Business, Sauder School of
Management Information Systems, Division of
DSpace
UBCV
Yang, Chenying
Doctor of Philosophy - PhD
University of British Columbia
The spatial distribution of economic activities is shaped by the way in which firms operate. I study firms' intra- and inter-national decisions and how their responses to policies affect the social welfare. First, I develop a quantitative model of multi-plant oligopolists where firms decide on plant locations, export and pricing, taking into account competition and cannibalization. I advance the existing trade literature on multinational firms by allowing for interdependent entry, oligopolistic rivalry and variable markups. Despite having a combinatorial discrete choice problem, I provide a toolkit to estimate the model in three steps. I present simulation-based evidence to show that neglecting interdependencies among plant locations within a multi-plant firm introduces quantitatively relevant differences in estimation. Second, I estimate the multi-plant firm model developed in the first essay focusing on the cement industry in the US and Canada. Estimates reveal important features of this industry, especially fixed costs as a key determinant of the market structure. I apply the estimated model to quantify firm-level responses to changes in environmental, trade and competition policies, and highlight the welfare implications of having multi-plant production. Results indicate that a carbon tax of $50/tCO2 in Canada will generate carbon leakage to the US which offsets 18% of the domestic emissions abatement, and also exacerbate the market distortion. A unilateral tariff increase of 20% reduces domestic welfare and does not lead to significant increase in number of plants in the US. I also analyze a hypothetical acquisition in which the efficiency gains of multi-plant firms offset the effects from competition-lessening. Last, I study firms' sourcing decisions through rules of origin (RoOs) in regional trade agreements. They are a set of criteria that define the origin of a product to qualify for preferential access. This chapter distinguishes trade diversion through RoOs from tariff reduction on intermediate goods, focusing on the automotive industry. I find that RoOs significantly distort where to source auto parts and the effect is nonlinear depending on the restrictiveness of rules. The shift from foreign to regional inputs increases before a stringent content rule backfires.
DECISIONS OF MULTINATIONAL FIRMS: PLANTLOCATION AND SOURCINGbyChenying YangB.Sc., Singapore Management University, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Business Administration in Strategy & Business Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2021© Chenying Yang, 2021The following individuals certify that they have read, and recommend to theFaculty of Graduate and Postdoctoral Studies for acceptance, the dissertationentitled:DECISIONS OF MULTINATIONAL FIRMS: PLANT LOCATIONAND SOURCINGsubmitted by Chenying Yang in partial fulfillment of the requirements for thedegree of DOCTOR OF PHILOSOPHY in Business Administration in Strat-egy & Business Economics.Examining Committee:Professor Keith Head, Sauder School of Business, UBCCo-supervisorProfessor John Ries, Sauder School of Business, UBCCo-supervisorProfessor Thomas Ross, Sauder School of Business, UBCUniversity ExaminerProfessor Kevin Song, Vancouver School of Economics, UBCUniversity ExaminerProfessor Eduardo Morales, Department of Economics, Princeton UniversityExternal ExaminerAdditional Supervisory Committee Members:Professor Sanghoon Lee, Sauder School of Business, UBCSupervisory Committee MemberProfessor A´lvaro Parra, Sauder School of Business, UBCSupervisory Committee MemberProfessor Hiroyuki Kasahara, Vancouver School of Economics, UBCSupervisory Committee MemberiiAbstractThe spatial distribution of economic activities is shaped by the way in whichfirms operate. I study firms’ intra- and inter-national decisions and how theirresponses to policies affect the social welfare.First, I develop a quantitative model of multi-plant oligopolists where firmsdecide on plant locations, export and pricing, taking into account competitionand cannibalization. I advance the existing trade literature on multinationalfirms by allowing for interdependent entry, oligopolistic rivalry and variablemarkups. Despite having a combinatorial discrete choice problem, I providea toolkit to estimate the model in three steps. I present simulation-based evi-dence to show that neglecting interdependencies among plant locations withina multi-plant firm introduces quantitatively relevant differences in estimation.Second, I estimate the multi-plant firm model developed in the first essayfocusing on the cement industry in the US and Canada. Estimates reveal impor-tant features of this industry, especially fixed costs as a key determinant of themarket structure. I apply the estimated model to quantify firm-level responsesto changes in environmental, trade and competition policies, and highlight thewelfare implications of having multi-plant production. Results indicate that acarbon tax of $50/tCO2 in Canada will generate carbon leakage to the US whichiiioffsets 18% of the domestic emissions abatement, and also exacerbate the mar-ket distortion. A unilateral tariff increase of 20% reduces domestic welfare anddoes not lead to significant increase in number of plants in the US. I also ana-lyze a hypothetical acquisition in which the efficiency gains of multi-plant firmsoffset the effects from competition-lessening.Last, I study firms’ sourcing decisions through rules of origin (RoOs) in re-gional trade agreements. They are a set of criteria that define the origin of aproduct to qualify for preferential access. This chapter distinguishes trade di-version through RoOs from tariff reduction on intermediate goods, focusing onthe automotive industry. I find that RoOs significantly distort where to sourceauto parts and the effect is nonlinear depending on the restrictiveness of rules.The shift from foreign to regional inputs increases before a stringent content rulebackfires.ivLay SummaryFacing policy changes, firms could respond by re-optimizing prices, re-formulatingimports and exports, or re-locating plants. These firm-level adjustments mayundermine the intended purpose of a policy and impose costs on the economy.Therefore, a good understanding of how firms decide where to produce, fromwhom to source, and how much to charge is crucial. The decisions are evenmore complicated when firms are multi-plant or multi-national.This thesis builds theoretical frameworks to illustrate the tradeoffs associ-ated with firms’ production location and sourcing decisions, and also pinpointsthe key differences between multi-plant and single-plant firms. The models canbe used to analyze a few pressing issues in the current policy debates, includinghow to effectively price carbon in emission-intensive and trade-exposed indus-tries, what the effects of greater trade protectionism in a country or a region are,and to what extent we should worry about the rising concentration.vPrefaceThis dissertation is original, unpublished, independent work by myself.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Location Choices of Multi-plant Oligopolists . . . . . . . . . . . . . . 81.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2 A Model of Multi-plant Firms . . . . . . . . . . . . . . . . . . . . . 161.2.1 Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2.2 The multi-plant firm’s problem . . . . . . . . . . . . . . . . 181.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.3 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.3.1 DGP in Monte Carlo simulations . . . . . . . . . . . . . . . 351.3.2 Multi-plant firm estimation . . . . . . . . . . . . . . . . . . 371.3.3 Results from multi-plant firm estimation . . . . . . . . . . 441.4 Single-plant Approximation . . . . . . . . . . . . . . . . . . . . . . 461.4.1 Monte Carlo results . . . . . . . . . . . . . . . . . . . . . . . 501.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 Multi-plant Oligopolists in the Cement Industry:Empirical Evidence and Policy Implications . . . . . . . . . . . . . . . 572.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57vii2.2 The Cement Industry . . . . . . . . . . . . . . . . . . . . . . . . . . 632.2.1 Industry background . . . . . . . . . . . . . . . . . . . . . . 632.2.2 Data description . . . . . . . . . . . . . . . . . . . . . . . . . 722.3 Multi-plant Production and Welfare Measures . . . . . . . . . . . 752.4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.4.1 Step 1: Estimation of local production capability, trade costs,and plant productivity dispersion . . . . . . . . . . . . . . 832.4.2 Step 2: Estimation of demand . . . . . . . . . . . . . . . . . 872.4.3 Step 3: Estimation of fixed costs . . . . . . . . . . . . . . . . 892.4.4 Fit of the model . . . . . . . . . . . . . . . . . . . . . . . . . 982.5 Quantitative Applications . . . . . . . . . . . . . . . . . . . . . . . 1012.5.1 The Greenhouse Gas Pollution Pricing Act . . . . . . . . . 1022.5.2 Trade with multi-plant firms . . . . . . . . . . . . . . . . . . 1152.5.3 Changes in firm operations . . . . . . . . . . . . . . . . . . 1202.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1253 Rules of Origin and Auto-Parts Trade . . . . . . . . . . . . . . . . . . . 1273.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1273.2 A Model of Global Sourcing under Rules of Origin . . . . . . . . . 1323.2.1 Consumer preferences and demand . . . . . . . . . . . . . 1333.2.2 Firm’s problem conditional on sourcing location . . . . . . 1343.2.3 Sourcing decisions . . . . . . . . . . . . . . . . . . . . . . . 1383.2.4 Aggregation and gravity . . . . . . . . . . . . . . . . . . . . 1393.3 Data and Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 1423.3.1 RTAs and RoOs . . . . . . . . . . . . . . . . . . . . . . . . . 1423.3.2 Tariff and trade . . . . . . . . . . . . . . . . . . . . . . . . . 1453.3.3 Part-level data . . . . . . . . . . . . . . . . . . . . . . . . . . 1473.3.4 Bilateral accessibility . . . . . . . . . . . . . . . . . . . . . . 1483.4 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162A Chapter 1 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171A.1 Model details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171A.1.1 Conditional joint distribution of the lowest two cost firms 171A.1.2 Price distribution . . . . . . . . . . . . . . . . . . . . . . . . 174A.1.3 Markup distribution . . . . . . . . . . . . . . . . . . . . . . 175A.1.4 Expected revenue . . . . . . . . . . . . . . . . . . . . . . . . 176A.1.5 Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178A.1.6 Best-response potential game . . . . . . . . . . . . . . . . . 180A.2 Model extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181A.2.1 Adding core productivity differences at firm level . . . . . 181viiiA.3 Simulation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183A.3.1 Delta Method for transformed parameters in SP approxi-mation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183B Chapter 2 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184B.1 Estimation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184B.1.1 Asymptotic standard deviation . . . . . . . . . . . . . . . . 184B.1.2 Additional tables . . . . . . . . . . . . . . . . . . . . . . . . 186B.2 Data appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189B.2.1 Implied trade across FAF zones . . . . . . . . . . . . . . . . 189B.2.2 Districts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191B.2.3 Locations of limestone deposits and cement plants . . . . . 193B.2.4 Other figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 195B.3 Comparison to separate entry decisions . . . . . . . . . . . . . . . 195C Chapter 3 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200C.1 Derivation of firm’s conditional inputs sourcing . . . . . . . . . . 200C.2 Derivation of country-level sourcing decisions . . . . . . . . . . . 201ixList of TablesTable 1.1 Estimated Parameters . . . . . . . . . . . . . . . . . . . . . . . . 45Table 1.2 Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Table 1.3 Single-plant Approximated Parameters . . . . . . . . . . . . . . 51Table 2.1 Distribution by plant and FAF zone . . . . . . . . . . . . . . . . 71Table 2.2 Average market share by plant and FAF zone . . . . . . . . . . 72Table 2.3 Estimation of trade costs . . . . . . . . . . . . . . . . . . . . . . 86Table 2.4 Estimation of demand . . . . . . . . . . . . . . . . . . . . . . . . 89Table 2.5 Estimation of fixed costs . . . . . . . . . . . . . . . . . . . . . . . 95Table 2.6 Model fit of plants number and distance to headquarter . . . . 100Table 2.7 Model fit of trade flows . . . . . . . . . . . . . . . . . . . . . . . 100Table 2.8 Counterfactual changes with $50 carbon levy on fuel in Canada 108Table 2.9 Counterfactual changes with $50 carbon levy on fuel and 33%BTA in Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Table 2.10 Counterfactual changes with OBPS in Canada . . . . . . . . . . 114Table 2.11 Decomposing sources of trade . . . . . . . . . . . . . . . . . . . 116Table 2.12 Counterfactual changes with 20% import tariff in the US . . . . 119Table 2.13 Counterfactual changes with Cemex-Eagle acquisition . . . . . 123Table 2.14 Counterfactual changes with collusion among all firms . . . . . 125Table 3.1 Description statistics on RTA and RVC . . . . . . . . . . . . . . 144Table 3.2 Baseline results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Table 3.3 Heterogeneous RoO effects . . . . . . . . . . . . . . . . . . . . . 155Table A.1 Convergence Rate Check of Best-Response Potential Game . . 180Table B.1 Robustness check: estimation of fixed costs . . . . . . . . . . . . 186Table B.2 Estimation of Trade Costs at Country Level . . . . . . . . . . . 187Table B.3 First-Stage Regression for Demand Estimation . . . . . . . . . . 188Table B.4 Fuel Costs and Energy Content . . . . . . . . . . . . . . . . . . . 189Table B.5 Trade Estimates for Cement and Nonmetallic Minerals . . . . . 190Table B.6 Summary Statistics of Districts . . . . . . . . . . . . . . . . . . . 193Table B.7 Estimation of entry without interdependency . . . . . . . . . . 197Table B.8 Counterfactual changes with $50 carbon levy on fuel in Canadawithout interdependency . . . . . . . . . . . . . . . . . . . . . . 198xList of FiguresFigure 1.1 Firm-level changes with number of plants . . . . . . . . . . . . 26Figure 1.2 Predicted entry probabilities and production capabilities bylocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 1.3 Fit for consumption and production . . . . . . . . . . . . . . . 46Figure 1.4 Entry probability across locations . . . . . . . . . . . . . . . . . 52Figure 1.5 Firm-level comparison using multi- v.s. single-plant fixed costsacross simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 1.6 Consumption and production using multi- v.s. single-plantfixed costs across locations . . . . . . . . . . . . . . . . . . . . . 53Figure 2.1 Cement shipping flow, 2016 . . . . . . . . . . . . . . . . . . . . 58Figure 2.2 Cement plants and consumption in 2016 . . . . . . . . . . . . . 66Figure 2.3 Distribution of distance for cement and trade in goods . . . . 67Figure 2.4 Inversely proportional cement trade to distance . . . . . . . . 67Figure 2.5 Cement trade intensity, 2016 . . . . . . . . . . . . . . . . . . . . 69Figure 2.6 Cement production and estimated capability by location . . . 87Figure 2.7 Estimated fixed costs and production capability by location . 98Figure 2.8 Model fit of trade flow over distance . . . . . . . . . . . . . . . 100Figure 2.9 Model fit of cement consumption and production . . . . . . . 100Figure 2.10 Change of plant locations with $50 carbon levy on fuel inCanada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Figure 2.11 Change of plant locations with $50 carbon levy on fuel and33% BTA in Canada . . . . . . . . . . . . . . . . . . . . . . . . . 109Figure 2.12 Change of plant locations with OBPS in Canada . . . . . . . . 112Figure 2.13 Welfare comparison of carbon policies . . . . . . . . . . . . . . 114Figure 2.14 Change of plant locations with 20% import tariff in the US . . 117Figure 2.15 Change of plant locations when Cemex acquires a small firm . 121Figure 3.1 Distribution of effectively applied tariff . . . . . . . . . . . . . 146Figure 3.2 Distribution of preferential margin on passenger car . . . . . . 146Figure 3.3 Distribution of cars export share within RTA . . . . . . . . . . 147Figure 3.4 Heterogeneity in car parts . . . . . . . . . . . . . . . . . . . . . 148Figure 3.5 Trade effects of RTAs under different RVC . . . . . . . . . . . . 154xiFigure B.1 Districts Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Figure B.2 Trade within the Same District . . . . . . . . . . . . . . . . . . 193Figure B.3 Cement and limestone resources location distribution . . . . . 194Figure B.4 Distribution of cement plant capacity . . . . . . . . . . . . . . 195Figure B.5 Change of plant locations with and without interdependencyfor $50 carbon levy on fuel . . . . . . . . . . . . . . . . . . . . . 198xiiAcknowledgmentsI want to start by expressing my deepest gratitude to my advisors. I could nothave hoped for a better committee. Thanks to Keith Head for providing in-valuable advice while pushing and challenging me, but most importantly forteaching me to become a better version of myself. Thanks to John Ries for al-ways making me think about the big picture and investing tremendous amountof time editing my work. Thanks to Sanghoon Lee for going through every stepof the derivation when I built the model and for bringing me to the world ofurban economics. Thanks to A´lvaro Parra for being the first person who steeredme to write an entry paper and for offering so many practical advice duringmy job market. Thanks to Hiroyuki Kasahara for always being my go-to per-son whenever I have econometrics questions and for giving me extremely help-ful feedback while you were on sabbatical. Without your encouragement andguidance, this work would not have been possible.To continue, I would like to thank everyone in the Strategy and Business Eco-nomics division: Vanessa Alviarez, Werner Antweiler, James Brander, ThomasDavidoff, Limin Fang, Ken Kikkawa, Guillermo Marshall, Scott Orr, Tom Ross,Tsur Somerville, Ralph Winter, and all other faculty members who have pro-vided generous support during my doctoral study. And thanks to Elaine Choxiiiand Helen Ho for their extraordinary responsiveness and help. I am fortunateto have amazing friends and colleagues with whom I walked along this jour-ney: Xiaonan, Cheng, Navid, Minkyeong, Wenyi, Qiyuan, Fan, Yuxiang, Alex,Jasmine, Sev, and Hao. And last but not least, thanks to Joyce and Ellie who feellike family.Finally, I am deeply grateful to my family. To my parents Hongwu Yang andYandong Qiao who always believe in me, support me to pursue my dreams andlove me unconditionally. Thanks to my partner Rain Gu for standing by me nomatter what happens and taking care of things while I struggled to get papersdone. Thanks to my cats Kiwi and Wiki who are my work companions andsources of joy, especially during the pandemic lockdown days.xivDedicationIn memory of my grandfather, Bengong Yang, who has been the most importantreason why I never give up. I hope you are proud of me.xvIntroductionResearch in international trade has shifted its focus from countries to firms thatengage in trade activities over the past two decades. The analysis of intrana-tional and international trade patterns is also inevitably related to the spatialdistribution of economic activities. This thesis answers two central questions inthe intersection of international trade, industrial organization and spatial eco-nomics, namely where firms produce and where they source inputs. Under-standing the tradeoffs associated with the spatial organization of firms helps usto predict what will happen to the market structure, equilibrium outcomes, andwell-being of economic agents when firms face cost shocks induced by policychanges. Through the following three chapters, this thesis shall explore the in-terdependency among firms, markets and government policies by developingmultinational firm models and resorting to computational methods to empiri-cally quantify equilibria within different contexts.In the first two chapters, I focus on a specific group, multi-plant firms, whichaccounts for substantial shares of aggregated trade and production in an econ-omy. There are two aspects of multi-plant firms that are particularly interestingyet challenging to solve. One is that the production location decision of multi-plant firms extends that of single-plant firms because, other than considering1competition with other firms, cannibalization among plants within the samefirm also matters. The location decision of one plant is thus interdependentwith another, making the problem combinatorial. When there is more than onemulti-plant firm on the market, the location game incurs an exponential increasein the number of possible plant configurations, further complicating the processof finding a pure strategy Nash equilibrium. The second aspect is that the pric-ing decision of multiple plants owned by a firm is strategic and depends on thefirm’s market power. A multi-plant oligopolist has an incentive to coordinatethe prices of its own plants and internalize the price competition, while strate-gically setting prices to compete with rival firms.Existing trade models that incorporate multi-plant firms achieve tractabilityeither by assuming away the endogenous interdependence of location choicesor else by ignoring the oligopolistic nature of firm competition. Imposing theseassumptions upon multi-plant or multi-national firms leads to abstraction fromrealities. Such misspecified models may yield spurious outcomes. I relax theseassumptions and allow for oligopolistic rivalries and variable markups, whiletackling the hard interdependent entry game in a computationally cost-savingway.Built upon the head-to-head oligopoly trade model formulated by Bernardet al. (2003), the theoretical framework employed in this thesis recognizes thegranularity of oligopolies as well as the plant cannibalization and pricing co-ordination featured in multi-plant firms. It yields generalized results which ef-fectively nest previous findings for single-plant firms. Specifically, a firm withmore favorably located plants faces lower costs of production and distribution,thereby enabling it to capture a larger fraction of proximal and domestic mar-kets. The set of plants a firm establishes is a source of competitive advantage2for it to exercise market power and raise markups. However, the marginal ben-efits associated with building more plants diminish because of business stealingamong the firm’s own plants. The framework also highlights the role of the spa-tial distribution of plants in terms of market prices and trade, which connectsthe extensive with the intensive margin. Due to the interdependency of produc-tion locations, a local change to one plant could potentially trigger global effectsacross all other plants, market aggregates, and eventually, welfare.Empirically, I overcome the challenges associated with this high-dimensionaldiscrete choice game. I estimate the multi-plant firm model in a three-step pro-cedure, leveraging gravity-type regressions, the analytical expression for mar-ket price given the spatial distribution of plants, and the solution algorithm fora combinatorial problem when the location game is submodular. The chaptergoes further to demonstrate that neglecting interdependencies among a multi-plant firm’s production locations introduces biases in estimation, which subse-quently could lead to inaccurate aggregated outcomes.This machinery of analyzing multi-plant firms is general enough to answervarious policy-related questions. I apply the multi-plant firm model to the ce-ment industry in the US and Canada, which is an emission-intensive, trade-exposed, and concentrated industry with outputs widely used in many con-struction and transportation projects. It has been the center of many policydebates. In the second chapter, I perform counterfactual experiments to quan-tify firm responses and welfare effects of environmental, trade, and competitionpolicies. Notably, multi-plant firms play an important role in these welfare im-plications.First, I examine the effects of the Greenhouse Gas Pollution Pricing Act in3Canada by comparing three carbon schemes, namely, carbon tax with and with-out border tax adjustment (BTA) and the output-based pricing system (OBPS). A$50/tCO2 carbon tax increases the operating costs of Canadian cement produc-ers relative to those in the US. Firms respond by moving production and asso-ciated emissions to “pollution havens,” leading to losses in the taxing economyand limited changes in total emissions. The problem is often termed “produc-tion and carbon leakage.” I find that change of plant locations is most aggressivein the case of the carbon tax alone in which 13% of the Canadian plants ownedby the top two firms will be closed. For a hundred tonnes of CO2 reduced inCanada, 18 tonnes “leak” to the US. BTA serves as a remedy for carbon leak-age. Specifically, imposing the same level of carbon tax to imported cementdecreases the amount of leakage per one hundred tonnes of CO2 abatementto 12 tonnes. However, it is not as effective in mitigating production leakagewhen the Canadian plants primarily produce to export. OBPS, effectively a re-bate to firms to lower the regulatory burden, retains the competitiveness of theCanadian cement industry and reduces production leakage. However, it cutscarbon emissions by a much smaller amount compared to the other two pricingregimes. These results illuminate key considerations when designing carbonpolicies for the cement industry. A high carbon tax may not be desirable for aconcentrated industry where multi-plant firms can change plant sites to unreg-ulated jurisdictions in the long run.Next, corresponding to rising US national protectionism during recent years,I focus on a unilateral tariff increase of 20% by the US towards the importedcement from Canada. The model predicts a seven-fold loss in the US than inCanada, and multi-plant firms will not move a significant number of plants tothe US.4Finally, I simulate a hypothetical acquisition of a leading US cement pro-ducer by the second largest player in North America. The acquisition actuallyboosts total surplus because efficiency gains of the multi-plant firm are greaterthan the harmful effects associated with lessening of competition. The exercisecontributes to the discussion about the Competition Act in Canada in terms ofwhat standards should be used to assess a merger.The other essential aspect of firm-level decisions is imports of intermediateinputs, in accordance with the growing importance of global production shar-ing. My third chapter studies firms’ sourcing decisions in a multi-country andmulti-product world. I use a policy instrument, rules of origin (RoOs), em-ployed by regional trade agreements (RTAs) as an external shock that will shiftfirms’ selection on which inputs to offshore and the countries from which to pur-chase them. RoOs are a set of criteria that define the origin of a product to qual-ify for preferential tariff treatment. The restrictiveness of rules is typically gov-erned by regional value content (RVC), meaning the share of value originatedfrom member countries must be above certain threshold. Hence, a firm facesthe tradeoff between cheaper inputs from suppliers outside the region and pay-ing higher (most favoured nation) tariffs when exporting final products to RTApartners. I develop a multi-country and multi-product sourcing framework inwhich firms decide the amount of import based on supplier-intermediate char-acteristics, destination-intermediate characteristics, and the bilateral accessibil-ity. RoOs are incorporated as implicit costs of importing intermediates fromcountries outside the RTA region. The framework entails a gravity trade modeland thus makes it possible to recover the effects of RoOs using aggregated tradedata.Focusing on the automotive industry, I survey rules of origin for 23 regional5trade agreements between 2000 to 2014. Exploiting the variation in RVC, thischapter identifies significant diversion in intermediate sourcing due to RoOsand the effect is nonlinear with respect to their restrictiveness. The shift fromforeign to regional inputs increases before a sharp decline when the requiredminimum RTA content reaches 65%. Impacts of RoOs are further decomposedto three channels: export destinations of final goods, magnitude of preferentialtreatments and value of intermediate goods. Results show that the RoO effectsare stronger when car exports are mainly intra-RTA, but indifferent to preferen-tial margins of cars or values of parts.The chapters proceed as follows. In Chapter 1, I study production locationchoices of multi-plant oligopolists. I first provide a study overview in Section1.1. I then lay out the multi-plant firm model in Section 1.2, followed by anestimation toolkit of the model in Section 1.3. An approximation using single-plant firm assumptions is presented and compared to the multi-plant estimatesin Section 1.4. The chapter ends with conclusions and a list of possible applica-tions in Section 1.5. In Chapter 2, I examine the policy implications of havingmulti-plant oligopolists in the cement industry. I discuss the study motivationand overall results in Section 2.1. Then I start with describing the dataset andproviding background of the cement industry in Section 2.2. Section 2.3 dis-cusses the model that characterizes important facts of the industry. The modelis then estimated structurally in Section 2.4, and in Section 2.5, I perform threesets of counterfactual experiments. I summarize the policy implications and fu-ture research directions in Section 2.6. In Chapter 3, I investigate the impactsof rules of origin on firms’ sourcing decisions of auto parts. I give an overviewof the policy and firms’ tradeoffs in Section 3.1. I first adapt the existing modelto include rules of origin as a form of trade frictions in Section 3.2. Data and6how I construct the variables related to the automotive industry are presentedin Section 3.3. The trade diversion effects of RoOs are estimated and furtherrefined to heterogeneous channels in Section 3.4. I discuss research implicationsand limitations in Section 3.5. I give a brief conclusion to the thesis at the end.7Chapter 1Location Choices of Multi-plantOligopolists1.1 IntroductionEvaluating how firms, especially multi-plant firms, operate spatially is a com-plex problem. A multi-plant firm confronts trade-offs in deciding where to lo-cate a set of plants and which plant to supply where, taking into account thecompetition with rival firms. A firm having too many plants close to consumersincurs higher fixed costs. Having too sparse plants implies higher costs fortransporting products to consumers. Further, given locations differ in produc-tion costs and plants can be heterogeneous in productivity, plants owned by thesame firm would cannibalize each other’s markets. The possibility of trade andcannibalization causes the plant entry decision in one location interdependentof the other, which the problem becomes combinatorial. The geographic dis-tribution of plants subsequently determines the goods flow and prices in each8market.In this chapter, I develop a quantitative spatial model of heterogeneous oligopoliststo study their decisions associated with multi-plant production. It is firmlygrounded at the intersection of trade and industrial organization theory. Withthis model, I aim to answer three main questions. First, what determines thenumber and location of plants for different firms? Second, how do markupsand prices vary by the spatial allocation of plants? Third, how important isallowing for multi-plant production and interdependent entry of plants?To shed light on these essential components of firms’ decisions, I set up aneconomy with a finite number of discrete locations that are heterogeneous inproductivities and input costs. Plants at each location are potential suppliers oflocal consumers and those in every other locations. The productivity of a plantdepends on local characteristics as well as a stochastic term that is realized postentry. Firms decide how many and which locations to build plants by balanc-ing their expectation on costs of production, costs of distribution and costs ofentry, while factoring competition within and across firms given the vector ofdemand. When competing, plants engage in head-to-head price competition ex-cept that those owned by the same firm coordinate. Therefore, for a multi-plantfirm, there are counteracting forces in determining the optimal set of produc-tion locations: coordination in prices set by the firm improves its competitiveadvantage against rivals through building more and favorably located plants,whereas cannibalization between its own plants decreases the marginal benefit.Plants are strategically added until marginal payoff cannot cover fixed costs ofbuilding. Across firms, plants are strategic substitutes.The model advances existing research in two aspects. First, firms are gran-9ular and oligopolies such that the model yields firm-market-specific variablemarkups. Existing work has long been using constant markup derived fromthe workhorse model of constant elasticity of substitution (CES) with monop-olistic competition.1 I relax those assumptions and incorporate strategic pric-ing among oligopolistic rivals, while keeping the markup distribution tractablewith an analytical expression. The key idea for tractability in the multi-plantfirm framework is to consider a nested structure in competition where plantswithin a firm do not undercut each other in price but plants across firms com-pete head-to-head similar to Bernard et al. (2003) (hereforce BEJK). By allow-ing the particular competition structure, a standard parametric distributionalassumption of plant productivities, and a continuum of consumers in each mar-ket, I align the multi-plant firm model in this chapter to many other canonicalmodels in the literature that conform to a gravity trade framework. It deliv-ers a closed-form expression for firms’ expected sales given the plant locationconfiguration.The model predicts that a firm with more and better located plants chargeshigher markups and captures a larger fraction of the market. The intuition isthat favorable plant bundle a firm owned lowers its average costs and improvesthe firm’s competitive advantage to outbid others. Introduction of entry andoligopolistic competition opens up the possibility to reexamine the connectionbetween extensive and intensive margin in the context of multi-plant or broadlymultinational firms. It highlights the role of spatial distribution of plants intrade besides the usual technological differences and geographic barriers. Asthe geographic configuration of plants shapes the relative competency of firms,it also reinforces differences in comparative advantage across locations.1Examples of using Dixit-Stiglitz type of model in studying multinational firm are Tintelnot(2017), Antras et al. (2017), and Hu and Shi (2019).10Second, the plant location game is interdependent and submodular, and yeta model with such feature can be fully estimated. Solving the interdependententry game facing a large set of potential locations implies a hard permutationproblem. When there are L number of possible production locations, a firmfaces 2L possible choices. A game with F number of players further complicatesthe combinatorial discrete choice (CDC) problem as it now involves 2FL com-binations. Due to the difficulty in tackling such a problem, some papers eitherassume away export platform sales or fixed costs of entry, or treat locations aspredetermined.2 There are additional theoretical challenges with respect to theexistence and uniqueness of high dimensional spatial equilibrium when playersare strategic substitutes.3 In games with strategic complements, it follows fromTopkis’ theorem (Topkis, 1978) and Tarski’s fixed point theorem (Tarski et al.,1955) that a pure strategy Nash equilibrium (PSNE) exists. For this reason, mostpapers that deal with combinatorial problems are applications of games withstrategic complements, such as Jia (2008) where chain stores exhibit positivespillover and Alfaro et al. (2021) where firms prefer to export to similar markets.However, little is known about games with strategic substitutes. One could ac-commodate by not solving the game but using a revealed preference approachto bound the model primitives (Holmes, 2011). In this chapter, I leverage thesubmodularity and aggregation property of the firm’s profit function to solvethe PSNE of a game with imperfect competition by applying a CDC solutionalgorithm designed in Eckert et al. (2017). I then provide a toolkit to separatelyidentify model primitives in three steps using rather aggregated and easily ob-2Examples are Helpman et al. (2004), Ramondo and Rodrı´guez-Clare (2013), Irarrazabal et al.(2013), and Head and Mayer (2019).3I take definitions from Jackson and Zenou (2015) p.103, where a game has strategic comple-ments when “an increase in the actions of other players leads a given player’s higher actionsto have relatively higher payoffs compared to that player’s lower actions”. On the opposite,games of strategic substitutes are “an increase in other players’ actions leads to relatively lowerpayoffs to higher actions of a given player”.11tained data. Conditions on key parameters to guarantee the existence of a PSNEcan be validated in steps prior to solving the location game.Specifically, the estimation procedure is the following. In the first step, grav-ity regressions and data on bilateral trade are used to estimate a composite oflocal TFP and input costs that determines the relative production advantageacross locations. I can also obtain an estimate of trade elasticity which regu-lates competition intensity among plants. In the second step, I estimate demandthrough nonlinear least squares using data on consumption and market charac-teristics. Instead of using price data which is subject to limited availability, I usethe model-derived price index constructed from the parameters recovered inthe last step. It is a function of the every potential suppliers’ costs and markuprule, weighted by its probability of serving the market. In the third step, I es-timate the fixed costs of building plants by fitting moments using the observedplant locations. A notable advantage is that the multi-plant firm model in thischapter can be estimated with minimum data requirement. Micro data on firmor plant-level market shares or prices is not needed for this exercise.Although I present in this chapter a model characterizing a rich set of multi-plant firms’ decisions and also provide a recipe to recover it without sacrificingtoo much on computational cost when one has limited data, a researcher maystill worry about the payoff for incorporating interdependent entry when study-ing multi-plant firms. After all, one could assume every plant entry decision isisolated, and thus, a firm decides to have a plant if and only if the expected vari-able profit associated from the particular plant is higher than its fixed cost of es-tablishing. The assumption is not as unreasonable as it appears to be. Think ofevery geographical unit is managed by a manager who has complete authorityto decide whether to have a plant and how much to charge, and the headquarter12has no influence on any decisions. In that case, plants and firms are conceptuallyequivalent. Here, I essentially take the other extreme: each firm has a big man-aging board who oversees entry and pricing. The reality could be somewherein between. Instead of arguing which premise is correct, the focus is whetherwe can approximate multi-plant firm decisions using single-plant assumptionsif the true data generating process (DGP) is the CDC model with oligopolisticmulti-plant pricing. I present simulation evidences that ignoring interdepen-dent entry generates remarkable biases. In particular, fixed costs are overesti-mated for large multi-plant firms because they are complement to the omittedfirms’ incentive of restraining entry to reduce cannibalization. On the contrary,fixed costs will be underestimated for smaller multi-plant firms because theyare contaminated by the omitted incentive of boosting entry to crowd out com-petitors. In general, the estimated parameters assuming separated entry do notperform well in predicting the “true” multi-plant firms’ decisions, and subse-quently could generate inaccurate aggregated outcomes if multi-plant firms arelarge and plant interdependency is strong.Canonical trade models that studying oligopolists, such as BEJK and Atke-son and Burstein (2008a), do not clearly distinguish a plant and a firm.4 This isconcerning given mounting evidences that support differences between the twoeconomic entities (i.e., Rossi-Hansberg et al., 2018; Hsieh and Rossi-Hansberg,2019; Aghion et al., 2019; and Cao et al., 2017), especially when multi-plant firmsare prevalent in oligopolistic industries. My model addresses the omission and4BEJK take different view of the world compared to the way Atkeson and Burstein (2008a)modeling oligopoly in trade. In Atkeson and Burstein (2008a), each firm produces a distinctgood in a specific sector and firms maximize profits given imperfect substitution within a sec-tor and across sectors. In contrast, BEJK model multiple producers producing the same goodand there are a continuum of imperfectly substituted goods. I follow BEJK by assuming firmsproduce a homogeneous good. I acknowledge that this assumption may limit the scope of in-dustries where the framework can be applied. However, an advantage for adopting BEJK is thatit requires less firm-level data than Atkeson and Burstein (2008a).13offers testable implications on prices, markups and market shares across firmswith different bundles of plants. As an extension of BEJK and the subsequentwork by Holmes et al. (2011, 2014), and De Blas and Russ (2015), the distribu-tions of costs and markups derived from the multi-plant firm model nest thosein single-plant setting.5 The model, therefore, yields more generalized insightson firm-level decisions regardless of single- or multi-plant owners.I also build on and contribute to a vibrant area of ongoing research that ex-plores interdependencies in firm-level decisions. In the international trade liter-ature that explores firms’ extensive margin with spillovers, this chapter sharesthe most similarities with Tintelnot (2017), Antras et al. (2017), and Alfaro et al.(2021). An obviously important application of my model is multinational firms.Similar to this chapter that studies substitutabilities in firms’ multi-plant pro-duction, Tintelnot (2017) focuses on multinational production facing positiveexport platform sales and cannibalization. Nevertheless, his work evaluates allpossibilities in a very small location set and the method is not easily scalable. Iovercome the challenge by combining theoretical properties from the submod-ular game with a solution algorithm for combinatorial discrete choice problem.Not about multinational firms per se, Antras et al. (2017) and Alfaro et al. (2021)speak to complementarities in firms’ global sourcing decisions and firms’ ex-port participation dynamics, respectively. In estimation, Antras et al. (2017) andthis chapter both employ a three-step procedure to separately identify demandand supply primitives. Alfaro et al. (2021) add time dimension to the combi-natorial choices of export destinations. However, none of these papers adopta game setting with multiple players. They all model a monopolistic compet-5Bernard et al. (2003) have markup distribution being impervious to any characteristics ofmarket structure. Subsequent papers by Holmes, De Blas and others generalize the model toincorporate the effects of finite number of firms in a market. My model is closer to the laterdevelopment that recognizes the granularity of firms.14itive market and treat firms as infinitesimal with constant markups, whereas Ihighlight a small group of sizable firms competing oligopolistically and exploit-ing geographical advantages to increase markups. This key difference makesmy model more suitable for analyzing policy questions in industries that aredominated by a few large firms.This chapter joins a literature in the field of industrial organization that ana-lyzes how retailers set up distribution networks in space, such as Jia (2008) andHolmes (2011). The technique to solve for combinatorial discrete choice is de-veloped based on Jia (2008). Jia (2008) imposes a “supermodular” condition onthe return function, meaning that there is only positive spillover among chainstores. Eckert et al. (2017) generalize Jia (2008) and use the repetitive fixed pointssearch algorithm to deal with either “supermodular” or “submodular” prob-lem. The algorithm is further developed by Hu and Shi (2019) to a continuumof monopolistically competitive firms over a monotonic type space. The recentpaper by Oberfield et al. (2020) handles the combinatorial optimization in an en-tirely different way. They derive a limit case where the optimal plant density isdifferentiable in a continuous space. On the other hand, an alternative approachto combinatorial problem is using moment inequality to partially identify pa-rameters without solving the model, such as Holmes (2011). The downside forthis method is the difficulty to perform counterfactual experiments.Other than interdependency in location choices, the chapter also broadlyrelates to multi-product firms when there is cannibalization among productswithin the same firm. Specifically, the endogenous markup distributions drawnfrom this chapter and Nocke and Schutz (2018) share the same shape.The remainder of the chapter is structured as follows. In Section 1.2, I lay out15the model and propositions derived from it. In Section 1.3, I start by describingthe data generating process from the multi-plant firm model, and then proposea method to consistently estimate it using commonly found data in the litera-ture. An approximation using single-plant firm assumptions is presented andcompared to the “truth” in Section 1.4. The chapter ends with conclusions anda list of possible applications in Section 1.5.1.2 A Model of Multi-plant FirmsThis section sets out a theory of production locations, export and prices formulti-plant firms with market power. A firm and a plant are distinct, albeitrelated, economic entities. A plant can potentially serve the demand locallyand elsewhere. A firm internalizes cannibalization within itself and competi-tion with rivals by deciding where to produce, and how much each of its plantsshould charge. For simplicity, all that differentiates a firm from other poten-tial entrants prior to entry are fixed costs of building plants.6 Once fixed costsare paid, plants are differentiated by production and trade costs associated withtheir locations, and a stochastic term that indicates their productivity level. Eachfirm selects its optimal plant sites by maximizing total expected single-periodprofits. I consider a partial equilibrium environment by focusing on interde-pendent entry and price competition between oligopolies in an industry.The model features a static simultaneous entry game with complete infor-mation. I identify the competition and cannibalization effects from the plants’spatial distribution pattern. This approach abstracts from a number of dynamic6The ex-ante heterogeneity across potential entrants can be extended to include firm-levelproductivity differences, but they are omitted for simplicity and would require additional datato be identified. I incorporate this extension in Appendix A.2.1.16considerations. For example, it does not allow for preemptive entry (Igami andYang, 2013; Zheng, 2016) nor does it allow for any learning process by firms(Arkolakis et al., 2018). One may also raise the concern about firms’ additionalconsiderations in a dynamic setting, such as how sunk costs and negative scrapvalues can deter relocation of a plant.7 In this regards, “relocation” decisionsunder a dynamic model are evaluated differently compared to “location” deci-sions under a static model. Since the main goal of this model is to study theinterdependency in multi-plant firms’ location decisions in a steady state andto compare long run equilibria under different policy regimes, incorporatingtransition dynamics is beyond the scope of this chapter. Empirically, given thedifficulty of solving the CDC problem, it is also extremely computational inten-sive to extend the framework to a dynamic setting unless imposing additionalassumptions.Formally, there is a finite number of discrete geographical units, m ∈M . Afirm, f ∈ F , chooses a subset of locations L f ⊆M to set up plants, where aplant is indexed by ` ∈L f .8 The firm owns N f = |L f | number of plants.I start with the description of demand and then turn to the problem of multi-plant firms.1.2.1 DemandDemand is characterized for a single product bought by a continuum of con-sumers i ∈Dm on a unit interval in m. The aggregated local demand is Qm units7Scrap values can be positive or negative depending on whichever is higher, proceeds fromselling the land or payments to cleanup.8I assume a firm cannot have more than one plant at a location. Essentially, a firm choosinga set of plants is equivalent to choosing a set of locations to produce.17of the good. I assume an isoelastic demand at the location level, given byQm = AmP−ηm , (1.1)where −η < −1 is the price elasticity of demand to be consistent with profitmaximization of monopolists.9 The local price index of the good is Pm, and theexogenous demand shifter is Am. I formulate local demand instead of demandof each consumer for reasons that will be clear later. To give a quick previewhere, firms only obtain knowledge on how consumers may differ after plantsare built. At the earlier stage when a firm still chooses plant locations, it expectsto charge the same price for all consumers in m. Therefore, to construct a firm’sexpected profits, I only need the demand information at the location level.101.2.2 The multi-plant firm’s problemA multi-plant firm decides where to establish production operations and howto serve consumers at every location. A finite number of oligopolists appointtheir plants to produce the same product facing the aforementioned demandfunction. The timing of game is that at t = 1, firms simultaneously decide theset of locations to build plants in order to maximize expected profits, and paythe respective fixed costs. The setF of potential entrants is given. At t = 2, firmslearn about the realized productivity of plants and decide to which consumerplants supply. Plants compete in price. For simplicity, I assume there is no fixedcost of exporting and every plant can be potential supplier of each consumer at9A special case of isoelastic demand is CES preferences.10One can easily add more structure to the demand side, such as CES of the good and substi-tutes at consumer level and then aggregate to a location. However, additional demand param-eters add no benefit in solving the firm’s problem but further complicate the calibration of themodel.18every location.11 I solve the model by backward induction.Production decisions given plant locationsEach location m ∈M is characterized by an exogenous productivity level Tm, aswell as local equilibrium characteristics that firms take as given, namely, the de-mand shifter Am and costs of input wm. Inputs to produce the good are immobileacross locations. Trade between any two locations bears an iceberg trade cost.For example, firm f has a plant in `. The cost of transporting the good from ` toa consumer at the center of m is τ`m.Conditional on firm f produces in a set L f of locations, for each location` ∈L f , the firm converts one bundle of inputs into a quantity Z f `i of the goodfor consumer i ∈ Dm at constant return to scale. The term Z f `i represents id-iosyncratic shock specific to a plant-consumer pair. Examples of such factors in-clude some degree of relationship specificity and internal distance between con-sumers in m towards the center. Rather than dealing with each Z f `i separately,I assume that they are realizations of independently and identically distributedrandom draws from a Fre´chet distribution. The cumulative distribution func-tion of the productivity that firm f ’s plant in ` isFdraw` (z) = Pr[Z f `i ≤ z]= exp(−T`z−θ).Dispersion of productivity is represented by θ . The bigger θ is, the more similarare the productivity draws.11Fixed costs of exporting at firm level could be incorporated, as in Tintelnot (2017), but theyare omitted for simplicity and would require additional data to be identified. However, if thefixed costs of exporting are associated with the set of plant locations, then a firm would nolonger select the minimum cost plant to serve a destination consumer, and the model wouldlose tractability.19Combining productivity, input and trade costs, the marginal cost of supply-ing the good from a plant in ` to consumer i in m is thereforeC f `im =w`τ`mZ f `i,∀` ∈L f , i ∈Dm. (1.2)It is distributed asFc`m(c) = Pr[C f `im ≤ c]= 1− exp(−φ`mcθ),where φ`m = T`(w`τ`m)−θ indicates the capability of location ` serving location m.A caveat here is that plants at the same location are ex-ante identical regard-less of ownership. The setup is analogous to Antras et al. (2017) where as long asthe productivity draws are from a location-specific distribution, any firm spe-cific term is absorbed. One may argue to include a firm’s core productivityparameter to shift its plants’ productivity as in Tintelnot (2017) such that moreproductive firm will build more productive plants on average. As I demonstratein Appendix A.2.1, it is straightforward to incorporate additional firm-level het-erogeneity into the benchmark model. However, estimation of the model be-comes substantially more data-hungry.12 Although firms are not endowed withcore productivities, we will show later that a firm having more plants at effi-cient (higher T ) locations implies a more productive firm overall. Therefore, theex-ante heterogeneity across firms is fully loaded on a firm’s number of plantsand their locations, i.e. the extensive margin.Plants engage in Bertrand competition in a nested structure. Every consumerin a location is served by its lowest-cost supplier. If firms are single-plant, the12To estimate the set of firm core productivity parameters, I would need each firm’s marketshare in every location which is not commonly available. I welcome researchers who have therelevant data to use the extended version of the model in the Appendix.20winning firm is constrained not to charge more than the second-lowest marginalcost, the standard setting in BEJK. In the case of multi-plant firms, the firmheadquarters decide prices of all their plants instead of plant managers. Thefirm headquarter will internalize competition between its own plants and coor-dinate their pricing. As a result, the winning plant will not undercut its sisterplants owned by the same firm, until the next lowest-cost plant is owned by acompetitor. The price charged is limited by the marginal cost of the lowest-costplant owned by the second-lowest cost firm. Instead of fully characterize costranking across all plants, what really matter are the lowest-cost plant within afirm and the two lowest-cost firms.First, define the kth lowest cost among firm f ’s plants serving consumer i inm as Ck, f i(m). The distribution of the lowest marginal cost can be easily derivedasFc1, fm(c) = Pr[C1, f i(m) ≤ c]= 1− exp(−Φ fmcθ), (1.3)whereΦ fm=∑`∈L f φ`m refers to the capability of a firm f serving location m. Theassumption of Fre´chet distributed productivities becomes handy in the deriva-tion due to its grounding in the extreme value theory. If a firm selects the bestavailable technology from a distribution, its productivity will also follow anextreme value distribution. While technical advantages dictate this choice, em-pirical distributions of productivity are typically bell-shaped in the literature,which also in favor of the Fre´chet specification.1313Another commonly used distribution is Pareto. Although Fre´chet and Pareto distributionboth have fat right tails, they are very different on the left side. The former density is bell-shaped whereas the latter density is downward-sloping throughout. Other candidate couldbe log normal that is very hard to be distinguished from Fre´chet, or truncated distributions.However, properties in truncated distributions are more obscured and hard to applied to mymodel without strong support of empirical evidences. A thorough examination and comparisonof distributions can be found in Head (2011) and Kotz and Nadarajah (2000).21Based on equation (1.3), the firm-level expected marginal cost to consumersin m isE[C1, f i(m)]= Γ(θ +1θ)Φ−1θfm . (1.4)More plants at favorable (high φ`m) locations necessarily lower the firm’s ef-fective marginal cost.14 Intuitively, one more production location grants thefirm an additional cost draw, and greater competition among plants. Althoughplants within the same firm coordinate their pricing strategies, they still fightfor being the ultimate supplier. Intense internal competition reduces the ex-pected marginal cost at the firm level. More plants also imply that the averageshipping distance to consumers is shorter and thus additional savings on tradecosts for firms. Moreover, the effect of an additional plant is larger when it is lo-cated somewhere cheaper to produce and closer to consumers. The propertiesof the minimum cost distribution for a multi-plant firm allow me to establishthe following result (the proof is straightforward and omitted in the main text).Proposition 1: An additional production location to the firm’s active locationset strictly decreases its lowest cost of supplying the good to all consumers inexpectation.Second, define C1,i(m) and C2,i(m) be the lowest and second-lowest marginalcost across all firms for consumer i in m. Conditional on sales originating fromfirm f ’s plant at location `, C1,i(m) ≡ C f `i(m) and C2,i(m) ≡ ming6= f ,g∈F{C1,gi(m)}. Ishow in Appendix A.1.1 that the conditional joint distribution of the lowest and14The implication is in contrast to Oberfield et al. (2020) in which they focus on the span-of-control cost and more plants will reduce a firm’s efficiency. Nevertheless, we both have thatfavorable locations reduce the marginal costs of plants and firms.22second-lowest firm-level cost of supplying the good to a consumer at m isFc12,m| f (c1,c2) = 1− e−Φmcθ1 − ΦmΦ fm(1− e−Φ fmcθ1)e−(Φm−Φ fm)cθ2 , (1.5)for c1 ≤ c2, where Φm = ∑ f∈F ∑`∈L f φ`m denotes the sourcing potential of loca-tion m over all plants. Notice that the conditional joint distribution is indepen-dent of which plant in firm f sells to consumers in m. The rationale is that thecost ranking between plants within a firm does not matter to the game exceptfor determining the firm-level minimum cost.When the number of firms approaches to infinity, the limit distribution ofequation (1.5) is what BEJK use for the joint distribution of two lowest costs.When firms are finite but single-plant, equation (1.5) takes the form of the jointdistribution in Holmes et al. (2011). Therefore, the two key features that dif-ferentiate my model from previous literature are granularity and multi-plantproduction. We would expect that the additional dimensions on extensive mar-gin based on BEJK type of model bring richer implications on how markupsvary across firms.I now turn to describe the price and markup distributions in this model.The competition structure implies a partially limit pricing strategy, where thelowest-cost plant charges a minimum between the monopoly price and the low-est marginal cost of its head-to-head competitors. Mathematically, the pricecharged to consumer i in m is Pi(m) = min{µ¯C1,i(m),C2,i(m)}, where the monopolymarkup µ¯ = η/(η−1).Conditional on sourcing from firm f , the firm decides its winning plant to23charge consumers in location m at a price following the distribution,F pm| f (p) = Fc12,m| f (p, p)+ΦmΦ fm(1− e−Φ fmµ¯−θ pθ), (1.6)with derivation shown in Appendix A.1.2. A closer look at equation (1.6) re-veals that the first term comes from the cost ladder, while the second term isderived from the probability to charge the monopoly price. Pass-through is zeroif the limit pricing prevails, and one otherwise. Combining with Proposition 1,a firm with larger and favorably located plant set lowers its average price. Theexpected price charged by firm f to consumers in m isE[Pfm]= Γ(θ +1θ)ΦmΦ fm((Φm− (1− µ¯−θ )Φ fm)−1/θ − (Φm−Φ fm)Φ− θ+1θm ) ,(1.7)Closely related, firm f ’s markup in location m is realization of a randomdraw from a shifted Pareto distribution truncated at the monopoly level,Fµm| f (µ) =1− 1(1−s fm)µθ+s fm 1≤ µ < µ¯1 µ ≥ µ¯, (1.8)where s fm = Φ fm/Φm indicates the relative competitiveness of firm f to its ri-vals. It is the sole shifter of the markup distribution. See Appendix A.1.3 forderivation. Specifically, for 1 ≤ µ < µ¯ , a firm owning more plants in favorablelocations charges higher markup. For µ ≥ µ¯ , I compute the probability of firmf charging monopoly markup given the second-lowest cost equals to1− e−Φ fm(µ¯/c2)−θ1− e−Φ fmcθ2.Therefore, knowing that the otherwise price charged will be c2, the firm is more24likely to exploit the maximum markup if it is more capable of supplying theproduct through plant allocation because the efficiency gap to its next lower costrival is wider. We observed that more dispersed plants indicated by smaller θalso increase the likelihood of charging the monopoly price.The markup distribution again generalizes what is in single-plant firm mod-els. In the case of infinite number of firms competing head-to-head, the markupdistribution converges to equation (11) in BEJK. I summarize results in the fol-lowing proposition.Proposition 2: Holding the competitors fixed, (i) an additional production loca-tion to the firm’s active location set weakly decreases its average price chargedto all consumers; (ii) an additional production location to the firm’s active loca-tion set weakly increases its average markup charged to all consumers.Lastly, I explore the implications of our model for the bilateral trade volumeacross locations, aggregating from firms’ decisions. With firms’ cost distribu-tions in equation (1.3), the probability that firm f supplies to a consumer in miss fm =∫ ∞0∏g6= f .g∈F(1−Fc1,gm(c))dFc1, fm(c) =Φ fmΦm. (1.9)Essentially, the probability equals to a firm’s relative competitiveness of sup-plying the good compared to all other head-to-head competitors. Since all con-sumers are uniformly distributed on a unit interval, the probability of supplyingto a consumer is the same as the expected fraction of consumers captured in m.Proposition 3: An additional production location to the firm’s active locationset strictly increases the share of consumers sourcing from it, holding the com-25petitors fixed.Similarly, suppose a setF` of firms produce at ` and N` = |F`|, the probabil-ity that location ` exports to a consumer in m iss`m =∫ ∞0∏k 6=`,k∈M(1−Fc1,km(c))dFc1,`m(c) =N`φ`mΦm, (1.10)where Fc1,`m(c) = 1− exp(−N`φ`mcθ) characterizes the distribution of the lowest-cost plant at ` across all firms entered. The probability represents location `’scompetitive advantage. The more plants, the higher local efficiency, the lowerinput costs and the lower trade costs in a location, the larger share m sourcingfrom it. Different from BEJK which do not have a measure of firms, this chaptershows more firms producing in a location is pro-competitive despite firms beingsymmetric for simplicity.Recall that φ`m = T`(w`τ`m)−θ , equation (1.10) can be transformed to resem-ble a standard gravity equation. The trade elasticity is shaped by the Fre´chetparameter θ as in Eaton and Kortum (2002).The model propositions derived from this section are summarized and rep-resented visually in Figure 1.1.Choice of plant locationsA firm chooses the set of plant locations from a finite discrete spaceM to max-imize the expected total profit summing over its plants. To complete the ex-pected total profit function, I first present the expected variable profit, with de-26Figure 1.1: Firm-level changes with number of plantsNotes: The figure displays a firm’s expected marginal costs of supplying thegood, expected prices, markups, and the fraction of consumers served, av-eraging across locations, with respect to the number of plants it owns. Pa-rameter values are the same as the Monte Carlo simulation in Section 1.3.1.The firm of interest here is firm B, taking firm M and small firms as given.The curve is drawn by adding firm B’s plant one by one, starting from thelocation with the highest profitability, until reaching its optimal plant set of26 plants.tails presented in Appendix A.1.4 and A.1.5.E[pi f]= κ∑mAm(R¯ fm−C¯ fm), (1.11)where the constant κ = Γ(θ+1−ηθ), andR¯ fm =(Φm− (1− µ¯−θ )Φ fm)− 1−ηθ − (Φm−Φ fm)Φ− θ+1−ηθm ,27C¯ fm =Φ fm×[(θ +1−η)(Φm−Φ fm)∫ µ¯1µ−θ−2(Φm− (1−µ−θ )Φ fm)− 2θ+1−ηθdµ+ µ¯−θ−1(Φm− (1− µ¯−θ )Φ fm)− θ+1−ηθ ].The expectation of variable profit is taken over random productivity draws forall plant-consumer pairs. It depends on the capability of supplying the goodfrom all of the firm’s plants and its competitors’. More importantly, each plantis not separately additive. Cannibalization effects defines multi-plant firms’ lo-cation problem to be combinatorial optimization.In order to have a well defined expected variable profit, I must restrict η −1 < θ . The same restriction has been seen in the literature, such as Eaton andKortum (2002), Eaton et al. (2011), and Bernard et al. (2003), with η representingdemand elasticity and θ being the heterogeneity of suppliers in production. Thecondition ensures that suppliers are competitive enough such that consumptionis not concentrated on a few of them. Mathematically, the condition is in needfor a well-behaved κ after taking the expectation over a function of Fre´chet dis-tributed stochastic term, knowing that Gamma function is sensitive to param-eter values at the negative support. One may contrast the condition to whatis in Antras et al. (2017) that guarantees the supermodularity of sourcing deci-sions. A clear difference is mentioned in Antras et al. (2017) footnote 11 whereθ in their setting is no longer heterogeneity of final good suppliers but inputproducers although η still remains to be demand elasticity among final vari-eties. The submodularity or supermodularity property of equation (1.12) willbe explained in more details in Section 1.2.3.Although the restriction on η and θ has little to do with submodularity ofthe profit function, discussing the comparative statics of a firm’s profit with28respect to these two parameters help us to understand the firm’s optimal plantlocation strategy. Figure 1.1 implies that a firm obtains positive marginal payoffby adding one more plant to its existing active set. However, when θ is highmeaning that plants are more homogeneous, the lowest cost among a firm’sown plants will not reduce much after building another plant. Furthermore,when demand is less elastic (low η), the firm’s variable profit responses weakerto cost reductions and gains less.A multi-plant firm incurs plant-specific fixed costs for setting them up, {FC f `,∀`∈L f }.15 Fixing the same set of plant locations, firms would expect exactly samevariable profits because plants at the same location are symmetric. Therefore,what drives one firm to have more plants than the other is having lower fixedcosts on average. Location choices are affected by the firm’s idiosyncratic fixedcosts at different locations and profitability given competitors’ fixed costs andlocation choices. A firm thus solvesmaxL f⊆ME[Π f (L f )]= E[pi f (L f )]− ∑`∈L fFC f `. (1.12)Finally, I close the model with the local price index, which is a composite ofprices that all firms charge to consumers in m.Pm = ∑f∈FE[Pm| f ]× s fm (1.13)= Γ(θ +1θ)Φ−1/θm ×[(1−N)+ ∑f∈F(1− (1− µ¯−θ )s fm)−1/θ ],15There is a strand of literature concerning greenfield entry versus merger and acquisition.However, the case of M&A need not to be fundamentally different from my benchmark model.Acquisition price can be seen as the fixed cost, except the case that the acquisition price dependson the seller’s residual value that is past dependent. If then, fixed costs are also endogenous andneed to be solved using a dynamic model.29where N = |F | is the given number of firms. The equation explains how varia-tion on local prices is channeled through plants spatial distribution globally.1.2.3 EquilibriumSo far, I have yet discussed in detail how to find the equilibrium of the inter-dependent production locations in this game-theoretic model. I will first showthe existence of equilibrium depending on important properties of firms’ profitfunctions. Then, I discuss how to address the issue of multiple equilibria likemany other simultaneous entry games with complete information.Existence of pure-strategy Nash equilibriumIn a single-agent location problem, with |M | number of potential productionlocations, a firm selects among 2|M | possible configurations. Theoretically, onecan use the brute force approach to calculate firm profits for all combinationsof locations and pick the set yielding the maximum profit. However, the com-putational cost grows exponentially when |M | gets large. In general, it is alsonot guaranteed that the optimal location set is unique for a discrete choice prob-lem even in the case of single player. So what is sufficient condition to ensurea global maximum and how to find the optimal in a cost-efficient way? For-tunately, Eckert et al. (2017) provide a solution where if the objective functionexhibits single crossing differences, we can iteratively and repetitively refine thecombinatorial discrete choice set and the process always converges to a uniqueequilibrium.Noticing that equation (1.12) is submodular in a multi-plant firm’s own strat-egy, meaning that the marginal value on total profit of adding location ` by firm30f is decreasing in the number of other locations that f entered. Specifically,from the propositions, the variable profit of a firm increases from expanding itsplant location set, but the marginal gain diminishes with more plants due toself-cannibalization. Submodularity in the firm’s profit function is a sufficientcondition for single crossing differences, suggesting that unprofitable locationswill remain to be unprofitable when enlarging the set and profitable ones willremain to be profitable when shrinking the set. Leveraging the monotonicity,Eckert et al. (2017) generalize the method that is first developed in Jia (2008) tothe case of submodular profit functions and further show that we can alwaysreach a unique maximizing vector by partitioning the lattice and repetitivelyapplying the algorithm. I will discuss how to implement the algorithm withmore details in Section 1.3.2.In a multi-agent location game, existence of equilibrium, and in particulara pure strategy Nash equilibrium (PSNE), becomes much more challenging.There are three aspects of complexity in the game described in my multi-plantfirm model: discrete choices as firms decide to enter or not, multidimensionalas each strategy is defined as a vector of ones and zeros, and strategic sub-stitutes as players face competition. Attributed by the first two points, for atwo-player |M |-location game, the domain of strategies is an enormous set of22|M | number of configurations. Although the third point seems to be preva-lent in many applications, tackling games that exhibit strategic substitutes isnot as straightforward. Past literature has shown that there are substantial im-balances in existence and characterization of equilibrium between games withstrategic substitutes and strategic complements (i.e. Vives, 1999; Jackson andZenou, 2015; Jensen, 2005). An advantage of studying a game with strategiccomplements is that a PSNE always exists following Tarski’s fixed point theo-31rem (Tarski et al., 1955) and Topkis’ monotonicity theorem (Topkis, 1978). Insuch case, the equilibrium set is a complete lattice and highly structured whereplayers benefit from coordination and typically the greatest PSNE is also Paretooptimal (Milgrom and Roberts, 1990; Zhou, 1994). However, existence of PSNEis not generally true in games with strategic substitutes.16The multi-plant firm model in Section 1.2 is a submodular game. With mul-tidimensional strategies, submodular games are games in which the marginalreturns to any component of the player’s strategy drop with increases in othercomponents of the player himself and the competitors’ strategies. I have demon-strated above that the profit function exhibits decreasing differences in a firm’sown strategy due to self-cannibalization. The same holds for the marginal profitto be decreasing in the firms’ joint strategy space due to competition. Thismodel does not yield forces that could make plants being strategic complementsto each other.17 Neither does it imply any admissible parameter setting thatleads to supermodularity of the payoff function. The most relevant papers inrecent development of proving existence of a PSNE in submodular games areDubey et al. (2006) and Jensen (2010). They restrict attention to aggregativegames in which the payoff of a player only depends on his own strategy andan aggregate of others’ strategies (or what’s called “quasi-aggregative games”in Jensen (2010) when the strategy set is multidimensional). In our context,the firm’s profit, equation (1.12), is a function of its own location strategy L fand a weighted additive aggregate of rivals’ locations, Φm.18 Submodularityimplies that the game contains strategic substitutes. Moreover, if the plant loca-16One can refer to Example 1 in Jensen (2005) where no equilibrium exists for a strategicsubstitutes game.17Introducing agglomeration forces could easily make the firm’s profit function intractable.18Mapping to the notation in Jensen (2010), the aggregator g(L ) = ∑ f∈F Φ fm(L f ). The in-teraction functions are σ f (L− f ) = ∑g 6= f ,g∈F Φgm(Lg). The shift-functions Ff (σ f (L− f ),L f ) =σ f (L− f )+Φ fm(L f ) = g(L ). Therefore, our multi-plant firm model is a quasi-aggregative gameby Definition 1 in Jensen (2010).32tion strategy sets are compact and the profit function is upper semi-continuous,using best-reply potential game properties, Jensen (2010) proves that a quasi-aggregative game of strategic substitutes has a PSNE.19 20 I will illustrate howto find the equilibrium in Section 1.3.2 using a duopoly game, although theoret-ically it can be extended to more than two players.Proposition 4: For a |F |-player, |M |-location game in Section 1.2 with profitfunction exhibiting submodularity for all players, the set of pure-strategy Nashequilibria is not empty.Multiple equilibriaA common concern in estimating discrete games is the existence of multipleequilibria. The fact that for a given set of parameters and covariates, there maybe more than one equilibrium outcome, raises the well-known coherency prob-lem in econometric inference (Heckman, 1978; Tamer, 2003). In the absence ofinterdependency across locations, for a 2×2×1 (two players choosing enter onelocation or not) game with competition, the Nash equilibria is that either firmenters and the other stays out. With interdependency, the game would accom-modate more equilibria.Surveying the literature, there are four main approaches to deal with the19According to Corollary 1 in Jensen (2010), the quasi-aggregative game has to satisfy As-sumption 1 and 2 for a PSNE to exist. Assumption 1 is satisfied because the location game pre-sented here features strategic substitutes and therefore every firm’s best-reply correspondenceis a decreasing selection. Assumption 2 is also satisfied through a monotonic transformation ofthe shift-functions.20Eckert et al. (2017) impose additively separable condition to a player’s profit function toprove existence of PSNE in a game exhibiting single-crossing differences, meaning that the profitfunction is additively separated to a player f specific part and a common part of all players’actions. This is a much stronger sufficient condition than what is needed in Jensen (2010).33multiplicity of equilibria.21 The first is to model the probabilities of aggre-gated outcomes that are robust to multiplicity. For example, in the simplest2×2×1 game, the number of entrants is unique although the firm identity isundetermined (Bresnahan and Reiss, 1990; Bresnahan and Reiss, 1991; Berry,1992). However, information on firm heterogeneity is lost. Should I use it in thischapter, I would not be able to estimate the fixed costs distributions which arefirm-location specific.Second, one can embrace the multiplicity and take a bounds approach (Cilib-erto and Tamer, 2009; Pakes et al., 2015). The method sets identify parameterswhich could be too large to be informative. Lack of point identification becomesdifficult when performing counterfactual exercises. Estimating a bound alsocauses inference to be computationally intensive, such as placing confidence re-gion on the set.The third approach to multiple equilibria—the one taken here—is to choosean equilibrium by imposing certain entry sequence. I simulate the data and es-timate the model by selecting the equilibrium that would be chosen by the lowcost firm. While I model the entry game as static, the assumption is convenientin avoiding multiple equilibria.22 In principle, estimates could be sensitive tothe equilibrium selected and the predetermined order of entry. I assume the“true” equilibrium is selected because the focus of the exercise is to investigatewhether assuming separated entry is a good approximation to interdependentplant location model. Introducing additional uncertainty complicates the com-parison.21Ellickson and Misra (2011) provide a thorough discussion on estimating static discretegames, especially methods for dealing with the issue of multiple equilibria.22The same approach has been taken by Jia (2008), Atkeson and Burstein (2008b), Eaton et al.(2012), Edmond et al. (2015) among many others.34More recent development of the literature is around specifying a more gen-eral equilibrium selection rule that is a function of covariates and observables,as in Bajari et al., 2010. The solution requires computing all equilibria and anequilibrium selection parameter as part of the primitives to be estimated to-gether with the model. Although this approach is more general than imposingcertain sequence of entry, the computational burden to calculate all equilibria inan interdependent entry game is too high.1.3 Structural AnalysisIn this section, I lay out an estimation procedure of the multi-plant firm modelwith commonly available data. Instead of using the real data set, I generatedata based on the multi-plant firm model and then present results to show con-sistency of the estimates to the true DGP.1.3.1 DGP in Monte Carlo simulationsI consider a region consisting of 50 locations with one single-plant local firmin each of the location.23 Each location independently draws logarithm of thedemand shifters A, local productivity T , and input costs w, all from a uniformdistribution on the open interval (4,6). As for trade costs, I set τ`m= (1+t)×d0.2`m ,where t is the 10% tariff for trade flow between any location dyads, and distanced`m is specified as one plus the absolute difference between any two index ` andm from 1 to 50.There are two large entrants deciding where to produce out of the 50 poten-23For simplicity, I assume a group of small firms to make each location a potential candidatefor production, i.e. finite input costs. Therefore, all locations can potentially sell to one another.35tial locations given the group of small incumbents. Productivities of plants aredistributed Fre´chet with shape parameter θ = 5. Price elasticity of demand is setto be −η =−2. Firm B (for “big”) and firm M (for “medium”) draw plant-levelfixed costs from a log-normal distribution, log(FCB`)log(FCM`)∼ NµF =1.52, ΣF =0.25 0.250.25 0.25 .Firm B on average is cheaper to build plants than firm M. Given that the exerciseonly have two firms, I let them have perfectly correlated draws with commonstandard deviation, suggesting same perception on fixed costs of establishingacross locations. Should I allow for imperfect correlation across firms, thereneed to be more firms to identify such parameter.Based on these “true” primitives of the multi-plant firm model, I simulatethe model 100 times to generate 100 sets of data. Averaging across all the sim-ulations, firm B has 26 plants and firm M has 13 plants consistent with firm Bfacing lower fixed costs.24 Firm B accounts for around 32% of the total expen-diture on the product over the 50 locations, and the share for firm M is 21%.Among consumers served by the two firms, the prices paid to firm M is on av-erage 0.98 times of the prices paid to firm B, and firm M faces marginal costs1.1 times of those for firm B. Hence, firm M’s average markup is lower. Sincethe datasets are generated from the multi-plant firm model, it is not surprisingto see that these comparisons between the two firms corroborate the proposi-tions. Aggregating firms’ exports to location level, the average domestic marketshare is 21% corresponding to the share of product consumed in a market thatis produced locally.24The average out of 100 simulations is rounded to the nearest integer.361.3.2 Multi-plant firm estimationThe typical dataset that econometricians observe involves a combination of ag-gregated data at location level and limited firm level data. Other micro data,such as prices or shipping flow for individual plant, is not necessarily avail-able to researchers. I hereby propose a procedure to estimate the full modelwith minimal data requirement, namely bilateral trade volume between loca-tions Q`m, trade costs τ`m, demand shifters Am, and each firm’s plant locations{L f ,∀ f = B, M, single-plant firms}. For simplicity, I assume iceberg trade costsare known truthfully, and so do the demand shifters.25 The key parameters ofinterest in estimation are then narrowed down to {θ ,η ,µF ,ΣF}.The estimation is performed in three steps. First, I use a gravity-type regres-sion to estimate the composite of locations’ production capability T`w−θ` and theFre´chet dispersion θ . The sourcing probability derived from the model providesa natural link between theoretical implication and the bilateral trade data. Next,I project local consumption on the model-consistent price index constructed us-ing the estimates from last step, and estimate the demand elasticity−η throughnonlinear least squares. What has been obtained in the first two steps is criticalfor constructing firms’ expected profit as a function of plant location configu-rations and fixed costs. In the final step, I match the predicted optimal plantlocations to the actual ones to pin down parameters that govern the fixed costdistribution via method of simulated moments. Separability in estimation al-lows me to reduce dimensionality of the problem and save computational cost.More importantly, I can verify that the profit function is well defined before25In practice, econometricians observe distance between locations and tariff rates instead ofthe ad valorem trade costs. They need to additionally estimate the trade cost elasticity withrespect to distance. Similarly, econometricians observe location characteristics and need to es-timate A as a function of the covariates. However, I assume these elasticities are known at truevalues here because they are not central to firms’ trade-offs in this chapter.37implementing the combinatorial optimization algorithm in the last step.Step 1: Estimation of location production capability and plant productivitydispersionThe first step is to estimate each location’s production capability summarizedby the term T`w−θ` , and the dispersion of plants’ productivities θ . To do so, Itake the plant locations as given and exploit differences in trade originated fromother local attributes, such as productivity, input costs, and trade costs. Recallthat equation (1.10) provides the probability of m sourcing from `. Empirically,the model-predicted sourcing probability is associated with the trade share involume, i.e. s`m =Q`mQm. Transform equation (1.10) to its estimable version,Q`mQm= exp[FE`+FEm−θτ`m+ ε`m], (1.14)where the origin fixed effect FE` = ln(N`T`w−θ`), and the destination fixed effectFEm = − lnΦm. I estimate the gravity regression via Poisson Pseudo MaximumLikelihood (PPML) due to the consistency it delivers under general conditionsand its capability of incorporating zeros as clearly explained in Silva and Ten-reyro (2006) and Head and Mayer (2014).Estimating equation (1.14), I obtain the Fre´chet shape parameter directlyfrom the trade elasticity. As for the component T`w−θ` for each location, I needto tease out the number of plants N` from the origin fixed effects. The modelpresumes that local efficiency and input costs are underlying economic condi-tions without general equilibrium feedback of plants spatial distribution on fac-tor markets. Consequently, I can substitute N` with the observed data on plant38locations.26 Another issue is that the location production capabilities can onlybe estimated up to a scale. Normalization affects the absolute level of variableprofits and subsequently fixed costs. I will explain how to recover the scaleparameter in step 2.After the first step, I obtain estimates of an efficiency and input costs combi-nation for each location and the key parameter θ . Effects of these componentson firm profits depend on the price elasticity, −η . I now turn to estimating thedemand.Step 2: Estimation of demandTo estimate demand featured in equation (1.1), I combine it with the local priceindex derived from the model. Recall in equation (1.13), the price index is afunction of the estimated location production capability and Fre´chet parameterθˆ , data on trade costs and plant locations, and the unknown price elasticity.Denote the estimated location production capability from step 1 as ln T˜`w−θ` =ln T̂`w−θ` +λ , where λ is the normalization parameter and T̂`w−θ` are the absolutelevels used in DGP. Then, lnPm(T̂`w−θ` ) = lnPm(T˜`w−θ` )+λ/θˆ . Assuming demandshifter Am is observed, I estimate the following using nonlinear least squaresbecause the price elasticity affects demand also through firm markups,lnQmAm= κ2−η lnPm(η ; T˜`w−θ` ), (1.15)where the constant κ2 = −ηλ/θˆ . Hence, not only the price elasticity is esti-mated, but also I adjust the level of local production capability to be used later26In DGP, I assume all locations have at least one plant. Therefore, I arbitrarily eliminatethe potential issue of zero plant and unidentified local characteristics. In real data, this prob-lem would restrict our potential location set to only those with observed positive production,causing selection bias.39for constructing comparable firm profits as in DGP.In practice, one should also find valid instruments for prices and perform theabove via generalized method of moments, even for the constructed price indexbecause the endogenous plant locations are also used to form the price index.Some candidates for price instruments could be cost shifters in nearby locations.In this Monte Carlo simulation, for simplicity, I assume away the endogeneityproblem so that all the estimation error can be traced to the last step of theestimation.27 I can then focus on examining how well the model-predicted plantlocations match the simulated data, and keep a clear comparison between theestimates under the multi-plant versus the single-plant firm assumption.Step 3: Estimation of fixed costsHaving the necessary elements for constructing firms’ expected payoff, the laststep is to solve for firms’ optimal location sets and estimate the fixed costs ofestablishing plants. The model does not yield a closed form solution to firms’location choices conditional on the location observables and estimated vectorof parameter values. Hence, I would need simulation methods to get the sim-ulated estimate of entry probability for each firm-location pair.28 I assume thefixed costs are log-normally distributed as in DGP with a common shape butdifferent mean. I then draw a 2×50-dimensional matrix of FC f ` for a large num-27Note that the trade costs and demand shifters are observed at true values, so the constructedprice index in the second step will perfectly match the simulated “true” price if η is at its truevalue. Using instruments generated from DGP in estimation will introduce additional error.28There is actually another level of simulation for firm markups. Notice that the expectedvariable profit function (1.12) involves numerical integration over the markup. I use a stratifiedrandom sampling method in order to obtain good coverage of the higher markup. I defineintervals from 1 to µ¯ = η/(η − 1), [1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.95, 1.97, 1.99, µ¯].I then draw 5 uniform random numbers within these intervals. The draws receive a weightinversely proportional to the length of the interval. The integral part of the profit function isapproximated by∫ µ¯1 f (µ)≈ ∑Ss=1ws f (µs).40ber of times.29 For each repetition, the firm maximizes total expected profits bychoosing where to build the set of plants taken rivals’ locations as given.In a duopoly game with 50 potential locations, firms select from 2100 which isa magnitude of 1030 number of configurations. The model requires (η−1)/θ <1. Estimates from the first two steps would verify whether the condition is sat-isfied. In this submodular game, marginal profit of adding a plant is strictlydecreasing with the size of the active plant set. A firm would always enter a lo-cation which subtracting it from the full set will bring negative marginal profit,and vice versa, he would always stay out of a location which adding it to thenull set brings negative marginal profit. Define firm f ’s marginal profit of in-cluding ` in a location strategyL f as∆`Π f (L f ) =Π f (L f ∪ `)−Π f (L f \ `).Specifically, the AE-Repetitive algorithm in Eckert et al. (2017) works as follows.In the single-player case, starting from L f =M which contains all locations,` ∈L 1f if ∆`Π f (M ) > 0. Also at the other extreme, starting from L f = /0 whichcontains no entries, ` 6∈L 1f if ∆`Π f ( /0)< 0. The first round of mapping confirmssome of the coordinates. Now iterate the mapping until a complete equilibriumlocation set is reached with no more refinement can be made. When there areindefinite coordinates, Eckert et al. (2017) prove that the set of possible vectorscan be sliced to any two subsets and then operate the mapping on each of thesubsets separately. Slicing and mapping is repeatedly done until a unique opti-mal location vectorL ∗f emerges.29For the fixed cost draws, I follow Antras et al. (2017) to use quasi-random numbers froma van der Corput sequence which have better coverage properties than usual pseudo-randomdraws. I use 300 simulation draws for estimation.41In the duopoly case, there will be multiple equilibria as explained in Section1.2.3. I assume the larger firm, firm B, enters first which leads to the equilib-rium most profitable for firm B. The same ordering is used in DGP. Therefore,firm B starts to solve for his best response using the algorithm by taking firmM enters nowhere. Then firm M finds his best response given firm B’s initialstrategy. Two firms take turn to react until both best responses converge. Sincethe duopoly game is submodular, the iteration reaches a PSNE, {L ∗B ,L ∗M}. Thespeed of convergence in a game with best-response potential properties is expo-nential derived in Swenson and Kar (2017).30I identify the fixed costs of building plants via method of simulated moments(MSM). With any guess of {µF ,ΣF}, I can solve for the equilibrium plant loca-tions for the two firms using the above-mentioned algorithm. Due to the smallfirm sample, I fix perfectly correlated location draws between the two firms asin DGP. Essentially, parameters of interest are µFB ,µFM,σF . Moments are to matchthe model-predicted and the observed values of (a) number of firm B’s plants;(b) number of firm M’s plants; (c) difference between the average productioncapability for locations that firm B produces and those that firm B stays out; (d)difference between the average production capability for locations that firm Mproduces and those that firm M stays out. The first two moments are informa-tive about the mean of fixed costs for the two firms. The last two moments helpto pin down the dispersion of fixed costs distribution. The smaller the disper-sion, the less entry decisions vary by fixed costs but more by local profitability.Thus, firms produce where the location production capability is higher relativeto others.30In Table A.1, I present examples of two firms choosing among different location sets. Theaverage time of convergence for 10 potential locations is around 0.09 seconds averaging 1000simulations. It takes a maximum of three rounds of iteration to find the best response for twofirms.42Formally, the vector of moment functions, g(·) ∈ R4, specifies the differencesbetween the observed equilibrium outcomes and those predicted by the model.The following moment condition is assumed to hold at the true parameter valueδ0 = {µF ,ΣF} ∈ R3,E[g(δ0)]= 0. (1.16)A MSM estimator is such thatδˆ = argminδ1|M |[ |M |∑`=1gˆ(δ )]′W[ |M |∑`=1gˆ(δ )], (1.17)where gˆ(·) is the simulated estimate of the true moment function and W is aweighting matrix.31 I use the identity matrix and weight the moments equally inthe following estimation of the simulated data because precision of the estimatesis not a first-order concern when comparing results from the interdependententry model to those assuming separated entry. In Chapter 2 when I estimatefixed costs using data from the North America cement industry, I apply theoptimal weighting matrix as robustness checks and present the results in TableB.1.The complexity when having spatial correlation is that the moment functionsg(·) are no longer independent across locations. In order for the method of mo-ments estimators using dependent cross section data to be consistent, Conley(1999) proves the sufficient condition is that the dependence among observa-tions should die away quickly as the distance increases. In the current modelsetup, competition between plants becomes weaker when locations are further31The discrete choice decisions makes the objective function non-smooth and the firm’s prob-lem not globally convex. The shortcoming is that I cannot guarantee the solution I find is theglobal optimum of the problem. To address this issue, I tried the particle swarm optimizationalgorithm to search through 100 starting points. All sets of starting points resulted in closeoutcomes.43apart due to trade costs.1.3.3 Results from multi-plant firm estimationTable 1.1 presents results of the three-step estimation procedure. It should beexpected that the first two steps estimate Fre´chet shape parameter θ and priceelasticity η perfectly because DGP and estimating regressions are based on ex-actly same set of equations in the model. There is not measurement error in-troduced either since I substitute the “true” data on demand shifters, trade costand number of plants when regressing (1.14) and (1.15). The estimated locationproduction capabilities from fixed effects in gravity regression are also perfectlycorrelated with the simulated data on T`w−θ` .Let’s focus on the estimated parameters governing the fixed cost distribu-tion. The estimated mean of the fixed costs distribution for firm B and firmM are close to the true parameters. They are also estimated with high level ofprecision indicated by the small average standard error and mean absolute de-viation. I also compute the simulated coverage probabilities of the confidenceinterval, and found them remarkably close to the nominal coverage probability:for the 95% confidence sets the simulated coverage probabilities are 97% and94% respectively. The results support that average fixed costs of firm B and firmM are well identified by matching the number of plants each firm owns. So isthe difference in average fixed cost of building a cement plant by the two firms.The estimated standard deviation σF is slightly upward biased, but the trueparameter value is still less than one standard error away from the estimate.The below 95% simulated coverage probability indicates that the dispersion offixed cost distribution is not as strongly identified as the mean. The sample of4450 locations and two firms can make the inference suffer from asymptotic sizedistortion besides lack of independence.Comparing the predicted plant entry probabilities for the two firms with thelocal profitability represented by the production capability across locations, Fig-ure 1.2 clearly illustrates a positive correlation between the two. More impor-tantly, the figure shows what’s left to be explained in entry decisions is drivenby variation in fixed costs across locations. The dominant role of fixed costs isparticularly striking for those with fewer plants, causing some locations withrelative production advantage do not appear to be attractive to firms.Table 1.1: Estimated Parameters(1) (2) (3) (4) (5)True values Avg. estimates Avg. std. err. MAD Simulated coverageθ 5 5.0 0 0 1η 2 2.0 0 0 1µFB 1.5 1.500 0.216 0.092 0.97µFM 2 2.155 0.286 0.087 0.94σF 0.5 0.693 0.235 0.105 0.83Based on estimates and estimated standard errors from 100 simulated datasets, the table reportsaverage of the estimates, average of the asymptotic standard error, and mean absolute deviation(MAD) of the estimates. Simulated coverage probabilities of the 95% (nominal coverage) confi-dence intervals are constructed as the following. First, compute the confidence interval for eachdataset using estimate± 1.96× standard error. Second, count the proportion of datasets for whichthe confidence interval contains the value of the true parameters.I examine the estimation results by describing the model’s fit of the data inTable 1.2. For the moments that were targeted to match in estimation, namelynumber of plants built by each firm, the prediction almost exactly fits the data.I also report the correlations between the predicted and observed number offirm B plants and firm M plants in each location, which is 0.64 and 0.60 respec-tively. These correlations are not targeted in estimation, but still indicate a rea-45Figure 1.2: Predicted entry probabilities and production capabilities by lo-cationEstimated plant entry probabilityEstimated Tw-θsonable fit. Since number of plants affect trade flow between locations, I furthercheck the correlation between predicted share of trade volume for each locationdyads and the observed shares used in the first-step gravity regression. They arehighly correlated at 96.5%. The fraction of consumption supplied by domesticproduction is also matched pretty well. Lastly, I use Figure 1.3 to compare thepredicted consumption and production across locations against the simulateddata. Both dimensions distribute tightly along the 45-degree line and explainmore than 90% of the data. Overall, multiple test results establish confidencein the proposed multi-plant firm estimation method accounting for interdepen-dent entry decisions.1.4 Single-plant ApproximationHaving described all the mechanisms in a multi-plant firm framework, I pro-ceed to address a pressing question when applying this model: does interde-46Table 1.2: Goodness of FitData Model predictedTargeted momentsFirm B number of plants 25.7 25.7Firm M number of plants 13.2 13.2Non-targeted momentsDomestic market share 0.210 0.216Corr of trade shares 0.965Corr (firm B entry prob, sample locations) 0.641Corr (firm M entry prob, sample locations) 0.600Statistics for simulated data and model prediction are averages across 100repetitions, and thus number of plants is not integer. Correlations are calcu-lated by stacking the respective variables from each repetition.Figure 1.3: Fit for consumption and production45° lineSimulated dataEstimation predictedslope = 1.013fit = 1(a) Consumption (average over 100 simu-lations)45° lineSimulated dataEstimation predictedslope = 1.032fit = .91(b) Production (average over 100 simula-tions)47pendent entry matter? Realistically, a multi-plant firm could operate in a con-tinuum degree of control over its plants, with one extreme being complete over-sight of all its production locations and the other being full delegation to localmanagers. The latter is equivalent to treating each establishment as a single-plant firm. The framework in this chapter highlights two distinct features inmodeling decisions of multi-plant firms (MP) compared to single-plant firms(SP). One is that multi-plant firms coordinate prices among plants owned. Pricesetting at the firm level instead of plant gives the firm incentive to expand plantset to crowd out rival firms. The other is that multi-plant firms internalize can-nibalization through strategically placing the set of plants. A firm has incentiveto reduce its number of plants or locate them further apart to minimize self-cannibalization. These two counteracting forces are absent in a world with onlysingle-plant firms. They compete head-to-head with all other plants and enterif the expected profit net of fixed costs of oneself is positive.Although imposing single-plant assumption is inconsistent with the multi-plant firm’s objective to maximize total profits of all its plants through bothpricing and entry decisions, it is an empirically handy approach for researchersespecially when studying discrete choice decisions because one does not needto solve combinatorial optimization. Therefore, in this section, I focus on mea-suring the difference in entry decisions by ignoring interdependent entry in es-timation for a multi-plant firm DGP. Specifically, the model is preserved withspillovers from price coordination and cannibalization, but instead of solvinga set of plant locations, I estimate the cost parameters assuming separate entryacross locations. One can think of this alternative as a case where a local man-ager decides whether to build a plant or not given all other plants’ locations.The profit he/she expects is distributed by the parent firm based on a fraction48of the firm’s total profit.Under the same model, now let’s compute the expected profit for firm f atlocation `. Because pricing strategy is coordinated at the firm level, the pricedistribution for every plant owned by the same firm is identical as shown inequation (1.6). Hence, the expected variable profit for a particular plant is pro-portional to the firm’s profit based on the share of consumers sourced from thisplant over all firm f ’s consumers. With the Fre´chet distributed productivities,the sourcing probability of consumers in m from plant ` over the set of firm f ’splants iss f `m =φ`mΦ fm. (1.18)Multiplying the probability by equation (1.11) and subtracting the associatedfixed costs, I obtain the expected profit of a plant owned by firm f at ` isE[Π f `]= E[pi f `]−FC f `, (1.19)where E[pi f `]= κ∑m s f `mAm(R¯ fm−C¯ fm).Maintaining the same parametric assumption that fixed costs follow a lognormal distribution shifted by firm ownership, and then taking logs of the plantentry condition E[pi f `]> FC f `, the empirical form of plant entry probability un-der single-plant approximation isPr[` ∈L f]=Φ(1σFlnE[pi f `]− µFfσF). (1.20)Since the focus is to compare separate versus interdependent entry, estimatingequations from the first two steps in the multi-plant firm procedure remain thesame. Aggregated outcomes at location level are not affected by the change of49entry assumption if keeping the observed number of plants the same. Therefore,I can use same estimates from the first two steps to calculate plant-level profit.Inverting the coefficient of the expected profit at plant f ` gives a direct estimateof the standard deviation of log fixed costs, σF . I estimate equation (1.20) asa binary probit with the constructed lnE[pi f `]on the right-hand side, togetherwith a firm dummy.321.4.1 Monte Carlo resultsTable 1.3 summarizes and compares the estimation results under SP separateentry assumption and MP interdependent entry assumption. I compute the av-erage fixed costs based on the mean equation of the log-normal distribution,exp(µ+σ2/2). The larger firm B’s fixed cost tends to be overestimated whenneglecting interdependency, while firm M’s fixed cost is slightly lower. WithSP approximation, the simulated coverage probabilities of confidence intervalfor the estimated distribution mean are substantially lower than the 95% bench-mark, 47% and 78% respectively. This result demonstrates clear bias in estimat-ing fixed costs without considering that plant locations are interdependent onone another. The standard deviation of log fixed costs is unexpectedly a closeand precise estimate to the true value. However, the under-performance in cov-erage probability of σF in the case of MP is not as salient as the poor coverageof µF in the case of SP.To understand why fixed costs are estimated to be higher in single-plantapproximation for firms with more plants, one has to link back to the two ex-ternalities that are neglected for single plants, coordination and cannibalization.32I cluster the standard error at location level to account for correlated draws. Coefficients foreach set of simulated data are significant at 1%.50Recall that I have demonstrated in Section 1.2.3 that marginal profit of a multi-plant firm is positive with the number of plants as the firm is in better position tocompete against rivals. There are two countervailing forces against expandingthe plant set: cannibalization effects and additional fixed costs. These two pushthe size of plant set to the same direction. Moreover, cannibalization intensifieswith the number of plants a firm owned. Hence, a large firm cares more aboutcompetition among its own plants and build fewer relative to the counterfac-tual SP scenario. The single-plant approximated fixed costs need to be higherto match the observed plants number from a multi-plant firm DGP. On the con-trary, for a multi-plant firm that is not as big, the concern for cannibalizationis weaker and biases on fixed costs drop with no constraint that the biases arenecessarily upward. I leave finding the cutoff in plants number that balancesthe MP and SP results for future research.Table 1.3: Single-plant Approximated ParametersTrue values Single-plant Multi-plant(1) (2) (3) (4) (5)Avg. estimates Coverage Avg. estimates CoverageµFB 1.5 1.698 0.47 1.500 0.97µFM 2 2.210 0.78 2.155 0.94σF 0.5 0.534 1 0.693 0.83Based on 100 simulated datasets, the table reports average of the estimates and simulatedcoverage probabilities of the 95% confidence interval. In column (2) and (3), for each dataset,I compute the parameters of interest transformed from the Probit coefficients estimated us-ing equation (1.20), and their corresponding standard error using Delta Method (refer to Ap-pendix A.3.1). Confidence intervals are then constructed. Next, I count the proportion ofdatasets for which the confidence interval contains the value of the true parameters. Column(4) and (5) are from Table 1.1.Suppose I use the overestimated fixed costs of firm B from SP approximationto predict its entry decisions, Figure 1.4 presents that firm B would have enteredall locations with significantly smaller probabilities, averaging across 100 sim-51ulated datasets. Firm M would also have entered less aggressively on average,but by a smaller difference. Across simulations, panel (a) in Figure 1.5 is a vi-sual illustration of the fixed costs results in Table 1.3. In panel (b), predictednumber of plants for the two firms are matched exactly to the observables usingmulti-plant firm estimated fixed costs, but under-predicted using single-plantapproximation. Researchers would predict 4 plants fewer (roughly 15%) forfirm B and 2 plants fewer (roughly 13%) for firm M.Figure 1.4: Entry probability across locations45° line.1.2.3.4.5.6.7w/ Single-plant FC (mean over simulations).1 .2 .3 .4 .5 .6 .7w/ Multi-plant FC (mean over simulations)Firm BFirm MFigure 1.5: Firm-level comparison using multi- v.s. single-plant fixed costsacross simulationsAverage fixed costsFirm B Firm MMulti-plant mean Single-plant mean(a) Fixed costs (mean over locations)05101520253035Number of plantsFirm B Firm MTrue mean Mean w/ Multi-plant FCMean w/ Single-plant FC(b) Number of plants (sum over locations)52Although the SP approximation underperforms at the firm level, the pre-diction on market aggregates does not appear to be deviated by a significantamount, if anything, slightly lower than the simulated consumption and pro-duction across locations shown by Figure 1.6. The reason is that consumptionor production depends on plants spatial distribution as well as location charac-teristics such as its production costs and efficiency, and accessibility to nearbylocations. These other factors remain to be consistently estimated under thesingle-plant assumption, and thus alleviate the biases in the predicted plant lo-cations. The three-step estimation procedure is appealing because separabilityensures some model primitives are intact from the firm entry assumptions.Figure 1.6: Consumption and production using multi- v.s. single-plantfixed costs across locations45° lineEstimation predictedSimulated datafitted SPfitted MP(a) Consumption (mean over simulations)45° lineEstimation predictedSimulated datafitted SPfitted MP(b) Production (mean over simulations)There are two things that could make the single-plant approximation dete-riorate. The first is that firms are large and own many plants. The second isthat the cannibalization effect is strong indicated by a higher θ . Both wouldstrengthen a multi-plant firm’s motive to build fewer plants and further differ-entiate the firm’s decisions from a single plant.53The takeaway from this exercise is that assuming separated entry decisionsfor multi-plant firms generates estimation biases which are heterogeneous acrossfirms depending on their sizes. In particular, it has trouble approximating plantlocations of large firms. Since large multi-plant firms typically control a domi-nant share of economic activities in an industry, failure to account for interde-pendent sets of plants may misguide us from the correct outcomes.1.5 ConclusionsIn this chapter, I develop a multi-plant oligopoly model with endogenous andinterdependent location decisions. On the intensive margin, the model derivesmulti-plant firms’ pricing and markup rule in closed forms that generalize find-ings for single-plant firms in BEJK and others. It also characterizes the extensivemargin of multi-plant production and quantitatively solves a firm’s optimal setof plant locations. The two margins interact in a way such that a set of prop-erties emerge. More and favorably located plants increase the production ad-vantage of a firm, improve its capability to compete against rivals, and enhancethe firm’s market power to charge higher markup. At the same time, there aretwo forces against the expansion of plant set: cannibalization and fixed costs.Marginal payoff of opening up new plants diminishes because of business steal-ing among a firm’s own plants. Hence, a firm strategically places an additionalplant to the right location until the marginal payoff cannot cover its fixed costs.The framework points to the importance of spatial interdependency raised frompositive and negative spillovers among plants within the same firm.A key contribution of this chapter is to overcome the empirical challenge ofsolving combinatorial discrete choice problem for a multi-player game. Under54a parametric restriction on demand elasticity and competition intensity amongplants, the game is submodular, meaning that all plants are substitutes. For afirm’s own plants, competition dominates the positive spillover from the firm’sincreased market power. Submodularity and aggregative property of the loca-tion game underpin the methodology to solve for combinatorial optimizationby eliminating many location configurations. I extend the algorithm in Eckertet al. (2017) for a game-theoretic framework and show that we can always find apure strategy Nash equilibrium. Moreover, the model generates a gravity tradeequation that can be leveraged to separately identify model primitives, whichfurther reduces the computational cost of estimating the full model.The chapter goes on to use simulated evidences to show that if the multi-plant firm model is the truth, assuming separated entry could make poor pre-dictions if firms are large and cannibalization effects are strong. Estimates froma binary Probit are biased, and the direction of biases depends on firm sizes.This machinery of analysing multi-plant firms can be applied to evaluate awide range of policies. Specifically, how firms respond to policy changes by re-organizing plants and subsequent effects on prices, market structure, and wel-fare. For example, it is a known issue that carbon tax would induce leakagethrough firms moving to pollution haven. Other shocks, such as trade war ormergers of competitors, could also generate unintended effects through firm-level responses. Since multi-plant firms are prevalent in many industries andcontrol a large share of production and trade, studying policy effects withouta careful treatment of multi-plant production is worrisome. One caveat is thatapplication of the model is restricted to firms producing a homogeneous good.Products such as cement, steel or paperboard are likely to be suitable candi-dates. It also depends on at which level the product of interest is classified. I55turn to quantitative applications of this model to the second chapter of my dis-sertation.56Chapter 2Multi-plant Oligopolists in theCement Industry:Empirical Evidence and PolicyImplications2.1 IntroductionFirm-level adjustments to regulatory changes could undermine the intendedpurpose of a policy and impose costs on the economy. A classic example is aregional carbon tax that increases the local operating costs relative to the unreg-ulated rivals. Firms respond by moving production and associated emissionsto jurisdictions with laxer standards, leading to employment loss in the taxingeconomy and limited changes in total emissions. The problem is particularlyacute when emissions damages are global, as in the case of carbon dioxide. The57recurrent concerns on the issue of carbon leakage prompt a need for new anal-ysis to understand the spatial organization of firms, especially in concentratedindustries where the welfare costs can be further exacerbated.In this chapter, I estimate a structural static model of the cement industrythat incorporates multi-plant oligopolists and their decisions on plant locations,export and pricing, focusing on the US and Canadian markets. While thereare important local players in most markets, a series of consolidation has re-sulted in the industry being dominated by few giant multi-plant manufactur-ers. This model is adapted from the multi-plant firm framework developed inthe first chapter of my dissertation. It analyzes the tradeoffs faced by a multi-plant firm in deciding where to locate a set of plants and which plant to supplywhere, taking into account the competition with rival firms and within itself.The model features competitive advantage of a firm with more and favorablylocated plants, but the marginal benefit diminishes due to cannibalization ef-fects among its own plants. In industries where fixed costs are high and goodsare tradable, the plant location decisions are interdependent of one another. Asa result, a local cost shock is likely to generate global impacts. Although ce-ment has been frequently regarded as a non-traded good, data actually tells theotherwise. Figure 2.1 clearly shows that cement is actively traded between lo-cations in the US and part of Canada. Therefore, multi-plant firms’ interdepen-dent location decisions are relevant and the model is a well-suited and realisticcharacterization of the cement industry.Using the estimation toolkit for the multi-plant firm model proposed in thefirst chapter of my dissertation and adjusting for the data limitations encoun-tered in this sample, I am able to recover the key costs faced by cement pro-ducers, namely fixed costs of establishing a plant, the cost of production, and58Figure 2.1: Cement shipping flow, 2016the cost of trade.1 Considering building cement plants is subject to an onerousregulatory process which largely depends on local knowledge and connections,fixed costs are firm-location specific. Fixed costs of building an average sizedcement plant are estimated to be around $200 million to $300 million, with het-erogeneity between firms such that the largest player is capable of saving $100million per plant compared to her competitor. The massive amount of fixedcosts investment makes it an important determinant of firms’ production lo-cations, which then indirectly contributes to the market structure, prices, andother aggregated outcomes. Consistent with the observed data, the firm ex-ploits its cost efficiency by building more plants than any of the producers in1Since I apply a static model, dynamic parameters, such as sunk costs, per-period investmentcosts, and scrap values, are not considered in this chapter. Ryan (2012) estimates the per-periodcost of investment is merely 0.5% compared to the cost of entry. He also finds that a cementplant needs to pay the environmental cleanup fee to exit which is higher than proceeds fromselling off the land and infrastructure. The average negative scrap value is at -$53 million whichis roughly a quarter of the entry cost. Although these dynamic parameters are essential whenfirms decide whether to relocate plants in the next period, they are not a focus of this chapter. Icompare firms’ adjustment in the long run under different policy scenario, considering policiessuch as carbon tax are not likely to be one-off or only last for a short period of time.59this region. I also estimate the production cost of cement for the top two ce-ment manufacturers. It costs $57 per tonne of cement for the largest firm and$65 for the second largest, implying an average gross margin around 42% and33% respectively. Trade costs are primarily driven by distances and whetherlocations are adjacent and belong to the same country. Other than unfoldingthe cost structure of this industry and pointing to the firm-level heterogeneity, Ican also measure the degree of competition and cannibalization using the esti-mated model. The result indicates a fierce competition among plants, which isconsistent with cement being a relatively homogeneous product.The payoff for assembling all this machinery comes from the ability to usethe estimated model to explore policies. As one of the largest manufacturingsources of carbon emissions, the cement industry is commonly assessed to beemissions-intensive and trade-exposed with high risk of carbon leakage (Euro-pean Commission white paper, Europejska 2009). The nature of cement and itswide use in infrastructure construction also makes the industry a critical com-ponent of the national economy, along with the widespread concern over risingconcentration. The cement industry, therefore, is at the center of many policydebates. Applying this framework, I try to answer some of the pressing ques-tions in these discussions by predicting multi-plant firms’ responses to changesin environmental, trade and competition policies and the associated impacts onwelfare.First, I examine effects of the Greenhouse Gas Pollution Pricing Act (the Act)in Canada. Three carbon pricing schemes are considered, namely carbon taxwith and without border tax adjustment (BTA), and the output-based pricingsystem (OBPS). The latter two policies serve as remedies for production or car-bon leakage. Indeed, I find that change in plant locations is most aggressive in60the case of carbon tax alone.2 The increase in unregulated regions’ emissionsover domestic emission reduction (leakage rate) is 18% for a carbon tax at $50per tonne of CO2. BTA is most effective in fighting carbon leakage. Specifically,imposing same level of carbon tax to imported cement decreases the leakagerate to 12% but cannot eliminate it because many Canadian plants that used toexport to the US still lose their competitive advantage and are substituted bythe US plants. On the other hand, OBPS, effectively a rebate to firms to lowerthe carbon tax, retains the competitiveness of the domestic cement industry butfails to achieve a significant amount of emissions abatement.The counterfactual exercises provide estimates of the losses to producers andconsumers net of increases in government tax revenue. Of course, the policiesprovide social benefits from reducing emissions. I calculate the required socialcost of carbon required to generate overall benefits. The critical social cost ofcarbon must be $50 in the case of OBPS and higher in the case of a $50/tonnecarbon tax. These results indicate that it may be undesirable to impose a highcarbon tax on a concentrated industry where firms can locate plants differentlyto unregulated jurisdictions in steady state.Second, motivated by the unilateral tariffs that the US imposed from 2017to 2019, I examine effects of a 20% tariff increase by the US towards importedcement from Canada. Results show that the protectionism strategy is not suffi-cient to bring plants back to the US, while it would lose seven times more thanits trade partner Canada in terms of welfare.Last, I simulate a hypothetical acquisition of a leading US cement producerby the second largest multi-plant firm in the region. Efficiency gains from the2Change in plant locations refers to different spatial allocations of plants in two steady stateswith and without implementing the policy, instead of transitional dynamics.61acquisition facilitates the firm to expand its territory and substantially increaseits market share to catch up with the top player. In a head-to-head price com-petition, these efficiency gains of the second largest firm are always passed onas price reductions of its competitors, which I refer to as “efficiency effects”.3Meanwhile, the second largest firm lessens the competition by acquiring one ofits rivals and raises anti-competitive effects. The model is granular enough topredict consumer-specific price changes. I find that consumers served by the ac-quisition parties suffer a higher price due to lessening of competition, whereasconsumers served by other firms enjoy a price drop due to the “efficiency ef-fects”. Depending on the composition, the average price could decrease despitehaving a more concentrated industry, in which case efficiency gains dominateanti-competitive effects of the acquisition and increase total surplus.The cement industry has been studied in past research on industrial organi-zation and environmental economics. Some have been focused on the impactsof environmental policies as what is done in my first set of counterfactual exer-cises, such as Ryan (2012) and Fowlie et al. (2016). These works use a dynamicsetting, but similar to what has been found in this chapter, the carbon tax regimesignificantly increases the cost of entry, exacerbates market distortions, and re-sults in welfare losses. However, they measure carbon leakage using an aggre-gated demand shift in imports without factoring in the foreign market structureor interconnection between the domestic and foreign through multi-plant firms.They found that at $50 carbon tax, increase in all foreign emissions is 16% of theemissions abatement in the US. The leakage rate is lower than mine in which the18% is for US-Canada alone, suggesting that neglecting plant location changesof multi-plant firms could lead to underestimation of carbon leakage.3The optimal pricing strategy in the head-to-head price competition is to charge the priceequal to the marginal cost of the second-lowest cost firm, or monopoly price, whichever is lower.62Others, such as Miller and Osborne (2014) and Miller et al. (2017), focus theiranalysis at pricing strategy of cement firms, or horizontal and vertical merg-ers and acquisitions as in Perez-Saiz (2015) and Hortac¸su and Syverson (2007).Prior work analyzes the cement industry as localized competition (Rosenbaum,1994; Jans and Rosenbaum, 1997; Newmark, 1998; Hortac¸su and Syverson, 2007;Salvo, 2010; Ryan, 2012). To my knowledge, this is the first study that exploitsthe tradable nature of cement and endogeneize the cement plant location de-cisions to be interdependent. The impacts of policies are then not only aboutfirms’ pricing decisions, but also on the extensive margin.The remainder of the chapter is structured as follows. I describe the dataset and provide background of the cement industry in section 2. Section 3 dis-cusses the model that characterizes important facts of the industry. The modelis then estimated structurally in section 4, and in section 5, I perform three setsof counterfactual experiments. Section 6 concludes.2.2 The Cement IndustryThis chapter draws on several key institutional details about the cement indus-try.2.2.1 Industry backgroundCement is used to form concrete, the most-used input in construction and trans-portation infrastructure. It is a fine mineral dust that acts as the glue after mixedwith water to bind the aggregates together. Cement comprises 10 to 15 percentof the concrete mix.63Different raw materials, such as limestone, sand and clay, are mixed andground into powder, from which clinker is produced after heating the powderin kilns with peak temperatures at 1400-1450◦ Celsius. Fossil fuels are burntto produce the extreme amount of heat. Fuel combustion accounts for roughlyhalf the amount of CO2 emitted from producing cement, and the rest comesfrom the chemical reaction, known as calcination. In total, for every tonne ofcement produced, around 0.8 tonne of carbon is released into the atmosphere(Van Oss and Padovani, 2003; Kapur et al., 2009).The final output, cement, is produced by grinding clinker with gypsum orsmall amounts of other components to control its properties. Hence, there isstill some differentiation in cement types depending on its properties that bettersuits for some projects but not others. For example, pozzolana cement is pre-pared by adding pozzolana to portland cement. It is widely used in bridges,piers and dams due to the high resistance to various chemical attacks. Rapidhardening cement attains high strength in early days and is used in road works.Sulfate resisting cement is used in construction exposed to severe sulfate actionby water and soil in places like canals. However, overall, cement is a ratherhomogeneous product.Costs of productionAccording to a report by the leading cement manufacturer, LafargeHolcim, thevariable cost of producing cement consists of equally contributed costs of ma-terials, energy and labor. Ryan (2012) addresses the importance of equipmentmaintenance cost that leads to an increasing marginal cost curve when produc-tion is beyond 87% of the capacity. He uses data from 1980 to 1999, a periodwhen the utilization rate remains to be high. However, in recent years, the US64Geological Survey database (USGS) shows that none of the survey region in theUS exceeds a plant utilization rate of 80%, and the average is merely around65% in 2016. Therefore, it is defensible to assume constant marginal cost whenestimating the model based on data from 2016 in this chapter.Around 85% of the intermediate inputs for cement manufacturing is lime-stone (Van Oss and Padovani, 2003). Since the transportation cost of limestoneis high, cement firms mostly use limestone extracted from quarries nearby andtransport using a belt conveyor, truck or marine. It is natural for one to mistak-enly presume that cement plant location is entirely determined by locations oflimestone quarries. I show in Appendix B.2.3 that there are almost 3000 lime-stone quarries widely distributed across the US and Canada so that upstreamsuppliers in cement production is not restrictive in general. At the downstream,there are more than 5000 ready-mix concrete plants (US Geological Survey, USCensus). Therefore, a cement plant tries to position closer to sources of inputwhile taking the market demand and competition into account.As for the energy use and cost of fuel, firms and governments have beenstriving to deal with environmental concerns in the cement industry. On thefirm side, they have improved the kiln technology to optimize fuel usage. Cur-rently, according to Portland Cement Association, around 93% of the cementproduced in the US is manufactured through the dry process, a more energyefficient technic. Many plants that use the outdated wet kilns were closed byearly 1990s, after which the number of plants have been quite stable in the US.4The steady plant number and spatial distribution in recent years make the datasuitable for analyzing equilibrium. On the government side, most policy inter-4“Wet” or “dry” refers to the moisture content of raw materials. The wet process needs moreenergy because the moisture needs to evaporate. For more details in exit of plants in the USplease refer to Table 1 in Miller et al. (2017).65ventions are focused on shifting fossil fuels to more environmentally friendlysubstitutes by imposing carbon price on fossil fuels. Around the world, coalstill provides 90% of energy consumed by cement plants.5 The share of coal ismuch lower for developed economies, for example, 40% for plants in the USand Canada.6 As there is no systematic relationship between the kiln technol-ogy and the the type of fuel burnt, firms’ transition from coal to alternatives hasbeen slow. Thus, it is reasonable to assume plants retain the same compositionof fuel types and combustion efficiency facing environmental policy changesand focus on analysing firms’ adjustment on production.Other than variable cost of production, building a cement plant requiresgreat amount of fixed cost investment. Past literature as well as firm accountingrecords report that the fixed cost for building a one million tonne cement plant isaround $200 million (Ryan, 2012; Fowlie et al., 2016; Salvo, 2010). It contributesto cement plants being scarce and discrete as shown in Figure 2.2. Firms, there-fore, face the proximity-concentration trade-off between paying fixed costs ver-sus bearing trade costs. More details of Figure 2.2 will be explained later.Active shipping flowIt has always been a myth that cement is too expensive to transport and thusonly locally consumed. Given the year, the cement trade share out of world pro-duction can reach as high as nearly 8%. Although trade in cement has been slug-gish since then, it remains to be active regionally. Across the US and Canada,data shows that trade in cement is comparable to other manufacturing prod-ucts. Figure 2.3 visualizes how trade decreases with distances for cement and5Source: https://www.globalcement.com/magazine/articles/974-coal-for-cement-present-and-future-trends6For a complete breakdown of fossil fuel usage and energy efficiency, please refer to TableB.4.66Figure 2.2: Cement plants and consumption in 2016all manufacturing goods in the US and Canada, and compare those with thebenchmark case of frictionless trade where each origin is equally likely to ex-port to a destination regardless of distance. Half of the cement in this regionis transacted within 300 kilometers, and it extends to 420 kilometers for man-ufacturing goods. Furthermore, there is still about 10% cement trading in longdistance beyond 900 kilometers. The figure also implies that trade costs increasewith distance. Figure 2.4 presents trade share decreases with distance and in-creases for contiguous partners, which are consistent with the standard gravityestimates.Active cement trade in this region also corresponds to the fact that cement67Figure 2.3: Distribution of distance for cement and trade in goodsFigure 2.4: Inversely proportional cement trade to distance(a) Exports (b) Imports68is not produced everywhere as seen in Figure 2.2. The grey border on the mapindicates 149 survey zones from Freight Analysis Framework (FAF), which in-clude census agglomerations, census metropolitan areas, and the remainderarea of province/state in the US and Southern Canada. Out of the 149 FAF zonesin my sample, only 73 of them have cement plants, whereas the rest are entirelysupplied through imports. Figure 2.5 shows the export intensity and importpenetration across the 73 FAF zones. On average, a zone exports 44% of its localproduction and imports 27% of its cement consumption.7 The positive corre-lation between export intensity and import penetration suggests intra-industrytrade in cement across locations. I exploit plant heterogeneity and buyer-selleridiosyncrasies to rationalize such pattern.Multi-plant firms take the possibility of cement trade into consideration whendeciding the set of production locations. Since a plant not only serves the localmarket, but also acts as an export platform, the entire set of potential locationsforms a network where what happens to one location has global influences.Therefore, plants owned by a multi-plant firm are interdependent on one an-other, making the location problem combinatorial.Multi-plant oligopolists and fringe firmsThe cement industry is highly concentrated with a few multi-plant oligopolists.In 2015, the top one world cement manufacturer, Lafarge from France, mergedwith the third largest, Holcim from Switzerland. The new giant owns 20% of7Since Canada Freight Analysis Framework is a logistics file, the origin of cement flow withinCanada may not be documented as its production location. Neither is the destination of ce-ment flow being its market for final consumption. Therefore, some Canadian FAF zone, suchas Hamilton, Oshawa, and Rest of Alberta (excluding Edmonton and Calgary), could have ex-tremely high export intensity and import penetration ratio because of re-export and re-import.I acknowledge the data limitation may cause measurement error.69Figure 2.5: Cement trade intensity, 2016BirminghamMobileALTucsonAZARLos AngelesSan FranciscoCADenverCOMiamiOrlandoTampaFLAtlantaGAChicagoILIndianapolisINIAKSLouisvilleMEBaltimoreMDDetroitMIKansasSt. LouisMOMTOmahaNVNMAlbanyNYDaytonOHTulsaOKORPhiladelphiaPittsburghNew YorkPACharlestonSCSDKnoxvilleTNAustinDallasSan AntonioTXSalt LakeUTVASeattleWAWVWYNSQC MontréalONOshawaTorontoHamiltonABEdmontonVancouver020406080100Export intensity(%)0 20 40 60 80 100Import penetration(%)USCanadacement plants in the US and Canada, followed by Cemex who owns another10% of plants in the region and headquartered in Mexico. Figure 2.2 shows thespatial distribution of these two multi-plant firms, and also a large group offringe belonged to the other 24 firms.8 Overall, the four-firm concentration ratiomeasured by installed capacity is 51% in the US and 86% in Canada. There areat most four cement plants in a single FAF zone.In the international market, Bernard et al. (2018) well document findingsabout multinational firms participating along multiple margins of internationalactivities. Similar patterns can be found for multi-plant firms regionally. Largest8Another key player in the region is Heidelberg. It announced to acquire Italcementi at theend of 2016. After one cement plant divesture requested by the Federal Trade Commission, itwould surpass Cemex as the second largest player in the region. However, my data ends beforethe acquisition actually happens. Besides, I don’t think Heidelberg and Italcementi prior to theshock are suitable for the equilibrium analysis.70Table 2.1: Distribution by plant and FAF zonePanel A: Percentage of firmsNumber of FAF zonesNumber of plants 1 2-4 5-10 11+ Total1 34.6 0.0 0.0 0.0 34.62-4 0.0 30.8 0.0 0.0 30.85-10 0.0 3.8 19.2 0.0 23.111+ 0.0 0.0 0.0 11.5 11.5Total 34.6 34.6 19.2 11.5 100.0Panel B: Percentage of capacityNumber of FAF zonesNumber of plants 1 2-4 5-10 11+ Total1 6.5 0 0 0 6.52-4 0 21.5 0 0 21.55-10 0 3.6 26.7 0 30.411+ 0 0 0 41.6 41.6Total 6.5 25.1 26.7 41.6 100Panel C: Percentage of plantsNumber of FAF zonesNumber of plants 1 2-4 5-10 11+ Total1 7.4 0 0 0 7.42-4 0 19 0 0 195-10 0 4.1 28.9 0 33.111+ 0 0 0 40.5 40.5Total 7.4 23.1 28.9 40.5 100cement firms produce in more locations, own more plants, and have greater pro-duction capacity at each location. In Table 2.1, I report joint distributions for 26cement firms by the number of plants owned and the number of productionlocations entered in my sample. Panel A reports the distribution in number offirms; panel B reports the distribution in market share measured by capacity;and panel C reports the distribution in share of plants owned. Comparing re-sults across the three panels, around 35% of cement firms are highly localizedwith a single plant at one FAF zone. These single-plant firms account for only6.5% of production capacity and 7.4% of cement plants. On the contrary, 3 firms71that own 11 or more plants across more than 11 FAF zones control around 42%of production capacity and 40.5% of plants. The positive correlation across dif-ferent margins of multi-plant firms’ operation ensures that the market is domi-nated by a few firms. Along the intensive margin, Table 2.2 shows the averagemarket share across locations where firms enter. The last row demonstrates thatfirms entering more locations on average obtain larger market share at each lo-cation through building larger plants. So do firms owning more plants shownby the last column.Table 2.2: Average market share by plant and FAF zoneNumber of plants Number of FAF zones1 2-4 5-10 11+ Mean1 29.7 0 0 0 29.72-4 0 39.2 0 0 39.25-10 0 37 38.3 0 38.111+ 0 0 0 47.1 47.1Mean 29.7 38.9 38.3 47.1 36.6Market share is measured by production capacity. FAF zoneswith only one firm producing, i.e. 100% local market share, areexcluded in computing the average to make sure the table is acomparison for capacity of each plant.In sum, although large multi-plant firms are dominant, the group of localand smaller cement producers is too big to ignore.2.2.2 Data descriptionThis chapter focuses on studying the cement industry in the contiguous US andthe part of Canada which have the most active commodity flow with the US.Data is collected from four main sets.First, cement plant locations are sourced from Global Cement Report pub-72lished by International Cement Review. The directory covers 2108 operatingcement plants worldwide in 2016, out of which 104 are in the US and 17 are inCanada. For each plant, the directory lists its name, ownership, location, andcapacity. With the plant ownership data, I can identify all the multi- and single-plant firms in the region.One limitation about this dataset is that without information on plant open-ing or closing, I have to work with the snap shot of plant data in 2016. Never-theless, it is valid to use the cross-sectional data for estimating a steady state fortwo reasons. One is that the number of plants and their spatial distribution inthis region have been relatively stable during the last two decades as mentionedin Section 2.2.1. The other is that despite the mega-merger happened in 2015, allthe divesture by LafargeHolcim post-merger was realized in 2016, which is ad-justed in my sample data.9 One caveat is that the third largest producer Heidel-berg announced to acquire Italcementi at the end of 2016, and it is not reflected inmy sample because the acquisition and divesture did not complete until 2017.10The close timing of these two M&As raises concern that there might be strate-gic interactions played in another game if the events were expected. However,modeling such game would be beyond the scope of this chapter.Second, bilateral cement trade flow is constructed from Freight AnalysisFramework by the US Department of Transportation, Canadian Freight Analy-sis Framework by Statistics Canada, and US Geological Survey database (USGS).Production locations and consumption markets are zones defined by the Freight9For a complete list of divesture, please refer to the information on FederalTrade Commission (FTC) website, https://www.ftc.gov/enforcement/cases-proceedings/141-0129/holcim-ltd-lafarge-sa-matter, especially the “Analysis of Agreement Containing Consent Ordersto Aid Public Comment” published on May 4, 2015.10FTC demand the divesture of one cement plant in Martinsburg, West Virginia. Source: https://www.ftc.gov/enforcement/cases-proceedings/151-0200/heidelbergcement-ag-italcementi-spa-matter73Analysis Framework, which are the smallest geo-unit available in these datasets.As mentioned earlier, it includes census agglomerations, census metropolitanareas, and the remainder area of province/state. After checking cement mergercases documented by the Federal Trade Commission, I find that metropolitanarea is also the unit of assessment for competition impacts. To some degree, itsubstantiates the definition of markets in my empirical analysis. Additionally,it’s rarely seen that a cement firm would have more than one plant in a FAFzone.11 The define geographical unit for location is consistent with my modelwhere a firm decides whether to have a plant or not instead of how many plantsfor a single location. Figure 2.2 shows cement consumption across FAF zones,in which Los Angeles and Dallas are the largest markets.The availability of trade data allows me to assemble a balanced panel of73 origins shipping cement to 149 destinations from 2012 to 2016, taking intoaccount that cement is only produced in the subset of FAF zones. Details ofhow to assemble the data from multiple sources and associated assumptionsare provided in Appendix B.2.1. The estimation is also complemented by bi-lateral trade in cement at country level where the data is obtained from UNCommodity Trade Statistics Database.Third, bilateral trade frictions are sourced from various datasets. At FAFzone level, distance is measured as great-circle distance between the zone cen-troid. Within a zone, internal distance is measured as great-circle distance be-tween the northeastern boundary and the southwestern boundary. The aux-iliary country-level regression uses CERDI-seadistance database and shippingdays measured in Feyrer (2018). The former computes sea distance as the short-11For the four locations that actually do contain two plants belonging to the same firm, Icombine plants to one. One of them is Cemex at a FAF zone in Florida.74est sea route between two highest traffic ports in respective country, and land-locked countries are associated with the nearest foreign port. The later calcu-lates round-trip shipping days between primary ports for each bilateral pairassuming an average speed of 20 knots with adjustments. The country-level re-gression also uses tariff data from the World Integrated Trade Solution by WorldBank and other gravity variables from CEPII research center.Lastly, to estimate demand, I collect input costs to construct instrument vari-ables for prices, including durable goods manufacturing wage, limestone prices,natural gas and electricity prices. They are sourced from the US Energy In-formation Administration, US Quarterly Census of Employment and Wages,Statistics Canada, Natural Resources Canada, and USGS Quebec Hydro. De-mand shifters including population and units of building permit issued are alsocollected from US Census and Statistics Canada. To map the consumption data,I collect all these variables from 2012 to 2016.2.3 Multi-plant Production and Welfare MeasuresI adapt the multi-plant firm model developed in the first chapter of my disserta-tion to the context of the cement industry and then list the welfare measures forpolicy evaluation. For consistency, I use the same set of notations as in the firstchapter. There are a finite number of discrete geographical units m ∈M , and agiven set of potential entrants F . Cement is tradable across these locations. Acement firm, f ∈F chooses a subset L f ⊆M to set up plants, and then com-petes in price with rival firms and decides which cement plant ` ∈L f to serveready-mix concrete producers.12 A firm’s plant set depends on the profitabil-12The majority of downstream consumers of cement are ready-mix concrete plants, the restare construction firms and individual users. Who are the consumers do not matter as long as75ity of each potential location, its own idiosyncratic fixed costs, and competitionforces among plants within and across firms.Considering there are more than 5000 concrete plants in the US, I treat con-crete producers i distributed continuously on a unit interval at each market m.Demand is isoelastic given by Qm = AmP−ηm where η > 1. The multi-plant firm’sproblem follows exactly the same structure as before, except that the constantmarginal cost of supplying cement from a plant in ` owned by firm f to a con-crete producer i in m is now richer asC f `im =W 1/3` E1/3` M1/3`Z f `iτ`m, (2.1)where location ` has worker wage W , energy price E and intermediate materialpriceM. They form a Cobb-Douglas composite of input costsw`=W1/3` E1/3` M1/3` ,and a third of the cost share each is consistent with the cement industry normmentioned in Section 2.2.1.13 Distribution of plants’ idiosyncratic shock Z f `i fol-lows a Fre´chet distribution with CDF, exp(−T`z−θ). By plotting the capacity ofcement plants in my sample in Figure B.4, the empirical distribution displaysa better fit to a bell shaped curve, and thus partially corroborates the use ofFre´chet despite that capacity is not a perfect approximation to Z f `i.Given that the plant productivities are distributed Fre´chet, the expected marginalcost of production, excluding transportation costs τ`m, for the lowest-cost plantthere are many of them to be approximated by a continuum interval.13Perez-Saiz (2015) also specifies a multiplicative expression for the marginal cost of cementplants. For technical reason, a Cobb-Douglas cost function simplifies the counterfactual exer-cises because cost shocks can be applied as ad valorem changes.76owned by firm f isE[C1, f i] = Γ(1+1θ)(∑`∈L fT`w−θ`)− 1θ. (2.2)A firm owning more plants at favorable locations would have lower productioncosts on average. The cost advantage continues to hold in terms of distribu-tion since a dense network with more plants implies a shorter average shippingdistance.In the multi-plant firm model, firms compete head-to-head in price for acommon product. The competition structure coincides with two important fea-tures of the cement industry. One is that cement is a homogeneous product.14The other is that according to Miller and Osborne (2014) and Miller et al. (2017),cement firms price to market and the price “reflect(s) the ability of the customerto source cement from competing manufacturers”. The multi-plant firm sets theprice such that plants owned by the same firm coordinate in pricing and under-cut those owned by the rivals. Optimal price is equal to the marginal cost of thelowest-cost plant owned by rivals, or the firm’s monopoly price, whichever islower. The expected price for firm f charging to concrete producers at m isE[Pfm]= Γ(θ +1θ)ΦmΦ fm((Φm− (1− µ¯−θ )Φ fm)−1/θ − (Φm−Φ fm)Φ− θ+1θm ) .(2.3)The production and distribution efficiency gains from having more and favor-ably located plants are incompletely passed through as price reductions of thefirm but raise its markup given the head-to-head pricing strategy.Combining the Fre´chet distributed plants and the nested competition struc-14The minor differences in types of cement can be absorbed by the plant-consumer idiosyn-cratic shock Z f `i because each type correspond to certain use of cement.77ture, the model gives rise to a gravity consistent probability of each market msourcing from plants at `,s`m =N`φ`mΦm, (2.4)where φ`m = T`(w`τ`m)−θ is a location `’s capability of supplying cement to m,and Φm = ∑`N`φ`m is the overall sourcing potential of m, summing across allcement production sites and the number of plants at each site N`. The moreplants entered (high N), more efficient a location (high T ), the cheaper costsof inputs (low w), and the smaller trade costs (low τ), the higher competitiveadvantage a location has against alternatives in supplying cement. The Fre´chetshape parameter θ governs the trade elasticity. Higher θ implies that cementplants are more homogeneous, competition is fiercer and trade is more elastic.After deriving the optimal price distribution and given the isoelastic de-mand, I obtain a closed-form expression for the multi-plant cement firm’s sales,taking expectation over the random productivity draws for all plant-consumerpairs,E[R f ] = κ∑mAm((Φm− (1− µ¯−θ )Φ fm)− 1−ηθ − (Φm−Φ fm)Φ− θ+1−ηθm), (2.5)where the constant κ = Γ(θ+1−ηθ)and the monopoly markup is µ¯ = ηη−1 . Afirm’s capability of producing and distributing cement is summarized byΦ fm =∑`∈L f φ`m, which depends on how many and where the plants are. More plantsat favorable locations will increase the firm’s competitive advantage and itssales. Subsequently, the model yields a multi-plant firm’s expected total profitsuch that the firm can find its optimal plant set to maximize the profit,L ∗f = arg maxL f⊆ME[pi f (L f ;L− f ,φ ,A,θ ,η)]− ∑`∈L fFC f `, (2.6)78where φ is a vector contains φ`m for all location-market dyads and A is a vectorof demand shifters for all markets. I defer the full expressions of the expectedvariable profit E[pi f ] to Appendix, but highlight the key elements constructingthe function here.Firm f pays the fixed costs FC f ` to build a cement plant at `. The fixed costsare non-negligible especially in the cement industry. Moreover, fixed costs ofbuilding cement plants are likely to be firm-location specific. It could reflecta multi-plant firm’s managerial and communication costs to locations furtheraway from the firm headquarter. Specifically in the cement industry, plant es-tablishment is subject to several layers of regulatory approval, such as envi-ronment clearances for mines, for handling effluents, and land procurement.Different regions are neither uniform in these procedures. Hence, a firm’s localknowledge would also make a significant difference. Theoretically, the varia-tion of fixed costs across firms are what differentiate them ex-ante. Recall thatthe model assumes plants at the same location draw from the same distributionregardless of firm identity, meaning that different firms produce at exactly sameset of locations have equal variable profits in expectation. Therefore, a firm withlow average fixed costs would build more plants than another with high fixedcosts.A multi-plant firm’s profit, unlike a single plant, sums all its plants’ profitthat each is a function of all other plants’ locations. As explained extensivelyin chapter one, one of the key takeaways from the multi-plant firm model isthat coordination and cannibalization counteracts among plants within a firmsuch that the firm’s profit increases with the number of plants but the marginalreturn diminishes. On one hand, a multi-plant firm internalizes price decisionsof its own plants and tends to build more plants to exploit the market power79against its rivals. On the other hand, the firm internalizes business stealingeffect and tends to build fewer plants. Plants are strategic substitutes and theprofit function exhibits submodularity. Interdependencies among plants makethe multi-plant firm’s location decision a combinatorial discrete choice problemthat requires powerful numerical tools to solve.Aggregating each firm’s optimal price, the local price index isPm = Γ(θ +1θ)Φ−1/θm ×[(1−|F |)+ ∑f∈F(1− (1− µ¯−θ )s fm)−1/θ ]. (2.7)Now, let’s introduce policy interventions or shocks that lead to firms’ adjust-ment in production locations after re-optimizing the profit function. The changecould come from costs of production, costs of trade, or a particular firm’s busi-ness operations. Because all plants are interconnected through spillovers, a lo-cal change could potentially cause a global reshuffling if the shock is sufficientlylarge. Changes to production and trade costs can be summarized as a shift fromφ 0 to φ 1. The new plant locations are L 1f and the original ones are L0f . Thesechanges in turn affect price indices to the new level P1m. Therefore, welfare effectsin producer and consumer surplus in the cement industry are∆PS= ∑f∈F(pi f (L 1f ;L1− f ,φ1,A,θ ,η)−pi f (L 0f ;L 0− f ,φ 0,A,θ ,η))(2.8)∆CS=11−η ∑m∈MAm((P0m)1−η − (P1m)1−η) . (2.9)Moreover, I define SCC as social cost of carbon which is the long-term damagedone by a tonne of CO2 emissions in a given year measured in monetary term.Noted that carbon damages are global regardless of origin, and hence, the valueof total carbon emission changes, domestic and foreign, is fully borne by ev-ery market. The social cost of carbon needs to reach the following minimum80threshold for a policy to be welfare improving for the domestic market,SCCD =∆PSD+∆CSD+∆GRD∆eD(1−λ ) , (2.10)where I define λ = −∆eF/∆eD, meaning the change in foreign emissions to thechange in domestic emissions, as the leakage rate. Changes in domestic gov-ernment revenue is ∆GRD. Similarly, if I analyse all markets as a whole for auniversal shock, the corresponding threshold becomesSCC =∆PSD+∆CSD+∆GRD+∆PSF +∆CSF +∆GRF∆eD(1−λ ) . (2.11)These “required” social costs of carbon are one way of evaluating counterfac-tual policy experiments in Section 2.5, taking into account the environmentalexternality.2.4 EstimationThe first chapter of my dissertation proposes a three-step procedure to estimateparameters in the multi-plant firm model. In this section, I show how to per-form the estimation procedure using the data on the cement industry for theUS and Canada described in Section 2.2.2. Observing equation (2.6), key prim-itives of the model are the Fre´chet dispersion parameter θ , demand elasticityη , a composite of locations’ production capability Tw−θ , trade costs τ , demandshifters A, and fixed costs FC (vectors are bolded).I specify trade costs as a function of observed determinants, denoted X`m,τ`m = exp(X′`mβτ), (2.12)81where β τ is a vector of the trade cost parameters. The vector X`m includes thestandard explanatory variables used in gravity equations: distance, contiguity,whether the dyads are located at the same state, province, or country. Thesevariables have been shown to matter for trade flows in the past literature. Sim-ilarly, demand shifters are characterized as a function of population and thenumber of building permits on new privately-owned residential constructionunits.15Am = exp(X′mβA), (2.13)where βA is a vector of demand parameters. Lastly, instead of estimating everyfirm-location specific fixed costs which are impossible to be identified. I specifythey are realizations from a log-normal distribution,log(FC f `)∼ N(X′f `βF ,(σF)2) . (2.14)The distributions of fixed costs are shifted by the distance between FAF zonesand the firm’s North American headquarter, as well as an interaction dummyof the firm and the country where FAF zones locate. Distance is a proxy formanagement and communication frictions faced by multi-plant firms, while thefirm-country dummy captures a firm’s local knowledge that affects buildingcosts of a cement plant.16 Therefore, what left to be estimated to fully recoverthe model is {Tw−θ ,θ ,η ,β τ ,βA,βF ,σF}.15Cement is also widely used for non-residential, commercial construction projects. Unfortu-nately, data on the volume of non-residential construction activities is unavailable.16Building a cement plant can take years to get the regulatory approval and is extremelycostly in administration. A cement firm who has local knowledge and relationship may beable to reduce the regulatory costs. For example, Lafarge merged with Canada’s largest cementproducer, Canada Cement Company, in 1970, and then experienced unprecedented growth.Cemex, on the other hand, invested in the US market after the anti-dumping duty order onimports of gray Portland cement from Mexico went into effect on August, 1990. Cemex thenshifted its strategy from export to FDI. In particular, it acquired Southdown in 2000 and RMCin 2005, which both owned assets throughout the US.822.4.1 Step 1: Estimation of local production capability, tradecosts, and plant productivity dispersionBased on the multi-plant estimation procedure, the first step is to estimate agravity type regression transformed from the sourcing equation (2.4),Q`mQm= exp[FE`+FEm−θX′`mβ τ + ε`m], (2.15)where the location fixed effect FE` = ln(N`T`w−θ`), and the market fixed effectFEm = − lnΦm. Our goal at this stage is to estimate θ through trade elasticity,trade costs parameters β τ from variations in standard gravity variables, andTw−θ from location fixed effects.When estimating equation (2.15), two issue occur specific to the sample Iused. One is that θ is not separately identified from β τ . To deal with the firstissue, I supplement the FAF-zone level gravity regression with a country-levelregression that exploits tariff variation to identify the trade elasticity. Distance atthe country level is replaced with measures of sea distance as explained in Sec-tion 2.2.2 to reflect the fact that international trade in cement is mostly sea-borne.Tariff refers to the logarithm of one plus the bilateral tariff as an ad-valorem costshock, of which the coefficient is an estimate of−θ .17 The trade cost parametersβ τ can subsequently be teased out. Estimating the trade elasticity at differentlevel of data is justified because the model provides nice aggregation propertiessuch that trade elasticity remains as −θ even at country level.17According to WTO, only 5 member countries specify tariff of cement in specific or othernon-ad valorem formats. It accounts for 0.6% of all tariff lines in HS chapter and across allmember countries. The majority uses ad-valorem tariffs. In estimating trade elasticity, I treattariff as cost shifters rather than demand shifters, assuming tariffs are imposed before markups.Cement manufacturers are typically the one building port facilities, importing cement fromabroad, clearing customs and the one selling cement domestically. Therefore, they do not haveincentive to markdown price but rather report it as a cost. See Costinot and Rodrı´guez-Clare(2014) for more detailed discussion.83The other is that in the US-Canada sample, cement plant and positive cementproduction only exist in 73 FAF zones, a subset of those that consume cement.I denote this subset as L ⊂M . Trade is restricted to be originated from theselected area, which is consistent with the theory where the number of plantsentered is multiplicative in determining the sourcing probability from a locationin equation (2.4). Estimates from the gravity trade regressions are not biasedeven with the selected sample. For the 73 FAF zones, estimates for the local pro-duction capability T`w−θ` are obtained from the estimated location fixed effectsadjusted by the observed number of plant assuming no general equilibrium ef-fects of plant locations to factor markets. However, what’s more problematicis that the production capability for the rest of the locations will remain to beunknown to econometricians. I assume that the zero-production locations haveinfinite costs such that cement firms will never build plants there in equilibrium,and thus, it is plausible to exclude them from firms’ choice sets. Observing Fig-ure B.3 that plots the spatial distribution of limestone quarries, we see that somestates and provinces without cement plants are also places where there is noor very limited resource for materials, such as Saskatchewan, Manitoba, NorthDakota, Nebraska, Wisconsin, Louisiana, and Mississippi. However, imposingthe assumption could bias the fixed cost estimates if the observed zeros are ex-post realizations of stochastic shocks.The baseline estimates are obtained by running equation (2.15) via PoissonPseudo Maximum Likelihood (PPML), but I also applied alternative specifica-tions to valid the results. Table 2.3 summarizes the first-step results. Column(1) to (3) report the results for the main sample - the US and Canada FAF zones,whereas column (4) and (5) regress on the auxiliary sample of 144 countries.As expected, OLS overestimates the effect of distance compared to PPML in the84presence of heteroskedastic gravity errors. The estimates obtained from runningPPML on trade flows and trade shares are very close although the latter imposesless weight to large flows. At FAF zone level, the effects of distance to other FAFzones and its internal distance between boundary points are separately esti-mated. The elasticity of distance to other zones is estimated to be around -1.2,which is consistent with what has been found in the past literature (around-1). The effect of internal distance is smaller around -0.4, suggesting that ce-ment is more than proportionally consumed at home location, a result accordswith the positive and significant home coefficient in the country-level regres-sion. The distance elasticity estimated using the country sample is also aroundthe same magnitude despite that distance is measured differently. All columnsshow more trade if locations are adjacent. State/province and country borderalso matter. Sharing common trade agreements boosts trade between countries,but not common language. The key parameter of interest in the country-levelgravity regression is the elasticity of trade with respect to trade costs. It mapsto the negative plant productivity dispersion parameter in the multi-plant firmmodel, i.e. −θ . Column (4) and (5) obtain similar estimates of the trade elastic-ity with an average of -11. The estimate is at the higher end of what is typicallyfound in the literature (around -5 in Head and Mayer (2014)), but justifiable bythe homogeneous nature of cement and less productivity dispersion of cementplants. For the following steps of estimation, I take θ = 11 and the estimatedtrade costs computed from Table 2.3, column (3) as my benchmark.Figure 2.6 plots the estimated cement production capability against the ac-tual production volume for each location in panel (a), and combined effect withthe number of plants in panel (b). The positive correlation in both figures sug-gests a credible ranking of the estimated location production capability. Com-85Table 2.3: Estimation of trade costsFAF zone sample Country sample(1) (2) (3) (4) (5)OLS, logQ`m PPML, Q`m PPML, Q`m/Qm PPML, Q`m/Qm PPML, Q`m/Qmlog dist`m,m 6=` -2.297a -1.174a -1.198a(0.032) (0.034) (0.032)log dist`` -1.499a -0.462a -0.455a(0.042) (0.037) (0.039)log sea dist`m -1.359a(0.157)log shipping time`m -1.067a(0.138)intra-nation`m 3.176a 1.048a 1.757a(0.134) (0.123) (0.239)intra-state`m 0.393a 0.546a 0.414a(0.100) (0.093) (0.086)contiguity`m 1.258a 1.401a 1.223a 2.740a 2.617a(0.073) (0.062) (0.075) (0.342) (0.410)log (1+ cement tariff`m), −θ -10.567a -11.633a(2.590) (2.711)language`m -0.449 -0.465(0.296) (0.291)RTA`m 1.559a 1.738a(0.323) (0.302)home`m 7.456a 7.749a(0.476) (0.625)Observations 25435 54385 54385 20736 20736R2 0.576 0.917 0.687 0.975 0.973For the regressions using the FAF zone sample for year 2012-2016, column (1)-(3) include origin-year anddestination-year fixed effects. The set of origins include 73 FAF zones across the US and Canada that have pos-itive cement production. The set of destinations are 149 FAF zones. For the regressions using the country-levelsample, column (4)-(5) include origin and destination fixed effects. Regressions use 144 countries’ squaredsample for year 2016. R2 is squared correlation of fitted and true dependent variables. Robust standard errorsin parentheses. Significance levels: c p<0.1, b p<0.05, a p<0.01.paring the two panels, the number of plants contribute towards explaining ce-ment production suggested by the improvement of R-square.18 Specifically,panel (b) should be a right shift of the scatter plot in panel (a) in which the de-gree of shift is different depending on the number of plants in each location. Forlocations that produce more cement than what is predicted by the production18The fit displayed in Figure 2.6 is the R-square by regressing log of production on log oflocation production capability and the control for average trade costs weighted by destinationmarket size. One can derive from equation (2.4) that ln∑mQ`m = lnN`T`(w`)−θ + ln∑m(τ−θ`m QmΦm),where the second term is the average trade costs controlled for in plotting.86capability, I observe that the shift tends to be larger indicating more plants lo-cated in these area. Vice versa, locations below the fitted line have fewer plants.In other words, lower input costs and higher local efficiency do not necessarilylead to more plants, suggesting that fixed costs of establishing plants matter andare likely to vary.Figure 2.6: Cement production and estimated capability by locationOH ALFLSCKYWAAZ TNPAFLWYAZMOWAFLMDUTOKORCOPAMIMOPAOKGATNONOHNVILEMTALNMINNYILSCVACOARMOSDCATXMIMEWVFLKSNYONGAALINIACATXUTMDTXQCPATXNSCAONABQCABONBC111213141516log of cement production in metric tons2 3 4 5 6 7 8 9log of estimated Tw-θ for each locationfit = .56(a) Exclude number of firmsOH ALFLSCKYWAAZTNPAFLWYAZMOWAFLMDUTKORCOPAMIMOPAOKGATNONOHNVILEMTALNMINNYILSCVACOARMOSDCATXMIMEWVFLKSNYONGAALINIACATXUTMDTXQCPATXNSCAONABQCABONBC111213141516log of cement production in metric tons2 3 4 5 6 7 8 9log of estimated NTw-θ for each locationfit = .68(b) Include number of firmsWith the estimates of local production capability, trade costs and the Fre´chetparameter θ , I now turn to estimating the price elasticity of demand −η andparameters in demand shifters βA.2.4.2 Step 2: Estimation of demandUsing estimates from the first step and the observed plant location data, I canconstruct local price index as a function of only one unknown, η . Combine itwith the demand function and specification of demand shifters, I estimatelnQm = X′mβA−η lnPm (η)+νm. (2.16)87Since η enters the demand function non-linearly, I apply Generalized Methodof Moments (GMM) with instruments for price. I use the average of local inputcosts and in nearby locations as price instruments, weighted by the trade costsinverse. The input costs include durable goods manufacturing earning, lime-stone prices, natural gas and electricity prices. Table 2.4 presents the results. Asexpected, the price elasticity corrected for endogeneity in column (2) is largerin absolute value compared to the estimate without instruments in column (1).The effects of two demand shifters, population and building permits allocated,are both estimated to be positive and significant with magnitude smaller thanone as what has been found by Ryan (2012).As a robustness check, I also estimate the demand using a more “reduced-form” approach with USGS survey data on cement market price instead of de-riving it from the model primitives. The classification of price survey area inUSGS is broader than FAF zones, consisting 28 clusters of states and provinces.I leverage the instruments to address the issue of measurement error and priceendogeneity. Column (3) in Table 2.4 presents a similar “reduced-form” priceelasticity to that in column (2). To verify validity of the instruments, I alsopresent the first-stage results in Table B.3. Cost shifters are significantly corre-lated with the cement prices. The F-statistic of the excluded instruments on theendogenous regressor is 21.64, and the Stock-Wright S statistic is 95.59, whichare all above the rule-of-thumb threshold of 10. Hence, the tests reject the weakIV concern and the instruments are most likely to be valid.Overall, I find that the price elasticity of demand for cement is -2.68. Theliterature studying the cement industry has yet reach a consensus about its de-mand elasticity. Jans and Rosenbaum (1997) estimate the US domestic demandelasticity of -0.81. Miller and Osborne (2014) estimate an aggregate demand88elasticity of -0.02, using the data from southwestern United States. Ryan (2012)estimates a range between -1.99 and -3.21, and later on -0.89 to -2.03 in Fowlieet al. (2016). My estimate falls along the interval where the literature has found,although being at the upper range. Estimates of η = 2.68 and θ = 11 also con-firm (η−1)/θ < 1 such that the firm’s profit function is well defined and can beevaluated properly in the multi-plant firm location game.Table 2.4: Estimation of demandModel consistent Pure empirical(1) (2) (3)NLLS GMM 2SLSlog pricem, η -1.382a -2.683a -2.117b(0.323) (0.627) (1.014)log building permitsm 0.424a 0.399a 0.536a(0.048) (0.051) (0.067)log populationm 0.653a 0.628a 0.562a(0.058) (0.059) (0.074)Observations 744 744 739All regressions include year fixed effects. The dependent variable is thelog of cement consumption in thousand tonnes. The last two columnsuse instruments, but not column (1). The set of markets include 149FAF zones during 2012-2016. All regressions include a year fixed effect.Robust standard errors in parentheses. Significance levels: c p<0.1, bp<0.05, a p<0.01.2.4.3 Step 3: Estimation of fixed costsIn the last two steps, I’ve estimated two types of costs faced by the cement firms,namely the trade cost based on the bilateral gravity terms, and the marginalcost of production formulated from the plant productivity distribution and therecovered location covariates. In the last step, I estimate parameters that gov-ern the fixed cost distribution by solving a combinatorial discrete location game89within a method of simulated moments (MSM) estimation. All the essential el-ements are prepared from previous steps to construct a firm’s expected variableprofit for each location configuration.To make the problem more tractable, I restrain the location game betweena duopoly, LafargeHolcim and Cemex, the two largest multi-plant cement pro-ducer in my sample. Meanwhile, as shown in Section 2.2.1 that fringe firmsare important, I allow for the rest of firms being incumbents where locationsare given and fixed, and all plants compete in price. Essentially, the timing ofevents is that small firms enter without anticipating LafargeHolcim and Cemexin the later period; the distribution of small firms then become covariates whichLafargeHolcim and Cemex take as given in making location choices. Once theentry decisions are made, all plants compete in price and profits are realized.Opposite to many papers that study Stackelberg competition and assume largefirms enter first, the timing assumption here is consistent with background ofthe cement industry in the US and Canada.19 The region was dominated bysmall local firms before large multinationals entered. The unique path of devel-opment is closely tied to the historical localization of cement and improvementof the transportation technology. Any ex-post regret by the small firms is ruledout by the one-shot static game.For a submodular game with combinatorial discrete choices over a large setof potential locations, the first chapter of my dissertation makes great effort incharacterizing and solving for an equilibrium. The submodular game featuredin the multi-plant firm model has a pure strategy Nash Equilibrium (PSNE). In19Papers that study Stackelberg competition assume that big firms enter first and choose theirprices anticipating the reactions of small firms. Next, small firms enter or exit the market andchoose their prices treating big firms’ choices parametrically (Etro 2006, Etro 2008, Andersonet al. 2020, Kokovin et al. 2017). Unlike mine, these papers endogeneize the entry and exit offringe firms.90a game with two players, it can be found by letting firms take turns to solve thebest location response using the algorithm from Eckert et al. (2017), given theother player’s current plant locations and fringe firms’ locations. Best responsesare solved iteratively until strategies of both players converge. Furthermore,PSNE may not be unique. To deal with multiplicity of equilibria, I leveragepredetermined sequential entry as equilibrium selection criteria and allow fordifferent ordering as robustness checks. As baseline, I estimate the model us-ing the equilibrium that is most profitable for LafargeHolcim, the largest playerand early entrant to North America in 1950s.20 Alternatively, I also estimatethe equilibrium that is most profitable for Cemex, and another one that giveseach firm regional advantage in moving first. Although I try to “solve” the co-herency problem in econometric inference, it continues to raise difficulties at thecounterfactual stage. For example, the moving sequence I used in estimation tocharacterize the data may no longer be valid under the counterfactual. Therehas not been an existing solution I’m aware that tackles this problem. However,what will alleviate the concern is when estimates across multiple equilibria donot vary significantly. We will show later that it is exactly the case with thecement sample in this chapter.Knowing how to solve for the firms’ optimal location strategy given a vectorof fixed costs, I can estimate the parameters governing the fixed costs distribu-tion via method of simulated moments. I draw a 2× 73-dimensional matrix offixed costs for 300 times. For each fixed costs draw, firms maximize total ex-pected profits by choosing where to build plants using the algorithm above. Ithen use the fraction of entry over 300 draws as the simulated approximation20Lafarge (prior to the merged entity LafargeHolcim), a leading French cement producer, builtits first cement plant at Richmond in western Canada as early as 1956. By the end of 1960s,Lafarge is the third largest cement producer in Canada. Lafarge’s market in the US expandedafter its acquisition of General Portland in 1983.91of entry probability for each firm in every location. Moments are to match themodel-predicted and the observed values of (a) number of LafargeHolcim/Ce-mex plants, in the sample, in Canada and in the US;21 (b) average distancefrom headquarter of LafargeHolcim/Cemex to plants;22 (c) difference betweenthe average production capability for locations that LafargeHolcim/Cemex pro-duces and those that it stays out. The moments are informative about the overallmagnitude of the fixed costs of entry, as well as how they vary by distance andthe identity of firm and the country of interest. Roughly, the mean of fixed costsis identified by the entry decision of firms in the first two sets of moments. Thelast set of moments helps to pin down the dispersion of fixed costs distribution.When the variance is large, the more entry decisions vary by fixed costs andless by local profitability. In another words, firms care more about fixed costs indeciding where to build plants and they could enter even if the local productioncapability is not as high.Denote the parameters of interest in the last step to be δ = {βF ,σF}, and thevector of differences between moments in data and simulated model is gˆ(δ ) =m− mˆ(δ ). X f is a vector of firm and firm-location level characteristics. φˆ and Aˆare vectors of location covariates and estimated trade costs between locations.At true parameter value,E[g(δ0;X f , φˆ , Aˆ, θˆ , ηˆ)]= 0.21Matching the number of plants in each country is relevant for the counterfactual exerciseswhere policies are imposed at country level.22For LafargeHolcim, I use its North America headquarter, which is at Chicago, Illinois, be-cause its unlikely that plant operations is managed by its global headquarter in Switzerlandgiven the firm size. Cemex is used as its global headquarter in Mexico.92MSM finds an estimate such thatδˆ = argminδ1|L |[ |L |∑`=1gˆ(δ )]′[ |L |∑`=1gˆ(δ )], (2.17)I also apply particle swarm optimization to search through a large number ofstarting points for a global optimum.For estimates using a dependent cross-sectional dataset to be consistent, asufficient condition is that the dependence between locations should die awayquickly as the distance increases (Conley, 1999). In the current model setup,trade cost to a market increases for a distant cement supplier, and then decreasesits probability of supplying to the market and weakens its role as a competitorto other locations. To ensure the speed of dependence decay, I further segregatethe 149 FAF zones to eight districts and assume that competition is negligibleacross them.23 The districts are categorized by USGS as relatively separatedmarkets. FAF zones on average export more than 88% of the cement productionand import more than 82% of the consumption within the same district. Moreinformation about each district is presented in the Appendix B.2.2. An alterna-tive way to restrain the geographic scope of the spillover effect is by assumingdependence only occurs for the set of locations within certain radius to eachlocation, as in Jia (2008). However, such method does not work in general forthe multi-plant firm model unless there are only two players. Existence of over-lapping across each location’s catchment area causes the firm profit function toviolate the submodularity (or supermodularity) condition which is essential forthe CDC solution algorithm in Eckert et al. (2017) to work.23Districts are Mountain and Pacific North, Mountain and Pacific South, West North Central,West South Central, East North Central, East South Central, New England and Middle Atlantic,and South Atlantic.93Cluster bootstrap is used to estimate the standard errors reported in Table2.5. District vectors are re-sampled 100 times with replacement to preserve thedependence among locations.24 Alternatively, one can also estimate based onthe asymptotic variance of the MSM estimator, which I report the results inTable B.1. Equation (2.17) implies that I use identity weighting matrix for thesample of 73 locations when performing the MSM estimation. As robustnesschecks, I present the standard error estimated using an identity weight, as wellas the optimal weighting matrix, while taking into account the spatial depen-dence within each district. The estimates are close with the optimal weightingmatrix exhibiting slight improvement in precision.Estimates of the fixed costs parameters for three different equilibria are dis-played in Table 2.5, corresponding to the scenario that is most profitable forLafargeHolcim (LFH), Cemex (CEX), or allowing LFH to have local advantagein Canada and CEX in Texas and Florida. Estimates are not significantly dif-ferent across equilibria, which ease the generality concern of the counterfactualresults. The equilibrium selection rule does not have “bite” here because theasymmetry between two oligopolists mitigates the effect of sequential move as-sumption in selecting equilibrium. Specifically, LafargeHolcim owns twice thenumber of plants than Cemex. Assuming Cemex moves first, the model mustrationalize the fact that Cemex enters half the number of locations as Lafarge-Holcim. It does so by making Cemex to acquiesce LafargeHolcim’s entry andchoose to forgo some locations expecting LafargeHolcim would enter. Estimatesreflect that Cemex has disadvantages in those locations. Vice versa, assumingLafargeHolcim moves first, the estimates need to be consistent with the patternsin the data and LafargeHolcim being the dominant player.24I recognize the potential concern of bootstrap when the number of clusters is small(Cameron and Miller, 2015; MacKinnon and Webb, 2017).94Table 2.5: Estimation of fixed costs(1) (2) (3)FavorLafargeHolcimFavorCemexLocal advantagefor two firmsβFcons -6.631 -6.126 -5.617(1.616) (1.688) (1.559)βFCEX-USA -0.406 -0.363 -0.280(0.373) (0.382) (0.372)βFLFH-CAN -3.734 -3.475 -3.480(1.867) (2.318) (1.992)βFdist 1.795 1.698 1.634(0.220) (0.245) (0.221)σF 2.790 2.581 2.694(0.481) (0.504) (0.503)The data shows Cemex does not have any cement plants in Canada,which makes it impossible to identify the Cemex-Canada dummy. Idrop the Cemex-Canada and LafargeHolcim-US dummies and pre-serve the other two and a constant.I find a location that is 10% more distant from the firm’s headquarter, theaverage fixed costs of establishing plants will be nearly 20% higher holding ev-erything else constant. The effect seems to be large considering communicationand management cost alone, but should be interpreted with caution. First, itcould reflect increasing information friction at locations further away from thefirm headquarter. Second, the literature on multinational production has doc-umented the costs of producing far from headquarters, i.e. MP cost. The base-line model does not feature the loss of productivity associated with transferringheadquarter services to production locations, but the friction could be well ab-sorbed by fixed costs. With limited plant-level data in this chapter, I cannotseparately identify differences in variable costs from fixed costs as in Tintelnot(2017). However, one can easily extend the model by incorporating a h( f )`-levelterm in the marginal cost of production. Third, the distance elasticity to fixed95costs may be upward biased due to the omitted home variable. Head and Mayer(2019) find that assembly cars at the brand’s home country is 9.5 more likely tohappen than choosing other assembly locations.The average fixed cost is much lower when LafargeHolcim builds a plantin Canada because the firm has accumulated local knowledge through its longpresence in Canada since 1956 followed by a wave of M&A activities with Cana-dian cement firms. However, Cemex does not share the country-specific ad-vantage in fixed costs shown by the insignificant coefficient. Variance of thefixed cost distribution is rather high, suggesting that firms’ entry decisions arepredominantly determined by fixed costs rather than local profitability. Theresult is consistent with high fixed costs investment in the cement industry doc-umented in Section 2.2.1. One may attempt to argue that the reason local prof-itability matters less and fixed costs appear to be high could be that the variableprofit modeled in the multi-plant firm framework fails to capture some impor-tant aspects. To rebut the argument, I perform external validity checks to showthat the estimated fixed costs are align with the industry facts.To check for external validity of the estimates, I transform the estimates totheir corresponding monetary value and compare the costs estimated from themodel to the cement industry standard. Recall that in the first step of the estima-tion, the production capability of each location is estimated up to a scale. Thenormalization can be computed by comparing the predicted local price in thesecond step to the USGS survey data on cement prices. Since the normalizationparameter enters the price index multiplicatively through Φm in equation (2.7),I run the observed cement price on the model prediction and obtain a slope of140.575, which would then be the amount to scale up the cost estimates.96Back-of-envelope calculation reveals that the average fixed cost across thecement plants owned by LafargeHolcim is estimated to be around $181 millionand that for the Cemex plants is around $280 million.25 The estimated averagefixed costs of building a cement plant are surprisingly close to the industry normof $200∼$300 million. The cost advantage of LafargeHolcim justifies itself beingthe leader in the US and Canada and having twice as many plants as Cemex.Computed from equation (2.2), the lowest production cost adjusted for thescaling among LafargeHolcim’s plants is estimated to be $57 per tonne of ce-ment. At an average price of $98 per tonne of cement based on equation (2.3),it implies a gross margin of 41.8% for LafargeHolcim. Similarly, the lowest pro-duction cost adjusted for the scaling among Cemex’s plants is $65 per tonne ofcement. At Cemex’s average price of $97, its gross margin is 33%. The higherefficiency and markup for LafargeHolcim than Cemex are consistent with themodel implications in which a firm having more plants will gain competitiveadvantage and market power.I further compare the estimated profit margins with the 2016 financial state-ments of the two firms to assess the plausibility of these estimates. Lafarge-Holcim reported a gross profit of $11,272 million on sales of $26,904 million,which is a profit margin of 41.9% and almost exactly matches with what hasbeen estimated. Cemex reported a gross profit of $4,756 millon on sales of$13,404 million, which is a profit margin of 35.5% and again very close to theestimated value. The costs of production are also close to the engineering costsof $60 in 2016 reported by the US Environmental Protection Agency.26 In sum,25Since I use static data for one year, the estimated fixed costs after adjusted for the scalingalso need to be computed in net present value. I use a 6% interest rate to discount.26EPA reports engineering estimates of average production costs of $50.3 per tonne of pro-duced cement in 2005 (RTI International, 2009). I convert into 2016 dollars.97these cross-firm comparisons corroborate the costs estimates from the multi-plant firm model.At location level, I analyse the interaction between the estimated productioncapability, the estimated fixed costs and the observed cement production by FAFzones. I copied panel (a) in Figure 2.6 to Figure 2.7 to be interpreted togetherwith the panel (b). It is clear that Nova Scotia, a province having moderateproduction capability, produces exceptionally small amount of cement. The in-consistency is reconciled by Nova Scotia having the highest fixed costs. On thecontrary, FAF zones in Texas are as capable in producing cement as Nova Sco-tia but among the lowest fixed costs locations, contributing to Texas being thelargest cement producer in the sample. Similar findings can be seen by compar-ing FAF zones in Alberta to those in Ontario. These differences in productioncapability and fixed costs of entry help explain the variation across FAF zones inthe number of plants located and subsequently the amount of production. Fig-ure 2.7, complemented by the firm-level comparison, highlights the importanceof heterogeneous fixed costs at plant level for matching the model to data.2.4.4 Fit of the modelTo check how well the model fits the data, I start by comparing predictions ofthe model for the moments it is targeted to match. As shown by Table 2.6, themodel fits the data generally well in the number of plants, total or regionally,for each firm and the average distance between plants and firm headquarters.The number of plants in Canada is slightly over-predicted and that in the USis slightly under-predicted. Since the number of plants affects a locations’ com-petitive advantage in supplying cement to every market, I also check the fit of98Figure 2.7: Estimated fixed costs and production capability by locationOH ALFLSCKYWAAZ TNPAFLWYAZMOWAFLMDUTOKORCOPAMIMOPAOKGATNONOHNVILEMTALNMINNYILSCVACOARMOSDCATXMIMEWVFLKSNYONGAALINIACATXUTMDTXQCPATXNSCAONABQCABONBC111213141516log of cement production in metric tons2 3 4 5 6 7 8 9log of estimated Tw-θ for each locationfit = .56(a)ABABBCNSONONONONQCQCALAL ALARAZAZCACACACOCOFLFLFLFLGAGAIAILILINIKSKYMDMDMEMIMIMOMO MOMTNENMNVNYNYOHOHOKOKORPAPAPAPASCSCSDTNTNTXTXTXTXUTUTVAWAWAWVWY5001500250035004500average fixed costs in million US$2 3 4 5 6 7 8 9log of estimated Tw-θ for each location(b)the model prediction to the trade data in Table 2.7. The predicted bilateral shareof import is able to explain 64.4% of the data variation. To check to what extentthe prediction is affected by the gravity errors, I regress the final prediction af-ter solving for the endogenous plant locations on the gravity-predicted importshare. The fit improves by around 20%. Restricting the sample to intra-districttrade further increases the fit by another 6.7%. If comparing the import shareis less convincing because it is indirectly targeted through the first-step gravityregression, I further compares the trade volume as shown in the last column ofTable 2.7. The degree of fit does not fall.Other than comparing trade flow, Figure 2.8 plots and compares the share oftrade by distance.27 The close fit is not surprising because I estimate the distanceelasticity of trade to be -1.198 to match the trade flow over distance, but it isreassuring that the estimation of fixed costs and solution for endogenous plant27The actual trade data is used for only the dyads within the same district to be comparablewith the estimation under such assumption. Same goes for the consumption and productiondata in Figure 2.9.99Table 2.6: Model fit of plants number and distance to headquarterLafargeHolcim CemexData Model Data ModelNumber of plants 22 22.50 11 11.02Number of plants, Canada 6 6.74 0 0.71Number of plants, US 16 15.76 11 10.31Average distance of HQ to plants (km) 369 330 271 283The predicted number of plants is not integer because they are summations of the simu-lated entry probabilities.Table 2.7: Model fit of trade flowsBilateralshare of importGravity-predictedshare of importGravity-predictedshare of importwithin regionBilateralimport volumeModel prediction 0.767 0.797 0.990 0.631(0.005) (0.003) (0.008) (0.004)Observations 10877 10877 1437 10877R2 0.644 0.850 0.917 0.645All regressions include a constant.locations are consistent and do not introduce additional bias.Figure 2.9: Model fit of cement consumption and production45° line11010010005000Data (log scale)10 100 1000 5000Model (log scale)log-log regression:slope = .941fit = .52(a) Consumption (thousand tonnes)45° line1010010005000Data (log scale)10 100 1000 5000Model (log scale)log-log regression:slope = .614fit = .65(b) Production (thousand tonnes)100Figure 2.8: Model fit of trade flow over distanceDataModel0.2.4.6.81Share of trade1 10 100 1000 5000Distance (km, log scale)Having checked the model performance through plants number and trade,lastly I compare the model predicted cement consumption and production againstthe data. Figure 2.9 shows that the model fits the data reasonably well in bothdimensions. The actual and predicted cement consumption across markets dis-tribute tightly along the 45-degree line. The prediction on production, althoughdeviates from the diagonal relationship, captures 65% of the data variation. Themultiple test results establish confidence in the following counterfactual exer-cises.2.5 Quantitative ApplicationsThe benefit of estimating a structural model is the ability to simulate counterfac-tual experiments once the underlying primitives are known. I apply the modelto three sets of quantitative exercises and investigate firm dynamics when mar-ket conditions change. Since the cement industry is associated with importantenvironmental concern, trade debate and major phase of consolidation, I access101the welfare implications for each of these aspects in this section. These quan-titative applications of the framework demonstrate a new way to evaluate awide variety of policies taking into account multi-plant production and spatialadjustment at the firm level.2.5.1 The Greenhouse Gas Pollution Pricing ActAccording to the World Bank’s 2019 State and Trends of Carbon Pricing Report,74 jurisdictions, representing about half of the global economy, are putting aprice on carbon. These regulations would directly affect the energy price andincrease the cost of production, especially for the carbon-intensive industries.Responsible for about 8% of the global CO2 emissions, the production of ce-ment is assessed to be in a high competitive and leakage risk category facingthe carbon levy. Therefore, governments aim to design policies such that firmscan afford, and industries can maintain competitiveness, while retaining the in-centives to reduce emissions.In 2018, Canada passed the Greenhouse Gas Pollution Pricing Act (the Act)which is a backstop system at the federal level that would raise the carbon priceto $50 per tonne by 2022. The Framework is composed of two carbon pricing ini-tiatives: a carbon tax on fossil fuels and an output-based pricing system (OBPS)for industrial facilities.28 Prior to the pan-Canadian approach, provinces such as28In practice, to account for the unique circumstances across different provinces, the federalbenchmark provides provinces with flexibility to implement their own carbon pollution pricingsystems. Fuel charge in the backstop system is only applied to Ontario, New Brunswick, Mani-toba, Saskatchewan, Alberta, Yukon and Nunavut. OBPS is applied to Ontario, New Brunswick,Manitoba, Price Edward Island, Saskatchewan, Yukon and Nunavut. Some exceptions are NovaScotia and Que´bec where implement cap-and-trade systems, Alberta where has its Carbon Com-petitiveness Incentive Regulation, and British Columbia where implements broad-based car-bon tax. However, these provincial regulations are assessed to meet the federal government’sminimum stringency benchmark requirements for pricing carbon pollution. For simplification,counterfactual analysis is based on a uniform change to all Canadian provinces.102British Columbia, Alberta, or Que´bec have already implemented certain pricingregimes on carbon. British Columbia, for example, applies carbon tax to emis-sions from the combustion of fossil fuel, but not to process emissions duringproduction such as the calcination of limestone. The primary interest is to eval-uate the welfare costs of these environmental regulations for both consumersand producers by comparing what the alternative spatial allocation of plantsand market structure would be in the long run.Carbon tax on fossil fuelsI first examine the effect of carbon pricing levied on fossil fuels considering theyare essential for generating energy in producing cement. The average cost offuel to produce a tonne of cement before the carbon levy is $12.44, calculatedbased on the amount of energy required for production, breakdown of fuel typeused, fuel prices and energy content tabulated in Table B.4.29 The computed pre-tax unit cost of fuel is close to $13.82 in Miller et al. (2017) using the 2010 data.After the carbon levy, rates for each fuel subject to the levy is set by the CanadianFederal Carbon Pricing Backstop Technical Paper such that they are equivalentto $50 per tonne of CO2 by 2022. The average cost of fuel for producing onetonne of cement post the levy becomes $29.37.30 As explained in Section 2.2.1, Iassume that there is no substitution of fuel to other carbon-saving sources afterthe policy in the short run.In equation (2.1), I specify that fuel is a third of the input costs in producingcement. Therefore, increasing the cost of fuel from $12.44 to $29.37 per tonne29Produce one tonne of cement requires energy 4.432 million BTU. Cost of fuel in 2016 =(42%×2.366+22%×5.003+13%×1.722+4%×12.223)×4.432= $12.44/tonne cement.30Levy on fuel by 2022 = (42%× (158.99/27.77)+22%× (0.0979/0.035)+13%× (0.1919/0.04)+4%× (0.1593/0.036))× 4.432 = $16.93, and hence cost of fuel in 2022 will be 16.93+ 12.44 =$29.37/tonne cement.103of cement is equivalent to 33% increase in the input cost w` or 96% decrease inlocal production capability T`w−θ` for all FAF zones in Canada. The change in alocation’s competitive advantage is exacerbated by the relatively large θ . Whenplants are not widely differentiated, a small increase in costs of production mayinduce immediate losses of market share, which explains why carbon policycould be a major threat to the competitiveness of the local cement industry.Responding to the rise in production costs, cement firms tend to move plantsto “pollution havens”. Figure 2.10 displays the comparison of spatial distribu-tion of plants before and after the carbon tax. Combining the top two cementmanufacturers, red indicates the share of plants predicted to close and greenindicates the share of plants predicted to open. FAF zones other than the 73 areexcluded from the potential location set and shaded in grey. The map showsthat there is some degree of plants closure throughout FAF zones in Canada,with the most striking exit ratio in Que´bec where more than 20% of the plantswill be shut down, followed by Great Vancouver metro area in British Columbia,Nova Scotia, Alberta and Ontario. As close substitutes, plants are shifted to thezones along the border in the US, near the pre-existing Canadian plants. Mar-kets that were previously served by Canadian plants would now source fromthe US plants that are not too distant. On the west coast, Washington and Mon-tana face the steepest increase in plants owned by LFH and CEX, around 16%more, whereas places in Oregon and Utah face a moderate expansion, and noplant opening in states further South. Despite similar distance to Canada, plantsare built in Utah but not Nevada because Utah is more efficient and cheaper toproduce cement. On the east coast, plants opening is weaker because there hasalready been a dense production network as shown in Figure 2.2.The first two columns in Table 2.8, panel (a) quantify the change in average104Figure 2.10: Change of plant locations with $50 carbon levy on fuel inCanadaprobability for building a plant in Canada or in the US, for each firm respec-tively. The model predicts that the probability of having a plant owned by eitherfirm in Canada drops around 10%. In contrast, the probability of having a plantin the US barely increases, which is consistent with the fact that constructionof a cement plant incurs high fixed costs. Across firms, the effect is heteroge-neous. LafargeHolcim, being the dominant player in the Canadian market, ishit harder by the negative cost shock. It loses more plants in Canada and is notable to recover by building more in the US. Note that the model overpredictsthe presence of Cemex in Canada, so theoretically Cemex could have benefitedfrom having a weaker competitor after the carbon tax.The average price in Canada for one tonne of cement is $26.82 higher (almosta third of the baseline price), out of which $16.93 is directly passed on from theincreased fuel prices and the rest from the rising market concentration. The pre-105diction is in line with Ganapati et al. (2016) and Miller et al. (2017) who find thatchanges of fuel cost are more than fully transmitted to cement prices. However,in the US, the impact on prices is driven by two opposing forces: downwardpressure from the intensified market competition through plants entering andthe upward pressure from the loss of cheap cement imported from Canada. Acarbon levy as high as $50 per ton of CO2 makes the latter slightly dominate.Associated with the price changes, consumers in both countries substitutecheaper alternatives for cement. In Canada, the amount of cement consumptiondrops by more than 52%. The contraction of production is even more promi-nent at around 58%, some of which “leak” to the US. The intensive margin inconsumption and production is actually quite responsive, although on the ex-tensive margin, the number of plants is not as flexibly adjusted. Implicitly, itindicates that the US cement plants achieve a higher utilization rate and Cana-dian plants will be under-utilized.31The effects of the carbon tax on trade in cement are enormous. The cementexport from Canada to the US almost vanishes. Instead, Canada is flooded withcement from the US, more than triple the amount before. Based on the changesin trade volume and consumption, import penetration of the US produced ce-ment into the Canadian market rises from 6% to 41%.As for welfare analysis, from equation (2.8) and (2.9), impacts of a $50 car-bon levy on fuel in Canada include the consumer loss around $310 million andthe producer loss around $68 million annually.32 Comparing to the 2016 Cana-31Data shows that the capacity utilization rate of a US cement plant is on average 70% in 2016,which leaves room for better utilization.32Producer surplus is calculated combining all firms including the small ones operating in theregion. The profit change of LafargeHolcim and Cemex comes from different plant locations andadjustment in prices, whereas changes of small firms’ profits are only from prices.106dian cement industry revenue of $7.4 billion, the combined loss is roughly 5%.Consumers bear about 82% of the tax burden, comparable to the 89% found byMiller et al. (2017) in their study of a US carbon tax. Using the carbon emis-sion intensity from fuel combustion at 0.4 tonne of CO2 per tonne of cement,the government revenue is around $97 million dollars. Producers could be fullycompensated by 70% of the revenue obtained from the carbon tax.Lastly, assuming that producing one tonne of cement emits 0.8 tonne of CO2,the leakage rate is around 18%. It implies that for a hundred tonne of CO2abated in Canada, approximately 20 tonne leaks. The leakage is particularlyproblematic when the emission damage is independent of the origin, as in thecase of carbon dioxide. Therefore, evaluation of the social benefit to Canadafrom carbon reduction should be based on net emissions, taking into accountthe amount of leakage.Summing over changes on consumer surplus, producer surplus and govern-ment revenue, the $50/t carbon levy on fossil fuels would be welfare improvingfor Canada provided a minimum social cost of carbon at $65/t.33 At a $50/tCO2carbon price set by the government, the policy generates welfare loss to Canada.There are two reasons for the carbon tax to be suboptimal. First, the market dis-tortion is exacerbated with the presence of oligopolists, as shown by the morethan complete pass-through of fuel costs. Second, the carbon pricing is incom-plete and creates carbon leakage whose damages are global. In this case, welfarelosses from these two channels overwhelm the gains from emissions abatementfor a social cost of carbon set at the current level of the carbon tax.33Based on EPA Social Cost of Carbon Fact Sheet (2016), the social cost of CO2 could rangefrom $14 to $138 in 2025. To break even in welfare terms, the required minimum social cost ofcarbon is (−310.50−68.04+96.86)/(−5.27+0.94) = $65/tCO2.107As one may expect a negative cost shock to Canada may benefit the US,the welfare evaluation shows otherwise. The US also loses around $25 milliondriven by higher prices faced by consumers. Just as the pollution of carbon isglobal, the effect of a carbon tax in one country also transmits to another throughmulti-plant production and trade.Table 2.8: Counterfactual changes with $50 carbon levy on fuel in CanadaPanel A: Impacts on market outcomes∆ Avg entry prob(%) ∆ Price($) %∆ Consum %∆ Prod %∆ TradeLFH CEX Canada USCanada -7.43 -2.13 26.82 -52.37 -57.63 -54.25 -94.67US 0.13 0.19 0.73 -1.04 1.38 224.83 1.02Panel B: Impacts on welfare and emissions∆ CS($M) ∆ PS($M) ∆ TaxRev($M) ∆ Emissions(Mt) Leakage rate(%)Canada -310.50 -68.04 96.86 -5.27 17.89US -35.54 10.70 - 0.94 -Border tax adjustmentAs demonstrated by the change in trade, downstream consumers turn to unreg-ulated imports after the imposition of carbon tax. A solution to such leakageis a border tax adjustment (BTA) that raises the effective price of unregulatedimports. In this section, I evaluate to what extent a BTA is effective and its wel-fare implications. Imposing the same level of carbon levy on fossil fuels to theimported cement from the US is equivalent to charging an ad valorem border taxof 33%.3434Note that trade costs τ and input costs w enter the sourcing probability from a location inthe same way through a power of−θ . From the previous section, I’ve calculated that the carbontax is equivalent to 33% increase in w, then immediately the border tax should be 33% to achievethe same level of carbon tax. Implicitly, I assume that the composition of fuel usage and relatedfuel prices are the same in Canada and in the US, which is an assumption has to be imposeddue to limited data. 33% border tax also means that the import penetration of the US cement inCanadian consumption will be kept as the same level (6%) as before imposing the carbon tax.108Augmenting the carbon tax on fuel with a BTA mitigates the loss of domesticmarket share to foreign producers, thus slowing the change of plant sites fromCanada to the US. Comparing Figure 2.11 to Figure 2.10, the exit rate for Cana-dian plants decreases and fewer locations in the US are seen with significantplant entry. Vancouver metro area and Que´bec lose the most plants of about15%, followed by Nova Scotia, Alberta and Ontario. New plants no long enterMontana, and the fraction of new plants in Washington, Oregon, Utah and FAFzones in eastern US all decline. Table 2.9 also presents smaller change in entryprobabilities compared to the case of carbon tax alone. Therefore, sufficient levelof BTA is indeed effective in reducing production leakage. However, Canada,as a net exporter of cement, will not overturn the closure of cement plants sincemany of them were used to primarily serve the US markets.Figure 2.11: Change of plant locations with $50 carbon levy on fuel and 33%BTA in CanadaBecause cement consumed in Canada bears the increase of carbon price re-gardless of the origin, the price of cement rises by another $5.42 for Canadian109consumers and total consumption drops further. In the US, fewer plants entrybesides the loss of import competition also exacerbates the price increase. Theproduction of cement and trade both move in the expected direction, with theaddition of BTA protecting domestic production and improving terms of trade.BTA, however, will not recover the loss of Canadian exports.Finally, Canada suffers additional $10 million loss in welfare compared tothe scenario without BTA, out of which the $2 million gain of producers cannotcompensate the extra $12 million loss of consumers. However, the governmentreceives additional tax revenue besides the carbon tax on domestic production.Using the percentage change in trade, the border tax revenue is approximately$10.7 million.35Border tax adjustment not only works to reduce the emissions leakage rate(18% to 12%), but also cuts down the total emissions in level by indirectly re-straining the US production through exports. However, BTA cannot eliminatecarbon leakage because Canadian exporters would still shift their productionto the US, and they consist a significant number of Canadian cement produc-ers. Overall, the threshold of the social cost of carbon, in order for Canada tobenefit from the policies, reduces to $61/tCO2.36 The welfare loss from carbonleakage is partially mitigated by implementing BTA, although the concentratedindustry is still under-producing.35The 2016 export value of cement from the US to Canada is $69.8 million according to TradeData Online from the Government of Canada. I use the same percentage change in trade volumeas trade value.36To break even in welfare terms, the required minimum social cost of carbon is (−322.76−66.27+108.9)/(−5.22+0.62) = $61/tCO2.110Table 2.9: Counterfactual changes with $50 carbon levy on fuel and 33%BTA in CanadaPanel A: Impacts on market outcomes∆ Avg entry prob(%) ∆ Price($) %∆ Consum %∆ Prod %∆ TradeLFH CEX Canada USCanada -6.70 -2.00 32.24 -53.61 -57.04 -53.61 -94.65US 0.08 0.15 0.75 -1.06 0.90 -53.61 0.99Panel B: Impacts on welfare and emissions∆ CS($M) ∆ PS($M) ∆ TaxRev($M) ∆ Emissions(Mt) Leakage rate(%)Canada -322.76 -66.27 108.90 -5.22 11.79US -36.30 10.93 - 0.62 -Output-based pricing systemI show in the previous section that a sufficient level of BTA on top of a car-bon tax is more likely to improve welfare than leaving it out. However, BTAis designed to level the playing field for domestic and foreign plants servingthe Canadian market. The gain is small if the majority of Canadian plants areexporters and compete in foreign. An alternative strategy that addresses theproduction and carbon leakage for all Canadian plants is to impose an output-based pricing system (OBPS) as adopted by the Act. OBPS prices carbon on thebasis of emission intensity, i.e. emissions per unit of output. The cement indus-try is subjected to an output-based standard at 95% of the sectoral average car-bon intensity (0.8tCO2/tonne of cement), which means an emitting limit of 0.76tonne CO2 per tonne of cement. Under OBPS, if a plant generates more emis-sions than 76% of her cement output, she faces a marginal rate at $50/tCO2 andis taxed for the portion exceeding.37 The objective of OBPS is two fold: one isthat it provides relief from fuel charge to emission-intensive and trade-exposed37Firms that emit a quantity below their limit will obtain surplus credits that can be sold tofirms that need credits for compliance. With limited firm-level data, I ignore the carbon tradingaspect of OBPS in this analysis.111industries so that domestic firms still retain some level of competitiveness com-pared to foreign; the other is that OBPS financially incentivizes firms to reducetheir emissions intensity and transit to cleaner technologies. This carbon pric-ing scheme comes with a notable side effect which is weaker pricing signal andsmaller carbon reduction in targeted industries. It could potentially cause largedistributional effects where some industries are protected at the costs of othersbeing heavily regulated. The recent work by Fowlie and Cired (2020) studies312 manufacturing sectors and finds that aggregate carbon reduction can stillbe achieved using a similar regime.Figure 2.12: Change of plant locations with OBPS in CanadaIn this section, I model the OBPS as a output-based “rebate” following CanadaGazette (2019). Given that 95% of the sectoral emission intensity is tax-free forthe cement industry, I assume 95% of the proceeds from OBPS will be returnedto the sector. Due to data limitations, the sample used for this analysis does notcontain information on firm- or plant-level carbon emissions intensity, nor is112the static model able to accommodate endogenous technological improvement.I take a simple heuristic approach and model the cement industry as one repre-sentative firm operating at the average 0.8tCO2 emissions intensity. The OBPSin this counterfactual exercise is effectively a lower carbon tax at the averagerate of $50× 0.8× (1− 95%) = $2 per tonne of cement. Compared to the 33%increase in the carbon tax case, it is equivalent to an ad valorem 2.76% increasein the production cost for Canadian plants.38 Predictions under this assump-tion will be an upper bound of OBPS on change in plant locations and a lowerbound on carbon reduction since firms are treated as passive tax payers withoutactively seeking cleaner production technology.Figure 2.12 shows that OBPS triggers the least change in plant sites amongthree carbon pricing schemes. Very few locations in the US are observed withentry, and some locations such as Nevada even suffer from plants exiting dueto expansion in the nearby area (Seattle). The results in Table 2.10 are not qual-itatively different from those in Table 2.8, if any, smaller in magnitude. As ex-pected, the number of plants, the amount of production, and the exports to theUS, have all been restored nearer to the baseline level. Mitigation on productionleakage is achieved at the sacrifice of weaker environmental targeting. Carbonemissions abatement is now 0.72 million tonne including the amount that leaks,which is around one sixth of the reduction in the case of carbon tax alone. Astriking finding is that the carbon leakage rate is almost 24%, higher than anyof the scenarios before. Therefore, OBPS does not curb emissions leakage inrelative terms, but it indeed lessens production leakage.Using the welfare measures to calculate the social cost of carbon for the OBPS38Consistent with the Act, I also adjust the calculation to cover both combustion and non-combustion emissions in OBPS, unlike only combustion for the fuel charge. The estimated av-erage Canadian plant production cost is $72.56 calculated from equation (2.2).113Table 2.10: Counterfactual changes with OBPS in CanadaPanel A: Impacts on market outcomes∆ Avg entry prob(%) ∆ Price($) %∆ Consum %∆ Prod %∆ TradeLFH CEX Canada USCanada -1.00 -0.23 3.15 -8.65 -10.35 -8.79 -27.54US 0.04 0.03 0.19 -0.29 0.33 11.75 0.31Panel B: Impacts on welfare and emissions∆ CS($M) ∆ PS($M) ∆ TaxRev($M) ∆ Emissions(Mt) Leakage rate(%)Canada -46.36 -9.57 20.50 -0.95 23.82US -9.57 2.67 - 0.23 -to be welfare-enhancing for Canada, the threshold is around $49 per tonne ofCO2.39 Among the three scenarios, this is the only case where a $50 carbonprice will improve welfare. By giving free allowances to cement producers,OBPS essentially cuts the regulatory cost and alleviates the downward pres-sure on production which has already been below the socially optimal level inthe concentrated cement industry. The market is not as distorted by the multi-plant firms as when charging a high carbon tax, and the consumer and producersurplus suffer smaller losses.In summary, Figure 2.13 visualizes the comparison of welfare effects amongthe three carbon pricing schemes. Judging from these measures, OBPS is morelikely to be welfare improving with a smaller social cost of carbon. The analy-sis provides some suggestive evidences to rationalize the government adoptingOBPS in a concentrated industry like cement, despite that emissions abatementcould be small. It points to two confounding factors when internalizing pollu-tion externality – change in market structure and emissions leakage.39To break even in welfare terms, the required minimum social cost of carbon is (−46.36−9.57+20.50)/(−0.95+0.23) = $49/tCO2.114Figure 2.13: Welfare comparison of carbon policies2.5.2 Trade with multi-plant firmsWith the recent political unrest and the US-Canada tension on key manufactur-ing inputs such as aluminum, there is potential risk for unilateral increase intariff. In this section, I show how the multi-plant firm model can be applied to atrade policy experiment, and evaluate the effects of tariff changes on firm-leveladjustment and welfare. Before the counterfactual exercise, I first decomposewhat are the driving forces of trade in the multi-plant firm model to better un-derstand how multi-plant production affects trade in this framework.Decomposing the forces of tradeAs a variant in the Ricardian world, the model captures the comparative advan-tage based on technological differences while incorporating the role for geogra-phy. The geographic features not only refer to trade barriers but also the spatialdistribution of plants. Trade is a mixed result of the three forces as presentedin equation (2.4): the variation in marginal costs of production represents dif-115ferences in efficiency across locations; trade costs reflect geographical barriersand fixed costs govern plant locations. Although the literature has provided ev-idence for the presence of three types of costs, little is known about their quan-titative importance. With the help of the estimated parameters, I am able tolet firms re-optimize their plant location sets and predict changes in aggregatedoutcomes, under different costs scenario.Table 2.11: Decomposing sources of tradeData BaselinemodelZerofixed costsInfinityfixed costsSame locationinput costsτ = 1everywhereImport penetration (%) 27 24 17 31 20 89Export intensity (%) 45 44 40 47 44 93In the case of infinity fixed costs, I assume the firm always has a plant at its headquarter or the nearest location to itsheadquarter if the headquarter is out of sample.Table 2.11 tabulates the results. The model closely fits the average importpenetration and export intensity in the data, with a small underestimation dueto the assumption of intra-district trade. If there were no fixed costs for settingup foreign plants, then every firm would have a plant in each location becausethe model features increasing firm payoff with the number of plants it owns, andtrade would decrease such that markets only import 17% of their consumptionand exports 40% of their production. Trade would not vanish because plants areheterogeneous. If, on the contrary, the fixed costs were extremely high such thatfirms would only have one plant in their headquarter but anywhere else, theimport and export share would rise to 31% and 47% respectively. Comparingthe changes caused by fixed costs to unifying technology across locations, I findthat the effect on trade of the latter is not as large as that of the former. If theunit input costs were equalized everywhere to the mean value, markets wouldreduce the incentive to trade and the import from foreign is less by 4%, a levelof change smaller than 7% in the cases of extreme fixed costs. Exports would116reshuffle based on trade costs ranking instead, and the share in production doesnot necessarily decline. The third factor is geographic barriers. If trade costswere eliminated for every dyad, markets freely trade with each other choosingthe location with the lowest input costs and the most plants, both import andexport share would rise to around 90%. Overall, I find that all three factorssignificantly contribute to the level of trade, with geographic barriers being themost important, followed by plants spatial setting, and location differences intechnology the least. While the traditional Ricardian model of trade emphasizeson technological differences, geography plays a more important role here.National protectionismGiven the cement consumption in Canada relies mostly on domestic produc-tion, changes to import tariff by Canada would not significantly affect firm dy-namics. On the contrary, Canada exports around 30% of its cement productionto the US, and it is also the largest foreign supplier for the US cement industry.Unilaterally increase of the import tariff by the US will shift plant location andtrade pattern in the region. I, therefore, examine firm dynamics and welfareimplications when the US increases the import tariff to 20%, a level most of theMFN rates in the cement industry fall below.Figure 2.14 shows the change of cement plants from Canada to the US. AllFAF zones in Canada face higher plant exit rate. New cement plants are built inthe US, such as Washington, Oregon, Montana, Utah and some eastern states.However, expansion in some US locations crowds out plants in the other, namelyNevada. Observing the first two columns of Table 2.12, one result contrastingwith previous findings in the environmental policy experiments is that the USexpects to have more entry than the number of plants shut down in Canada,117Figure 2.14: Change of plant locations with 20% import tariff in the USimplying that the US demand of cement is large enough to support more play-ers if prohibiting imports.40 However, if the government intends to bring plantsback to the US, with a 20% tariff, the effect is quite small. The largest changein Table 2.12 happens at the intensive margin. Export of cement to the US, inparticular, decreases by about 85%, which makes the share of Canadian exportin its production of cement drop to 5%, a much lower rate than the baseline of30%.The welfare analysis highlights the importance of multi-plant productionand oligopolistic competition when evaluating trade policies. Specifically, Canadaexperiences an increase in price and producer surplus, while consumer surplusdeclines. The result is opposite to the effects of tariffs on exporting country40The top two firms combined increase the entry probability to any FAF zone in the US by0.23%, multiplying 63 potential FAF zones results in 0.145 more plants. In contrast, the two firmsdecrease the entry probability to any FAF zone in Canada by 1.37%, multiplying 10 potentialFAF zones results in 0.137 fewer plants.118in traditional trade theory. However, decomposing the firm-level adjustmentsreveals that when multi-plant firms close their Canadian plants facing the nega-tive trade shock, their average efficiencies of supplying cement also deteriorate,which then lead to higher prices and smaller market share.41 While large multi-plant manufacturers are hit harder by the trade shock, small local Canadianproducers expand their domestic market share. Hence overall, the producersurplus in Canada actually rises, but the gain is distributed to smaller producersfrom large multi-plant firms. As for the importing country, the US, consumerssuffer a big loss which is more than what can be compensated by producers’gain and tariff revenue combined. With the quantifiable welfare changes, I canconclude that a 20% unilateral tariff increase does more damage to the US itselfthan to its opponent.Table 2.12: Counterfactual changes with 20% import tariff in the USPanel A: Impacts on market outcomes∆ Avg entry prob(%) ∆ Price($) %∆ Consum %∆ Prod %∆ TradeLFH CEX Canada USCanada -1.00 -0.37 0.17 -0.43 -7.48 -0.43 -84.70US 0.10 0.13 0.66 -0.93 0.90 0.52 0.90Panel B: Impacts on welfare and emissions∆ CS($M) ∆ PS($M) ∆ Tariff Rev($M)Canada -2.55 0.36 -US -31.81 9.45 8.404241In my model, small single-plant firms are assumed to be sticky and do not exit facing thecost shocks. Their prices and market share, however, will respond based on competition withlarge multi-plant firms. One could rationalize the setting consider the following. Facing a neg-ative cost shock, a single-plant firm has the outside option of exiting which leaves him zeropayoff if no scrap value. A multi-plant firm has the option to reshuffle its plants and remain tobe profitable. The exercise here is for trade cost shocks that are not big enough to induce theclosure of small firms.42I estimate the percentage decrease in trade value using the percentage change in trade vol-ume. In 2016, Canada export cement to the US for a total of 274.7 million dollars.1192.5.3 Changes in firm operationsMerger and acquisitionThis section is inspired by expressions of concern over rising concentration thathave appeared in many industries, especially for products that are relatively ho-mogeneous, like cement. Since the largest cement manufacturer in the US andCanada, LafargeHolcim, is the outcome of a merger in recent years. What if thesecond largest firm Cemex acquires a medium-sized firm in this region? Thetarget chosen in this experiment is a leading US cement producer, Eagle Mate-rials Inc, who owns six US cement plants in 2016 and headquartered at Dallas,Texas.43 Since the technology in producing cement does not vary much acrossfirms, I assume cost synergies of the acquisition flow from managerial efficien-cies, such as the knowledge and connections in FAF zones that Cemex has notyet established a presence. In practice, it is reduction in fixed costs measuredthrough changes in location proximity to headquarter, from Monterrey in Mex-ico to Dallas in the US.Let’s name the hypothetical entity CemexEagle. Given the estimated modelprimitives, I allow LafargeHolcim and CemexEagle to re-optimize their plantsets. The left panel in Figure 2.15 displays aggressive plant entry for Cemex-Eagle, radiating from the headquarter Dallas and most severely affecting Okla-homa, Kansas, Illinois, Missouri, and Wyoming. The momentum continues toCanada. Lower fixed costs lead to the expansion of CemexEagle, and in turn alarger set of plants improves the firm’s production and distribution efficiency.43Eagle Materials Inc was the second largest locally owned cement manufacturer in 2016, justfollowing Ash Grove Cement Company which owned eight US plants. However, Ash GroveCement Company was acquired by CRH plc, an international building materials group, at theend of 2017. Eagle Materials Inc, remaining to be independent, is now the largest US ownedcement producer in 2020.120Meanwhile, comparing CemexEagle to the two separated entities before acqui-sition, I find that the firm also internalizes some plants with overlapping catch-ment area in the South. On the other hand, LafargeHolcim, closes plants innumerous places across Canada and the US, especially those where CemexEa-gle surges. Although the plant redistribution generally follows the expectation,not every location has Cemex rising and LafargeHolcim shrinking. For exam-ple, what happens at Wyoming, Nevada and Tucson metro area in Arizona areresults from changes in nearby locations, suggesting interdependency across lo-cations.Figure 2.15: Change of plant locations when Cemex acquires a small firm(a) Cemex post-acquisition (b) LafargeHolcimThe first segment in Table 2.13 presents market shares of the top two cementfirms before and after the acquisition. Although LafargeHolcim faces a small de-cline of market shares in Canada and the US, it still remains to be the dominantplayer. Cemex, after acquiring Eagle Materials, significantly enlarges its marketshare in both countries, and almost catches up with its rival in the US. In termsof producer surplus, CemexEagle obtains higher profits than the two firms pre-acquisition combined because the expansion of plant set shortens the deliverydistance to markets, improves the firm-level productivity, and subsequently in-121creases its competitive advantage for supplying cement. Correspondingly, itscompetitors lose. The overall producer surplus in both countries declines.The model is granular enough to predict price changes faced by consumersof each firm. In a head-to-head price competition where the optimal price equalsto the next lowest cost or monopoly price, any efficiency gain by a firm impliesa tighter pricing constraint of its rivals. Hence, consumers served by firms otherthan CemexEagle will enjoy a price drop. On the opposite side, prices generallyincrease for consumers of Cemex or Eagle Materials because for CemexEagle,competition is lessen. Therefore, how the average price or the aggregated con-sumer surplus changes depends on the fraction of consumers captured by thesefirms before and after. Knowing that LafargeHolcim’s customers are always themajority, the average price drops and consumers gain overall. It is critical thateven small efficiencies reduce some prices in this framework. Based on the totalsurplus standard, the acquisition would bring gains in efficiency (managerial ef-ficiency, production efficiency and distribution efficiency for CemexEagle) thatoffset the effects from lessening of competition.Although this is a hypothetical acquisition simulation, the implications areclosely related to arguments surrounding Canada’s Competition Act, Section96(1). It states that “the Tribunal will allow a proposed merger to proceed evenif the merger leads to a substantial lessening of competition providing the ef-ficiency gains uniquely attributable to the merger offset and are greater thanany lessening of competition” (Mathewson and Winter, 2000). The statementmakes Canada unique amongst other leading antitrust jurisdictions in treatingefficiencies to outrank anti-competitiveness. A real and possibly the most con-tentious case in Canada is the merger of Superior Propane and ICG Propanethat used the efficiency defence to get approved (Mathewson and Winter, 2000;122Rosenfeld, 2003; Zerbe and Knott, 2004). Therefore, the counterfactual exercisein this section allows us to re-examine the state of competition policy in Canada,specifically for the cement industry.Table 2.13: Counterfactual changes with Cemex-Eagle acquisitionMarket share, pre (%) Market share, post (%) ∆ PS($M) ∆ Price($) ∆ CS($M)CEX LFH CEX-EAGLE LFHCEX-EAGLE LFH SmallCanada 4.65 41.83 6.21 40.95 2.62 -2.34 -1.13 -0.22 2.95US 10.12 18.64 16.05 18.52 18.57 -5.30 -21.66 -0.01 22.82Collusion among firmsCement manufactures are frequently accused of collusion. The literature findsthat cement cartels exist in countries such as Brazil, India and South Africa (Har-rington, 2015; Salvo, 2010). The sum of cement cartel activity in Appendix Table1 of Connor (2014) mentions no cartel investigations in cement in either Canadaor the US up to December 2013.44 In the absence of direct evidence pointingto collusion in the North American cement industry, the assumption oligopolis-tic Bertand-Nash pricing seems reasonable. As I have shown in Section 2.4.3,the markups emerging from this assumption are similar to those reported inaccounting data.In terms of regulations, Canada has made significant amendments to theCompetition Act after 2009 by strengthening its anti-cartel enforcement. Mostcollusive arrangements are now automatically illegal without the need for es-tablishing proof of undue economic impacts. The amount of fines and impris-onment has also been raised substantially.45 Overall, The Canadian anti-cartelenforcement is closely aligned with the US, and penalties are high compared to44There was a cartel charge in the US ready-mix concrete industry in 2010.45Maximum fines were increased to CAD 25 million per count from CAD 10 million per count.Individual prison terms were increased from 5 years to 14 years.123many other jurisdictions including the EU (Connor, 2016).With the estimated model primitives, I can then evaluate what would hap-pen to production and welfare in the case of collusion. In this section, I exam-ine a limiting case where all firms collude, including the largest two and smallfirms. This can be seen as a mega multi-plant firm owning all plants in the USand Canada and charging monopoly price to consumers. This case is nested inmy baseline model, and the mega firm’s expected variable profit isE[pi]= κµ¯−η(µ¯−1)∑mAmΦη−1θm , (2.18)where κ = Γ(θ−η+1θ). And every entity in the cartel earns Φ fm/Φm fraction ofthe firm’s variable profit in m. The market price index isPm = Γ(θ +1θ)µ¯Φ−1/θm . (2.19)Table 2.14 presents changes of the market equilibrium if all firms colludeat the monopoly markups, holding the spatial distribution of plants fixed asbaseline. Compared to the baseline case, prices increase substantially in bothcountries, along with drop in production by about 60%. The cement cartel sig-nificantly harms consumers in both countries, which only 40% can be offset bythe gain of producers. Linking back to the environmental concern in the cementindustry, if one considers benefits from carbon reduction associated with theshrinking cement production, the cartel would theoretically improve social wel-fare of North America as long as the social cost of carbon is above $29/tCO2.4646To break even in welfare terms, the required minimum social cost of carbon is (−344.71−1914.70+139.31+791.74)/((−0.5817×11.34−0.5928×85.4)×0.8) =$29/tCO2.124Table 2.14: Counterfactual changes with collusion among all firms%∆ Price %∆ Consum %∆ Prod ∆ CS($M) ∆ PS($M)Canada 36.78 -57.99 -58.17 -344.71 139.31US 39.87 -59.30 -59.28 -1914.70 791.742.6 ConclusionsIn this chapter, I estimate a spatial multi-plant oligopoly model with endoge-nous and interdependent location decisions. The framework goes quite far inmatching data of the US and Canadian cement industry. The estimation revealskey costs faced by cement plants, including cost of production, trade cost andfixed cost of entry. Using the structurally estimated parameters, I quantitativelyevaluate the effects of environmental regulations, trade policies, and competi-tion policies on firm dynamics and market aggregates.An increase in carbon tax would result in firms to locate plants to nearby“pollution havens” in the long run. It causes production leakage which furtherpushes down the domestic production below its socially optimal level and ex-acerbates market distortions in the concentrated cement industry. Moreover, itinduces carbon leakage to unregulated markets where the increase in carbonemissions offsets emissions abatement and creates environmental damages inthe taxing country. The welfare losses from these two channels make carbon taxa suboptimal policy. Two remedies are evaluated. First, a border tax adjustmentcan mitigate carbon leakage, but is not effective in reducing production leak-age if plants were primarily exporters. Second, an output-based pricing system,which works as rebates to firms to lower the carbon levy, alleviates produc-tion leakage but performs poorly in cutting down carbon emissions if firms arenot incentivized to adopt carbon-efficient technologies. The comparison across125three carbon pricing regimes provides insights to policy makers in regulatingcarbon for a emission-intensive, trade-exposed and concentrated industry, likecement.In addition, examination of unilateral tariff changes confirms the long-existingconsensus that countries gain from free trade. The chapter also goes beyondin analyzing the effects of tariff on the market structure of exporting countryand detecting heterogeneous effects between multi-plant and single-plant firms.Lastly, the acquisition simulation provides a case where the majority of con-sumers can actually gain from rising concentration due to improved efficiency.It contributes to the discussion about Canada’s Competition Act in cases whereefficiency effects outweigh losses in an anti-competitive merger.The chapter has a broader goal that the multi-plant oligopoly framework andthe associated estimation strategy I introduced can extend the reach of empiricalresearchers when evaluating policies and other spatial organization problems.I have demonstrated in this chapter that this framework is applicable to threedifferent topics which are traditionally studied in isolation by economists. Eval-uations of the seemingly irrelevant policies are in fact intrinsically connectedthrough analyzing firms’ responses. Therefore, an integrated framework ofmulti-plant production is in need to connect the dots of several issue altogether.126Chapter 3Rules of Origin and Auto-PartsTrade3.1 IntroductionSince 2016, a set of free trade agreements have drawn unprecedented attentionled by the formation, renegotiation, or separation of some world’s largest free-trade areas, namely the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), the United States-Mexico-Canada Agreement (USMCA),the Regional Comprehensive Economic Partnership (RCEP), and the EU-UKTrade and Cooperation Agreement (TCA). One central detail that governmentshave been wrestling with is how to determine whether a product is eligible forpreferential treatment in an agreement, especially when it comes to sensitivesectors, such as the auto industry. CPTPP adopted a generous rule of regionalvalue content (RVC) on duty-free vehicles at 45%, which means that automo-biles need to be manufactured using at least 45% of content created intra-FTA.127There has been vigorous opposition in some member countries, such as Canada,arguing that the liberal rule contradicts what is demanded by the US in USMCA,an increasingly stricter standard from 62.5% to 75%. In Asia, RCEP consolidatesvarious rules in the existing five “ASEAN+1” agreements. Firms no longer needto reformulate the production to comply with different rules, and instead theymanufacture products to qualify a single set of RCEP criteria, which is fairly lowat 40%. As for the EU-UK trade deal, there has been back and forth negotiationson the content rule of electric vehicles.Debate over these trade agreements sheds light on a commercial policy in-strument which used to be less transparent: rules of origin (RoOs). It functionsas a set of criteria to determine the origin of products and whether productscan be granted preferential tariff treatment. Complementary to the preferen-tial terms among FTA members, RoOs are designed to curb exports from thirdcountries to transship goods to the FTA through the member with the lowestexternal tariff (trade deflection).1 As such, researchers historically regard RoOsas a “supportive” role for regional integration. Nevertheless, with the dramaticgrowth of intermediate goods trade which accounts for almost two thirds ofinternational trade (Johnson and Noguera, 2012), the production chain of finalgoods evolves to be an increasingly sophisticated network across industries andgeographical locations. A commonly cited case is Apple iPod in Dedrick et al.(2010), whose production involves memory chips from South Korea, batteryfrom Japan, controller chip from the US and assembly in China. The answerto where a final product originates is thus no longer straightforward. In thiscontext, rules of origin reshape firms’ input allocation by defining a product’s“nationality”.1In this chapter, I define that trade diversion occurs when an importer chooses a less efficientsource because of regional preferences, whereas trade deflection occurs when tariffs on onedestination cause the exporter to send her goods to a different destination.128Rules of origin distort sourcing decisions beyond the traditional trade di-version effects of preferential tariffs.2 If RoOs are not too liberal to leave firmsunconstrained, a final good producer faces a dichotomy. On one hand, she canenjoy the low tariff when exporting final goods to the trade bloc in exchange forprocuring a required share of inputs within the region which could be less cost-effective sources. On the other hand, she can source from the cheapest inputsuppliers anywhere but lose the origin status and pay MFN tariffs when cross-ing partners’ borders. Given export decisions, firms choose whether to complywith the rules or not. For compliers, RoOs divert trade of intermediate inputs tothe free trade region even without tariff reduction for inputs. For non-compliers,there could be other margins of firm adjustment, such as reorganizing export orrelocating production. A restrictive RoO could backfire when more firms defythe rules or even shift the production to countries with laxer requirements.I develop a theoretical model to analyze firm’s decisions on where and howmuch to source each input facing the rules of origin constraint in a multi-countryand multi-product world. The key focus of this model is to incorporate RoO asimplicit costs of importing intermediates from countries outside the free traderegion. Built upon Antra`s and Chor (2013) and Antras et al. (2017), the modelallows marginal products of different inputs in producing the final good to varybut is silent on the extensive margin decisions on offshoring which is the focusin Antras et al. (2017). Having different marginal product of inputs helps tobuild a micro foundation featuring heterogeneity in intermediate imports alongthe product dimension. The model yields a gravity trade equation for everyintermediate goods, and guides the estimation to be tractable.2See Caliendo and Parro (2015), Amiti and Konings (2007), and Bas and Strauss-Kahn (2015)for studying effects of tariff liberalization.129Legal complexity and inconformity of rules of origin presents a major em-pirical challenge in studying their effects.3 The practice with regard to RoOsvaries across regional trade agreements and industries, with some defined interms of change in tariff headings, others the regional value content (RVC) cri-terion and yet others requirements of manufacturing or processing operation.For this reason, the existing empirical papers on RoOs have focused on a singletrade agreement (Anson et al. 2005, Conconi et al. 2018 and Head et al. 2021 onNAFTA, Sytsma 2019 on EU Generalized System of Preferences). To accommo-date the lack of uniformity in rules across sectors, they either use a syntheticindex approach as in Estevadeordal (2000) or count the number of linked finalgoods that are subject to RoOs like Conconi et al. (2018), or else exploit an eventstudy.4 This chapter differs in focusing on a single industry, the automotive,where global sourcing is prevalent and, most importantly, regional value con-tent criterion is consistently applied by different RTAs. It allows me to rankRTAs according to the regulated share of value originating from member statesout of the value of a car as a measure of RoO restrictiveness. Using observedRVC thresholds avoids measurement error in self-constructed indices, and isconsistent with the way my framework and other theoretical papers have mod-eled RoOs.Leveraging the derived gravity equation on trade in intermediates and vari-ation in local content requirements across RTAs, I first unpack the effects of re-gional trade agreements on intermediate goods trade to two distinct channels:3Rules of origin are very detailed in regional trade agreements. For example, NAFTA’s annexon rules of origins is close to 200 pages.4The index constructed by Estevadeordal (2000) and also used in Anson et al. (2005) mea-sures the restrictiveness of preferential rules of origin from 1 being the least restrictive to 7 beingthe most restrictive. It is based on the type of rules implemented, technical rule being the mostrestrictive practice, followed by value content and lastly change in tariff classifications. Conconiet al. (2018) consider the input-output linkage in counting the number of sourcing restrictionsthat affect intermediate goods in each sector.130preferential intermediate tariffs and rules of origin on downstream outputs. Iexamine RoO annexes on the automotive industry for 23 RTAs from 2000 to2014, which cover 40 major economies and 26 HS6-digit auto parts. Resultsshow that RoOs indeed facilitate trade diversion. The impact of RTAs on inter-mediates trade would be equivalent to the removal of 19% ad-valorem tariff whenthe associated content rule is below 60% and equivalent to 53% tariff removalwhen RVC is above 60%. Furthermore, the degree of trade diverted is humpshaped with respect to the restrictiveness of RoOs. As the content rule goesbeyond 65%, the average shift of foreign sourced inputs to regionally sourcedones is about the same magnitude to RTAs with less than 50% RVCs, suggestingmore firms defy the rules and relocate their production elsewhere.Beyond the trade diversion effects of RoOs, the chapter further exploresfirms’ heterogeneous responses to RoO changes. Specifically, I test whetherexport destinations of cars, the magnitude of preferential benefits, and differ-ent car parts would vary the results. When the majority of foreign consumersare intra-RTA or the preferential margin on car exports is high, car exporters’benefits from complying RoOs are likely to outweigh costs. At country level,increase in the number of compliers leads to larger diversion in intermediatessourcing. Moreover, RVC thresholds may work differently across parts depend-ing on what gets to be redistributed first. I find where cars are sold matters tothe sourcing of car parts, but the effect of exported cars’ preferential margin isweak. There is neither systematic difference in RoO effects across parts.This chapter adds to a growing body of literature on rules of origin. Much in-terest on earlier works has been on theory (Krishna and Krueger, 1995; Krueger,1997; Falvey and Reed, 2002; Krishna, 2005; Ju and Krishna, 2005). Recently, em-pirical studies start to rise. The most closely related paper is Conconi et al. (2018)131in which they use difference-in-difference to show RoOs reduce the growthrate of imports of intermediate goods from third countries to Mexico relativeto NAFTA partners by around 45%. Anson et al. (2005) also document nega-tive impact of RoOs on imports and that the compliance costs of NAFTA RoOson Mexican exporters amount to 47% of the preferential margin. Sytsma (2019)finds the RoO in EU to Bangladesh textile exporters cuts three-fourths of thepreferential margin. Several other papers provide evidences that liberalisingrules of origin increases export (Andersson, 2016; Tanaka, 2021; De Melo andPortugal-Perez, 2014). The most recent study by Head et al. (2021) focuses onthe auto industry as well. They establish a RoO Laffer curve where productionof car parts within USMCA first expands and then contracts with increasingcontent requirement, taking into account adjustment on firm types (compliant-unconstrained, compliant-constrained, and non-compliant) and relocation ofassemblers. Their theory is corroborated by some of the empirical results inthis chapter.The chapter continues as follows. I first adapt the existing model to includerules of origin as a form of trade frictions. Derived from the model, trade elas-ticities can be estimated separating the effects of RoOs from others in a RTA.Refinements are then performed to test for any heterogeneous effects related toexport decisions and intermediate goods characteristics.3.2 A Model of Global Sourcing under Rules ofOriginI develop a multi-country and multi-product sourcing model that characterizeshow much and where final good producers import every intermediate inputs.132Geography is categorized by countries where intermediate suppliers locate, fi-nal good producers locate, and markets where final goods are sold. To studyrules of origin, I restrict the second and third type of locations to the same setwhich is bonded by a free trade agreement, whereas locations of intermediatescan be global. Compliers of RoOs are constraint in sourcing from countries out-side of the FTA region as if a hypothetical tariff on intermediates is imposedbetween FTA members and other countries.3.2.1 Consumer preferences and demandConsider a free trade bloc N consisting of countries where individuals havecommon preferences. For model tractability, I let trade in cars entails zero costsamong FTA member countries and assume away any frictions including dis-tances, and thus, there is no price arbitrage. It allows me to model aggregateddemand for the entire bloc instead of each country. A representative consumerinN values the consumption of different varieties of cars from a set Ω accord-ing to a standard constant elasticity of substitution (CES) aggregatorU =(∫ω∈Ω(ϕω q˜ω)ρdω)1/ρ, ρ ∈ (0,1), (3.1)where ϕω represents the quality of variety ω perceived by all consumers in thebloc and q˜ω is its consumption in physical units. Denote E as the total expendi-ture on the automotive industry summing across the member countries. Maxi-mizing utility subject to the budget constraint∫ω∈Ω pω q˜ωdω = E gives rise to thefollowing demand featuring a constant price elasticity for variety ω :qω = Aω p− 11−ρω , (3.2)133where qω ≡ ϕω q˜ω is the quality-adjusted output. The variety-specific demandshifter, Aω = E (Pρϕω)1/(1−ρ), depends on the industry-wide demand for the setof countries and consumers’ taste towards the variety of car. I assume firmstreat Aω as exogenous. P is the standard price index accounting for the tastedifferences across varieties available to these markets.3.2.2 Firm’s problem conditional on sourcing locationEach differentiated variety is produced by a single car manufacturer who lo-cates at ` ∈ N within the bloc. Firms are then also indexed by ω . They areheterogeneously defined by their core productivity δω . Production of final carvarieties requires assembly of a continuum bundle of intermediates, denoted byj on an unit interval. Firms decide how much and where to procure parts giventhe demand of its variety within the trade bloc characterized by equation (3.2).Sourcing of parts, however, is not restricted to the member countries only, buta broader set I . I leave firms’ export decisions to markets outside of the tradebloc and the joint determination of both exports and imports for future exten-sions. Instead, I focus on the group of firms who are always constrained by rulesof origin and choose to comply, named “compliant-constrained” in Head et al.(2021).Intermediates are produced by competitive parts suppliers from a countryset I where each supplier is denoted by ji where i ∈ I . A part supplier en-gages either in a relationship-specific production or in an outside option withvalue zero. Since every part is fully customized to a variety of car, neither canparts suppliers resell to alternative buyers. In a case where contracts betweencar assemblers and parts suppliers are perfectly enforceable and complete, as-134semblers make an offer to pay p j in exchange for x j amount of compatible inputsj for each part. Suppose the optimal sourcing strategy is {i∗( j),∀ j ∈ [0,1]}, thequality-adjusted volume of a car variety ω follows a CES production function,qω = δω(∫ 10(ψ jx j(i∗)ω)αd j)1/α, (3.3)where ψ j captures the marginal product of different car parts which is non-negative and continuously differentiable.5 Intermediate inputs are combinedwith a symmetric elasticity of substitution equal to 1/(1−α) where α ∈ (0,1).They are imperfectly substitutable along the quality dimension, but not the en-gineering process. For example, an assembler may compensate inferior wheelswith leather seats cover to meet the same level of quality perceived by con-sumers.With complete control over the investments and prices of all components,a car manufacturer maximizes his profits by offering the optimal contract suchthat only the lowest cost parts suppliers {i∗( j),∀ j ∈ [0,1]} would participate.Mathematically,max{x jω ,p jω} j∈[0,1]piω = A1−ρω δρω(∫ 10(ψ jx jω)αd j)ρ/α−∫ 10p jωx jωd js.t. p jωx jω − c j(i∗)ωx jω ≥ 0.(3.4)Part j supplier in country i∗ incurs unit cost c j(i∗)ω . I show in Appendix thatsolving this problem delivers the optimal amount of input j, pricing, and asso-5Another way is to ignore substitutability and model a Leontieff production function whichis a special case of the CES specification.135ciated firm profits to bex∗jω =Aωψ j(ρδρω) 11−ρ (v∗jω) 11−α V ρ−α(1−α)(1−ρ)ωp∗jω = c j(i∗)ωpi∗ω = (1−ρ)Aω (ρδωVω)ρ1−ρ ,(3.5)where v∗jω = ψ j/c j(i∗)ω indicates the marginal product per unit of cost and Vω =[∫ 10(v∗jω) α1−αd j] 1−ααis an aggregator of cost-adjusted quality of all intermedi-ates. The discussion of whether the quality-adjusted investment on inputs arecomplements or substitutes depending on the relative size of α and ρ followssimilar rationale in Antra`s and Chor (2013) and Alfaro et al. (2019). When ρ issmaller than α and demand of a final car is more elastic, any additional invest-ment on quality improvement of a particular part can significantly reduce thatof other parts, making them substitutes in quality terms. The suppliers’ partic-ipation constraint is binding for the lowest cost parts producers, which leavesthem with the same payoff as the outside option at zero. Car assemblers extractall the rents.Now let’s characterize the marginal cost of part j supplier from country ishipping to assembler ω at `,c jiω` =wiz jiωτ ji`ri`di`, (3.6)where wi is a composite index of wages and material prices for car parts pro-duction in sourcing country i. Delivery of car parts is subject to a set of tradefrictions from i to `, namely ad-valorem tariffs on parts τ ji` = 1+ t ji`, non-pricefactors such as distance that shifts transportation cost di`, and implicit costs onparts due to rules of origin placed on final cars ri`. For RoO compliers who find136the rules to be binding, ri`> 1 if the part is sourced outside the region, i.e. i /∈N ,and ri`= 1 otherwise. There could be other groups of firms who never find RoOsbinding and those who choose not to abide the rule, in either case ri` = 1 regard-less whether county i belongs to the regionN or not. Modeling the endogeneityof ri` which depends on firm-level decisions and identifying marginal switcherswould further complicate the model and require more disaggregated data in es-timation.6 With limited data, I keep the model parsimonious but bear in mindthat firms’ heterogeneous responses to RoOs are embedded in ri` which will beinvestigated empirically in Section 3.4.Another caveat is that firms may progressively source parts within the FTAregion until the minimum requirement is met. The effective RoO constraint ondifferent parts would then vary depending on their relative contributed valueand cost advantages, although technically, the same content threshold is statedwithout specification to different parts. Solving which part is reallocated to do-mestic sourcing and which part remains foreign is a complicated combinatorialproblem. Nevertheless, I extend ri` to r ji` in the empirical section and investigatewhether effects are heterogeneous across parts.Productivities of the compatible inputs, z jiω , are supplier-assembler specific.I treat productivities of part j from country i for a car assembler ω as inde-pendent draws from the Fre´chet distribution with CDF, exp(−z−θ). Hence, themarginal product per unit cost of a part, v jiω = ψ j/c jiω`, is distributed asPr(v jiω ≤ v)= exp(−φ ji`v−θ), (3.7)where φ ji` = ψθj(wiτ ji`ri`di`)−θ indicates country i’s potential in supplying part6The recent study by Head et al. (2021) makes theoretical contribution in modeling thesemargins.137j to country `. The shape parameter θ governs the force of comparative advan-tage across suppliers from different countries for a specific part. The lower theθ , the higher the variability of productivities. Note that different car manufac-turers who assemble their respective varieties at the same location would expectidentically distributed parts suppliers.3.2.3 Sourcing decisionsObserving equation (3.5), car manufactures choose the optimal part supplierwho offers the lowest price of the part or equivalently the highest value perunit cost from the set of countries I .7 With equation (3.7) and properties ofthe Fre´chet distribution, the distribution of value per unit cost for parts that areactually procured by car assemblers at ` isPr(v∗jω ≤ v)= 1− exp(−Φ j`v−θ), (3.8)where Φ j` = ∑k∈I φ jk` is the sourcing capability of a country ` for a part j. Theprobability that i∗ is selected for part j used in cars assembled at ` equals toPr(argmaxi∈Iv jiω = i∗)=φ ji∗`Φ j`. (3.9)An alternative interpretation is that equation (3.9) is the share of assemblers in` that source from part supplier ji∗. More assemblers choose parts suppliersfrom i∗ if they have low costs to serve ` relative to others. Specifically, whenRoOs are effective, sourcing within the FTA region has competitive advantageagainst sourcing outside, holding other cost factors equal. Following Eaton and7Implicitly, I assume all countries from the setI are capable of producing compatible inputsfor every variety of car. Relaxation of this assumption will not affect the model structure. Agravity-type trade equation which is essential for the empirical estimation still holds.138Kortum (2002), another implication about the Fre´chet distributed productivitiesis that the distribution of value per unit cost for part j that country ` sourcesfrom a particular country is independent of the sourcing country’s identity andequals to the distribution in (3.8). Consequently, the share of assemblers in `that source from ji∗ is also the corresponding expenditure share.3.2.4 Aggregation and gravityFrom the optimal sourcing decisions of inputs in equation (3.5), the shippingflow of part j from the lowest-cost supplier to a car assembler ω in value termisX jω = ρ11−ρ EPρ1−ρ (ϕωδρω )11−ρ(v∗jω) α1−α Vρ−α(1−α)(1−ρ)ω . (3.10)To get the expected trade flow of part j from a country i∗ to country `, I needto aggregate the above taking into account the measure of heterogeneous firmsin `, their associated cost distributions when i∗ is the source country, and theprobability of choosing country i∗. Now, let’s tackle each of the components.I assume free entry for car manufacturers with entry cost F` for every ` ∈N . Equation (3.10) reveals that the preference-based ϕω and cost-based δω areisomorphic in trade. Therefore, instead of separately specifying each variable,I assume the composite ϕωδρω is drawn from a Pareto distribution with shapeparameter η where η > 1/(1− ρ). Free entry condition and variable profit inequation (3.5) give rise to the entrant’s lowest productivity and quality cutoffbeing (ϕωδρω) 11−ρ=F`(1−ρ)ρρ1−ρ EPρ1−ρVρ1−ρω. (3.11)Firms which above the threshold enter and actively source inputs from all po-139tential suppliers since there is no fixed costs of importing.Aggregating the variety-specific part usage in (3.10) to country ` where as-sembly of a set Ω` varieties is processed, I obtainX j` = κF` Ω`(Φ j`Φ`) α(1−α)θ, (3.12)where constant is κ = ηρη(1−ρ)−1 , andΦ`=(∫ 10 Φα(1−α)θj` d j) (1−α)θαis a sourcing capa-bility index of country ` across all the parts. The equation implies that if a part ishigher value-added to the final car and also enjoys cost advantage among all thepotential suppliers, it will be used more in producing the quality-adjusted finaloutput relative to other parts. The relative difference is governed by the degreeof substitution across parts and productivity dispersion across suppliers. Thederivation is presented in the Appendix, which takes advantage of the settingwhere the cost distribution of parts that are actually sourced by a country is thesame regardless of the identity of firms (varieties).Combined with the sourcing probability in equation (3.9), export from coun-try i∗ to ` for part j isX ji∗` = κ F` Ω`Φ− α(1−α)θ` Φα(1−α)θ−1j`︸ ︷︷ ︸dest., part-destψθj w−θi∗︸ ︷︷ ︸part, orig.(ri∗`di∗`)−θ︸ ︷︷ ︸orig-destτ−θji∗`︸︷︷︸part-orig-dest. (3.13)The model yields a gravity trade equation at product level aggregating fromfirms’ decisions. Trade in intermediate inputs is rising in marginal productof a car part and measure of assemblers, and decreasing in cost of parts pro-duction and trade frictions between the country pair for the input. Due to thesubstitutability across intermediate inputs introduced in the model, country `’s140sourcing capability of other parts also affects trade negatively. Depending onthe relative size of α versus θ , the effect of sourcing capability of country ` forthe part j is ambiguous. If intermediate inputs are less substitutable (small α)and input producers from different countries are less dispersed (high θ ), thenincrease in Φ j` due to improvement in supply by any other origins will reducesourcing of the part from i∗ because business stolen by parts suppliers fromother origins dominates expansion of the market for part j. The trade elasticityremains −θ as in Antras et al. (2017) when the extensive margin in sourcing issuppressed and all firms are capable of sourcing inputs from all countries.Although this chapter does not intend to structurally recover all the modelprimitives for counterfactual analysis, the gravity equation provides powerfulguidance for understanding trade flows of intermediate inputs and estimatingtrade elasticities. Once observed variables measuring each type of friction areintroduced, namely tariffs, rules of origin restrictiveness and non-price factors,I can apply the empirical counterpart of equation (3.13) to estimate each of theireffects on trade.As an extension of the benchmark model, I have mentioned in Section 3.2.2that the effective RoO friction when sourcing outside of the trade bloc couldvary by parts if there is systematic differences in which part to be shifted in-wards first and which part to always be left out, which makes it r ji`. The exten-sion will not change the rest of the deviation, and the gravity equation becomesX ji∗` = κ F` Ω`Φ− α(1−α)θ` Φα(1−α)θ−1j`︸ ︷︷ ︸dest., part-destψθj w−θi∗︸ ︷︷ ︸part, orig.d−θi∗`︸︷︷︸orig-dest(r ji∗`τ ji∗`)−θ︸ ︷︷ ︸part-orig-dest. (3.14)I will provide more details in Section 3.3.3 about constructing the proxy for r ji`,and compare empirical results in equation (3.14) to (3.13).1413.3 Data and Variables3.3.1 RTAs and RoOsRules of origin are critical components in regional trade agreements. In thischapter, I study a period from 2000 to 2014 covering 23 RTAs and 40 majorcar and parts production countries including the U.S., Canada, Mexico, Brazil,China, Japan, South Korea, Thailand, India, 28 EU countries, Iceland, Norway,and Turkey. These RTAs are either still active in 2014 or once have been activeduring the studied time period. Information on each specific RTA such as yearsof entry into force and deactivation, parties involved, relevant articles and an-nexes about RoO provisions is provided by WTO Regional Trade AgreementDatabase and member countries’ government websites.The restrictiveness of rules of origin in this chapter is measured through theminimum of regional value content required in order to be treated with pref-erential terms. Concentrating on a single industry, the automotive, allows meto exploit the observed thresholds rather than relying on relatively subjectiveindices. One may raise concern on whether RVC is sufficient to represent thestringency of rules of origin. RVC rules are normally used in combination withchange of tariff classifications which requires any non-originating input must besourced outside the same category with the final good at certain level. For ex-ample, consider a passenger car falling under HS sub-heading 8703.21-8703.90.NAFTA rules of origin require the following:“A change to subheading 8703.21 through 8703.90 from any other heading, pro-vided there is a regional value content of not less than 62.5 percent under the net cost142method.”The first part means that non-originating input in a passenger car requiresa HS heading change, i.e. not coming from heading 8703 (“motor cars & vehi-cles for transporting persons”). The second part imposes additional constraintwhich the cost of inputs sourced within NAFTA has to be at least 62.5% of thetotal net cost for a final car. Considering car parts that are mostly under theheading of 8708 (“parts & access for motor vehicles”) and 8407 (“spark-ignitionreciprocating or rotary internal combustion piston engines”) but none underthe same heading with passenger cars, the change of classification restriction isclearly not binding. What matters for the sourcing of car parts is mainly theRVC threshold.8 In general, the fact that change of classification rule is unbind-ing in the automotive industry applies to other RTAs as well. Therefore, RVC isa valid instrument for RoO stringency, at least for cars.How regional value content is calculated goes further in details. Generallytwo methods are used, transaction value or net cost. The first is based on valueof non-originating materials in which RVC is equal to one minus the share ofnon-originating materials’ value in adjusted price of the good.9 The net costbased approach replaces transaction price to net cost of the good and calculatesRVC using the share after subtracting value of non-originating materials overtotal net cost of the good. Most RTAs in my sample use the net cost method for8The recent replacement of NAFTA with USMCA increases RVC threshold to 75%, and alsointroduces new regulation on labor value content that requires 40-45% of auto content be madeby workers earning at least $16 per hour, as well as 70% percent of both the steel and aluminumused in car production must originate within the region. However, the two new requirementsare not commonly used across RTAs. I ignore clauses other than RVC for now but acknowledgethat my measurement of stringency could be at the lower bound.9As global value chain becomes more fragmented, production of non-originating interme-diates could involve the use of originating materials as inputs. However, the value flow backhome through imported foreign intermediates is not counted intra-RTA. So technically from theglobal value chain perspective, RoOs are more restrictive than it appears to be.143cars. However, some also provide transaction value method as an alternativeand either can be used with slightly different threshold, in which case I choosethe more stringent content rule.Table 3.1: Description statistics on RTA and RVCEIF Year Car RVC (%)North American Free Trade Agreement (NAFTA) 1994 62.510pan-Euro-Mediterranean cumulation system / PEM Convention 1997 60EU - Mexico 2001 60EFTA - Mexico 2002 40Accession of China in Asia Pacific Trade Agreement (APTA) 2002 45Japan - Mexico 2005 65ASEAN - China 2005 40EFTA - South Korea 2007 55Japan - Thailand 2008 40ASEAN - South Korea 2008 40ASEAN - Japan 2009 40ASEAN - India 2010 35EFTA - Canada 2010 50India - MERCOSUR 2010 60India - South Korea 2010 40India - Japan 2012 50EU - South Korea 2012 55South Korea - U.S. 2012 55South Korea - Turkey 2013 55Note: Pan-Euro-Mediterranean cumulation system is based on a network of Free Trade Agreements havingidentical origin protocols with contracting parties including the EU, EFTA, Turkey, and participants in theBarcelona Process, and others. Four other FTAs are part of PEM Convention and not separately listed above.EFTA countries consist of Iceland, Norway, Switzerland, Liechtenstein during 2000-2014. NAFTA countriesare the US, Canada and Mexico. Brunei, Cambodia, Indonesia, Laos, Malaysia, Myanmar, Philippines, Singa-pore, Thailand, and Vietnam form ASEAN. MERCOSUR comprises Argentina, Brazil, Paraguay and Uruguay.Countries that are bolded in these organizations, as well as China, Japan, South Korea, and India are includedin the regression analysis of this chapter.A list of regional trade agreements in my sample and their respective valuecontent rules on the automotive industry is presented in Table 3.1. RVC rangesfrom 35% to 65%, but at the level of country pairs, most are concentrated at60% as a harmonising initiative by the EU except for the agreement with SouthKorea. The lack of variation becomes problematic when I include both a RTAdummy and RVC in a regression due to high collinearity, which I have carefully10The RVC for light vehicles was first set to be 50% during 1994-1998, and then modified to be56% in 1998-2002. It is finally raised to 62.5% from 2002 until the recent replacement to USMCA.144dealt with in the empirical section.3.3.2 Tariff and tradeTo estimate the gravity equation of trade in intermediate inputs in (3.13), I col-lect trade and tariff data for HS6-digit car parts from UN Comtrade and theWorld Integrated Trade Solution (WITS). 26 categories are identified for carparts including engines, transmissions, brake system, steering and suspensioncomponents, electrical equipments, seats and other parts. Final good is re-stricted to passenger cars.Figure 3.1 reports distributions of cars and car parts effectively applied tariffsacross country-pair-year observations, excluding a large number of zero tariffs.Effectively applied tariffs would be the MFN rates if a country pair does notform RTA and preferential tariffs otherwise. Variation in tariffs takes into ac-count the phase-out schedule and two partial scope agreements. As in panel (a),India has over 100% tariff on passenger cars, followed by China at around 86%before joining the WTO but gradually lowering the tariff thereafter. The MFNtariff on passenger cars for Thailand is as high as 74%, while that for Brazil andMexico is around 30% to 45%. Countries such as the US and Canada have lowrate at about 1% - 5%, and Japan zero tariff although the high automobile stan-dards impede foreign cars from stepping into the market. Car parts generallyface lower tariffs compared to what are imposed on finished cars due to tariffescalation. China had relatively high tariff on auto parts at 45% before becom-ing a member of the WTO and reduced it to around 10% until 2014. Thailandand India are at the top tier of countries which set high MFN rates on parts at30% - 40%, followed by Brazil and Mexico at around 20%. Tariffs on parts in the145US, Canada and Japan are largely approaching zero.Figure 3.1: Distribution of effectively applied tariff051015Density0 .2 .4 .6 .8 1(a) Passenger cars051015Density0 .1 .2 .3 .4 .5(b) Car partsUnlike applied tariffs on cars, Figure 3.2 shows preferential margins definedas the difference between the MFN and preferential tariffs are not as dispersedbut highly concentrated at 10%. It is consistent with the fact that most MFNrates on passenger cars are around 10% as presented in Figure 3.1, panel (a).11Countries that are located at the thin right tail are India, Mexico and a few smallEuropean economies who witness substantial tariff decline after forming RTAs.Figure 3.2: Distribution of preferential margin on passenger car010203040Density0 .2 .4 .6 .811Figure 3.1, panel (a) and Figure 3.2 are not exactly the same because phase-out tariff sched-ule and PSAs are included in the former but not the latter. The difference between MFN andeach year’s phase-out tariff is included when plotting Figure 3.2.146Although the model does not explicitly solve firms’ decisions on export ofcars, equation (3.10) incorporates the market demand within RTA in determin-ing import of intermediates at the firm level. Theoretically, firms are more likelyto obey rules and source pars internally if they mainly serve the markets withinRTA. In practice, I construct the share of intra-RTA trade over total export incars to test the hypothesis.12 Along the distribution of intra-RTA export sharein Figure 3.3, China, India, Thailand and Japan who are at the lowest boundaround zero have fewer trade agreements signed with the rest of countries inmy sample, whereas they are major car exporters worldwide. On the contrary,Mexico and some small European countries almost entirely rely on export toNAFTA countries and the EU. The US and Germany are at the mean where 60%of their car exports flow to RTA members.Figure 3.3: Distribution of cars export share within RTA01234Density0 .2 .4 .6 .8 13.3.3 Part-level dataTo estimate equation (3.14), I introduce parts characteristics, namely unit prices,to be interacted with the RVC level in the analysis. The unit price at the HS6-12Production of cars that serves the domestic market (i.e. trade with itself) is not included inthe measurement because it is not subject to RoOs.147classified auto part is computed as the sum of total value traded by the US di-vided by the corresponding physical volume based on the primary quantity unitmeasured at HS10 digit before averaging to HS6. Average prices across originsand years are used to test for any heterogeneity in effects of RoO by the natureof each part.Figure 3.4 panel (a) shows that most parts cost below $500, before jumpingto thousand-dollar engines, transmissions and starter motors. Brake system andspark plugs are the least costly parts when assembling a car.13 Panel (b) visu-alizes tariffs across parts averaging over country pairs and years. Comparedto Figure 3.1, much of the variation in tariffs of auto parts stems from countrypairs and years instead of the product dimension.Figure 3.4: Heterogeneity in car parts01000200030004000US$ Parts −−−−−−−−−−−−−−−−− Spark ignition piston engines >1000cc Spark ignition piston engines >250cc but not >1000cc Spark ignition piston engines >50cc but not >250cc Drive axles with differential Transmissions Starter motors Generators and alternators Fuel/lubricating/cooling medium pumps for engines Glow plugs and other ignition or starting equip Sound signalling equipment Motor vehicle parts nes Seats Radiators Parts for spark−ignition type engines nes Wheels including parts and accessories Steering wheels Shock absorbers Mufflers and exhaust pipes Distributors and ignition coils Clutches and parts Bumpers and parts Parts and accessories of bodies nes Parts of electrical ignition or starting equip Parts of pumps for liquid whether or not fitted Brake system parts nes Spark plugs Price −−−−−−−−− $3774 $2850 $1808 $1575 $1357 $1179 $716 $591 $500 $389 $374 $324 $290 $253 $248 $222 $203 $193 $181 $169 $153 $151 $137 $133 $113 $21(a) Unit price.03.04.05.06.07.08 Parts −−−−−−−−−−−−−−−−− Brake system parts nes Wheels including parts and accessories Parts and accessories of bodies nes Bumpers and parts Seats Spark ignition piston engines >250cc but not >1000cc Drive axles with differential Transmissions Mufflers and exhaust pipes Radiators Shock absorbers Clutches and parts Steering wheels Motor vehicle parts nes Spark ignition piston engines >50cc but not >250cc Sound signalling equipment Glow plugs and other ignition or starting equipSpark plugsSpark ignition piston engines >1000ccDistributors and ignition coilsParts for spark−ignition type engines nesParts for electrical ignition or starting equipStarter motorsGenerators and alternatorsFuel/lubricating/cooling medium pumps for enginesParts of pumps for liquid whether or not fitted Pref. Tariff −−−−−−−−− 8.3% 7.8% 7.7% 7.5% 7.5% 7.4% 7.3% 7.2% 7.1% 7.1% 7.1% 7.1% 7.0% 6.9% 6.5% 6.4% 6.3% 6.2% 6.2% 5.5% 5.5% 5.3% 5.2% 5.1% 4.2% 3.4%(b) Applied tariff143.3.4 Bilateral accessibilityThe last set of data needed for estimating the gravity equation are the standardexplanatory variables, including distances, whether two countries are adjacent13Price for spark plugs are denoted at 6 units to fit a common car’s usage.14Average applied tariffs exclude zero-tariff observations to be comparable with Figure 3.1.148or share a common language, as non-price cost shifters. These variables havebeen shown in past literature to matter for trade flows.Another variable controlled for is customs union (CU). Unlike FTAs, mem-ber states in a CU would have a common external tariff in which case tradedeflection is eliminated. Therefore, the rationale for having rules of origin islargely weakened, which is why RoOs are typically absent from CU arrange-ments.15 In the last year of my sample 2014, 28 EU countries and therefore 756out of 1560 bilateral trading pairs belong to a customs union.16 For the wholesample, about 35% of observations are part of a CU, 25% belong to a FTA orPSA, and the rest do not form any regional trade agreements. I include a cus-toms union dummy in the following regression analysis to avoid omitted vari-able bias.3.4 Empirical AnalysisThe primary goal of this chapter is to verify whether rules of origin create tradediversion in intermediate goods from non-RTA countries to member states us-ing an example of 26 types of auto parts. With time dimension added, I spec-ify the implicit trade friction from RoOs as a function of observables betweencountry i and `, denoted Ri`t . It includes indicators of whether the two coun-tries belong to a customs union or connected by a regional trade agreement,and interactions with the regional value content requirements. The non-pricetrade costs are a function of distance, and a time-invariant vector of dummies15See Georges (2008) for the effects of removing RoO by a hypothetical move from NAFTA toCU. They also mentioned that the European Commission set preferential RoOs for exceptionsto the principle of free circulation.16Intra-national trade data is excluded because production data for each of the 26 auto partsis not available.149describing the bilateral relationship, denoted Di`. Ad-valorem tariff for part j isτ ji`t . Explicitly, they areri`t = exp(R′i`tβr), di` = exp(D′i`βd), τ ji`t = 1+ t ji`t ,where β r and β d are vectors of trade cost parameters.The gravity trade equation (3.13) describing product trade flow betweencountries can be transformed to its estimable form,X ji`t = exp[FE j`t+FE j+FEit−θR′i`tβ r−θD′i`βd−θ ln(1+ t ji`t)+ ε ji`t], (3.15)where the importer-part-year fixed effect is FE j`t = ln(F` Ω`tΦ− α(1−α)θ`t Φα(1−α)θ−1j`t),the exporter-year fixed effect is FEit = −θ ln(wit), and the part fixed effect isFE j = θ ln(ψ j).17 The equation is estimated using Poisson Pseudo MaximumLikelihood (PPML) for its consistency and capability of incorporating zeros asclearly explained in Silva and Tenreyro (2006) and Head and Mayer (2014).Two issues emerge from the data. One is that the production data for HS6-digit car parts across countries and years is not readily available, which meansthe intra-national trade is missing from the panel. It could cause biases in theestimation of the effect of distance on trade when internal distances are not ac-counted for. What’s more concerning is that the impact of RTAs can be down-ward biased when RTAs divert trade from domestic to foreign sales.18 However,our target of interest, the effect of RoO restriction, may survive the problem be-cause use of content from the country itself or its RTA partners is treated the17I assume the product fixed effect does not vary by year because technology in producingcars is stable in years and the marginal product ψ of a part is not likely to vary.18See Yotov et al. (2016), chapter 1 for more discussion on including intra-national and inter-national trade in the estimation of structural gravity.150same to meet the rule. So there is no further distortion between intermediatetrade diverted to the importer itself or other RTA members unless cumulationrules other than full cumulation is applied.19 The other is that as mentioned inSection 3.3.1, RVC thresholds are highly concentrated at 60% due to the commonpractice by the EU countries. In fact, over 20% of the observations have RVC at60% and that is about 90% of those that form a RTA, which leads to a collinear-ity problem when both the RVC and RTA dummy are included in a regression.To separately identify the RoO effect, I replace the continuous RVC variable toa group of dummies – country pairs that are subject to RVC below 60%, equal60%, and above 60%. It is as if I compare effects under different quantiles. Ihereby interpret the estimated coefficients with great caution.Table 3.2 reports the main results. Throughout the five columns, estimateson the standard gravity variables have the expected direction but smaller mag-nitude than what have been found by the literature. Distance has the elasticityaround -0.6 instead of the benchmark -1 reported in Head and Mayer (2014),contiguity around 0.35 compared to 0.6, and the estimated effect of commonlanguage is not significant. The downward biases are likely to be caused bythe missing intra-national trade in the sample. Customs union which is the EUcountry dyads here has a much larger effect on trade. Using the mean coeffi-cient at 1.56, it implies that customs union entered into force increases trade incar parts by more then threefold on average.20 Other RTAs increase trade byaround 274 percent based on the coefficient in column (1) which is at the higher19Cumulation rules define the geographic area from which inputs can be sourced withoutlosing its originating status. It can follow full cumulation, diagonal cumulation or bilateralcumulation. Under full cumulation, intermediates from RTA partners can be used uncondition-ally. Diagonal cumulation is that firms can import intermediate goods from any RTA membersas long as the intermediates are produced under the same rules. Bilateral cumulation is themost restrictive where firms can only import intermediates from itself or produced in the im-porting country. See Bombarda and Gamberoni (2013) for more details. Throughout the chapter,I assume full cumulation is used.20For an indicator variable, the effect is interpreted as exp(1.56)−1≈ 3.76.151Table 3.2: Baseline resultsDep. Var parts export ji`t , PPML(1) (2) (3) (4) (5)ln disti` -0.652a -0.634a -0.593a -0.588a -0.496a(0.105) (0.111) (0.119) (0.121) (0.115)contiguityi` 0.398a 0.382a 0.344b 0.356b 0.266c(0.140) (0.146) (0.172) (0.152) (0.152)languagei` 0.034 -0.006 0.010 -0.022 0.081(0.237) (0.237) (0.240) (0.214) (0.225)CUi`t 1.520a 1.560a 1.469a 1.529a 1.740a(0.262) (0.272) (0.385) (0.386) (0.326)ln (1+parts tariff ji`t) -4.093b -4.321a -4.705a -3.830b -2.362(1.984) (1.633) (1.783) (1.911) (1.690)RTAi`t 1.320a -1.548(0.277) (1.379)RTAi`t× RVCi`t 5.003c(2.784)RTAi`t×1(RVCi`t <60%) 0.831a 0.875a(0.113) (0.131)RTAi`t×1(RVCi`t =60%) 1.177a 1.213a(0.385) (0.389)RTAi`t×1(RVCi`t >60%) 1.994a 2.074a(0.519) (0.543)RTAi`t×1(RVCi`t ≤50%) 0.471a(0.167)RTAi`t×1(50%<RVCi`t <60%) 1.186a(0.314)RTAi`t×1(RVCi`t =60%) 1.263a(0.356)RTAi`t×1(60%<RVCi`t <65%) 2.676a(0.389)RTAi`t×1(RVCi`t ≥65%) 0.699a(0.225)Observations 607971 607971 607971 592693 607971R2 0.884 0.885 0.886 0.922 0.888The parts are defined at HS 6-digit level and their export in US dollar current value. It in-cludes international trade flow between 40 countries from 2000 to 2014, but not intra-nationdue to missing parts production data. All columns except (4) include product, origin-year, anddestination-product-year fixed effects. Column (4) includes fixed effects for origin-product-year and destination-product-year. Standard errors are multi-clustered at origin, destination,and product level in parenthesis. Significance levels: c p<0.1, b p<0.05, a p<0.01.152end among past findings. The trade elasticity−θ identified through tariffs vari-ation is consistent with the literature between -4 to -5, although the effect isweakened when adding more RTA interactions in columns (4) and (5).Now, let’s focus on our parameter of interest, the effect of RoOs. Giventhe limited variation across RVC thresholds in the sample RTAs, column (2)presents undesirable results which validates the existence of the collinearityproblem. I deal with the issue by grouping the RVCs into three range. Col-umn (3) shows that import of intermediates from RTA partners is 130% largerthan importing from third countries when RVC is below 60%. The impact isequivalent to removing 19% of the ad-valorem tariff.21 As the RVC is higher, a60% content rule amounts to the equivalent of a 28% tariff on auto parts andhigher than 60% implies a 53% equivalent tariff effect. The escalating tradediversion effects suggest that more restrictive RoOs amplify the shift of inter-mediates from outside to the RTA region, holding everything else among RTAsin the three groups the same. Column (4) employs the same specification ascolumn (3) but substitutes product-origin-year fixed effects for the separatedproduct fixed effects and origin-year fixed effects. Results are quite robust. Tofurther decompose the effects of RoO, I run column (5) where there are fivegroups of RTAs defined by their respective RVC level. Figure 3.5 visualizesthe coefficients, their confidence intervals and effects on intermediates trade.Interestingly, we observe a humped shape relationship between the degree oftrade diverted and RoO restrictiveness. More imports of intermediates occurwithin the RTA until the RVC hits a peak at somewhere between 60% to 65%,supporting the argument that firms would reallocate more inputs intra-RTA tosatisfy the tightened content rule and maintain the originating status of their fi-21The effect is calculated by (exp(0.831) − 1) × 100% ≈ 129.6% and tariff equivalent as(exp(0.831/4.705)−1)×100%≈ 19.32%.153nal output. However, beyond 65%, increase in trade of car parts within the RTAdeclines sharply. Although the endogenous adjustment of firms changing fromcompliers to defiers is not explicitly modeled in the previous theoretical section,the empirical results here are a mix of intensive and extensive margin. The RVCrequirement beyond 65% is too stringent for firms to comply, and they may relo-cate elsewhere offsetting the trade diversion effects of RoO. The results resonatewith the Laffer curve modeled in Head et al. (2021) where stricter content re-quirements initially expand production but eventually contract it, but insteadof performing a simulation exercise, I show the nonlinear effects of RoO withreal data.Figure 3.5: Trade effects of RTAs under different RVC050010001500Effects on trade (%)01234Estimates and CI(0,50%](50%,60%)60%(60%,65%)[65%,1)RTA by RVCAs an extension of our baseline results, I further investigate what channelscontribute to the RoO effects and whether there is any heterogeneity depend-ing on firms’ export status and parts imported. Building on the preferred esti-mates in column (3) of Table 3.2, I interact the RTA-RVC group dummies withthree more variables, namely the share of export within the RTA, the preferen-tial margin on cars exporting to other RTA members, and the average price of154Table 3.3: Heterogeneous RoO effectsDep. Var parts export ji`t , PPML(1) (2) (3) (4)ln disti` -0.497a -0.593a -0.592a -0.498a(0.113) (0.121) (0.119) (0.113)contiguityi` 0.342b 0.328b 0.345c 0.330b(0.154) (0.164) (0.187) (0.168)languagei` 0.015 -0.010 0.010 0.013(0.240) (0.249) (0.246) (0.245)CUi`t 1.754a 1.439a 1.471a 1.744a(0.334) (0.402) (0.385) (0.344)ln (1+parts tariff ji`t) 1.087 -5.362a -4.692a 0.669(2.205) (1.865) (1.800) (2.182)RTAi`t × 1(RVCi`t <60%) 0.505a 0.912a 1.186a 1.098b(0.084) (0.182) (0.391) (0.461)RTAi`t × 1(RVCi`t =60%) 1.171a 1.341b 1.120 1.571(0.422) (0.530) (1.060) (1.285)RTAi`t × 1(RVCi`t >60%) 1.325a 1.442b 1.944b 0.978(0.472) (0.590) (0.828) (0.864)RTAi`t × 1(RVCi`t <60%) × expshRTA(i)`t 0.084a 0.099a(0.017) (0.019)RTAi`t × 1(RVCi`t =60%) × expshRTA(i)`t 0.021 0.019(0.020) (0.021)RTAi`t × 1(RVCi`t >60%) × expshRTA(i)`t 0.070a 0.071a(0.013) (0.016)RTAi`t × 1(RVCi`t <60%) × expmarginRTA(i)`t -1.994 -4.882(3.479) (3.519)RTAi`t × 1(RVCi`t =60%) × expmarginRTA(i)`t -3.198a -4.806a(1.166) (1.409)RTAi`t × 1(RVCi`t >60%) × expmarginRTA(i)`t 4.092c 2.346(2.360) (2.165)RTAi`t × 1(RVCi`t <60%) × ln (part price j) -0.057 -0.076(0.064) (0.069)RTAi`t × 1(RVCi`t =60%) × ln (part price j) 0.009 0.003(0.143) (0.151)RTAi`t × 1(RVCi`t >60%) × ln (part price j) 0.008 -0.003(0.105) (0.112)Observations 604929 604929 604929 604929R2 0.888 0.886 0.886 0.888All columns include product, origin-year, and destination-product-year fixed effects. Standard errorsare multi-clustered at origin, destination, and product level in parenthesis. Subscript RTA(i)` refer tothe RTA both country i and ` belong. expshRTA(i)`t is country `’s share of car export to the RTA part-ners over `’s total car export. expmarginRTA(i)`t = ln(1+MFN tariffRTA(i)`t −pref tariffRTA(i)`t)is thepreferential margin on country `’s car when exporting to the RTA partners. Unit value of part j isderived as described in Section 3.3. Significance levels: c p<0.1, b p<0.05, a p<0.01.155auto parts. First, when RTA member countries are important markets for car ex-porters at country `, firms would benefit from complying the rules and enjoy thepreferential treatment. Hence, keeping the RVC constant, greater proportion ofintra-RTA trade in final goods implies more firms would become compliers andoverall import more intermediates regionally. Results in column (1), Table 3.3,verify my hypothesis. For RTAs with RVC either below or above 60%, sourc-ing of car parts by country ` from its RTA partner i increases significantly withthe share of cars exported by ` to the same RTA in its total export.22 The effectdisappears when RVC is equal to 60% because they are mainly agreements of athird country and the EU where goods are freely circulated.The second refinement comes from preferential tariff margin of exporting fi-nal goods. Car exporters incline to abide by the rules when the benefit from ahigher tariff margin dominates the cost of sourcing from inefficient suppliers.Therefore, trade diversion is stronger with preferential margin in car exports.For RTAs with high content requirements, we observe such effect in column(2). Nevertheless, it is not significant when RoOs are generous and has unex-pected sign when RVC is 60%. The negative effect of preferential margin at 60%is again attributed to EU and EFTA countries where parts are already freelytraded. When they sign RTA with a country outside of Europe (for example,Mexico), the country who experiences large tariff reduction does not source asmuch European parts as European countries themselves. Comparing column(2) to (1), another observation is that the intensive margin on tariff reductiondoes not have enough power in explaining trade diversion of inputs as the ex-tensive margin effect of car exports share. Hence, in column (4) when I include22One reason that could alter the interpretation of results in export share is that consumerhave taste preference towards final cars that assembled using domestic parts. If then, increasingintra-RTA export share does not increase imports of car parts through firms’ responses to RoObut through the demand side. However, whether consumers have perfect knowledge on carparts used for assembly is an empirical question.156all three sets of interactions, the effects of intra-RTA export share remains to besignificant but not those of preferential margin on cars.Lastly, equation (3.14) sets the foundation for testing whether RoOs have thesame effect on different car parts. Observing column (3), I do not find system-atic pattern across parts with different prices. There can be two counteractingforces. On one hand, sourcing decision tends to be pivotal for expensive partsand should be sourced within the RTA region. On the other hand, the buyer-seller relationship may be more sticky for expensive parts. For example, suppli-ers outside of the RTA offer a bigger discount or the part has higher specificity.The mixed effects will not be clearly identified without firm-level data.The last column in Table 3.3 combines all three forces. Results stay consistentwith those from separately added variables. In addition, with modifiers to theRoO effects, the RTA×RoO interactions lose their significance although the signsare still as expected.3.5 ConclusionsThis chapter opens up the RTA black-box by separating the effects of tariff re-duction from rules of origin. Specifically, I estimate the distortive effect of rulesof origin on intermediate goods trade by exploring a particular dimension ofsourcing restrictions, regional value content. A clear takeaway from results byapplying the framework to the automotive industry is that car assemblers doreformulate sources of parts when facing more restrictive rules of origin. WhenRVC is above 60%, RTA is equivalent to a 53% ad-valorem tariff on the affectedintermediate goods. The trade diversion effect of RoOs, however, is not linearbut following a humped shape. The increase in import of intermediates within157a RTA first rises with more restrictive content rules but eventually falls downwhen more firms becoming RoO defiers.Going beyond the main effects of RoOs, I test three channels in which RoOtakes effect heterogeneously: the share of export to RTA region in total exportof final goods, preferential margin of final goods subsidized by RTA members,and the unit price of intermediates. Car exporters who target RTA markets findRoOs matter, and thus trade diversion is stronger with larger intra-RTA car ex-port. The other two channels, preferential margin on cars export and parts’prices, do not exhibit significant and robust effects. More disaggregated firm-level data is necessary to identify the mixed forces in these two.Theoretically, I build a multi-country and multi-product sourcing model tostudy where and how many inputs firms import. Rules of origin is incorpo-rated in the framework as a ad-valorem trade costs on intermediates. It derives agravity trade equation at product level that becomes handy in estimation. Thisis not a full-fleshed characterization of RoOs since I do not model export de-cisions of firms and firms’ choices of whether to comply with the rules of not.There should be future attempts on adding these elements to the model andestimate it structurally with finer data.It would also be interesting to study the RoO effects along the entire valuechain. When goods cross borders multiple times in a fragmented productionprocess, trade costs can accumulate and compound before the goods are soldfor final consumption. Therefore, production which is labeled non-originatingcan be very costly. The aspects of global value chain provide a full agenda forfuture research.Despite having limitations, this chapter contributes to the existing literature158by examining the effect of rules of origin across a wide span of trade agree-ments. It also provides guidance for policy makers in setting the optimal re-gional value content threshold by providing evidences on its nonlinearity. Thischapter serves as an exploration of the optimal RVC, while leaving future workto build upon.159ConclusionThis thesis studies firms’ participation in the international economy along mul-tiple margins, focusing on the set of production locations and input sourcing.I develop theoretical frameworks to characterize the tradeoffs and mechanismsassociated with how firms, markets and government policies interact. Specifi-cally, the role of multi-plant firms is highlighted and distinguished from single-plant firms. They are featured as oligopolies whose plant location decisions areinterdependent and pricing decisions are strategic, taking into account competi-tion with rivals and cannibalization within themselves. Since multi-plant firmsare dominant intra- and inter-nationally, a thorough analysis of their operationsare crucial to accurately predict aggregated outcomes.Applying these frameworks to two industries, cement and automotive, Iquantify the impacts of policies on different economic agents and social welfare.The three essays provide strong evidence in support of unintended effects ofpolicies generated from firm-level responses, suggesting the necessity of morecareful policy design.First, when pricing carbon to internalize pollution externality, firms can moveplants to “pollution havens”, which worsens the market distortion in the reg-ulated area when firms exhibit market power and exacerbates the problem of160carbon leakage. Second, practising national protectionism by increasing tariffsgenerates significant amount of welfare loss to the importing economy. Depend-ing on fixed costs of establishing plants, a level of tariff as high as 20% may evenbe insufficient to cause a different spatial distribution of plants, and thus, expan-sion of the protected industry can be quite limited but consumers suffer a bigloss. Similarly, another trade instrument, rule of origins, that is supposed toprotect regional integration will backfire when rules are so restrictive that firmsstart to shift their production outside the region and source inputs elsewhere.Last, the efficiency gains from mergers and acquisitions are magnified throughplant entry and exit post M&As. It is possible that the efficiency improvementis large enough to push prices down for a majority of consumers, although less-ening of competition still imposes upward pressure on prices to others. Overall,consumer surplus can increase but is distributed differently after firms merging.This thesis has a broader goal to extend the reach of empirical researcherswhen evaluating policies or other spatial organization problems from firms’ per-spective. For future research, it would be interesting to add the time dimensionto the analysis and study dynamic responses of firms and industries. Manyother dimensions of firms’ decisions, such as interdependency in exporting andimporting, margins at the product level when firms carry multiple products orbrands, are also left to be explored. Moreover, this thesis is within the scopeof partial equilibrium. Studying general equilibrium effects on factor marketswould be another exciting avenue to pursue.161BibliographyAghion, P., Bergeaud, A., Boppart, T., Klenow, P. J., and Li, H. (2019). A theoryof falling growth and rising rents. 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Columbia Business School Research Paper, (16-37). → page 17Zhou, L. (1994). The set of nash equilibria of a supermodular game is acomplete lattice. Games and economic behavior, 7(2):295–300. → page 32170Appendix AChapter 1 AppendicesA.1 Model detailsFor simplicity of derivation, I invert the marginal cost and derive the followingbased on a plant’s cost-adjusted productivityZ˜ f `im =Z f `iw`τ`m. (A.1)A.1.1 Conditional joint distribution of the lowest two costfirmsSince the conditional joint distribution of the lowest two costs is the same as thatof top two productivities, the joint distribution of the first and second highestcost-adjusted productivity to market m conditional on firm f ∗ from `∗ winning171the consumer isF12,m(z1,z2;`∗, f ∗) = Pr(Z˜1m(i)≤ z1, Z˜2m(i)≤ z2 | Z˜1m(i)>V)(A.2)= Pr(Z˜1m(i)≤ z2 | Z˜1m(i)>V)+Pr(z2 ≤ Z˜1m(i)≤ z1, Z˜2m(i)≤ z2 | Z˜1m(i)>V),where V ≡max{Z˜2m(i),S} and S≡max`∈L f∗ , 6`=`∗{Z˜ f ∗`m(i)}, given z1 > z2.The distribution of S isFSm(s;`∗, f ∗) = Pr(S≤ s;`∗, f ∗) = exp(−(Φ f ∗m−φ`∗m)s−θ) .And the distribution of V isFVm (ν ;`∗, f ∗) = Pr(V ≤ ν ;`∗, f ∗) = exp(−(Φm−φ`∗m)ν−θ).The first part of equation (A.2) can be simplified asPr(Z˜1m(i)≤ z2 | Z˜1m(i)>V)=Pr(V < Z˜ f ∗`∗m(i)≤ z2)P f ∗`∗m(A.3)=Φmφ`∗m∫ z20[F˜draw`∗m (z2)− F˜draw`∗m (V )]dFVm (V ;`∗, f ∗)= exp(−Φmz−θ2).Next, the second part of equation (A.2) is equal toPr(z2 ≤ Z˜ f ∗`∗m(i)≤ z1, Z˜2m(i)≤ z2, Z˜ f ∗`∗m(i)>V)P f ∗`∗m=Pr(z2 ≤ Z˜ f ∗`∗m(i)≤ z1, Z˜2m(i)≤ z2, Z˜ f ∗`∗m(i)> S)P f ∗`∗m,172where the equality is by definition of Z˜2m(i). The numerator can be further sim-plified asPr(z2 ≤ Z˜ f ∗`∗m(i)≤ z1, Z˜2m(i)≤ z2, Z˜ f ∗`∗m(i)> S)= Pr(z2 ≤ S≤ Z˜ f ∗`∗m(i)≤ z1, Z˜2m(i)≤ z2)+Pr(S≤ z2 ≤ Z˜ f ∗`∗m(i)≤ z1, Z˜2m(i)≤ z2)=∫ z1z2[F˜draw`∗m (z1)− F˜draw`∗m (S)]∏f 6= f ∗F˜1, fm(z2)dFSm(S;`∗, f ∗)+∫ z20[F˜draw`∗m (z1)− F˜draw`∗m (z2)]∏f 6= f ∗F˜1, fm(z2)dFSm(S;`∗, f ∗)=φ`∗mΦ f ∗m(e−(Φm−Φ f∗m)z−θ2 e−Φ f∗mz−θ1 − e−Φmz−θ2).The second part of equation (A.2) is thereforePr(z2 ≤ Z˜1m(i)≤ z1, Z˜2m(i)≤ z2 | Z˜1m(i)>V)=ΦmΦ f ∗m(e−(Φm−Φ f∗m)z−θ2 e−Φ f∗mz−θ1 − e−Φmz−θ2).(A.4)Summing equation (A.3) and (A.4), the joint distribution of highest two cost-adjusted productivities conditional on f ∗ from `∗ selling to i in m isF12,m(z1,z2;`∗, f ∗) =ΦmΦ f ∗me−(Φm−Φ f∗m)z−θ2 e−Φ f∗mz−θ1 − Φm−Φ f ∗mΦ f ∗me−Φmz−θ2 .The associated p.d.f. isf12,m(z1,z2;`∗, f ∗) =Φm(Φm−Φ f ∗m)θ 2z−θ−11 z−θ−12 e−(Φm−Φ f∗m)z−θ2 e−Φ f∗mz−θ1 .173A.1.2 Price distributionThe price of consumer i in market m isPm(i) =min{ 1Z˜2m(i),µ¯Z˜1m(i)}.Conditional on firm f ∗ serves the consumer in the market, the complement ofthe price c.d.f. is1−FPm (p; f ∗) =Pr(p≤ 1Z˜2m(i)<µ¯Z˜1m(i)| Z˜1m(i)>V)︸ ︷︷ ︸T1+Pr(p≤ µ¯Z˜1m(i)≤ 1Z˜2m(i)| Z˜1m(i)>V)︸ ︷︷ ︸T2.Derive each component, I have the firm termT1 =∫ ∞p−1∫ p−1z1/µ¯f12,mdz2dz1+∫ p−10∫ z1z1/µ¯f12,mdz2dz1=ΦmΦ f ∗me−(Φm−Φ f∗m)pθ − Φm−Φ f ∗mΦ f ∗me−Φmpθ − ΦmΦ f ∗m+(Φm−Φ f ∗m)µ¯θ ,and the second termT2 =∫ ∞0∫ µ¯/pµ¯z2f12,mdz1dz2=ΦmΦ f ∗me−Φ f∗mµ¯−θ pθ − Φm/Φ f ∗m(Φm−Φ f ∗m)µ¯θΦ f ∗m+(Φm−Φ f ∗m)µ¯θ .Combining the two and subtracted by one, I get the price distribution exactlyequals to equation (1.6).174A.1.3 Markup distributionThe markup equalsµm(i) =min{µ¯,C2m(i)C1m(i)}.Conditional on firm f ∗ serves the consumer i in market m, for the range belowthe monopoly markup, the distribution isFµm (µ; f∗) = Pr(Z˜1m(i)Z˜2m(i)≤ µ | Z˜1m(i)>V).Let’s first calculate the complement of the c.d.f.,1−Fµm (µ; f ∗) = Pr(Z˜2m(i)≤ µ−1Z˜1m(i) | Z˜1m(i)>V)=∫ ∞0∫ µ−1z10f12,m(z1,z2; f ∗)dz2dz1=ΦmΦ f ∗m+(Φm−Φ f ∗m)µθ .The conditional markup distribution is thenFµm (µ; f∗) = 1− 1µθ − Φ f∗mΦm (µθ −1)= 1− 1(1− s f ∗m)µθ + s f ∗m ,where s f ∗m=Φ f ∗m/Φm. Given the markup µ ∈ (1,∞), it’s obvious that limµ→1Fµm (µ; f ∗)=0 and limµ→∞Fµm (µ; f ∗) = 1.The markup distribution is truncated at the monopoly markup,Fµm (µ; f∗) =1− 1(1−s f∗m)µθ+s f∗m 1≤ µ < µ¯1 µ ≥ µ¯.The markup increases with the number of locations a firm builds plants. More-175over, I will show below that the probability of a firm earning monopoly markupincreases with its number of plants.Define Fµm (µ; f ∗,z2) as the probability that 1 ≤ Z˜1m(i)Z˜2m(i) ≤ µ , given the second-lowest cost and firm f ∗ wins the consumer. It can be simplified asFµm (µ; f∗,z2) = Pr(Z˜2m(i)≤ Z˜1m(i)≤ µZ˜2m(i) | Z˜2m(i) = z2)=∫ µz2z2 f12,m(z1,z2)dz1∫ ∞z2 f12,m(z1,z2)dz1=e−Φ f∗m(µz2)−θ − e−Φ f∗mz−θ21− e−Φ f∗mz−θ2.Therefore, the probability of firm f ∗ charging monopoly markup is1−Fµm (µ¯; f ∗,z2) =1− e−Φ f∗m(µ¯z2)−θ1− e−Φ f∗mz−θ2.Taking first order derivative with respect to Φ f ∗m, we see that the probability ofthe firm earning monopoly markup strictly increases with its producing capa-bility Φ f ∗m. Since Φ f ∗m increases with firm’s number of plants, it implies thatthe more plants a firm builds, the higher likely it can charge monopoly markup.A.1.4 Expected revenueBefore calculating the expected revenue and cost, it is useful to state the GammaLemma proved in appendix 5.1 of Holmes et al. (2011).Gamma Lemma:176(i) For ω > 0 and θ −η+1> 0,∫ ∞0zη−θ−2e−ωz−θdz= ωη−θ−1θ1θΓ(θ −η+1θ)(ii) For ω > 0 and 2θ −η+1> 0,∫ ∞0zη−2θ−2e−ωz−θdz= ωη−2θ−1θ(θ −η+1θ 2)Γ(θ −η+1θ).The conditional expected revenue isE[R fm | f = f ∗]= AmE[pm(i)1−η],which is the expected revenue for cement sold to destination market m, condi-tional on sourcing from firm f ∗, and fixing firm f ∗’s plant locations. The expec-tation is taken with respect to the random price realization. The demand shifterAm = exp(αm).For pm(i) =min{1Z˜2m(i), µ¯Z˜1m(i)}, we have the expectationE[pm(i)1−η]=∫ ∞0∫ z1z1µ¯(1z2)1−ηf12,m(z1,z2)dz2dz1︸ ︷︷ ︸T1+∫ ∞0∫ z1µ¯0(µ¯z1)1−ηf12,m(z1,z2)dz2dz1︸ ︷︷ ︸T2.The first term can be simplified after changing the order of integration and ap-plying the Gamma Lemma,T1 =ΦmΦ f ∗m(Φm−Φ f ∗m)Γ(θ −η+1θ)[(Φm− (1− µ¯−θ )Φ f ∗m)η−θ−1θ −Φη−θ−1θm].177The second term can be simplified toT2 = µ¯−θΦmΓ(θ −η+1θ)(Φm− (1− µ¯−θ )Φ f ∗m)η−θ−1θ.Combining the two terms, I have the conditional expected revenue equals toE[R fm | f = f ∗]= AmΓ(θ −η+1θ)Rˆ f ∗ms f ∗m,where Rˆ f ∗m=(Φm− (1− µ¯−θ )Φ f ∗m)η−1θ −(Φm−Φ f ∗m)Φη−θ−1θm , and s f ∗m=Φ f ∗m/Φm.The unconditional expected revenue is therefore,E[R fm]= AmκRˆ fm, where κ = Γ(θ −η+1θ).A.1.5 CostsThe conditional expected cost of a firm isE[C fm | f = f ∗]= AmE[pm(i)1−ηµ],for µ = Z˜1m(i)Z˜2m(i) when pm(i) =1Z˜2m(i)and µ = µ¯ when pm(i) = µ¯Z˜1m(i) . Hence,E[pm(i)1−ηµ]=∫ ∞0∫ z1z1µ¯(1z2)1−η z2z1f12,m(z1,z2)dz2dz1︸ ︷︷ ︸T1+∫ ∞0∫ z1µ¯0(µ¯z1)1−η 1µ¯f12,m(z1,z2)dz2dz1︸ ︷︷ ︸T2.The simplification of the firm term is more involved. I need to replace z1 byµz2 and change the order of integration (refer to the appendix of Holmes et al.178(2011)). The first term equals toT1=Φm(Φm−Φ f ∗m)(θ−η+1)Γ(θ −η+1θ)∫ µ¯1µ−θ−2(Φm− (1−µ−θ )Φ f ∗m)η−2θ−1θdµ.Unfortunately, there is no closed-form expression for the integral. Therefore, Iapply the numerical approximation in the empirical section.Applying the Gamma Lemma and taking the same steps as deriving the sec-ond term in the expected revenue function, the second term here can be simpli-fied toT2 = µ¯−θ−1ΦmΓ(θ −η+1θ)(Φm− (1− µ¯−θ )Φ f ∗m)η−θ−1θ.Combining the two terms, I derive the conditional expected cost equals toE[C fm | f = f ∗]= AmΓ(θ −η+1θ)Cˆ f ∗ms f ∗m,whereCˆ f ∗m =Φ f ∗m[(θ −η+1)(Φm−Φ f ∗m)∫ µ¯1µ−θ−2(Φm− (1−µ−θ )Φ f ∗m)η−2θ−1θdµ+ µ¯−θ−1(Φm− (1− µ¯−θ )Φ f ∗m)η−θ−1θ].The unconditional expected cost is thereforeE[C fm]= AmκCˆ fm.179A.1.6 Best-response potential gameA best-response potential game is where potential functions infer the differencein the payoff due to unilaterally deviation of each player to the best response. Itis introduced in work of Monderer and Shapley (1996) and later on developedin Voorneveld (2000). Under the condition of a finite game where the numberof players is finite and each of them has a finite strategy space, a best-responsepotential game always has pure strategy Nash equilibrium and more interest-ingly, every learning process based on best-response of the players converges toan Nash equilibrium.Moreover, starting from any arbitrary location decisions, if players simul-taneously deviates to their unique best replies in each period, the process ter-minates in a Nash equilibrium after finite number of steps. Swenson and Kar(2017) found that the convergence rate is exponential. Table A.1 shows examplesof 6 to 12 locations and two firms. Each is solved for 1000 times. The maximumnumber of rounds to find an equilibrium is three. When the potential numberof locations is larger and therefore the strategy space is larger, it takes longer tofind an equilibrium but still converges to a solution relatively fast.Table A.1: Convergence Rate Check of Best-Response Potential GameNumber oflocationsAverage time(seconds)Average number ofBR roundsMax number ofBR rounds6 0.0198 1.0830 37 0.0429 1.1010 28 0.0494 1.0190 29 0.0596 1.1830 310 0.0934 1.1230 311 0.0963 1.1980 212 0.1275 1.1130 2180A.2 Model extensionsA.2.1 Adding core productivity differences at firm levelSuppose the firm’s endowed core productivity also characterizes its plants’ marginalcost of production,C f `m(i) =w`τ`mZ fZ`(i),where Z`(i) are draws from the Fre´chet distribution exp(−T`z−θ), and Z f arefirm-specific parameters.The c.d.f. of the plant’s cost-adjusted productivity Z˜ f `m(i) =Z`(i)w`τ`m/Z fis thenF˜drawf `m (z) = exp(−φ f `mz−θ),where φ f `m = Zθf φ`m = Zθf T` (w`τ`m)−θ . The distributions of plants’ productivitiesat the same location are shifted by firms’ core productivities, although the shapeparameter remains the same. Plants owned by an efficient firm are on averagemore productive than those owned by inefficient firms at the same location. Ex-ploiting the properties of extreme value distribution, the distribution of a firm’shighest cost-adjusted productivity in supplying the product to market m isF˜1, fm(z) = exp(−Φ fmz−θ),whereΦ fm=∑` I f `φ f `m. The firm’s capability not only depends on plants spatialsetting but also its core productivity.Other than the difference in the formulation of Φ fm, what followed in com-pleting the multi-plant firm model all remains the same. Specifically, the proba-181bility that a location exports good to a market becomess`m =∑ f I f `φ f `mΦm.Transforming the sourcing probabilities into the gravity-type regression, onegets the same form as in equation (1.14), but with the location fixed effects beingFE` = ln(T`w−θ` ∑ f I f `Zθf). Therefore, one can no longer separately identify thelocation characteristics T`w−θ` from the firm productivities Z f without the helpof additional firm-level data.The gravity model, however, still holds at plant level where s f `m =φ f `mΦm con-ditional on firm f has a plant at location `, and the estimable form isE[Q f `mQm| I f ` = 1]= exp[FE f +FE`+FEm−θX′`mβ τ],where FE f = θ lnZ f and FE` = ln(T`w−θ`). Plant-market-level trade flow in vol-ume will be needed in performing the first step of the estimation.182A.3 Simulation detailsA.3.1 Delta Method for transformed parameters in SPapproximationFrom equation (1.20), we have the transformed parameters of interest asG(b) =µ̂FB =− b(I{ f=B})b(lnE[pi f `])µ̂FM =−b(I{ f=M})b(lnE[pi f `])σ̂F = 1b(lnE[pi f `]) ,where b(lnE[pi f `]) is the estimated coefficient of lnE[pi f `], and b(I{ f = ·})) arecoefficients of respective firm dummy.Using delta method, the approximate variance of the transformed(µ̂FB , µ̂FM, σ̂F)isV (G(b)) = J(G(b))V (b)J(G(b))′,where b is the vector of coefficients andV (b) is their variance covariance matrix.J(G(b)) is the Jacobian matrix of G(b) with respect to b, which isJ(G(b)) =− 1b(lnE[pi f `]) 0b(I{ f=B})b(lnE[pi f `])20 − 1b(lnE[pi f `])b(I{ f=M})b(lnE[pi f `])20 0 − 1b(lnE[pi f `])2 .183Appendix BChapter 2 AppendicesB.1 Estimation detailsB.1.1 Asymptotic standard deviationIn the third step of the estimation, I estimate the parameters that govern thefixed costs distribution using the Method of Simulated Moments (MSM) adaptedto the dependent cross-sectional data. One modification is to segregate the en-tire sample to eight regions to preserve the weak dependence as locations arefurther apart. Another modification with spatial dependence is regard to theasymptotic normality of the MSM estimators, specifically the variance covari-ance matrix. Following Conley (1999) and Conley and Ligon (2002), the asymp-totic covariance matrix of moment functions should beV0 = ∑`′∈R`E[g(δ0;X f , φˆ , Aˆ, θˆ , ηˆ)g(δ0;X f , φˆ , Aˆ, θˆ , ηˆ)′],184and its sample analogue isVˆ =1|L | ∑` ∑`′∈R`[gˆ(δ )gˆ(δ )′],where R` is the set of locations belong to the same region as location `.1Adjusted for spatial correlation, the asymptotic distribution is√|L |(δˆ −δ0) d−→ N(0,(1+S−1)(G′0W0G0)−1G′0W0V0W0G0(G′0W0G0)−1),where the K×P gradient matrix G0 = E[Oδ ′g(δ0)]and S is the number of sim-ulation for the fixed cost draws. In practice, I take 600 simulation draws froma van der Corput sequence for a good coverage. However, in the case of smallsamples, the standard asymptotic reasoning may be inappropriate. I instead re-port the bootstrapped standard errors in the baseline estimation. Nevertheless,Table B.1 below displays the asymptotic standard errors for comparison.Associated with the covariance matrix, one can also use the optimal weight-ing matrix,W0 =V−10 instead of an identity matrix. Theoretically, using a consis-tent estimator of the optimal weighting matrix, the MSM estimates are asymp-totically efficient, with the asymptotic variance beingAvar(δˆ ) = (1+S−1)(G′0V−10 G0)−1/|L |.I show in the Table B.1 column (3), (6) and (9) the 2-step estimators, where thefirst step is performed using identity weight on moments and then compute theoptimal weight using the first-step estimates to be fed in the second-step esti-1The variance covariance estimator is not always positive semidefinite. I follow Jia (2008)and use a numerical device to weight the moment by 0.5 for all the neighbors.185mation. In most cases, the 2-step estimates are more efficient than the identityweighted estimates. The estimates themselves are consistent and close.Table B.1: Robustness check: estimation of fixed costsFavorLafargeHolcimFavorCemexLocal advantagefor two firms(1) (2) (3) (4) (5) (6) (7) (8) (9)βFcons -6.631 -6.631 -6.643 -6.126 -6.126 -6.038 -5.617 -5.617 -5.616(1.616) (1.048) (0.209) (1.688) (1.268) (0.138) (1.559) (0.621) (0.165)βFCEX-USA -0.406 -0.406 -0.313 -0.363 -0.363 -0.303 -0.280 -0.280 -0.234(0.373) (1.707) (0.180) (0.382) (0.661) (0.145) (0.372) (0.318) (0.158)βFLFH-CAN -3.734 -3.734 -3.698 -3.475 -3.475 -3.430 -3.480 -3.480 -3.587(1.867) (0.724) (1.702) (2.318) (1.046) (0.255) (1.992) (1.133) (1.616 )βFdist 1.795 1.795 1.803 1.698 1.698 1.700 1.634 1.634 1.648(0.220) (0.130) (0.018) (0.245) (0.073) (0.021) (0.221) (0.080) (0.025)σF 2.790 2.790 2.568 2.581 2.581 2.437 2.694 2.694 2.591(0.481) (0.472) (0.159) (0.504) (1.342) (0.105) (0.503) (0.411) (0.104)Column (1), (4) and (7) are baseline estimates in Table 2.5 using identity weighting matrix and bootstrappedstandard errors. Column (2), (5), and (8) are estimates using identity weighting matrix and asymptotic standarderrors. Column (3), (6) and (9) are 2-step estimates using optimal weighting matrix and asymptotic standarderrors.B.1.2 Additional tablesTable B.2 provides alternative specifications for the first-step gravity-type re-gression using the country-level sample. Table B.3 presents the first-stage re-sults of the demand estimation using the price survey data. Table B.4 providesdetails in computing fuel costs for the carbon tax on fossil fuel counterfactualexercise.186Table B.2: Estimation of Trade Costs at Country LevelGreat circle distance Sea distance Shipping time(1) (2) (3) (4) (5) (6) (7) (8) (9)OLS, logQ`m PPML, Q`m PPML, Q`m/Qm OLS, logQ`m PPML, Q`m PPML, Q`m/Qm OLS, logQ`m PPML, Q`m PPML, Q`m/Qmlog (1+ cement tariff`m) 2.808 -10.980a -10.749a 1.451 -12.635a -10.567a 1.460 -13.648a -11.633a(3.716) (3.248) (2.736) (3.712) (3.475) (2.590) (3.787) (3.441) (2.711)log dist`m -2.160a -1.997a -2.083a -1.471a -1.201a -1.359a -1.321a -1.097a -1.067a(0.259) (0.285) (0.254) (0.170) (0.121) (0.157) (0.182) (0.134) (0.138)contiguity`m 3.916a 1.685a 2.255a 4.005a 2.286a 2.740a 3.609a 1.693a 2.617a(0.423) (0.362) (0.420) (0.427) (0.286) (0.342) (0.497) (0.368) (0.410)language`m 0.296 -0.380 -0.462 0.361 -0.340 -0.449 0.424 -0.377 -0.465(0.354) (0.285) (0.300) (0.356) (0.277) (0.296) (0.360) (0.282) (0.291)RTA`m 0.293 0.972a 1.224a 0.801b 1.231a 1.559a 0.829b 1.261a 1.738a(0.421) (0.272) (0.323) (0.397) (0.268) (0.323) (0.396) (0.270) (0.302)home`m 8.306a 6.323a 5.893a 9.823a 7.895a 7.456a 9.547a 7.394a 7.749a(0.869) (0.711) (0.733) (0.744) (0.441) (0.476) (0.836) (0.543) (0.625)Observations 1100 20736 20736 1100 20736 20736 1100 20736 20736R2 0.719 0.999 0.973 0.715 0.999 0.975 0.709 0.999 0.973All regressions include origin and destination fixed effects. Regressions use 144 countries’ squared sample and for year 2016. R2 is squared correlation of fitted and true dependent variables.Robust standard errors in parentheses. Significance levels: c p<0.1, b p<0.05, a p<0.01.187Table B.3: First-Stage Regression for Demand Estimationlog pricemlog (∑ 6`=mnatural gas`/d`m) 0.410a(0.073)log (∑ 6`=melectricity`/d`m) -0.159(0.125)log (∑ 6`=mwage`/d`m) 1.238a(0.146)log (∑ 6`=mlimestone`/d`m) -0.046(0.067)log natural gasm -0.037a(0.012)log electricitym -0.032c(0.017)log wagesm 0.099a(0.031)log limestonem 0.022b(0.009)log building permitsm 0.025a(0.006)log populationm -0.038a(0.006)F test of excluded instruments 21.64Stock-Wright LM S statistic 95.59Observations 739First-stage regression for the column (3) in Table 2.4. Price is from thedata based on survey regions and then assigned to the 149 FAF zones.d`m is the distance between a location-market pair. The regression in-clude year fixed effects from 2012 to 2016. Variables other than thenumber of building permits and population are excluded instruments.Robust standard errors in parentheses. Significance levels: c p<0.1, bp<0.05, a p<0.01.188Table B.4: Fuel Costs and Energy ContentEnergy Source Breakdown (%) Energy Content Price, 2016 ($/mBTU) Levy, 2022Coal (coke) 42 27.77 mBTU/t 2.366 $158.99/tNatural gas 22 0.035 mBTU/m3 5.003 $0.0979/m3Petroleum coke 13 0.04 mBTU/L 1.722 $0.1919/LHeavy fuel oil 4 0.036 mBTU/L 12.223 $0.1593/LBased on the Portland Cement Association’s US and Canadian Portland Cement Labor-Energy Input Survey, the amount of en-ergy required to produce one tonne of cement is 4.432 million BTU. The rest of 11% energy is provided by electricity and 7% byother sources which will not be accounted in computing cost of fuels, and neither covered by carbon tax on fossil fuels.Source: Energy Consumption Benchmark Guide: Cement Clinker Production, Energy Fact Book 2019-2020 (Natural ResourcesCanada), Technical Paper on The Federal Carbon Pricing Backstop, US Energy Information Administration energy conversioncalculators.B.2 Data appendixB.2.1 Implied trade across FAF zonesThere are three groups of trade to consider, across Canada-FAF flow, across US-FAF flow and US-FAF-Canada-FAF flow. For the first group, the cement tradeacross Canadian FAF zones are directly provided by the Canadian FAF survey.The drawback of using Canadian Freight Analysis Framework is that it is a lo-gistics file built upon a carrier survey where the origins and destinations are notnecessarily the points of production or final consumption. The US Freight Anal-ysis Framework, on the other hand, is based on the US Commodity Flow Survey(CFS) and collects data on shipments from the point of production to the pointof consumption. As for the second group, the limitation of obtaining acrossUS-FAF flow is that the commodities in the US FAF survey is classified at 2-digit level of Standard Classification of Transported Goods (SCTG). Cement is asubcategory belongs to nonmetallic mineral product. To derive US-FAF cementtrade, I assume that the cement trade is proportional to nonmetallic mineraltrade by the fraction of cement consumed in nonmetallic mineral consumptionby destination FAF zone. Because the US Geological Survey only provides ce-189ment consumption by state but not by FAF zone, I further assume that the con-sumption ratio of cement over nonmetallic mineral is the same for every FAFzone within the same state.Table B.5: Trade Estimates for Cement and Nonmetallic MineralsGreat circle distance Sea distance Shipping timelog dist`m -2.105a -1.255a -1.095a(0.090) (0.051) (0.068)log dist`m× industry -0.032 -0.056 -0.022(0.078) (0.053) (0.077)contiguity`m 1.072a 1.668a 1.186a(0.160) (0.139) (0.196)contiguity`m× industry 0.100 0.074 0.082(0.184) (0.171) (0.222)language`m 0.437a 0.675a 0.735a(0.143) (0.133) (0.143)language`m× industry 0.083 0.084 0.086(0.161) (0.159) (0.170)RTA`m 0.540a 0.838a 0.939a(0.131) (0.129) (0.135)RTA`m× industry 0.237 0.204 0.244(0.188) (0.194) (0.205)industry 0.008 0.219 -0.207(0.639) (0.459) (0.210)Observations 33842 33842 33842R2 0.397 0.398 0.325The dependent variable is share of export volume. All regressions include origin and destina-tion fixed effects and are performed using PPML. Sample is for year 2016 and 144 countries.Trade with own is dropped in the sample since the data is unavailable in the nonmetallic min-eral products. Different columns use different measurement of distance. R2 is squared correla-tion of fitted and true dependent variables. Robust standard errors in parentheses. Significancelevels: c p<0.1, b p<0.05, a p<0.01.Calculating cement trade between a Canadian FAF and a US FAF zone ismore complicated. From Statistics Canada, I obtain the cement trade betweenCanadian provinces and US states. How to allocate the trade from the state/province190level to the each FAF zone? The implied trade is computed by utilizing Cana-dian FAF zone-US cement trade, US FAF zone-Canada cement trade and the dis-tance between each US-Canada FAF zone pair. One key variable given by the USCommodity Flow Survey is the distance band between origin and destinationwhere there is positive cement shipment. Comparing the distance between eachUS-Canada FAF zone dyads with the distance band and considering the zoneswith positive cement production, I significantly reduce the sample of pairs tothose that are likely to have positive cement trade. The next step is to computetrade in this restricted sample. Trade between each FAF zone pair is derived byproportioning the state-province trade where the zones locate by total exportand import of the originating zone and the destination zone. The assumptionis that within the same state-province pair, one zone cannot export to a destina-tion more than its nearby zone if its total export is smaller. I acknowledge therestrictiveness of the assumption due to data limitation.Since some parts of cement trade data is implied from trade in nonmetal-lic minerals, I validate that the trade coefficients are not significantly differentbetween this two group using country-level data as shown in Table B.5. Otherproducts included in the nonmetallic minerals category are glass, bricks, andceramic products. The result is not unreasonable given that product character-istics of cement and other nonmetallic minerals are similar, such as both beingheavy to trade.B.2.2 DistrictsMap in Figure B.1 and Table B.6 shows the division of sample to 8 districts andan overview of cement market. The area greyed out in the districts map are FAF191zones without cement production. Consumption and production are roughlythe same for each district, indicating smaller share of trade with outside. Ex-plicitly, Figure B.2 shows the distribution of FAF zones trading within the samedistrict. Out of the 73 producing zones, all of them export at least 50% to otherFAF zones within the same district and more than three quarters export morethan 80% within the same district. As for the importing cement markets, thedistribution is a little dispersed. But still, three quarters of the 149 markets im-port more than 80% from FAF zones located within the same district and morethan 90% of the markets import at least half of their cement consumption withinthe district. Trade flow validates my assumption of districts being relativelyseparated from one another. The competition among plants across districts isnegligible.Figure B.1: Districts Map192Table B.6: Summary Statistics of DistrictsConsumption(million ton)Production(million ton)Number ofmarketsNumber oflocationsNumber ofplantsMountain and Pacific North 10.2 10.4 20 10 13Mountain and Pacific South 13.9 14.2 13 9 16West North Central 8.8 8.8 13 7 11West South Central 16.5 16.1 17 7 15East North Central 15.8 16.5 22 12 19East South Central 4.3 4.1 11 6 8New England and Middle Atlantic 10.9 10.5 28 10 18South Atlantic 16.2 16.1 25 12 17Figure B.2: Trade within the Same District0.1.2.3.4Fraction0 20 40 60 80 100Share of export within district (%)(a) Exports0.1.2.3.4.5Fraction0 20 40 60 80 100Share of import within district (%)(b) ImportsB.2.3 Locations of limestone deposits and cement plantsFigure B.3 maps the distribution of cement plants versus limestone resources.The information is obtained from US Geological Survey. There are 2909 lime-stone quarries in the US and 40 in Canada. Most of the FAF zones studied in mysample have at least one limestone quarry available. Obvious exceptions areSaskatchewan and North Dakota where no limestone is available and neithercement plants. These locations where access to limestone is limited are out ofthe potential set of locations to set up cement plants in my study.193Another issue is that large cement firms such as LafargeHolcim and Cemextypically use limestone mined from their own quarries, process and transport itto their cement plants right after extraction. The vertical integration of limestonequarries and cement plants is is not a focus of this chapter. Since the cementplants are usually few kilometers away from the limestone quarries, the locationchoice of cement plants studied in this chapter can be regarded as decisions foran integrated set of facilities, including mining activities and further processing.Figure B.3: Cement and limestone resources location distribution194B.2.4 Other figuresFigure B.4: Distribution of cement plant capacityp50 p75p95p99ParetoLog-normal-1001020predicted quantiles0.2.4.6observed density-10 -5 0 5observed quantiles (ln xi)B.3 Comparison to separate entry decisionsThis section examines the difference in estimation and counterfactual results ofhaving multi-plant firms making interdependent plant location choices versusentering each location separately.Because the price distribution for every plant owned by the same firm is thesame, the expected variable profit for a particular plant is its fraction of marketsupplied out of all the markets captured by its parent firm, multiplied by thefirm’s expected variable profit. Therefore, the expected total profit of a plant195owned by firm f at location ` isE[Π f `]= E[pi f `]−FC f ` =∑mφ`mΦ fmAmκ(Rˆ fm−Cˆ fm)−FC f `. (B.1)Suppose an economist ignores the interdependency of plant location choiceswithin a multi-plant firm, he then mistakenly treats the probability of plant en-try as the probability that expected profits of having a plant owned by firm f atlocation ` exceed fixed costs of building it. An alternative interpretation is thatmanagers of the firm are delegated to make myopic decisions on entry althoughthey know that prices after entering are still coordinated by the headquarter.Preserving the parametric assumption that fixed costs follow a log normal dis-tribution shifted by proximity to firm headquarter, and then taking logs of theplant entry condition E[pi f `]> FC f `, I obtain the the following myopic versionof probability of plant entry in empirical form:Pr[I f ` = 1]=Φ(1σFlnE[pi f `]−X′f `βFσF). (B.2)Inverting the coefficient of the calculated profitability of plant ( f , `) gives a di-rect estimate of the standard deviation of log fixed costs, σF . I estimate equation(B.2) as a binary probit with the constructed lnE[pi f `]on the right-hand side, to-gether with the distance between location and firm headquarter in logarithmand a constant.The estimated fixed cost is significantly different as seen in Table B.7.Thestandard deviation of the fixed costs distribution is calculated to be σF = 1.63.The mean parameters of the fixed costs distribution are βFdist = 0.605 and βFcons =0.338. Scaling these estimates to monetary term, the average fixed costs of build-ing a LafargeHolcim plant is $61 million and those of a Cemex plant is $54 mil-196lion. Comparing with the accounting costs or baseline estimates taking into ac-count for interdependencies across plant locations, the fixed costs here are muchlower. The reason is that multi-plant firms benefit from having more plants, andthus entry to a particular location can be profitable at firm level but not at plantlevel. Neglecting parent firm’s coordination but only the head-to-head compe-tition among plants leads to fewer entry. Therefore, in order to match the samenumber of plants, the fixed costs estimated based on separated entry need to besmaller than those for interdependent entry. Econometrically, the probit regres-sion at plant level is no longer i.i.d, I may need to use the spatial interdependentprobit models in Franzese and Hays (2008) to correct for the bias.Table B.7: Estimation of entry without interdependencyProbitconstant -0.207(1.494)ln distance to HQ f ` -0.371b(0.188)ln variable profits f ` 0.613a(0.171)Observations 146R2 0.136Robust standard errors in parenthe-sis.The differences in estimates cause departure in counterfactual policy evalu-ations. Table B.8 tabulates results by using the myopic fixed costs estimates forcalculating the market equilibrium in the baseline and counterfactual using themulti-plant firm model. Comparing Table B.8 to Table 2.8, the degree of plantlocation changes is stronger when fixed costs are low. Subsequently, averageprice in Canada faces a steeper increase with more concentrated market. Pricein the US, however, increases to a smaller amount facing more domestic com-197petition. The welfare loss and carbon leakage in Canada are both more severethan the baseline scenario. On the contrary, the loss of US is milder.Figure B.5 further compares change of plant locations in two scenarios withand without considering interdependent plant locations. Each dot indicates theprobability of at least one player from the top two enters the location. Myopicdecisions of separate entry generate larger deviation from 45 degree line, indi-cating larger exit rate in Canada and entry rate in the US.Similar comparison can be done for all counterfactual analysis which is work-ing in progress for now.Table B.8: Counterfactual changes with $50 carbon levy on fuel in Canadawithout interdependencyEntry Probability∆Price∆Consumption∆%Production∆%Trade∆%CS∆PS∆LFH CEX Canada USCanada -9.27 -6.93 27.91 -54.08 -59.53 -56.52 -95.09 -316.81 -65.42US 0.52 0.34 0.48 -0.67 1.56 259.51 1.11 -24.39 7.97The columns on entry probability, price, consumer surplus and producer surplus refer to change in level in their respectiveunit. The unit of entry probability is in percentage. Price is US dollar per tonne. Consumer surplus and producer surplusare in millions of US dollars. The consumption, production and trade columns refer to percentage change in volume.198Figure B.5: Change of plant locations with and without interdependencyfor $50 carbon levy on fuel45° line0.2.4.6.81Counterfactural top 2 entry prob0 .2 .4 .6 .8 1Baseline top 2 entry probw interdependency, USw interdependency, Canadaw/o interdependency, USw/o interdependency, Canada199Appendix CChapter 3 AppendicesC.1 Derivation of firm’s conditional inputs sourcingIn this Appendix, I provide more details on assembler’s behavior conditional onsourcing location. Notice first that by solving first order condition of equation(3.4), I obtain the following optimal decision of parts quantity:x∗jω ={A1−ρω θρωρ[∫ 10(ψ jx∗jω)αd j] ρα−1 ψαjc j(i∗)ω} 11−α. (C.1)Let Z∗jω =∫ 10 (ψ jx∗jω)αd j. Plugging this expression into the above x∗jω and trans-form it into a function of Z∗jω delivers the following,Z∗jω =∫ 10ψαj(A1−ρω θρωρ(Z∗jω)ρα−1ψαjc j(i∗)ω) α1−αd j.200Solving this equation, it’s straightforward to verifyZ∗jω = ρα1−ρ Aαωθαρ1−ρω∫ 10(ψ jc j(i∗)ω) α1−αd j 1−α1−ρ . (C.2)Lastly, substitute (A-2) back to (A-1), from which we can conclude the optimalx∗jω is given by equation (3.5).C.2 Derivation of country-level sourcing decisionsFrom equation (3.10), I need to integrate it to the country level over a set ofvarieties. Denote u= ϕωδρω and u is the corresponding lower bound. Notice thatthe distribution of v jω and Vω is invariant to ω , therefore integration of thesevariables can be replaced by the integration over v, multiplied by the measureΩ`. G(v) is the distribution in equation (3.8). G(u) is the Pareto distribution withshape parameter η . Then, we haveX j` = ρ11−ρ EPρ1−ρ∫ω∈Ω`(ϕωδρω )11−ρ(v∗jω) α1−α Vρ−α(1−α)(1−ρ)ω dω= ρ11−ρ EPρ1−ρ(∫ ∞uu11−ρ dG(u))×Ω`×∫ω∈Ω`(v∗jω) α1−α Vρ−α(1−α)(1−ρ)ω dω=ηρη(1−ρ)−1 F` Ω`∫ω∈Ω`(v∗jω) α1−α V− α(1−α)ω dω=ηρη(1−ρ)−1 F` Ω`(∫ ∞0vα1−α dG(v))×[∫ 10∫ ∞0vα1−α dG(v)d j]−1.Using the derived distribution of v, we have∫ ∞0vα1−α dG(v) = Γ(1− α(1−α)θ)Φα(1−α)θj` . (C.3)Therefore, substituting (A-4) back to (A-3) obtains equation (3.12).201
Thesis/Dissertation
eng
Business Administration - Strategy and Business Economics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Head, Keith
Ries, John C.
Decisions of multinational firms : plant location and sourcing
Text