You may notice some images loading slow across the Open Collections website. Thank you for your patience as we rebuild the cache to make images load faster.

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Essays on legal financial institutions Pizarro, Jose 2019

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
24-ubc_2019_september_pizarro_jose.pdf [ 1.68MB ]
Metadata
JSON: 24-1.0380616.json
JSON-LD: 24-1.0380616-ld.json
RDF/XML (Pretty): 24-1.0380616-rdf.xml
RDF/JSON: 24-1.0380616-rdf.json
Turtle: 24-1.0380616-turtle.txt
N-Triples: 24-1.0380616-rdf-ntriples.txt
Original Record: 24-1.0380616-source.json
Full Text
24-1.0380616-fulltext.txt
Citation
24-1.0380616.ris

Full Text

Essays on Legal Financial InstitutionsbyJose PizarroB.Eng. Industrial Engineering, University of Chile, 2006M.Sc. Economics, University of Chile, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Business Administration)The University of British Columbia(Vancouver)August 2019c© Jose Pizarro, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduate andPostdoctoral Studies for acceptance, the dissertation entitled:Essays in legal financial institutionssubmitted by Jose Pizarro in partial fulfillment of the requirements for the degree of Doctor of Philosophyin Business AdministrationExamining Committee:Ron GiammarinoCo-supervisorJack FavilukisCo-supervisorGiovanni GallipoliSupervisory Committee MemberMichael DevereuxUniversity ExaminerViktoria HnatkovskaUniversity ExamineriiAbstractAn important focus of the financial literature has been the role of legal institutions in the developmentof financial markets, and its impact on the long-run economic growth and welfare.This work contributes to this literature by studying the impact of three legal institutions on assetprices, the decisions of firms and households, and the sustainability of regulated markets. The firstlegal institution considered in this thesis is the personal bankruptcy code. Specifically, I study howthe protection that this institution provides to households impacts the loan market equilibrium. Thesecond legal institution is the total allowable catch (TAC) in the fishing industry. This institutionlimits the annual catch of a renewable resource (fish) in a geographic area. I research how to definethe exploitation limits incorporating financial incentives to the problem, and if this institution can helpto achieve a financially and ecologically sustainable harvest. Finally, the third legal institution studiedin this thesis is the tax code, specifically, how the treatment of corporate losses, and the possibility ofcarrying them forward in time, ties in with the future equity risk and return of a firm.All institutions are described in detail and discussed empirically and theoretically. The resultsof my research show that they have a significant impact on the decisions of market agents and inthe determination of asset prices. From the study of the personal bankruptcy code, I find that higherhousehold protection at bankruptcy relates to a lower quantity of loans to households, and lowerdelinquency rates, indicating that riskier households are being priced out of the market, affectingtheir welfare. With respect to the TAC regulation, I find that for a representative fishery it is optimal topreserve a significant part of the resource for future harvesting, even in the presence of multiple sourcesof uncertainty. Finally, after evaluating the effect of Tax Loss Carry Forwards on the firms’ risk andreturns, I find that its magnitude is highly significant in positively forecasting standard equity riskmeasures, that they significantly predict equity returns, even when accounting for standard measuresof risk.iiiLay SummaryThis thesis studies the impact of three legal institutions on asset prices, the decisions of firms andhouseholds, and the sustainability of regulated markets. First, I study the personal bankruptcy code,and how it affects the household’s and lenders’ loans decisions, and consequently, the equilibrium ofloan markets. Second, I study the regulation of the harvest of fish and how the use of a total allowablecatch can help to achieve a financially and ecologically sustainable exploitation. Finally, I study the taxcode, specifically, how the treatment of corporate losses and the possibility of carrying them forwardin time ties in with the equity risk and return.The overall results of my research indicate that these legal institutions have a significant impacton the decisions of economic agents and that their implications are relevant for investors, households,lenders, and governmental institutions.ivPrefaceThe research project in Chapter 2 was solely performed and identified by the author.The research included in Chapter 3 is based on unpublished research with Eduardo S. Schwartz(Simon Fraser University). In this co-authored project, both authors worked on all aspects of the paper.My personal share of contribution to this research amounts to about one half.The research included in Chapter 4 is based on unpublished research with Jack Favilukis (Univer-sity of British Columbia) and Ron Giammarino (University of British Columbia). In this co-authoredproject, all authors worked on all aspects of the paper. My personal share of contribution to thisresearch amounts to about one third.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Personal Bankruptcy, Loan Market Equilibrium, and House Prices . . . . . . . . . . 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Legal and Institutional Background . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.1 Data and Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Household Loans and The Homestead Exemption . . . . . . . . . . . . . . . 162.2.3 Lending Expenses and The Homestead Exemption . . . . . . . . . . . . . . 212.2.4 House Prices and The Homestead Exemption . . . . . . . . . . . . . . . . . 222.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.1 The Households’ Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.2 The Bank’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.3.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3.4 Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.5 Equilibrium Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36vi2.3.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 The Valuation of Fisheries Rights with Sustainable Harvest . . . . . . . . . . . . . . . 453.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2 A Valuation Model of Marine Fisheries Rights . . . . . . . . . . . . . . . . . . . . . 473.3 Parameter Estimation for the British Columbia Halibut Fishery Case . . . . . . . . . 503.3.1 British Columbia Halibut Biomass Dynamic Parameters . . . . . . . . . . . 513.3.2 British Columbia Halibut Price Dynamic Parameters . . . . . . . . . . . . . 523.3.3 British Columbia Halibut Fishery Costs Parameters . . . . . . . . . . . . . . 543.3.4 Risk Adjusted Fishery Discount Rate . . . . . . . . . . . . . . . . . . . . . 553.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.4.1 The Value-Function Iteration Approach . . . . . . . . . . . . . . . . . . . . 563.4.2 Model Parameters, Grids Dimensions and Limits . . . . . . . . . . . . . . . 573.4.3 Value Function and Harvesting Policies for the British Columbia Halibut Fish-ery Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.4.4 Multiple Sources of Uncertainty and their Impact on the Simulated Biomassand Harvest Dynamic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654 Tax Loss Carry Forwards and Equity Risk . . . . . . . . . . . . . . . . . . . . . . . . 664.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.2 Simple Binomial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.2.1 Case 1: 0≤Φ≤Πd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.2.2 Case 2: Πd ≥Φ<Πu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2.3 Case 3: Φ≥Πu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.3 Quantitative Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.3.2 Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.4 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4.2 TLCF and risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4.3 1986 Tax Reform Act . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.1 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91viiA Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97A.1 Complementary Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97A.2 House Prices Trends 1999-2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98A.3 U.S. Court data on Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98A.4 PSID data of households’ wealth portfolio and the magnitude of the homestead ex-emption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100A.5 Final Period Optimal Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102A.6 Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103B Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115B.1 Value-Function Algorithm Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 115B.2 Price Dynamic Estimation for the British Columbia Halibut . . . . . . . . . . . . . . 116B.3 Biomass and Harvest Dynamic for the British Columbia Halibut Using a Social Dis-count Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119B.4 Alternative Cost Function Parametrizations for the British Columbia Halibut and theirImpact on the Simulated Biomass and Harvest Dynamic . . . . . . . . . . . . . . . 120B.5 Impact of an increase in the Biomass Volatility on the Simulated Biomass and HarvestDynamic for the British Columbia Halibut . . . . . . . . . . . . . . . . . . . . . . . 122C Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124C.1 Variable Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124viiiList of TablesTable 2.1 FFIEC Performance Report Summary Statistics . . . . . . . . . . . . . . . . . . 13Table 2.2 Homestead Exemption by State, 2001-2016 . . . . . . . . . . . . . . . . . . . . 15Table 2.3 Loans to Households and Homestead Exemption . . . . . . . . . . . . . . . . . . 17Table 2.4 Household Secured Loans and Homestead Exemption . . . . . . . . . . . . . . . 18Table 2.5 Household Unsecured Loans and Homestead Exemption . . . . . . . . . . . . . . 20Table 2.6 Lending Expenses and Homestead Exemption . . . . . . . . . . . . . . . . . . . 21Table 2.7 House Prices and Homestead Exemption . . . . . . . . . . . . . . . . . . . . . . 23Table 2.8 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Table 2.9 Loans and interest rates - Estimated pooling equilibrium for K = 1 and K = 3 . . 38Table 2.10 Loans and interest rates - Separating equilibrium for K = 1 and K = 3 - Ψ= 0.00 39Table 2.11 Loans and interest rates - Pooling equilibrium for K = 1, separating equilibriumfor K = 3 - Ψ= 0.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Table 2.12 Housing Equilibrium - Pooling equilibrium for K = 1, separating equilibrium forK = 3 - Ψ= 0.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Table 3.1 Estimated Parameters for the Biomass Dynamic, 1996-2017 . . . . . . . . . . . . 52Table 3.2 Ex-Vessel Real Price Dynamic Parameters, 1996-2017 . . . . . . . . . . . . . . . 53Table 3.3 British Columbia Halibut Fishery Revenues, 2007 and 2009 . . . . . . . . . . . . 54Table 3.4 Fishery’s risk adjusted rate of return . . . . . . . . . . . . . . . . . . . . . . . . 56Table 3.5 Fishery Betas, Available Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Table 3.6 Estimated Parameters for the British Columbia Halibut Fishery . . . . . . . . . . 58Table 3.7 Grid Dimensions and Limits for Numerical Solution . . . . . . . . . . . . . . . . 58Table 3.8 Value Function for Different Levels of Uncertainty at the Current State . . . . . . 63Table 3.9 Simulations for Models with Different Levels of Uncertainty . . . . . . . . . . . 64Table 4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 4.2 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Table 4.3 TLCF Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Table 4.4 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80ixTable 4.5 Portfolio Sorts on TLCF and Standard Risk Measures . . . . . . . . . . . . . . . 81Table 4.6 TLCF and Future Market Beta . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Table 4.7 TLCF and Future Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Table 4.8 TLCF and Future SMB Beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Table 4.9 TLCF and Future HML Beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Table 4.10 TLCF and Future Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Table 4.11 TLCF and Future returns, 1986 change in tax code . . . . . . . . . . . . . . . . . 86Table A.1 Non-Business Chapter 7 Filings Summary Statistics . . . . . . . . . . . . . . . . 99Table A.2 Non-Business Chapter 7 Assets and Liabilities Summary Statistics . . . . . . . . 100Table A.3 PSID State Level Average Wealth, Summary Statistics . . . . . . . . . . . . . . . 101Table A.4 PSID State Level Average Home Equity and Unsecured Debt, Summary Statistics 101Table A.5 Credit Card Loans and Homestead Exemption . . . . . . . . . . . . . . . . . . . 103Table A.6 House Price Index Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . 104Table A.7 House Prices and Homestead Exemption Groups . . . . . . . . . . . . . . . . . . 104Table A.8 U.S. Census New House Units Permits and Homestead Exemption Categories . . 105Table A.9 Construction and Land Development Loans and Homestead Exemption Categories 105Table A.10 Household Secured Loans and Homestead Exemption Categories . . . . . . . . . 106Table A.11 Household Secured Loans by Type and the Homestead Exemption . . . . . . . . 107Table A.12 Total Secured Loans and Homestead Exemption . . . . . . . . . . . . . . . . . . 108Table A.13 Commercial Loans and Homestead Exemption . . . . . . . . . . . . . . . . . . . 109Table A.14 Household Unsecured Loans and Homestead Exemption Categories . . . . . . . . 110Table A.15 Credit Card Loans and Homestead Exemption . . . . . . . . . . . . . . . . . . . 111Table A.16 Loans Yield and Homestead Exemption . . . . . . . . . . . . . . . . . . . . . . . 112Table A.17 Ratio Homestead Exemption over House Prices: 2011 - 2016 . . . . . . . . . . . 113Table B.1 Price Dynamic Estimation: Multiple Models . . . . . . . . . . . . . . . . . . . . 118Table B.2 Summary Statistics for the Differences in the Harvesting Policy: Benchmark Caseminus Social Discount Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Table B.3 British Columbia Halibut Fishery Revenues, 2007 and 2009 . . . . . . . . . . . . 120xList of FiguresFigure 2.1 Cash-on-Hand for unemployed household (i, j) = {(i,u)}, as a function of thehome equity E(i, j)1 , for the Homestead Exemption K. . . . . . . . . . . . . . . . 29Figure 3.1 Logistic Natural Growth Function for for the parameters γ = 0.8, Imax = 150 . . 48Figure 3.2 International Pacific Halibut Commission Regulatory Regions. Source: Interna-tional Pacific Halibut Commission (IPHC). . . . . . . . . . . . . . . . . . . . . 50Figure 3.3 British Columbia halibut stock assessment and landings, 1996-2017. Source: In-ternational Pacific Halibut Commission (IPHC). . . . . . . . . . . . . . . . . . . 51Figure 3.4 British Columbia Halibut Biomass Growth and the Non-Linear Least SquaredModel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 3.5 British Columbia Halibut Ex-Vessel Real Price and Logarithmic Returns, 1996-2017. Source: Fisheries and Oceans of Canada - Quantities and Values . . . . . 53Figure 3.6 Value Function of the British Columbia Halibut Fishery . . . . . . . . . . . . . . 59Figure 3.7 Optimal Harvesting Policy of the British Columbia Halibut Fishery . . . . . . . 60Figure 3.8 Simulated Paths for the Price, Optimal Harvesting Policy, and Biomass for theBritish Columbia Halibut Fishery . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.9 Median, 1th and 99th Percentiles of the Simulated Harvesting Policy and Biomassfor the British Columbia Halibut Fishery . . . . . . . . . . . . . . . . . . . . . . 62Figure 3.10 Percentile 1th and 99th of the Simulated Harvesting Policy for the BenchmarkCase and the Only Biomass Uncertainty Case for the British Columbia HalibutFishery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 4.1 Tax Loss Carry Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 4.2 Firm Risk and Tax Loss Carry Forward . . . . . . . . . . . . . . . . . . . . . . 71Figure 4.3 Expected return as a function of TLCF . . . . . . . . . . . . . . . . . . . . . . . 74Figure A.1 House Price Index State Average, The Zillow Home Value Index (ZHVI) and theFederal Housing Finance Agency (FHFA) House Price Index (HPI). Data from1999 to 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98xiFigure A.2 House Price Index For States with High and Low Homestead Exemption, FederalHousing Finance Agency (FHFA) House Price Index (HPI). Data from 1999 to2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Figure B.1 Autocorrelation for the Logarithm of the British Columbia Halibut Price, 1996-2017. Source: DFO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Figure B.2 Median Simulated Biomass and Harvesting Policy for Different Cost FunctionParametrizations of the British Columbia Halibut Fishery . . . . . . . . . . . . . 121Figure B.3 Median, 1th and 99th Percentiles of the Simulated Harvest for the Biomass Volatil-ity Case, Increased Biomass Volatility Case, and the Benchmark Case, For theBritish Columbia Halibut Fishery. . . . . . . . . . . . . . . . . . . . . . . . . . 123xiiAcknowledgmentsI would like to express my special gratitude to my thesis advisors, Jack Favilukis and Ron Gi-ammarino. Your guidance, patience, support and advice were crucial for my research; I appreciateand treasure everything you have done for me. I will remain forever grateful.My gratitude is also with Eduardo Schwartz. Having the opportunity to work hand to hand withyou gives me almost the same pride than calling you my friend.More broadly, I would like to thank the rest of the UBC Finance faculty.Quiero expresar mi gratitud a mis padres, mis hermanos y mis amigos en Chile, Canada y Korea.A pesar de la distancia, su carino y apoyo han estado siempre conmigo.More importantly, I would like to express my infinite thanks to my beloved wife, Dilara. Thankyou for your support, friendship and companion, there are no words to express how much better mylife is with you.Lastly, I would like to acknowledge the financial support provided by University of British Columbiaand the Social Science and Humanities Research Council of Canada (SSHRC) over my graduate stud-ies.xiiiChapter 1IntroductionAn important focus of the financial literature is the study of the role of law in the development offinancial markets, and its impact on long-run economic growth and welfare of the agents. As Beckand Levine (2005) mention:“. . . financial markets in countries where legal systems enforce private property rights, supportprivate contractual arrangements and protect the legal right of investors, savers are more willingto finance firms and financial markets flourish. In contrast, legal institutions that neither supportprivate property rights nor facilitate private contracting inhibit corporate finance and stunt financialdevelopment”.The objective of this thesis is to study the impact of three legal institutions on asset prices, thedecisions of firms and households, and the economic sustainability of regulated markets. These insti-tutions directly define property rights, support contractual arrangements, and define the tax paymentof a firm, key legal regulations in place for financial markets around the world.The first legal institution I study is the personal bankruptcy code, in particular, how the character-istics of this institution affect the households’ and lenders’ loans choices, and consequently, the loanmarket equilibrium. The second legal institution that I study is the regulation of the harvest of naturalresources, with a focus on the potential of this institution to help achieve a financially and ecologicallysustainable exploitation of renewable natural resource (e.g. fish). The third legal institution I study isthe tax code, specifically, how the treatment of corporate losses for tax shield benefit interacts with thefirm’s equity risk and return.The results of my research show that these legal institutions have a significant impact on thedecisions of market agents and in the determination of asset prices, that they are relevant not onlyfor academics, but also for investors, households facing financial distress, lenders evaluating grantingpolicies, and governmental institutions designing regulations.The first studied legal institution is the U.S. personal bankruptcy code. Whitin the code there areseveral exemption laws that determine how much of the household’s wealth will be shared with thelenders in case of default on their unsecured obligations. Specifically, the bankruptcy code allows1the household to keep a fraction of its wealth, and in the case that its wealth is fully exempted, theirunsecured loans will be fully discharged providing them with a fresh financial start.In the personal bankruptcy code, the most important form of protection for the household assets- and the main focus of my research - is the homestead exemption1, which protects the household’shome equity and varies widely at state level across the U.S. For example, if a household’s home equityis below the state’s homestead exemption, the household will keep the full value of its home equity2 and its unsecured debt will be discharged. On the other hand, if the household’s home equity isabove the state’s homestead exemption, the house will be liquidated to repay (fully or partially) theunsecured loans. Therefore, the magnitude of the homestead exemption is extremely important todetermine the outcome of the personal bankruptcy procedure for the household and the lender. Amore detailed example and discussion of the legal aspects of the homestead exemption is included inChapter 2.Based on its impact on the outcome of the bankruptcy procedure, the homestead exemption affectsthe households demand for unsecured loans, its housing consumption and financing choices, as it de-termines the housing net wealth that the household will have at bankruptcy. On the other hand, lenderswill act rationally accordingly to the homestead exemption magnitude in the state that the household islocated. As a higher exemption affects the recovery that the lenders will have at bankruptcy, the lenderwill incorporate the magnitude of the homestead exemption into their pricing decisions and supply ofloans, potentially affecting the access that households will have to loans.One may conjecture that a higher exemption will increase moral hazard on the part of the house-holds, leading to a higher demand for loans from riskier borrowers, and to higher delinquency rates.The lenders will respond with higher interest rates, therefore, it is not clear what the aggregate effectof a higher homestead exemption magnitude will be in equilibrium as these two effects will competein opposite directions. Chapter 2 of this thesis is an empirical and theoretical analysis of the impact ofthe homestead exemption on the secured and unsecured loan markets.The empirical analysis shows that states with a higher homestead exemption have lower loans tohouseholds, and lower delinquency rates. For the interest rates I find that they are lower in stateswith higher homestead exemption, but the effect is not statistically significant. These results areinteresting and somewhat counter-intuitive, because a higher protection may be expected to increaseboth delinquency and loan rates as the default punishment shrinks and riskier households increasetheir loan demand.In the theoretical analysis I show that personal bankruptcy is a complex option, whose value andexecution depends on house prices, secured and unsecured loans, their respective interest rates, and thehomestead exemption. Most importantly, the empirical findings are explained by a theoretical model1The homestead exemption also exists in other countries, for example, in Canada it varies from $0 in Ontario to $40,000in Alberta2The housing net wealth is the difference between the market value of the primary residency of the household and themortgage outstanding balance.2in which an increase in the lender’s monitoring results in a change from a pooling to a separatingequilibrium, that is, from an equilibrium on which households are pooled by loan type regardless oftheir riskiness, to one on which they are separated by loan type and default riskiness. The changein the equilibrium characteristics ends up reducing the loans to riskier households and consequentlyreducing both the overall loans granted and the delinquency rate. The model also shows that a higherhomestead exemption relates to a higher demand for housing, resulting in higher housing prices in theequilibrium. The model also implies a reduction of overall social welfare as the protection becomesmore generous.The second legal institution I study in this thesis is the total allowable catch (TAC) for fisheries,which regulates the annual limit of the total harvest for a natural resource, specifically a fish specie, ina defined geographical region. My co-author and I propose and calibrate an economic model to definethe optimal limit to the annual harvest. We evaluate the consequences of the proposed approach bysimulating the dynamics of the resource if the proposed methodology is implemented. The results ofthis exercise indicate that our approach is economically sustainable in the long run.The fishing industry is an interesting and important example of a regulated natural resource withstrong implications for employment and sustainability, as it provides a living for 10 percent of theworld’s population (Greiff (2017)). Beyond its clear importance, Ye and Gutierrez (2017) documentthat more than 30% of the fish stocks have been overfished during the last decade, even with severalregulation efforts in place. This persistent problem is the main motivation of our work.This research is presented in Chapter 3 and has two main components. First, we theoreticallydevelop a stochastic optimal control approach to determine the harvest policy that maximizes thevalue of the resource, we model a fishery as a complex function on the variables underlying the valueof the industry, in this case, the resource stock (biomass) and the fish price. Uncertainty is introducedin the analysis by allowing these variables to follow dynamic stochastic processes.The practical implications of the proposed model are also addressed in this work by applying itto the British Columbia halibut fishery. The required data to calibrate and implement the model isobtained combining multiple sources of information and includes time series for the halibut biomass(stock), total harvest (landings), and the whole sale price for commercial fishing boats.The model results show that for the representative halibut fishery in British Columbia it is optimalto preserve the resource for future harvesting, and that if the significant negative shocks occur to theresource then it is optimal to drastically reduce exploitation, even fully stopping the harvest in somestates.Our results also show that the optimal harvesting policy exhibits strong financial incentives toavoid the extinction and preserve the natural resource for future extraction. These results are not onlyuseful for fisheries, but most importantly, they are also useful for governments and regulators, as itformalizes a quantitative model to determine the total allowable catch (TAC), based on real availabledata, that balances sustainability and economic incentives.The final legal institution studied in this work is the corporate tax code. My co-authors and I focus3on the Tax Loss Carry Forwards (TLCFs), which arise because the corporate tax code does not allowNet Operating Losses (NOLs) to automatically generate payments from the government to the firm.Instead, the tax coded allows operational losses to generate immediate refunds if the firm can applythe losses to prior taxable income (Tax Loss Carry Backs), or if this is not possible, to carry themforward. The consensus, starting with Modigliani and Miller (1963), is that corporate taxes and taxshields reduce a firm’s equity risk. In this work we show that this is not necessarily the case.This research is presented in Chapter 4 and is also separated in two main components. First, atheoretical study of the relationship between TLCFs and the firm’s equity return. We start with a oneperiod binomial model and show that the relationship between risk and TLCFs is non-monotonic. Wethen show that if the firm has existing non-TLCF tax shields, then the relationship between TLCFsand risk may be strictly positive rather than non-monotonic. We then solve a realistic, dynamic modelof a firm, and calibrate it to the data. In this model, the relationship between TLCFs an risk is positiveand quantitatively important for risk.In the second part of this work, my co-authors and I empirically study the relationship betweenthe Tax Loss Carry Forward and asset prices. We show that TLCFs are positively related to standardmeasures of risk, like factor betas and future volatility. We then show that TLCFs are also positivelyrelated to equity returns. Importantly, in our regression analysis of return and TLCFs we find thatTLCFs can predict future returns even when we condition on standard measures of risk. Hence, ourstudy shows that the TLCF is indeed significant for the firm’s equity return and risk and that theinclusion of standard measures of risk account for some but not all the risk generated by TLCFs.The remainder of this thesis is organized as follows. The research on the personal bankruptcy codeis presented in Chapter 2. The research on the total allowable catch (TAC) for fisheries is presentedin Chapter 3. Chapter 4 includes my research on Tax Loss Carry Forwards and finally, Chapter 5concludes.4Chapter 2Personal Bankruptcy, Loan MarketEquilibrium, and House Prices2.1 IntroductionThe corporate bankruptcy code has been an important focus of the financial literature, but recently thepersonal bankruptcy code has drawn significant attention, as its importance became clear during theGreat Recession (Mian and Sufi (2010)). During this period of economic downturn, the householdsability to meet their financial obligations eroded, consequently making the option to file for personalbankruptcy valuable for them, as it provides protection to the households’ assets from the lenderscollection.In particular, a household can file for either Chapters 7 or 13 of the personal bankruptcy code.For both chapters all the lenders’ collection efforts must stop. If it chooses Chapter 13, the householdproposes a repayment schedule, and its liabilities are reorganized without seizing any assets. If thehousehold chooses to file for Chapter 7 instead, it keeps a fraction of their assets, while a fraction oftheir unsecured loans may be discharged.Under Chapter 7, the households will keep a fraction of their assets determined by state-specificlaws called exemptions. Exemptions can be classified into two main categories: personal exemptions,which protect the household’s personal belongings1, and the homestead exemption, which protects thehousehold’s home equity2 of its primary residence.As Berkowitz and Hynes (1999) show, the homestead exemption is the most important protectionfor the households at bankruptcy, in magnitude and use. However, it is important to notice that themagnitude of this exemption varies significantly across states, thus directly affecting the financial1The personal exemption protects cash, jewelry, clothes, furniture, and other personal property.2The home equity is defined as the net value between the real estate fair value and the outstanding balance of the loanssecured by this property.5benefit from this legal procedure for similar households in different locations3. Thus, the homesteadexemptions has the potential to significantly affect the behavior of households and lenders, as theoutcome of the bankruptcy procedure drastically changes depending on the location of the household.For the households, a more generous homestead exemption increases the households’ home equitythat they will keep after bankruptcy, while increasing the possibility of a significant discharge ofunsecured loans.For the lenders, a more generous homestead exemption increases the credit risk of these loans,given that the recovery after bankruptcy will be lower, and consequently they may increase the chargedrates or monitoring in order to reduce their expected credit losses4.In this work I study the personal bankruptcy procedure. Specifically, how the magnitude of thehomestead exemption affects the households demand for loans, their housing consumption and fi-nancing choices. I also study how the magnitude of the homestead exemption relates to the lenders’decisions, specifically how it affects their incentives to monitor in the presence of asymmetric infor-mation.To fulfill my goal I develop an empirical and theoretical analysis of the impact of the homesteadexemption on the secured and unsecured loan markets.In the empirical analysis, I look to quantify the relationship between the magnitude of the home-stead exemption, household secured and unsecured loans and house prices5. The results indicate thatthere is a positive and significant correlation between housing prices and the homestead exemption.Additionally, in states with a higher homestead exemption, banks issue fewer loans to households, andthese loans exhibit lower delinquency ratios.Although the FFIEC data includes interesting information of the mortgage loans in the banks’balance sheet at state level, unfortunately no information is provided on if they are securitized. Al-though this procedure affects the mortgage interest rates and the bank’s granting policies, as Ghent3Consider a household whose sole asset is its home, valued at $100,000, with a mortgage outstanding of $70,000. Hence,the home equity, the net between the house value and the mortgage debt is $30,000. The household also owes $30,000 froman unsecured loan. If the household decides to file for Chapter 7 and happens to be situated in North Dakota, the homesteadexemption will then be $100,000, and the home equity will in turn be fully protected. In such a case, the household willkeep its house, and the unsecured loan will be fully discharged despite having wealth to repay. If the same household islocated in Missouri, were the homestead exemption is $15,000 (as the home equity is not fully exempted), the house is soldfor $100,000, the secured lender receives $70,000, and the remaining $30,000 are shared between the household (who keepsthe exempted amount of $15,000), and the unsecured lender, who recovers the remaining $15,000.4Although secured loans have priority during bankruptcy, there are several costs related to foreclosing the property insuch situation, hence making the repossession process longer and more expensive, as Berkowitz and Hynes (1999) docu-mented. In turn, the riskiness of the secured debt is also affected by the personal bankruptcy procedure, even if these loansare finally repaid.5In order to address this goal, I constructed both a state- and national-level panel database for the U.S., combininglending data from the Federal Financial Institutions Examination Council (FFIEC) with the household characteristics fromthe Bureau of Economic Activity, the Census Bureau, the American Community Survey, and the Panel Study of IncomeDynamics. It is important to mention that significant changes to the personal bankruptcy procedure were made by theBankruptcy Abuse Prevention and Consumer Protection Act of 2005 (BAPCPA). This act increased the filing cost to be paidby the households, made credit counseling mandatory, and, most importantly, allowed only households whose income isbelow the state median to be able to file for Chapter 7. Based on these significant changes within the bankruptcy code, theempirical analysis presented focuses on the ten-year period between 2006 and 2016.6(2011) shows, my work focuses on cases on which the households have positive home equity, so theyfile for Chapter 7 to protect their house. In such case, the mortgage loan is fully repaid by either thehousehold or the trustee, as positive home equity implies that the value of the house is enough to repaythe mortgage. My analysis focuses mostly on the effects of the homestead exemption in unsecuredloans and house prices, as the recovery after bankruptcy of these loans is directly determined by thehomestead exemption.Although the FFIEC data includes interesting information of the mortgage loans in the banks’balance sheet at state level, unfortunately no information is provided on whether or not they are secu-ritized. Although securitization affects the mortgage interest rates and the bank’s granting policies, asGhent (2011) shows, my work focuses on cases on which the households have positive home equity,so they file for Chapter 7 to protect their house. In such cases, the mortgage loan is fully repaid by ei-ther the household or the trustee, as positive home equity implies that the value of the house is enoughto repay the mortgage. My analysis focuses mostly on the effects of the homestead exemption in un-secured loans and house prices, as the recovery after bankruptcy of these loans is directly determinedby the homestead exemption.This findings are interesting as the homestead exemption makes bankruptcy more attractive tohouseholds, so an increase in the exemption should increase the demand from households with higherdefault probability, thus negatively affecting the riskiness of the loan pool, but it will also affect theincentives of the lender, as the loans delivery becomes riskier and lower on expectation. To understandthe economic forces behind these results, I develop a theoretical model.For the theoretical analysis, I follow Mitman (2016) in terms of constructing an equilibrium model;I include households facing idiosyncratic income risk as well as a representative lender (bank) whocompetitively supplies loans. Households get utility from non-durable and housing consumption, anduse secured and unsecured loans in order to finance consumption. The households have the option tofile for bankruptcy with a homestead exemption that protects their home equity.The lender is assumed to be initially unable to observe the riskiness of the household’s income,however it has the option to invest in a monitoring technology, and eliminate this information asym-metry6. If the bank does not invest in the monitoring technology, the lending market corresponds toa pooling equilibrium, on which the households pay the same interest rate for secured and unsecuredloans. If the bank invests in the monitoring technology it will deviate to a separating equilibrium. Thisis, the bank will offer a unique contract to each household type, for secured and unsecured loans.The economic mechanism of the model indicates that a more generous homestead exemption willincrease the demand for housing, as the household will keep a greater amount of its home equity duringfinancial distress. The exemption increase also makes unsecured loans more likely to be discharged atbankruptcy, in turn boosting the lender’s potential credit losses.6These choices are consistent with the concern expressed by the New York Bankers Association in regards when an in-crease in the state’s exemption was discussed: “Increasing exemptions will cause creditors to re-examine their underwritingguidelines, limiting the numbers of consumers and small businesses deemed credit-worthy”. New York Bankers Association2012 (Cerqueiro et al. (2016))7If the bank lends without knowing the household’s type, households with higher income risk poolwith the less risky ones. If the homestead exemption rises, the risky households’ demand for unsecuredloans increases, as the bankruptcy benefit increases. On the other hand, the low risk households’unsecured loans demand goes down, as the bank increases the interest rate charged. Consequently, fora higher homestead exemption, the pooling total amount will increase, as does the interest rate, andthe delinquency ratios. This results are inconsistent with the findings of my empirical analysis.Now, if the bank optimally invest in the monitoring technology, the bank will offer a uniqueunsecured loan contract for each household type. The low risk households’ interest rate will fall incomparison to the pooling equilibrium, as they are no longer priced together with riskier households,so safer households will increase their demand for unsecured loans. In contrast, the risky householdswill now face a higher unsecured loan rate, and consequently will reduce their leverage. The modelresults show that for most of the tested parametrizations, these combined effects generate an overalldecrease in the amount of loans, with an improvement in the overall credit quality of the loan portfolio.This reduction is consistent with the empirical evidence showing that a higher exemptions is related tolower fraction of secured loans issued, with lower interest rates, lower delinquency, and higher overallhousing prices.To conclude, this paper contributes to the literature by studying the impact of the magnitude of thehomestead exemption on the household’s and lender’s problem, by presenting a deeper analysis of thelenders’ problem and incentives, by including information asymmetry and household heterogeneityin a theoretical setting, and by finding that the observed cross-sectional patterns on the secured andunsecured loan markets are consistent with an increase in the lenders’ monitoring efforts.2.1.1 Legal and Institutional BackgroundLaws covering personal bankruptcy were last modified in formulating the Bankruptcy Abuse Preven-tion and Consumer Protection Act of 2005 (BAPCPA), which started from a presumption of abusepresented by the lenders. BAPCPA made several changes, specially to the filing process, increasingits cost and complexity, and making financial counseling mandatory.My work focuses on Chapter 7, which starts when the household visits a state licensed financialcounselor. The couselor evaluates the household’s asset and liabilities, and the overall eligibility foreach personal bankruptcy chapter. Among the eligibility requirements, the most important is the stateincome mean test, design to allow only households whose income is below the state’s income mean tofile.If the financial counselor concludes that the household is eligible for Chapter 7, it will collect therequired documentation and file its case with the state legislature. A state Trustee will be assigned tothe case, and will notify all the involved lenders that their collection efforts must stop.In Chapter 7 the secured lenders can enforce claims against assets that they directly financed. Thesituation is more complex for the unsecured lenders, as their recovery after default will be directly8related to the magnitude of the non-exempted assets. Then the Trustee evaluates the value of thehousehold’s assets, and based on the state specific exemption laws, the Trustee determines the unex-empt value of the asset. If this unexempt value is large enough to generate a positive recovery to thelenders, the asset is liquidated. The distribution of the unexempted value among the lenders is definedby the Trustee, based on the outstanding loan amount and seniority.In particular, for the focus of my work, the homestead exemption, if the household’s home equityvalue of its primary residency is above the homestead exemption, the residency will be liquidated, thesecured lender is fully repaid first, then the household receives the exempted value, and finally, theremaining unexempted value will go to the unsecured lenders.After the Trustee finalizes the valuation and distribution of the household assets, the case is closedand all unpaid unsecured debt is discharged. Under Chapter 7 the household’s future earnings arecompetently protected, and, if required, the household will be allowed to file again for Chapter 7 after8 years.Although it is beyond the scope of my work, I briefly describe the Chapter 13 of the personalbankruptcy code. In this chapter, the Trustee does not liquidate any of the household’s asset, butevaluates a 3 to 5 years repayment plan, calculated using estimations of the household’s expectedfuture income and living expenses. At the end of the proposed plan, any remaining unsecured debt isdischarged. If the repayment plan is in place, any failure to meet the agreed payments will withdrawthe case and the lenders will be allowed to reinstate their collecting efforts.After the personal bankruptcy case is closed, the household credit report will record the Chapter13 case information for seven years, and the Chapter 7 information for ten years.2.1.2 Related LiteratureMy work contributes to the literature studying the relation between the homestead exemption mag-nitude and the unsecured lending to households. Gropp et al. (1997) find that in states with higherhomestead exemptions, households with lower wealth are more likely to be denied unsecured loans.Severino and Brown (2017) use the Federal Reserve Bank of New York Consumer Credit Panel/E-quifax (CCP) debt balances from 1999 to 2005, and the changes to the homestead exemption at statelevel, finding that an increase in the homestead exemption relates to higher credit card debt holdingsby the households. Grant (2010) use data from the consumer expenditure survey (CEX) from 1980 to2003, finding that an increase in the homestead exemption reduces the average level of unsecured debtheld, and such effect disappears for homeowners. All of these works use data for the pre-BankruptcyAbuse Prevention and Consumer Protection Act of 2005 (BAPCPA) period, where debtors of all in-comes levels could file for bankruptcy under Chapter 7. This paper presents novel results by focusingon how the lenders’ behavior is affected by the exemption magnitude, and by the study of the post-BAPCPA period.The relationship between the homestead exemption and the households’ secured debt has also been9studied, Lin and White (2001) use data from the Home Mortgage Disclosure Act (HMDA), from 1992to 1997, to show that the probability of acceptance of a mortgage application is negatively related withthe homestead exemption magnitude. Using similar data Pence (2006) finds that smaller mortgagesare originated in states with more friendly foreclosure laws. Chomsisengphet and Elul (2006) use arandom sample of the HMDA data, from 1999, to show that the use of a credit score to infer the appli-cants quality, reduces the probability of receiving a mortgage loan for low score households, and thatafter controlling for the credit score, the homestead exemption magnitude becomes not significant.Berkowitz and Hynes (1999) and Severino and Brown (2017) find no significant impact of the mag-nitude of the homestead exemption over the secured lending. My work contributes to this literatureby evaluating the impact of the homestead exemption on secured bank lending for the post-BAPCPAperiod, and also by presenting a model on which secured lending is available for households whilealso house prices are an equilibrium result.The effect of the homestead exemption on the secured and unsecured debt is a relatively newstream in the literature. Mitman (2016) studies the effect of the Bankruptcy Abuse Prevention andConsumer Protection Act (BAPCPA) and the Home Affordable Refinance Program (HARP) on thebankruptcy rates and foreclosures. He finds that higher exemptions are related to lower bankruptcyrates but higher foreclosure rates. Hintermaier and Koeniger (2016) build a structural model to studythe debt-portfolio choices over the life cycle, focusing on matching the observed cross-sectional dis-tributions of secured and unsecured debt. The model is calibrated using the Survey of ConsumerFinances (SCF), showing that home equity of unsecured debtors remains in most cases under the ex-empted amount. In both cases the lender problem does not incorporate any monitoring nor informationasymmetry, and house prices are risky but exogenous. My work contributes by providing an analysison how the lender’s behavior and incentives are affected by the magnitude of the homestead exemp-tion in the presence of information asymmetry, while also evaluating its effects on the lending marketequilibrium and the house market equilibrium.The model presented in the following sections shares several features with the literature that stud-ies the macroeconomic effects of the personal bankruptcy code. In these models, the unsecured loanmarket is modeled following the work of Livshits et al. (2007) and Chatterjee et al. (2007). The se-cured loans model presented in my paper shares features with Athreya (2006), studied the role ofbankruptcy exemptions, in a model with secured and unsecured credit, all households are homeown-ers. Jeske et al. (2013) construct a model on which households optimally consume housing, financedwith a mortgage loan, which is priced incorporating default risk. My model shares several featureswith Mitman (2016), which includes a set of heterogeneous households facing idiosyncratic incomerisk. They use secured and unsecured loans to purchase real estate and non-durable consumption. Asin my model, households default separately on unsecured and secured loans, at the cost of giving uptheir housing wealth, but as mentioned, my work contributes to the literature by analyzing the effectof higher homestead exemption on the lender’s behavior and incentives, and consequently, on the loanmarket equilibrium.10Corradin et al. (2016) study the relationship between the homestead exemption and the demand forreal estate. They use data from 1996 - 2006 and find that demand for real estate is relatively high, if themarginal investment in home equity is covered by the exemption. My work contributes to this topicas I provide a novel economic model on which real estate prices are determined in equilibrium, andtherefore, it allows to analyze the impact of the magnitude of the homestead exemption on equilibriumhouse prices.Recent work from Indarte (2019) revisits the relationship between the debt relief generosity andbankruptcy filings, using a extensive database on mortgage borrowers. Her results indicate that anincreases in the homestead exemption only weakly incentivize further filing. Although in this work Istudy the lending market before the household filing for bankruptcy, my results relate to those in herwork, as I show that a higher exemption reduces the lending to riskier households, as the delinquencyratios7 of the loan portfolio indicate. Henceforth, the weak effect on filings may be the consequenceof a more severe granting policy, that restricts the riskier households at the moment of entering themarket, limiting the expected credit losses and bankruptcy filings.A potential issue that the empirical analysis of the relation between the homestead exemptionmagnitude and house prices is reverse causality, as higher house prices could lead to the set of higherhomestead exemptions. However, Hynes et al. (2004), and the novel work of Auclert et al. (2019),show that the historical homestead exemption magnitude is the best predictor of its current level, evenwhen compared to contemporaneous economic indicators, which alleviates these concerns. This resultis consistent with the evolution of the homestead exemption presented in Table 2.2, as it shows thatmany states have adjusted in few occasions the homestead exemption magnitude in the last 20 years,and in most cases it was an inflation adjustment, despite the significant changes in the real estateprices, and risk characteristics, observed during the same period.Finally, my paper contributes to the extensive literature in credit monitoring and loan allocation.Stiglitz and Weiss (1981) show that lenders could set an upper limit to the increase in interest rates,leading to a decrease in the equilibrium rates and loans. In my model the economic mechanism isconsistent with credit rationing, as it will be optimal for the lender to identify the riskiness of theborrowers, raising the loan rates to riskier households, generating an equilibrium on which a lowertotal amount of loans, with lower rates, and delinquency. The influential work of Bester (1985) revisitsthe screening problem in credit markets, shows that if the banks can screen investor riskiness, there isno credit rationing, although safer households will require a higher amount of collateral.Credit allocation, lending standards, and information asymmetries has been studied in the bank-ing literature, although most works focus on contracts, market competition, and mechanism design.Dell’Ariccia and Marquez (2004) perform a theoretical analysis on competition among financial in-termediaries, and its effects on credit allocation under asymmetric information. They show that banks7The delinquency ratio show the fraction of the total loans hold by bank that exhibit more than 90-days overdue payments.Usually at this point the bank will evaluate the initiation of legal collection of the loans, will finally may push the householdsto file for bankruptcy.11do not finance risky borrowers in markets with strong information asymmetries. Dell’Ariccia andMarquez (2006) show that lower information asymmetries lead to banks screening out bad borrowers,by demanding a high amount of collateral, in equilibrium. I present a model on which heterogeneousborrowers use two different type of loans, one with requires collateral (secured) and one unsecured,and the option to default on each loan, to smooth consumption, while the lender optimally price debtin the presence of information asymmetry, showing that riskier borrowers exhibit lower debt if thelender identify them.The rest of the paper is organized as follow, Section 2.2 includes the Data Description and Sum-mary Statistics, the empirical study of the relation between Real Estate Prices and the HomesteadExemption, and Household Loans and the Homestead Exemption. Section 2.3 presents the economicmodel, a scheme of the equilibrium computation, the model calibration, and the numerical results.Finally, Section 2.4 present the main concussions of this paper.2.2 Empirical Analysis2.2.1 Data and Summary StatisticsTo test the empirical relation between the magnitude of the homestead exemption, house prices, andbanks lending to households, I perform a series of panel regressions using a database that combinesmultiple sources and covers the period from 2006 to 2016, post the Bankruptcy Abuse Prevention andConsumer Protection Act of 2005 (BAPCPA).The data employed in this analysis is obtained from multiple sources. First, House prices are ob-tained from the Federal Housing Finance Agency (FHFA). The House Price Index (HPI) is defined as:“a weighted, repeat-sales index measuring the average price changes in repeat sales or re-financingson the same properties using single-family house prices”8. To complement this data I use the Zil-low Home Value Index (ZHVI) as an alternative house price measure. This index is defined as: “atime series tracking the monthly median estimated sale prices (Zestimates) value in a geographicalregion”9.The lending data is obtained from the Federal Financial Institutions Examination Council’s (FFIEC)Uniform Bank Performance Report (UBPR)10 defined as “a multi-page financial analysis of a com-mercial bank or savings bank that files the Consolidated Reports of Condition and Income (Call Re-port)”. These reports are periodically filed by U.S. banks, state-chartered banks members of theFederal Reserve System, and saving associations regulated by the Federal Deposit Insurance Corpo-ration.The FFIEC data is obtained at state-level, and the reports include performance and credit allocationratios, calculated using the information of all the insured banks operating in the state. Among the8https://www.fhfa.gov/DataTools/Downloads/pages/house-price-index.aspx9https://www.zillow.com/research/data/10https://www.ffiec.gov/ubpr.htm12Table 2.1: FFIEC Performance Report Summary StatisticsThis table presents the summary statistics for the FFIEC Uniform Bank Performance Report. The analyzed loans areseparated into the categories Secured Loans (which are the total real estate loans as a fraction of all loans issued by thebank), unsecured household loans (loans to individuals, which include personal loans, credit card debt, and auto loans), andCommercial Loans (loans to business). Secured loans are dis-aggregated into household secured loans (family real estateloans which includes loans to finance family residences and home equity loans), and commercial secured loans (commercialreal estate). Panel A shows the median, 10th percentile and 90th percentile for the fraction of total loans, Panel B shows theaverage category loan yield, which is the average interest paid by the loans in each portfolio, and finally Panel C present thedelinquency ratio for each portfolio, which is the ratio of overdue payments to the total amount of loans in the portfolio.Panel A: Loan Allocation (As a fraction of Total Loans)N Median 10th 90thSecured Loans 672 72.60 52.89 82.81- Household Secured Loans 672 27.06 11.41 41.13- Commercial Secured Loans 672 41.71 31.59 59.27Unsecured Households Loans 672 5.86 1.88 11.19- Credit Card Loans 672 0.06 0.01 0.27Commercial Loans 672 14.17 10.21 19.40Panel B: Loans Annual Yield (Interest payments over the total loans in the category)N Median 10th 90thSecured Loans 672 3.92 2.03 5.00- Household Secured Loans 672 4.88 0.00 6.58Unsecured Households Loans 672 8.09 6.60 9.29- Credit Card Loans 672 10.23 7.95 13.27Panel C: Loan Delinquency Ratio (Past due payments over the total loans in the category)N Median 10th 90thSecured Loans 672 1.07 0.46 1.89- Household Secured Loans 672 1.35 0.53 2.46Unsecured Households Loans 672 1.50 0.59 2.40- Credit Card Loans 672 1.60 0.69 3.26full set of reported ratios, I focus on the loan portfolio, which is categorized into secured loans andunsecured loans to households. Beside the credit allocation, I use the information on annual interestpayments (denoted annual yield), and the delinquency ratio for each loan type.Demographic data is obtained from the U.S. Census Bureau, the American Community Survey(ACS) and the Economic Census databases, and includes population, education, age, gender, and mar-ital status. Data on income and employment is obtained from the U.S. Bureau of Economic Analysis(BEA) database.With respect to the bank lending data, the Federal Financial Institutions Examination Council’s(FFIEC) Uniform Bank Performance Report includes the median loan portfolio of all the bank oper-ating in each U.S. state, from 2006 to 2016. This dataset is summarized in Table 2.1.Panel A of Table 2.1 presents the average loan portfolio for banks operating in each U.S. state.The three main categories correspond to 93% of the total loans (the rest are allocated in the category13“other loans”, which include loans to governmental institutions, or other financial institutions). Themain category is secured loans (real estate loans), and within the category, 27% of the total loans areallocated to secured loans to households (residential mortgage loans). Unsecured loans to householdsare almost 6% of the total loans.Panel B of Table 2.1 shows that credit card loans are associated with a higher annual yield, and thespread in the yields between secured and unsecured loans to households are more than 3%. Finally,Panel C shows the delinquency ratios, where the highest past due percentages are in the unsecuredloan portfolio.The Homestead ExemptionThe homestead exemption defines the amount of home equity that a household will keep after filingfor personal bankruptcy under Chapter 7. Here, I present its historical values, obtained from severalpublications of the manual “How to File for Chapter 7 Bankruptcy” by Nolo Legal (Elias and Renauer(2001,2009,2016)).There are U.S. states that allow the households to choose between the federal exemptions or thestate exemptions. For the empirical analysis I will assume the household will choose the code provid-ing greater homestead exemptions11.Table 2.2 presents the respective homestead exemption (in USD), from 2001 to 2016. At the endof the table I include the federal homestead exemption. Two main characteristics of the homesteadexemption are noticeable from this Table, first, that there is a significant heterogeneity across states,going from unlimited in states like Arkansas, Florida and Texas, to zero in New Jersey. The secondhomestead exemption characteristic is that several states have adjusted their exemption level in alimited number of times, during the last 20 years, as in the cases of Alabama, Arkansas, Connecticut,Florida, and Illinois.With respect to the cross-sectional value, the median state is Maine with a $95,000 exemption, the10th percentile is $15,000 in Missouri, and the 90th percentile is $500,000 in Massachusetts.11The states that allow households to select the exemption set are Alaska, Arkansas, Connecticut, District of Columbia,Hawaii, Kentucky, Massachusetts, Michigan, Minnesota, New Hampshire, New Jersey, New Mexico, New York, Oregon,Pennsylvania, Rhode Island, Texas, Vermont, Washington, and Wisconsin.14Table 2.2: Homestead Exemption by State, 2001-2016Homestead Exemptions (in USD) from 2001 to 2016, obtained from the manual ”How to File for Chapter 7 Bankruptcy”manual, published by Nolo Legal (2001, 2009, 2016).State 2001 2007 2011 2016Alabama $10,000 $10,000 $10,000 $30,000Alaska* $64,800 $67,500 $70,200 $72,900Arizona $100,000 $150,000 $150,000 $150,000Arkansas* Unlimited Unlimited Unlimited UnlimitedCalifornia $75,000 $75,000 $100,000 $100,000Colorado $60,000 $90,000 $120,000 $150,000Connecticut* $150,000 $150,000 $150,000 $150,000Delaware $0 $50,000 $100,000 $125,000Florida Unlimited Unlimited Unlimited UnlimitedGeorgia $10,000 $20,000 $20,000 $43,000Idaho $50,000 $50,000 $100,000 $100,000Illinois $30,000 $30,000 $30,000 $30,000Indiana $30,000 $30,000 $35,200 $38,600Iowa Unlimited Unlimited Unlimited UnlimitedKansas Unlimited Unlimited Unlimited UnlimitedKentucky* $10,000 $10,000 $10,000 $10,000Louisiana $25,000 $25,000 $25,000 $35,000Maine $25,000 $70,000 $95,000 $95,000Maryland $0 $0 $21,625 $22,975Massachusetts* $100,000 $500,000 $500,000 $500,000Michigan* $34,850 $31,900 $35,300 $37,775Minnesota* $200,000 $200,000 $360,000 $390,000Mississippi $75,000 $75,000 $75,000 $75,000Missouri $8,000 $15,000 $15,000 $15,000Montana $120,000 $200,000 $500,000 $500,000Nebraska $12,500 $12,500 $60,000 $60,000Nevada $125,000 $350,000 $550,000 $550,000New Hampshire* $60,000 $200,000 $200,000 $240,000New Jersey* $34,850 $0 $0 $0New Mexico* $120,000 $120,000 $120,000 $120,000New York* $20,000 $100,000 $150,000 $165,550North Carolina $20,000 $37,000 $70,000 $70,000North Dakota $80,000 $80,000 $100,000 $100,000Ohio $10,000 $10,000 $43,250 $265,800Oklahoma Unlimited Unlimited Unlimited UnlimitedOregon* $33,000 $39,600 $50,000 $50,000Pennsylvania* $34,850 $40,400 $43,250 $47,350Rhode Island* $34,850 $300,000 $300,000 $500,000South Carolina $69,700 $100,000 $106,750 $116,510South Dakota Unlimited Unlimited Unlimited UnlimitedTennessee $7,500 $7,500 $7,500 $7,500Texas* Unlimited Unlimited Unlimited UnlimitedUtah $40,000 $40,000 $40,000 $60,000Vermont* $150,000 $150,000 $150,000 $125,000Virginia $10,000 $10,000 $10,000 $10,000Washington* $40,000 $40,000 $125,000 $125,000West Virginia $30,000 $50,000 $50,000 $50,000Wisconsin* $40,000 $40,000 $150,000 $150,000Wyoming $20,000 $20,000 $20,000 $20,000Federal exemption $34,850 $40,400 $43,250 $47,350*: States in which households are allowed to choose between the federal or state homestead exemption.152.2.2 Household Loans and The Homestead ExemptionTo study the effect of the homestead exemption on the credit market, I use the FFIEC Uniform Re-port, specifically the state level data including credit allocation, yield rates and delinquency ratios forall banks operations. Unfortunately these reports only include ratios, so no information over dollaramounts is available.An advantage of this data is that it provides information from banks. Most of the prior literaturehas focused on the household. In my work I will analyze the lender’s problem in more detail, un-derstanding how they choose to allocate their loans among unsecured and secured debt, highlightinghow the difference in risk and the magnitude of the homestead exemption will relate to the lender’sincentives for monitoring. This is a novel feature of my database, and an important contribution of mywork.To analyze the relation between the homestead exemption and the bank’s credit allocation I startby estimating the empirical correlation between the magnitude of the homestead exemption and thefraction of the total bank’s loan allocated to households. The baseline specification is:Lhst = αs+αt +β log(Homestead)st +ΓXst + εst (2.1)where Lhst denotes the median bank allocation to households loans type h as a fraction of total loans inits portfolio, located in state s, at year t. αs and αt denote the state and year fixed effect respectively.log(Homestead)st is the logarithm of the dollar amount of the homestead exemption in state s at yeart. Xst denotes economic and demographic controls for county i, at year t.Among the economic and demographic controls, I include the state average age of the head ofhousehold, education level, family size, income, unemployment among others. All regressions includeyear and state fixed effects, and in all standard errors are robust.Taking into account the changes in the personal bankruptcy code induced by the 2005 BAPCPAact, the panel is constructed from 2006 to 2016. The appendix for this section includes regressionsusing categorical variables to separate states by the magnitude of their exemption, showing that themain results presented in Table 2.3 are also obtained using such specification.16Table 2.3: Loans to Households and Homestead ExemptionThis table present the estimations for FFIEC Loans to Households at state level. The total loans to household are the sumof the FFIEC loans categories residential mortgages to families (denoted household secured loans) and individual loans(denoted household unsecured loans). The LHS variable is the median over all the commercial banks insured by the FFIEC.The main control is the logarithm of the Homestead Exemptions. All regressions include the house price index, the logarithmof the income per-capita, the percentage of the population with high school diploma, the unemployment rate, the percentageof households under poverty level, the percentage of households lead by married couples, the percentage of households leadby a female, the number of households with children, the median state age, and the fraction of the state population of whiterace as controls. Standard errors are heteroskedasticity-robust.(1) (2)Household Loans Household Unsecured Loans% of Total Loans % Total Household Loanslog(Homestead Exemption) -0.96 0.01(t-stat) (-2.17) (0.21)House Price Index 0.00 -0.01(t-stat) (-0.36) (-1.69)log(Income) -14.41 -0.15(t-stat) (-1.99) (-2.67)High School 0.12 0.00(t-stat) (1.32) (-2.14)Unemployment 0.56 0.00(t-stat) (2.76) (-1.55)Under Poverty -1.77 -0.07(t-stat) (-0.71) (-2.41)Married Couples 0.63 0.03(t-stat) (1.13) (0.06)Female Householder 0.34 0.46(t-stat) (0.51) (0.79)Families with Child 0.09 -0.02(t-stat) (0.31) (-0.14)Age -0.05 0.02(t-stat) (-0.08) (4.29)Race -0.81 -0.13(t-stat) (-3.32) (-5.75)Year-FE Yes YesState-FE Yes YesAdj. R-Squared 0.96 0.95Observations 433 433Sample 2006-2016 2006-2016Table 2.3 indicates that the overall amount of loans allocated to households decrease as the home-stead exemption increases, but the relative amount of secured to unsecured loans are not affected bythe magnitude of the exemption.These results are surprising because one may expect that as the homestead exemption increases,households will feel more protected, and household demand for loans will rise. Instead, I find anoverall reduction in the amount of loans, pointing to a supply effect. This is also why a carefulanalysis of the lender’s incentives, and how they are affected by the magnitude of the exemption. To17better understand the lender’s behavior, in the next two subsections I focus on just the secured, andthen just the unsecured loans.Household Secured Loans and The Homestead ExemptionThe households secured loans studied here include the FFIEC 1 to 4 family residential mortgages andmultifamily (more than 5) family residential mortgages. Home equity loans are reported as part of 1to 4 family residential mortgages. Table 2.4 shows the results for the regressions specified in Equation(2.1) for the household’s secured loans.Table 2.4: Household Secured Loans and Homestead ExemptionThis table present the estimation for household secured loans (FFIEC Family Real Estate Loans). The LHS variables arethe median percentage from the total loans, the loan annual yield, and the delinquency ratio. All correspond to the medianvalue over all the FFIEC insured banks at state level. The main control is the logarithm of the Homestead Exemptions. Allregressions include the house price index, the logarithm of the income per-capita, the percentage of the population with highschool diploma, the unemployment rate, the percentage of households under poverty level, the percentage of households leadby married couples, the percentage of households lead by a female, the number of households with children, the medianstate age, and the fraction of the state population of white race as controls. Standard errors are heteroskedasticity-robust.(1) (2) (3)Household Secured Loans Household Secured Loans Household Secured Loans% of Total Loans Yield Delinquency Ratiolog(Homestead Exemption) -0.98 -0.07 -0.14(t-stat) (-2.67) (-1.41) (-3.09)House Price Index 0.00 0.01 -0.11(t-stat) (-0.17) (7.6) (-1.66)log(Income) -6.70 -2.23 -0.68(t-stat) (-1.08) (-2.91) (-1.02)High School 0.17 0.00 0.01(t-stat) (2.45) (0.03) (1.05)Unemployment 0.55 -0.04 0.04(t-stat) (3.6) (-1.47) (1.95)Under Poverty 4.00 0.13 7.73(t-stat) (1.91) (0.38) (2.92)Married Couples 0.61 -0.05 0.11(t-stat) (1.28) (-0.84) (2.1)Female Householder 0.17 0.03 0.10(t-stat) (0.31) (0.44) (1.42)Families with Child 0.09 0.04 0.02(t-stat) (0.37) (1.6) (0.92)Age 0.01 -0.14 0.00(t-stat) (0.01) (-2.32) (0.07)Race -0.35 0.09 -0.03(t-stat) (-1.9) (3.54) (-1.73)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.94 0.98 0.87Observations 433 433 433Sample 2006-2016 2006-2016 2006-201618Column (1) of Table 2.4 shows that the amount of loans allocated to secured debt for householdsis negatively correlated with the magnitude of the homestead exemption. Column (2) shows thatthe correlation between the secured loans annual yield and the homestead exemption is negative, butnot significant. Column (3) shows that the delinquency ratio is negatively, and significantly, relatedto the homestead exemption. These three effects combined are surprising. One may have expectedthat a higher bankruptcy protection would be related to a higher demand for loans, driven by riskierhouseholds, leading to higher interest rates and a higher delinquency ratio.The economic mechanism presented in my model relates these empirical findings with the supplyside of the lending market equilibrium, specifically, with the lender’s behavior. As the lender’s creditrisk exposure increases with the homestead exemption, the lender will be better off by identifyingand pricing each households accordingly to their risk, therefore their incentives to monitor becomemore important, even if monitoring is costly. This supply response to a higher homestead exemptionwill cause a reduction in the secured loans to households, while improving the overall quality ofthe portfolio. Because of the reduction of loans to riskier households, the higher quality portfoliowill have lower delinquency rates, and therefore lower interest rates, although this last effect is notsignificantive.In relation to previous work, my results are consistent with the pre-BACPAC analysis presented inLin and White (2001) and Chomsisengphet and Elul (2006) which use HMDA data, but differ from theones reported in Severino and Brown (2017) who find no significant effect over the secured lending ina the FRBNY/Equifax panel for the same period.The appendix for this section includes regressions using categories for the homestead exemptionto explicitly include the unlimited states, having no significant effect over the discussed results.Household Unsecured Loans and The Homestead ExemptionUnsecured loans to households are included in the FFIEC reports as “loans to individuals for house-hold, family, and personal expenditures” and include credit card loans, revolving credit plans otherthan credit cards, automobile loans, and other consumer loans. Table 2.5 shows the results for theregressions specified in Equation 2.1 for the households unsecured loans.19Table 2.5: Household Unsecured Loans and Homestead ExemptionThis table present the results for regressions of the Household Unsecured Loans (FFIEC loans to individuals), including ratioof household unsecured loans to the total bank loans, the loan category annual yield, and the delinquency ratio. The maincontrol is the logarithm of the homestead exemptions, but also include the logarithm of per-capita income, the percentageof the population with high school diploma, the unemployment level, the percentage of households under poverty level,the percentage of households lead by married couples, the percentage of households lead by a female, and the number ofhouseholds with children. Standard errors are heteroskedasticity-robust and clustered at the state level.(1) (2) (3)Unsecured Loans Unsecured Loans Unsecured Loans% of Total Loans Yield Delinquency Ratiolog(Homestead Exemption) 0.02 -0.21 -0.16(t-stat) (0.09) (-0.90) (-2.41)House Price Index 0.00 0.00 0.00(t-stat) (-0.57) (-0.75) (-2.63)log(Income) -7.71 7.18 -1.60(t-stat) (-2.39) (1.78) (-1.86)High School -0.05 0.01 0.01(t-stat) (-1.3) (0.52) (0.46)Unemployment 0.01 0.11 0.01(t-stat) (0.07) (1.37) (0.19)Under Poverty -5.77 2.74 0.15(t-stat) (-4.51) (1.96) (0.35)Married Couples 2.08 23.15 -2.49(t-stat) (0.09) (0.75) (-0.42)Female Householder 0.17 0.54 -0.02(t-stat) (0.58) (1.44) (-0.26)Families with Child 0.00 0.15 0.01(t-stat) (0.01) (1.37) (0.23)Age -0.06 0.53 -0.04(t-stat) (-0.24) (2.27) (-0.57)Race -0.46 0.05 -0.01(t-stat) (-3.75) (0.48) (-0.41)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.67 0.98 0.66Observations 433 433 433Sample 2006-2016 2006-2016 2006-2016The results presented in Table 2.5 indicate that there is no significant correlation between thehomestead exemption and the unsecured loans to households (Column (1)). The relationship betweenthe homestead exemption and the unsecured loan annual yield is negative, but not significant (Column(2)). The delinquency of the unsecured loans is negatively and significantly related to the homesteadexemption magnitude. Thus, although the loan allocation and interest payments are not significantlyrelated the exemption magnitude, the unsecured loans portfolio has a better creditworthiness in stateswith higher bankruptcy protection.My results are interesting as a positive, and significant, effect on the loan allocation and inter-est paid might have been expected. Specifically, in states with higher homestead exemptions, the20unsecured loans become more likely to be discharged at bankruptcy, henceforth, households wouldincrease their demand for this type of loans. This would also lead to higher interest rates and higherdelinquency since the higher loan demand is due to moral hazard. However, this is not consistent withthe empirical results. Thus the presented results are more likely related to the lender’s supply of loans,as in the case of a higher possibility of discharge, the lender may decide to reduce the loans to riskierhouseholds to avoid further losses, overall improving the credit worthiness of the loan portfolio.2.2.3 Lending Expenses and The Homestead ExemptionThe results for secured and unsecured loans results indicate that the loan market equilibrium is po-tentially affected by the lender’s supply of loans. In states with a higher exemption, the lender maydecide to reduce the loans to riskier household to avoid further losses, overall improving the creditworthiness of the loan portfolio.The proposed economic mechanism behind my empirical findings is related to the monitoringefforts from the lender. To explore the empirical evidence for this channel, I use as a proxy for moni-toring three different bank expenditure measures, the average expenditure in personnel, the efficiencyratio12, and the total salary expenses as a percent of the total assets.Table 2.6: Lending Expenses and Homestead ExemptionThis table present the results for regressions for different measures of bank expenditures at state level obtained from theFFIEC database, and include the average expenditure in personnel, the efficiency ratio, and the total salary expenses overthe total assets. The main control is the logarithm of the homestead exemption, but the regressions also include the logarithmif the per-capita income, the percentage of the population with high school diploma, the unemployment level, the percentageof households under poverty level, the percentage of households lead by married couples, the percentage of households leadby a female, and the number of households with children. Standard errors are heteroskedasticity-robust and clustered at thestate level.(1) (2) (3)Average Expenditure Efficiency Total Salary Expensesin Personnel Ratio Over Total Assetslog(Homestead Exemption) 1.33 0.29 0.55(t-stat) (0.82) (0.64) (1.48)log(Income) -0.97 1.79 -1.94(t-stat) (-0.16) (2.00) (-2.60)Controls Yes Yes YesYear FE Yes Yes YesState FE Yes Yes YesAdj. R-Squared 0.41 0.94 0.77Observations 433 433 433Sample 2006-2016 2006-2016 2006-2016Table 2.6 shows that although the correlation between the homestead exemption and various mea-sures of bank expenditures is positive, although the effect is not significant. This evidence, although12Defined as the total bank expenses (excluding interest expense) over the total bank revenue.21weak, points in the direction of higher monitoring in states with higher exemptions. Currently most ofthe monitoring is done using technological tools, e.g. credit scores and data analysis, unfortunately,the limitations in the available data prevent a more thorough analysis of this hypothesis, as a moredetailed information of the bank operations is required to be conclusive here.2.2.4 House Prices and The Homestead ExemptionThis section studies the empirical correlation between the magnitude of the homestead exemption andhouse prices. Specifically, I estimate county level panel regressions, including the logarithm of thehomestead exemption value in dollars. To address for county level specific characteristics, I includeeconomic and demographic controls, age of the head of the household, education level, family size,income, unemployment among others. All regressions include year fixed effects, and standard errorsare clustered at state level.The baseline specification is:hpit = αs+αt +β log(Homestead)st +ΓXit + εit (2.2)where hpit denotes the house prices index in county i, located in state s, at year t. αs and αt denote thestate and year fixed effect respectively. log(Homestead)st is the logarithm of the dollar amount of thehomestead exemption in state s at year t. Xit includes economic and demographic controls for countyi, at year t.As mentioned, the changes introduced by the Bankruptcy Abuse Prevention and Consumer Protec-tion Act (BAPCPA) at 2005 into the bankruptcy procedure are significant, hence the presented resultsfocus on the 2006 to 2016 period.22Table 2.7: House Prices and Homestead ExemptionThis table presents the results for regressions of two house price indexes, the FHFA House Price Index (HPI) and the ZillowHome Value Index (ZHVI) per Sq.Ft. The main variable of interest is the logarithm of the homestead exemption. Controlsalso include the per-capita Income, the percentage of the population with high school diploma, the unemployment level,the percentage of households under poverty level, the percentage of households lead by married couples, the percentage ofhouseholds lead by a female, and the number of households with children. Standard errors are heteroskedasticity-robust andclustered at the state level.(1) (2)FHFA House Price Index Zillow Home Value Index (ZHVI) per Sq.Ft.log(Homestead Exemption) 0.29 0.11(t-stat) (2.89) (3.76)log(Income Per Capita) 5.16 2.91(t-stat) (4.60) (4.60)High School -1.19 -6.02(t-stat) (-0.43) (-2.35)Unemployment -1.02 -1.14(t-stat) (-2.62) (-0.91)Under Poverty -4.50 0.43(t-stat) (-2.58) (0.28)Married Couples -0.99 -0.68(t-stat) (-2.30) (-0.17)Female Householder -0.83 -0.22(t-stat) (-1.48) (-0.67)Families with Child 0.30 0.12(t-stat) (1.30) (3.04)Age -9.24 -7.43(t-stat) (-4.13) (-2.28)Year-FE Yes YesAdj. R-Squared 0.46 0.15Observations 12,612 6,267Sample Available 2006-2016 2006-2016Table 2.7 shows that the magnitude of the homestead exemption is positively and significantlycorrelated with the house price levels at county level. Although the magnitude of the correlation,considering the variation in house prices observed during the last decade, is modest. This result isinteresting, and the model results are consistent with this positive price effect, however this is not themain result of my work.13To conclude this section, I summarize the empirical results. An increment in the magnitude of thehomestead exemption is related to higher house prices, fewer loans to households, specially focusedon lower secured loans. These loans exhibit better credit quality, as a higher homestead exemptionrelates to lower delinquency ratios on secured and unsecured loans. Finally, there is a negative effecton the secured and unsecured loan interest rates, but these effects are not statistically significant.13Although I abstract from modeling and discussing the supply of housing, is possible to think that it might be relatedwith the homestead exemption magnitude. In the appendix of this section I show that states with higher exemptions alsoissued fewer housing permits and fewer loans to real estate development. To analyze this effect in detail a deeper model ofthe housing market is required, and at the moment, this goes beyond the scope of this work.232.3 ModelConsider a model of a credit market with two types of households i ∈ {g,b}, who live for two periods,t ∈ {0,1}, and differ in their income distribution at t = 1. In each period the households consume anon-durable good and a durable good, interpreted as housing.Households finance their consumption through secured and unsecured loans. These loans areoffered by a perfectly competitive representative lender (the bank). Loans are issued at t = 0, andmature at t = 1, moment at which the households also decide whether to exercise their option todefault in each one of these loans.The credit market is assumed initially to exhibit asymmetric information, as the households knowtheir type, but the bank does not. Although the bank has the option to invest in monitoring technology,at a fixed exogenous cost Ψ, that allows it to perfectly observe the household type. If the bank doesnot invest, it will offer a pooling contract for secured and unsecured loans, this equilibrium is denotedthe pooling equilibrium, as a unique interest rate is offered for the aggregate pool of secured andunsecured loans. Now, if the bank invests, it will offer a unique contract for secured and unsecuredloan, and for each type of household, this market equilibrium is denoted the separating equilibrium.The model operates in the following way. In the first period the bank evaluates the pooling equi-librium in the credit market, and based on its estimations, decides whether to invest in the monitoringtechnology or not. The bank then posts the secured and unsecured loan interest rates for any levelof the households’ demand. The households consider the available loan contracts, and select thosewhich maximize their expected utility. In the second period, the household income is realized, and ifeligible, the households decide whether to file for personal bankruptcy, consequently defining the loanpayments, which are finally collected by the bank.The details of the model are presented in the following subsections. First, the households’ problemis detailed, including their consumption, repayment and default choices for all loans. Then, the bank’sproblem is described, including the pooling equilibrium, the separating equilibrium and the conditionsunder which each equilibrium will be observed. Finally, the model is solved, and the results arecontrasted with the empirical findings previously presented.2.3.1 The Households’ ProblemThe economy is inhabited by a set of households of mass 1, who consume housing, a durable goodassumed to be housing, supplied in fixed quantity h¯, and a non-durable consumption good, suppliedexogenously in perfectly elastic manner, with a price of one. The households are located in a statewith a homestead exemption of K dollars.At t = 0 all households have the same income y0, but at t = 1 the households may receive anemployed income, y1 = ye, or become unemployed (u), and receive y1 = yu, yu < ye. Households canbe either type g or type b, being the difference between these types the probability of transitioning toemployed at t = 1, pi i. Households type b are assumed to be riskier as pig > pib, this is, households type24b have a greater probability of becoming unemployed. The fraction of households type g is denotedα .At t = 1 households can be identified by their emplyment status and their type, this is (i, j) wherei ∈ {g,b} and j ∈ {e,u}.The households demand one-period secured loans from the bank Mi0, using the housing stock ascollateral, and one-period unsecured loans Bi0, to finance consumption at t = 0. RiM denotes the grosssecured loaninterest rate, RiB the gross unsecured loan interest interest rate.At t = 0 household i ∈ {g,b} maximizes:maxci0,hi0,Bi0,Mi0[u(ci0)+φu(hi0)]+E0{β[u(c(i, j)1)+φu(h(i, j)1)+βδu(p1h(i, j)1)]}(2.3)where u(ci0)is the utility from the consumption of the non-durable good ci0, φu(hi0)denotes theutility from the service flow derived from the housing stock hi0, β is the household’s discount factor,and δu(p1h(i, j)1)is the utility derived from bequest the housing stock at the end of t = 1. Householdsare risk-averse, with a Constant Relative Risk Aversion (CRRA) utility function:u(c) =c(1−γ)(1− γ)At t = 0, the households purchase their housing stock at price p0. As housing is a durable good,households maintain their stock until t = 1, when they can trade their stock at price p1.The maximization in Equation (2.3) is subject to the t = 0 flow budget constraint:ci0+ p0hi0 ≤ y0+Bi0+Mi0 (2.4)The secured loan is subject to the collateral constraint:0≤Mi0 ≤ p0hi0 (2.5)then the loan-to-value is allowed to be 1, but its value will be an equilibrium result.The unsecured loan is subject to the constraint:− y0 ≤ Bi0 ≤ y0 (2.6)then the maximum loan-to-income ratio is 1, and households may save as much as their income ifdesired14.14The interest rate on deposits is rL, fixed, exogenous, and assumed as the opportunity cost of the bank.25At t = 1, households type i will be part of the set (i, j) ∈ {(i,e),(i,u)}, and will maximize:maxc(i, j)1 ,h(i, j)1 ,d(i, j)B ,d(i, j)Mu(c(i, j)1)+φu(h(i, j)1)+βδu(p1h(i, j)1)(2.7)d(i, j)B and d(i, j)M denote the default choices for unsecured and secured loans. B(i, j)1 and M(i, j)1 denote theunsecured and secured loan repayments.The flow budget constraints at t = 1 is:c(i, j)1 + p1h(i, j)1 ≤ y(i, j)1 + p1h(i, j)0 −M1(p1,hi0,Mi0,RiM)−B1(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 ,K) (2.8)Equation (2.8) shows durable nature of the housing stock, as it remains as part of the households’wealth at t = 1. The right-hand-side of the budget constraint corresponds to the cash-on-hand that thehouseholds have after deciding if filing for personal bankruptcy, and will be denoted by:W (i, j)1 = y(i, j)1 + p1hi0−M1(p1,hi0,Mi0,RiM)−B1(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 ,K)The households’ optimal consumption and housing policies at t = 1 are solved analytically, as afunction W (i, j)1 , and are included in the appendix.A useful economic quantity for the analysis of the the households’ default choices, and loan pay-ments, is the home equity:E(i, j)1 = p1hi0−Mi0RiM (2.9)The following subsections present the debt payments and default policies for the secured andunsecured loans, which lead to the solution of the household problem at the last period, based on thethe cash-on-hand, and the rest of the economic quantities of the model.Secured Loan Payments and DefaultHouseholds will repay their secured loans if the home equity is positive (E(i, j)1 ≥ 0), otherwise, theywill default on their secured obligations, and the housing stock will be foreclosed by the bank. Thus,the households’ secured loan default policy is:dM(p1,hi0,Mi0,RiM)=1 if E(i, j)1 < 00 if 0≤ E(i, j)1and the debt repayment is:M1(p1,hi0,Mi0,RiM)=p1hi0 if E(i, j)1 < 0Mi0RiM if 0≤ E(i, j)1(2.10)26Unsecured Debt Payments and DefaultThe unsecured debt payments are directly related to the financial benefit of filing for personal bankruptcy.Beside this point, and as previously mentioned, an important change that the 2005 BAPCPA intro-duced is that only households whose annual income is below the state median are allowed to file forbankruptcy. Thus, I assume that employed households (income above the state median) will alwaysrepay their unsecured loans, and unemployed households will evaluate if filing for bankruptcy.Employed Households Unsecured Loan Payments and DefaultEmployed households (i, j) ∈ {(g,e),(b,e)} will repay their unsecured loans, then their default andrepayment policies are:dB(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 = ye,K)= 0B1(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 = ye,K)= Bg0RgB if (i, j) = {(g,e),(b,e)} (2.11)The employed households cash-on-hand after repaying their unsecured loans is:W (i, j)1 = ye+max{p1hg0−Mg0 RgM,0}−Bg0RgB if (i, j) = {(g,e),(b,e)} (2.12)Unemployed Households Unsecured Loan Payments and DefaultFor the unemployed households, (i, j) ∈ {(g,u),(b,u)}, the unsecured debt payments are determinedby the financial benefit from filing for bankruptcy. Thus, unemployed households will file for bankruptcyif their cash-on-hand after bankruptcy is greater than after fully repaying their unsecured loans.If an unemployed household files for bankruptcy, the state Trustee evaluates the liquidation ofthe household’s assets, specifically its house. If the home equity is below the homestead exemption,E(i, j)1 ≤ K, then the Trustee does not liquidate the house, and fully discharges the unsecured loan.Now, if the home equity is above the homestead exemption, E(i, j)1 > K, then the Trustee liquidates thehouse, repays the secured loan, gives the household the exempted value K, and the remaining value,min{E(i, j)1 −K,B0RB}, goes to repay the unsecured lender. These cases are detailed in the rest of thissubsection.Case 1: E(i, j)1 < 0In this case, as the household does not have home equity, it will default on its unsecured loan ifthe payment is greater than a fixed filing cost C ∈ [0,yu], which is associated to legal fees. Formally:dB(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 = yu,K)=1 if Bi0RiB >C0 if Bi0RiB ≤C27and the unsecured loan payment is:B1(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 = yu,K)=0 if Bi0RiB >CBi0RiB if Bi0RiB ≤C (2.13)The cash-on-hand of the unemployed household (i, j) ∈ {(G,u),(B,u)} with negative Home Eq-uity, E(i, j)1 < 0 is:W (i, j)1 =yu−C if Bi0RiB >Cyu−Bi0RiB if Bi0RiB ≤C (2.14)Case 2: 0≤ E(i, j)1In this case, the household’s cash-on-hand after bankruptcy is the sum of its income, plus the homeequity after bankruptcy, min{E(i, j)1 ,K}, minus the bankruptcy cost. If this amount is greater than thecash-on-hand after paying the unsecured loan, yu +E(i, j)1 −Bi0RiB, the household files for bankruptcy,thus the default policy is:dB =1 if yu+min{E(i, j)1 ,K}−C ≤ yu+E(i, j)1 −Bi0RiB0 if yu+min{E(i, j)1 ,K}−C > yu+E(i, j)1 −Bi0RiBand the unsecured loan payment is:B1 =min{Bi0RiB,max{E(i, j)1 −K,0}}if yu+min{E(i, j)1 ,K}−C ≤ yu+E(i, j)1 −Bi0RiBBi0RiB if yu+min{E(i, j)1 ,K}−C > yu+E(i, j)1 −Bi0RiB(2.15)The unemployed households, (i, j)∈{(G,u),(B,u)}, cash-on-hand after filing for personal bankruptcyis:W (i, j)1 = max{yu+min{E(i, j)1 ,K}−C,yu+E(i, j)1 −Bi0RiB}(2.16)To summarize this subsection, Figure 2.1 shows the cash-of hand, for the described cases, as afunction of the household’s home equity E(i, j)1 :28E(i, j)10 K K+Bi0RiB−Cyu+K−CW (i, j)1yu−CFigure 2.1: Cash-on-Hand for unemployed household (i, j) = {(i,u)}, as a function of the homeequity E(i, j)1 , for the Homestead Exemption K.The green line in Figure 2.1 illustrates the Case 1, as in this case, if the household has no homeequity to protect, it will file for bankruptcy if the unsecured loan amount is greater than the filing cost,as the unsecured loan is discharged for sure. The remaining lines in the figure illustrate Case 2. Theblue line shows the case when the home equity is fully protected by the homestead exemption, thus theunsecured loan is discharged. The red line represents the case on which the home equity is above thevalue of the homestead exemption, then the household keeps the exempted value K, and the remaininghome equity goes to repay a fraction of the unsecured loan. Finally, the brown line shows the caseon which the household fully repays its unsecured loan, as there is no financial benefit in filing forbankruptcy.Figure 2.1 shows a strong non-linearity in the households’ cash-on-hand, induced by the personalbankruptcy procedure. This non-linearity will required the use of numerical techniques to solve themodel.2.3.2 The Bank’s ProblemThere is a competitive representative bank, which supplies one-period secured and unsecured loans tothe households. Loans are granted at t = 0, and payments are collected at t = 1.Initially, the bank faces imperfect information about the households’ type, that is, the bank cannotidentify if the household is either type g or b, so it first evaluates the pooling equilibrium. The conceptof pooling assumed here follows Dubey and Geanakoplos (2002), as it implies that the bank offers aunique rate consistent with the expected aggregate payment of the pool. These contracts are observedin several markets as they reduce the information needed to quantify the risk of the loan, as no bilateralnegotiations are sustained and the bank only looks to characterize the aggregate pool repayment.Perfect competition in the model relates to the deterrence principle introduced by Riley (1979)informational equilibrium, and in its application to credit markets as presented in Milde and Riley29(1988). This refinement indicates that any potential defector from the pooling equilibrium is likely tobe deterred, if predictable reactions by others will make its initial defection unprofitable, making thezero-profit contract the only one observed in equilibrium.A key characteristic of the model is that the loan repayments are not only affected by the householdtype - idiosyncratic income risk - but also by the magnitude of the homestead exemption K, the focus ofanalysis of this work. As shown in the household’s problem, a higher homestead exemption increasesthe financial benefit from filing for personal bankruptcy, thus increasing the default probability andreducing the loan payments. Therefore, the expected pool payments are negatively affected by themoral hazard and adverse selection problems present in the pooling equilibrium. In such case, the bankincentives to invest in monitoring, and migrate from a pooling equilibrium to a separating equilibrium,will increase as the credit losses from riskier households escalate.The monitoring technology is included in the model as an option owned by the bank. If the bankpays a fixed cost Ψ, it will be able to identify the households’ type at t = 0. If the bank invests, itdeviates from the pooling equilibrium by offering separating contracts. A key assumption is that thebank will only accept household in their respective contract, as attempt from riskier households tomimic with safer households will be immediately rejected.Formally, the bank’s decision at time zero involves two steps. In the first the bank evaluates theinvestment in monitoring based on the equilibrium it thinks will prevail. If the bank believes that thepooling equilibrium will prevail, then the bank’s best action should be not to invest, as monitoring isunprofitable. Now, if the bank considers that the separating equilibrium will prevail, then the bank’sbest action should be to invest in monitoring, and not monitoring should be unprofitable. In the second,based on the monitor/don’t monitor decision. the bank posts interest rate offers to borrowers. Then,the households solve their maximization problem considering the available loan contracts, choosingthe one that maximizes their expected utility. In the second period of the model, the household’s riskyincome is realized, and the option to file personal bankruptcy evaluated, consequently defining theloan payments, which are finally collected by the bank.The option to invest in the monitoring technology, and deviate from the pooling equilibrium to theseparating equilibrium, is determined by the profitability of the alternative separating contracts. If thecost of the monitoring technology is greater than the benefit of deviating to the separating equilibrium,then the bank will stay on the pooling equilibrium. Now, if the cost is lower, then the bank will havea clear incentive to pay for the monitoring technology and offer the separating contracts. As theother banks in the market will also recognize the same profit opportunity, all banks in the market willdeviate, and the only contract that will remain is the zero-profit separating contract (which includesthe cost of monitoring technology).The profit from investing in the monitoring technology is measured as following. If a bank investsin the monitoring technology, it deviates from the pooling equilibrium by offering an alternative sep-arating contract. This contract is only available for safer households - type g - and charges a slightlylower interest rate than the pooling secured, and unsecured, loan contracts. As the riskier households30are not accepted in these new contracts, and the charged interest rates are almost the same, these de-viation contracts will exhibit positive profits, while the previously offered pooling contract becomecostly.The relationship between the cost and the deviation benefit is fundamental for the existence of apooling equilibrium, as if the monitoring cost is low, the separating equilibrium will be observed al-ways, as if any bank offers the pooling equilibrium, only risky households will demand such contracts,leading to losses. On the other hand, if the monitoring cost is high, the banks will not have significantincentives to deviate from the pooling equilibrium, as all the potential benefit from such deviation willbe paid in monitoring.To understand how the monitoring technology modifies the bank’s problem, I present the pool-ing equilibrium and the separating equilibrium, and formalize the conditions under which it will beprofitable for a bank to deviate.The Pooling EquilibriumIf the bank decides not to invest in the monitoring technology, it will face imperfect information aboutthe households’ type, thus the bank will charge the same interest rate for each loan type. The interestrates will be determined by the aggregate loan demands, and expected loan repayments. As the lendingmarket is competitive, the expected return on each type of loan will equate to the bank’s opportunitycost15, RL = 1+ rL.For the secured loans Mi0, the bank solves for the interest rate RM that satisfies the market equilib-rium condition:∑i={g,b}fiMi0 =1(1+ rL)E0[∑(i, j)={(g,e),(g,u),(b,e),(b,u)}f(i, j)M1(p1,hi0,Mi0,RM)](2.17)where fi and f(i, j) are the mass of each set of households:fi =α if i = g(1−α) if i = b (2.18)f(i, j) =αpig if (i, j) = (g,e)α(1−pig) if (i, j) = (g,u)(1−α)pib if (i, j) = (b,e)(1−α)(1−pib) if (i, j) = (b,u)(2.19)For the unsecured loans Bi0, the bank solves for the interest rate RB that satisfies the equilibriumcondition:15The opportunity cost can be interpreted as the deposit rate paid by the bank31∑i={g,b}fiBi0 =11+ rLE0[∑(i, j)={(g,e),(g,u),(b,e),(b,u)}f(i, j)B1(p1,hi0,Mi0,RM,Bi0,RB,y(i, j)1 ,K)](2.20)These market equilibrium conditions reflect the pooling loan contract and the competitive lendingassumption, as there are no expected profits beyond the opportunity cost.The Separating EquilibriumIf the bank decides to invest in the monitoring technology, it pays the fixed cost Ψ and it is able toidentify the households’ type. The technology is assumed to be paid once at the first period, t = 0.This cost is transferred to the loan interest rates, and it reduces the expected profits from lending, thusit affects the interest rates charged for each loan.As in the imperfect information problem, the lending markets are competitive, but in this caseeach rate has to individually satisfy the equilibrium conditions. For the secured loan Mi0, the interestrates RgM and RbM are found individually for each household type i ∈ {g,b} by solving the followingequilibrium condition:fiMi0+Ψ fiMi0∑i={g,b} fi(Mi0+Bi0) = 1(1+ rL)E0[∑(i, j)={(i,e),(i,u)}f(i, j)M1(p1,hi0,Mi0,RiM)](2.21)For the unsecured loan Bi0, the interest rates RgB and RbB are found by solving:fiBi0+Ψ fiBi0∑i={g,b} fi(Mi0+Bi0) = 1(1+ rL)E0[∑(i, j)={(i,e),(i,u)}f(i, j)B1(p1,hi0,Mi0,RiM,Bi0,RiB,y(i, j)1 ,K)](2.22)From these equilibrium conditions, it is possible to notice that if the total expected profit of thebank is computed, this is, the sum of Equations (2.21) and (2.22) for both households’ types, the totalcost paid for the monitoring technology is the fixed cost Ψ.Conditions to Invest in the Monitoring TechnologyBased on the information available before investing in the monitoring technology, that is, preferences,distributions, but not the households’ type, the bank estimates the expected loan demands for the creditpool. The bank uses these estimations to compute the potential profit from investing in the monitoringtechnology. This profit is measured as follows, first the bank pays the fixed cost Ψ, and offers anhypothetical alternative contract with a slightly lower interest rate than the estimated pooling contract,but in this new contract only type g households will be accepted.As the type g households have a lower default probability than the riskier households (type b), thealternative separating contract is profitable, being the upper bound of the investment profit induced by32the same pooling contract, but just including safe households. Formally:Πg =1(1+ rL)E0[∑(i, j)={(g,e),(g,u)}f(i, j)M(i, j)1 +B(i, j)1]− fg(Mg0 +Bi0)(2.23)where {M(i, j)1 ,B(i, j)1 } are the loan payments, for the pooling equilibrium loans to the safe household(type g), {Mg0 ,Bg0}.Then, the bank will invest in the monitoring technology if Πg >Ψ, that is, by an amount sufficientto at least cover the monitoring costs16. In such case, the market equilibrium observed will be aseparating equilibrium.Notice that in the separating equilibrium the only contracts offered by the bank are those withzero-profit17. If the bank offers a profitable separating contract, there is a “reaction” from the rest ofthe market that will take the safer households away from the bank, by offering an alternative separatingcontract. This is the reactive equilibrium introduced by Riley (1979), as the deviating bank will bedeterred from offering the potentially profitable separating contract by the possibility that the rest ofthe market will underbid it out of the market.2.3.3 EquilibriumTo find the equilibrium of the presented model, it is important to define the strategies to be consideredby the households and the bank. The optimal households’ strategy is the amount of secured andunsecured debt to demand. Their beliefs are constructed over the interest rates that the bank willcharge them for any amount of debt. For the bank, its strategy concerns whether to invest in themonitoring technology or not, and what interest rate to charge for any amount of debt requested bythe households. The bank’s beliefs are constructed over the market competition and the householdbehavior, and are fundamental to estimate the household’s loan payments.Specifically, the bank believes that the credit market is perfectly competitive, as the representativebank behavior and offered contracts are determined by the notion of deterrence. This concept isimportant as it will discipline the market, as any potential defector from an equilibrium is likely to bedeterred if predictable reactions by others will make his initial defection unprofitable.For the separating equilibrium, as the bank can identify the riskiness of the households, it will offersecured and unsecured loan contracts to each household type, so the off-equilibrium path beliefs forthe households that support the separating equilibrium and solve the incentive compatibility problem,are that only safe household are accepted in the low-risk household contract, so riskier households arerejected for sure if they apply to the safer household contract, deterring them from trying to mimic.Now, given that the high-risk contract will have a higher interest rate than the low-risk contract, the16Notice that in the definition of Πg the monitoring cost is not included. If this cost is included the investment conditionbecomes Πˆg =Πg−Ψ> 017This net profit will include the monitoring cost Ψ33safer households will never apply to such loan as it will reduce their expected utility through higherfuture payments.Formally, the equilibrium of the presented model are the households’ policy functions for non-durable consumption{ci0,c(i, j)1}, housing stock consumption{hi0,h(i, j)1}, borrowing policies{Mi0,Bi0},loan repayments{M(i, j)1 ,B(i, j)1}, the house prices {p0, p1} and the interest rates for the secured andunsecured loans{RiM,RiB}such that:1.{hi0,h(i, j)1},{ci0,c(i, j)1},{Mi0,Bi0}, and{M(i, j)1 ,B(i, j)1}are the optimal decision rules for thehousehold problem, Equations (2.3) and (2.7), subject to the the constraints, Equations (2.4),(2.5), (2.6) and (2.8).2. The housing market clears:(a) t = 0:∑i={g,b}fihi0 = h¯(b) t = 1:∑i={g,b}∑(i, j)={(i,e),(i,u)}f(i, j)h(i, j)1 = h¯3. The interest rates{RiM,RiB}solve the lender’s problem for the optimal households’ borrowingpolicies{Mi0,Bi0}and loan repayments{M(i, j)1 ,B(i, j)1}.(a) Pooling Equilibrium:i.∑i={g,b}fiMi0 =11+ rLE0[∑i={g,b}∑(i, j)={(i,e),(i,u)}f(i, j)M1(p1,hi0,Mi0,RiM)]ii.∑i={g,b}fiBi0 =11+ rLE0[∑i={g,b}∑(i, j)={(i,e),(i,u)}f(i, j)B1(p1,hi0,Mi0,RM,Bi0,RB,y(i, j)1 ,K)](b) Separating Equilibrium:i. For each i ∈ {g,b}:fiMi0+Ψ fiMi0∑i={g,b} fi(Mi0+Bi0) = 1(1+ rL)E0[∑i={g,b}∑(i, j)={(i,e),(i,u)}f(i, j)M1(p1,hi0,Mi0,RiM)]ii. For each i ∈ {g,b}:fiBi0+Ψ fiBi0∑i={g,b} fi(Mi0+Bi0) = 1(1+ rL)E0[∑i={g,b}∑(i, j)={(i,e),(i,u)}f(i, j)B1(p1,E(i, j)1 ,Bi0,RB,y(i, j)1 ,K)]344. The aggregate non-durable consumption is exogenously supplied, and defined as:(a)C0 = ∑i={g,b}fici0(b)C1 = ∑i={g,b}∑(i, j)={(i,e),(i,u)}f(i, j)c(i, j)1The supply is assumed to be perfectly elastic, thus the aggregate non-durable consumption ateach period {C1,C2} are always at equilibrium and sold at unit price.2.3.4 Model CalibrationFollowing Athreya (2006) , Jeske et al. (2013), and Mitman (2016), the preference parameters areβ = 0.95, φ = 0.1, γ = 3.9, and δ = 2. The bequest parameter δ has a wide range of values in therelated literature, I assume it to be 2, which gives the bequest motive relevance, but it is not the maindriver of the results.I assume that the fraction of good households is α = 0.713, which resembles the U.S. state averageof prime lenders. This distribution can be related to the model as I distinguish between good andbad credit households. The transition probabilities are set up to make the fraction of unemployedhouseholds in the second period similar to the fraction of bad households (type b) in the first period.(pig,u pig,epib,u pib,e)=(0.83 0.170.42 0.58)The households’ income at t = 1 can either be ye = 3 or yu = 1. These values are selected togenerate a sizable income risk for both household’s types. The income at t = 0 is set to equal theaggregate income at t = 1, so there is no aggregate uncertainty in the model.y0 =∑i={g,b}∑(i, j)={(i,e),(i,u)} f(i, j)y(i, j)1∑i={g,b} fi= 2.64Finally, the lender’s discount rate is set to rL = 0.03, which is similar to the historical U.S. TreasuryBills annual return, a common proxy for the deposit rate. The personal bankruptcy cost is set to bezero for simplicity. The model was solve for positive dead-weight costs, and if this value is positiveand not large enough to deter all households from defaulting, the presented conclusions remain.To resume, Table 2.8 presents all the selected parameters.35Table 2.8: Model ParametersThis table presents the parameters used to solve the model, obtained from Athreya (2006), Jeske et.at. (2013), and Mitman(2016).Parameter Description Value Commentβ Time discount factor 0.95 Mitman (2016)γ Risk aversion 3.91 Jeske et al. (2013)φ Housing consumption utility 0.10 Mitman (2016)δ Bequest motive 2.00α Household Distribution 0.713 Mian and Sufi (2011)ye Employed income 3yu Unemployed income 1In the next section I include a brief description of the solution algorithm.2.3.5 Equilibrium ComputationThe model equilibrium is computed in two steps, first the bank posts pooling contracts that the house-holds use to compute their optimal consumption and borrowing policies. As a function of the aggregatehouse prices and the posted interest rates for the secured and unsecured loans { p˜0, p˜1}, and{R˜iM, R˜iB}.The household’s optimal policies are computed using backward induction. For a given p˜1, house-holds’ housing stock h˜i0 and loans{M˜i0, B˜i0}, the optimal consumption and debt repayment policies att = 1 can be solved analytically. Using these optimal policies, the households searches over the set offeasible loans, housing and non-durable consumption at t = 0 until their utility is maximized.Once the households’ problem is solved for the given aggregate prices, their optimal demandfor loans{M˜i0, B˜i0}, and the expected loan repayments{M˜(i, j)1 , B˜(i, j)1}, are used to evaluate if thesequantities satisfy the bank’s conditions presented in Equations (2.21) and (2.22). If for the initial loanrates{R˜iM, R˜iB}the equilibrium conditions are not met, the lender will either raise or reduce the ratesdepending on the excess or lack of expected excess profit for each type of loan.With respect to the housing market, if for the initial prices { p˜0, p˜1} there is an excess or lack ofhousing demand, these prices are increased or decreased respectively.Once the house prices and interest rates are updated, the household’s problem is solved using thenew market prices, their consumption and borrowing policies are re-calculated, and the equilibriumconditions are re-checked individually. This process is repeated until the described market equilibriumis achieved.Once that the pooling equilibrium is computed, the bank evaluates the profit from deviating to theseparating contract using Equation (2.23). If the deviation is profitable the bank repeats the equilibriumcomputation but now solving the separating equilibrium following the same described procedure, butthe interest rate of each loan type, for each household type, is computed independently.362.3.6 Numerical ResultsTo understand the effects of the magnitude of the homestead exemption on the loan market equilib-rium, and to the incentives of the bank to monitor, I solve the presented model using the presentedparameters and methodology.The model is solved for two levels of the homestead exemption, K = 1, and a K = 3. These valuesare selected so the homestead exemption is in most cases above, or below, the home equity.In the first stage the bank decides whether to invest or not in the monitoring technology. Thischoice is made using the estimated deviation profit as presented in previous sections. Based on theestimated deviation profits, I identify the values of the monitoring technology costΨ that support eachpotential equilibrium. Then, in the second stage, I find the market equilibrium for several monitoringcosts in the identified ranges, and the results are discussed, specifically its relation with the empiricalresults.Stage 1: The Bank’s Investment DecisionAs the bank initially faces imperfect information about the households’ type, it cannot identify if thehouseholds are either type g or b, so it first evaluates the option to invest in the monitoring technology.As mentioned, the bank uses the estimated pooling equilibrium to decide whether to invest in themonitoring technology. In that case, the households enter the loan pool, they commit to an identicalinterest rate payment per loan unit demanded, however, different households will have a different pay-ment policy, as they payments are related to their future income (which is risky and different for eachtype), the option to file for personal bankruptcy, and their previously made payment commitments.For the selected parameters, the estimated pooling equilibrium is:37Table 2.9: Loans and interest rates - Estimated pooling equilibrium for K = 1 and K = 3This table presents the equilibrium results of the lending market for the pooling equilibrium. The key characteristic analyzedis the value of the homestead exemption K. The rest of the model parameters are presented in the calibration section.Panel A: Equilibrium Demand for LoansK = 1 K = 3M0(g) 0.58 0.00M0(b) 0.64 0.00B0(g) 0.29 0.66B0(b) 0.47 1.51D0 0.95 0.91Panel B: Equilibrium Loans Gross RatesK = 1 K = 3RM 1.03 -RB 1.51 1.64For the estimated pooling equilibrium, the bank’s profits from investing in the monitoring tech-nology, as shown in Equation (2.23), are Πg(K = 1) = 0.05 and Πg(K = 3) = 0.15, therefore itsincentives to invest in the monitoring technology increase with the magnitude of the homestead ex-emption. Specifically, if the monitoring cost Ψ is lower than Πg(K = 1), then the bank will deviate tothe separating equilibrium for both levels of the homestead exemption, and consequently the poolingequilibrium will not be observed.If Ψ is greater than Πg(K = 1), but lower than Πg(K = 3), then the bank will deviate from thepooling to the separating equilibrium just for the high exemption level. Then the pooling equilibriumwill be observed for low exemption, but the separating equilibrium will be observed for the highexemption.Finally, ifΨ is greater thanΠg(K = 3), then the pooling equilibrium is observed in the loan market,as the separating contract profitability is not large enough to compensate the monitoring technologycost.In the following section, the separating equilibrium is computed using the different values of Ψ,that are relevant for the described cases, this is, on which the bank has incentives to deviate effectivelyfrom the pooling equilibrium.Stage 2: Loan Market EquilibriumIn this section, and based on the level of the monitoring cost, I identify three different potential loanmarket equilibriums. In the first, the monitoring cost Ψ is lower than Πg(K = 1), then the separating38equilibrium is observed for both levels of the homestead exemption. In the second, Ψ is greater thanΠg(K = 1) but lower than Πg(K = 3), which implies that the separating equilibrium is only observedfor the high homestead exemption level. Finally, in the third case Ψ is greater than Πg(K = 3), thusthe bank does not invest in the monitoring technology, so for both homestead exemption levels theloan market equilibrium is the pooling equilibrium.Case: 0≤Ψ<Πg(K = 1)For the selected parameters, this case happens for a monitoring cost in the range 0 ≤ Ψ < 0.05.Several values in this range where tested, but the main intuitions are the same as in the case Ψ= 0.00,which will be presented next.In this case, as monitoring is profitable for both levels of the homestead exemption, the bank willalways invest and the pooling equilibrium will not be observed, then for both levels of the exemptionsa different interest rate is charged for each household type, and loan type.The separating equilibrium in the loan market for Ψ= 0.00 is:Table 2.10: Loans and interest rates - Separating equilibrium for K = 1 and K = 3 - Ψ= 0.00This table presents the numerical results for the equilibrium in lending market. The key characteristic subject of analysis inthis table is the value of the homestead exemption K..Panel A: Equilibrium Demand for LoansK = 1 K = 3M0(g) 0.54 0.00M0(b) 1.04. 0.00B0(g) 0.39 1.21B0(b) 0.00 0.78D0 0.96 1.09Panel B: Equilibrium Loans RatesK = 1 K = 3RM(g) 1.03 -RM(b) 1.03 -RB(g) 1.20 1.23RB(b) - 2.35Table 2.10 shows that for the separating equilibrium, with monitoring cost in the range 0 ≤ Ψ <0.05, the total amount of loans increases. This increment is driven by loans to safer households,thus, for the selected parameters, the presented separating equilibrium shows an increment in the total39amount of loans, with a reduction in the riskiness of the loan portfolio, as the fraction of loans to therisky households goes from 31% to 21%.The separating equilibrium is not consistent with the empirical findings, as it shows a counter-factual increment in the total amount of loans, driven by the safer loans, as the riskier householdsexperience a a reduction on their loans. For alternatives values of Ψ in the presented range, the totalamount of loans still increases as in the presented case, although the difference between the low andhigh homestead exemption cases is smaller.It is important to remark that as the bank is able to identify the riskiness of the households afterinvesting in the monitoring technology, it will offer a contract to each household type for secured andunsecured loans. This off-equilibrium path beliefs solve the incentive compatibility problem, as it isclear that the riskier households (type b) will be better off mimicking the safer households.The key assumption is that as the bank has already perfectly identified the households, so it willonly accept safe households in the low-risk contract, so riskier households are rejected if they applyto the low-risk contract. For the high-risk contract, the bank accepts any household in the pool. Theinterest rate in the high-risk contract is calculated for risky households, so accepting a safe householdwill make the contract profitable, although, because this contract is not optimal for safer households,this case will not happen in equilibrium.Case: Πg(K = 1)<Ψ≤Πg(K = 3)For the selected parameters, this case happens for a monitoring cost in the range 0.05 < Ψ ≤0.15. As in the previous case, several values in this range where tested, but the presented results arecalculated for Ψ= 0.10, the mid point of the range.In this case, monitoring is profitable only for the higher level of the homestead exemption, thus thebank will invest only in such case, and the pooling equilibrium will be observed for low homesteadexemption, as in this case, the profit of deviating from the pooling equilibrium does not compensatethe cost of the monitoring technology.Table 2.11 presents the pooling equilibrium for K = 1, and compares it with the separating equi-librium in the loan market for K = 3, and Ψ= 0.10.40Table 2.11: Loans and interest rates - Pooling equilibrium for K = 1, separating equilibrium forK = 3 - Ψ= 0.10This table presents the numerical results for the equilibrium in lending market. The key characteristic subject of analysis inthis table is the value of the homestead exemption K..Panel A: Equilibrium Demand for LoansK = 1 K = 3M0(g) 0.58 0.00M0(b) 0.64 0.00B0(g) 0.29 1.03B0(b) 0.47 0.71D0 0.95 1.09Panel B: Equilibrium Loans RatesK = 1 K = 3RM(g) 1.03 -RM(b) 1.03 -RB(g) 1.51 1.35RB(b) 1.51 2.59Table 2.11 shows that for the separating equilibrium, with a monitoring cost in the range 0.05 <Ψ ≤ 0.15, the total amount of loans decreases, and this reduction is focused on the loans to riskierhouseholds, thus, for the selected parameters, the separating equilibrium shows a decrease in the totalamount of loans, with a reduction in the riskiness of the loan portfolio, as the fraction of loans to therisky households goes from 34% to 22%.For this case, as the homestead exemption increases, the bank’s incentives to monitor also rises,making the bank deviate to the separating equilibrium. The observed results of this deviation areconsistent with the empirical findings, as it shows a reduction in the total amount, mainly focused onthe secured loans, complemented with a reduction of the loans to riskier households.In comparison to the previous case, the increment in the cost of the monitoring technology be-comes important for the loan demands. The monitoring cost makes loans more expensive to thehouseholds, as the bank transfers the monitoring technology cost to the rates. This is the channelbehind the reduction in the total amount of loans, in comparison to previous case on which the cost ofthe technology is lower.In this line, for alternatives values of Ψ in the presented range, the total amount of loans stillincreases (as in the previous case) if the cost of the technology is among the smallest values of theinterval, but for values near the center of the interval and up, the decreases in loans described is41consistently observed. A separating case with a monitoring cost larger that the higher bound of theidentified range was tested. In such case, households are observed to only demand secured loans anddo not default, as just by the transfer of the monitoring costs, the loan interest rates become highenough to avoid increasing them further by defaulting, even for the safer households.Therefore, the results of this case indicate that, from the presented alternatives, the observed em-pirical evidence is consistent with a bank choosing optimally to monitor for a higher homestead ex-emption magnitude. The magnitude of the monitoring cost is important not only to determines theincentives of the bank to deviate to the separating equilibrium, it also affects the loan interest rates thatthe households will pay. As the bank transfer the investment cost, the interest rates raise and the totalamount of loans decreases, in comparison to the pooling equilibrium observed for the low homesteadexemption.Now, as this case matches the main empirical findings presented, it is useful to review the equi-librium of the housing market observed for this case. Table 2.12 presents the housing equilibriumfor the pooling equilibrium with K = 1, and compares it with the housing market equilibrium for theseparating equilibrium with K = 3, and Ψ= 0.10.Table 2.12: Housing Equilibrium - Pooling equilibrium for K = 1, separating equilibrium forK = 3 - Ψ= 0.10This table presents the numerical results for the equilibrium in the housing market. The key characteristic subject of analysisin this table is the value of the homestead exemption K..K = 1 K = 3h0(g) 5.06 5.47h0(b) 4.85 3.83P0 0.31 0.37Table 2.12 shows, as in most of the parametrizations tested, that a higher homestead exemptionrelates to higher prices (P0), as type g households increase their demand for housing. These house-holds have a lower probability of becoming unemployed and a higher expected income, hence, theyexchange future income for the possibility of having a greater housing sock, that will provide theminsurance against negative income shocks, through their option to file for personal bankruptcy. Thisincrement in the type g households’ housing demand is the channel behind the positive relation be-tween the homestead exemption and house price, and is driven by the increment in their loans, as theyhave a higher amount of wealth in the first period available to invest, while at the same time, riskierhouseholds are more constraint, being forced to reduce their housing consumption to sustain theirnon-durable consumption. Another factor to remember here is that the safer households constitute abigger fraction of the total of households, so smaller changes in their behavior will have a higher effectin the market price.42Case: Πg(K = 3)<ΨIn this case, the bank does not invest in the monitoring technology, hence the market equilibriumis the same as the pooling equilibrium presented in Table 2.9.Table 2.9 shows that for the low homestead exemption K = 1, the households favor secured loansas their interest rates are lower. For a low homestead exemption, the financial benefit from personalbankruptcy is limited, as the households will keep only a small fraction of their wealth at default.This said, they will not demand high amounts of unsecured loans, as most of its home equity will becollected to repay them.For a higher homestead exemption K = 3, the financial benefit from filing for personal bankruptcyis higher than for K = 1, consequently, the households will demand a higher amount of unsecuredloans, as in most cases, if they file for personal bankruptcy they will keep most of their home equity.This increment in the unsecured loan demand is stronger for riskier households, as they have a higherprobability of becoming unemployed, and therefore, of filing for bankruptcy and do not repay theirunsecured loan.This effect is also reflected in the change in the aggregate loan demand, as for K = 1 the loansto risky households correspond to 34% of the portfolio, while for K = 3 its loan share rises to 48%,showing the traditional result that as the increment of the homestead exemption (or the benefit frombankruptcy) relates to a reduction of total amount of loans, but in the pooling equilibrium, the riskinessof the portfolio rises. These results are not consistent with the presented empirical evidence, as I foundthat the the loan portfolio becomes safer as the homestead exemption increases.In this case, the increment in the moral hazard and adverse selection increase the bank’s incentivesto deviate from the pooling contract, by investing in the monitoring technology. Investing allows thebank to offer a new separating contract just for the safer household. As this contract will only acceptshouseholds with a higher probability of repayment, it generates positive profits, and the previouslyoffered pooling contract exhibit loses, as only the riskier, higher default probability households, areleft in it.2.4 ConclusionIn this paper I study how the magnitude of the homestead exemption relates to the supply and demandfor loans. As the homestead exemption specifies the amount of home equity that a household willbe entitled to keep at bankruptcy, one might expect that a higher exemption will increase the moralhazard on the part of the borrowers, leading to higher demand for loans, with higher delinquencyratios, while the lenders will respond with higher interest rates. Surprisingly, I find the opposite in thestate-level panel that I constructed, as the regression analysis shows that states with a higher homesteadexemptions relates to fewer secured loans granted, lower delinquency ratios on secured and unsecuredloans, lower interest rates, and higher house prices.To understand the economic mechanism behind these empirical results, I follow Mitman (2016)43and construct an equilibrium model on which a set of households face idiosyncratic income risk. Thesehouseholds get utility from non-durable and housing consumption, financing them with their income,secured and unsecured loans, and have the option to file for bankruptcy in a process that captures themain features of the personal bankruptcy code. Loans are provided by a competitive lender that pricedefault risk using the overall debt position and assets holdings of the household. Lenders are assumedto initially be unable to observe the riskiness of the future households income, but can invest in acostly monitoring technology to eliminate this information asymmetry.The mechanism of the model is as follows. A more generous homestead exemption increases thehousehold benefits after filing for bankruptcy, providing implicit insurance to the households againstnegative income shocks. The loan demand increases as the financial benefit of bankruptcy increases,while the demand for housing also increases pushing house prices up. These bankruptcy benefits forthe households are mirrored by a rise in the credit losses faced by the lender. As unsecured debt ispartially or fully discharged, the lender price each loan accordingly to its specific credit risk.Although, in the case on which the lender can pay for the monitoring technology, the low riskhouseholds no longer provide subsidies to the riskier households, eroding their potential pooling ad-vantage as they are now subject to higher interest rate as the exemption increases and the monitoringcosts are transferred. For the theoretical results consistent with the empirical findings, this effectproduces an aggregate reduction in the secured loans, as the bank deviates from the pooling equilib-rium observed for low levels of the homestead exemption, to a separating equilibrium for a higherexemption, on which low risk households increase their demand for unsecured loans, while the totalaggregate amount of debt is reduced. This mechanism is consistent with the empirical evidence indi-cating that higher exemptions lead to a lower fraction of secured loans issued, with lower rates anddelinquency, with higher overall house prices.44Chapter 3The Valuation of Fisheries Rights withSustainable Harvest3.1 IntroductionThe economic sustainability of fisheries is an ongoing concern for consumers, fishers, governments,intergovernmental organizations, and academics. Overfishing occurs when more fish are caught thanthe natural population growth, and as Ye and Gutierrez (2017) indicate, during the last decade theworldwide percentage of stocks classified as overfished remained stable at 30%, pointing to a failureof self-regulation and a misalignment between economic incentives and conservation. This is thestarting point of several efforts from governments and institutions around the world to regulate thesemarkets and achieve a sustainable equilibrium.The Food and Agriculture Organization of the United Nations (FAO (2008)) indicates that animportant part of solving the overfishing problem is to “adjust fishing capacity to sustainable levelsthrough policy and regulations, including judicious use of subsidies and eradication of illegal, un-reported and unregulated fishing.” Nowadays one of the most used policy devices is the IndividualVessel Quota (IVQ) system, an allocation of extraction rights of the total annual fish catch (TAC)in the form of transferable quota shares which limits not only the total catch, but also controls theindividual fisher’s landings.Although the IVQ policy has been successful in limiting overexploitation, there is still an ongo-ing discussion on the optimal economic level of the quota. This paper develops a methodology ina dynamic setting to determine the total annual fish catch which maximizes the value of the natu-ral resource. This optimal TAC not only maximizes the value of the resource, but also assures thesustainability of the resource.This chapter develops and implements a stochastic optimal control approach to determine theharvest (the control) that maximizes the value of the resource by modeling fisheries as a complexfunction on the variables underlying the value of the industry, in this case, the resource stock (biomass)45and the fish price. Uncertainty is introduced in the analysis by allowing these variables to followdynamic stochastic processes. The model has some features similar to Morck et al. (1989) for forestrybut in this case the resource growth is specific for a fish population, and operational cash flows aremodeled as an explicit function of the biomass and the total harvest. In addition, we allow for a moregeneral price specification. For the biomass growth uncertainty we follow Pindyck (1984) and use alogistic growth function which explicitly captures the possibility of overpopulation and depletion. Forthe price of fish, we use a general log-normal price dynamics and let the data determine the particularform to use in our implementation of the model.To make the problem tractable we consider the case where several competitive price taking fish-eries can be represented by a single fishery endowed with the total annual fish catch (TAC) whoseproperty rights are well defined. To simplify the model we also assume that the fishery faces no taxesand that production can be opened and shut down at no cost; though these features could be easilyincorporated in the model.The model is solved using a value-function iteration algorithm instead of the more traditional par-tial differential equation approach. The solution approach solves for the optimal dynamic harvestingpolicy of a representative fishery, and then uses this policy to value the marine harvesting rights. Thesolution also allows us to study how the optimal level of harvesting relates to the two state variables inour model, the biomass and the fish price, and how these rights will optimally evolve with stochasticchanges in the state variables. Based on the optimal policy it is possible to simulate the dynamicsof the biomass subject to stochastic shocks and optimal harvesting, illustrating how the biomass willevolve over a specific time horizon.Most of the current literature on fisheries assumes that prices are constant or evolve deterministi-cally (Clark and Kirkwood (1986), Sethi et al. (2005)). A significant improvement of our model is thatit includes stochastic prices which turns out to be an important issue. Our analysis also expands the lit-erature by including in the cost function not only fixed operational costs, but also variable costs whichare related to the biomass through the fisheries efficiency (catchability), and a quadratic componentwhich incorporates an increasing marginal cost.To examine the model implications, we apply it to the British Columbia halibut fishery. Combin-ing multiple sources of information, we constructed time series for the halibut biomass, total harvest(landings), and price, and using this data all required parameters of the model are estimated. Our esti-mates show that the volatility of the fish price growth is comparable in size to the estimated volatilityof the biomass growth, showing that when previous literature assumed that the fish price followeda deterministic path the fishery’s valuation problem is significantly underestimating the uncertaintyfaced by the fishers.The model results show that it is optimal for the representative fishery to preserve the biomassfor future harvesting, and that if the biomass suffers significant negative shocks then it is optimal todrastically reduce exploitation, even fully stopping the harvest in scenarios of low biomass or lowresource prices. That is, the optimal harvesting policy exhibits strong financial incentives to avoid the46extinction of the natural resource.The valuation of natural resources under uncertainty is a problem in which the Real Option ap-proach has proven to be appropriate in other contexts, as the work of Brennan and Schwartz (1985)and the significant body of work that followed indicate, but until now it has not been fully applied tomarine fisheries1.This paper is also related to the research on the valuation of marine resources usingReal Options. The closest paper to ours are Murillas (2001) and Poudel et al. (2013), in which thisapproach is used to value capital investments in fisheries using a model with uncertainty in the growthof the fish and in the capital, a linear production cost function with no fixed cost, but no uncertainty inthe resource price.Finally, this paper contributes to the marine fisheries literature by presenting empirical estimationsfor all the parameters required to solve the model. Data for the British Columbia halibut fishery is usedbecause of its availability. Data was collected from several sources including the International PacificHalibut Commission (IPHC) and Fisheries and Oceans Canada (DFO). Cost data is hard to find, asClark et al. (2009) already indicated, so we use the two available financial surveys performed for theDFO by Nelson (2009) and Nelson (2011) to identify the parameters of the modeled cost function.In summary, this paper presents an approach for valuing fisheries under the optimal harvestingpolicy, including a full parameter estimation for its implementation to study the optimal policies andvalue marine fishery rights for the British Columbia halibut. This approach is not only useful to valueextraction rights for a current level of our state variables, it also allows us to understand how it evolvesover time and presents evidence for the value of conservation of the natural resource and the possibilityof achieving an economic sustainable equilibrium.This section proceeds as following. The valuation model is presented in section 3.2. Section3.3 provides a detailed estimation of the model parameters for the British Columbia halibut fishery.Section 3.4 shows the numerical result for the estimated calibration and quantifies the impact of theinclusion of price volatility into the model. Finally, Section 3.5 gives our concluding remarks. Detailson the solution algorithm, the estimation and selection of the stochastic price model, a sensitivityanalysis for the cost function parameters, and the impact of the use of a social discount rate on theharvesting policy are provided in the Appendix.3.2 A Valuation Model of Marine Fisheries RightsIn this section we develop a dynamic stochastic economic model to study how fisheries should opti-mally harvest the resource. The value of the marine fishery is assumed to depend on two stochasticvariables: the biomass and the price of fish.Following Pindyck (1984) the dynamic of the biomass of the resource is assumed to follow:It+1 = It +G(It)−qt + ItσIε It+1 (3.1)1Exception are Nøstbakken (2006) and Kvamsdal et al. (2016)47Figure 3.1: Logistic Natural Growth Function for for the parameters γ = 0.8, Imax = 150where It is the biomass at year t, G(It) is the annual expected rate of growth of the biomass, qt is theannual harvesting rate and the stochastic control in the model, σI is the volatility of the unanticipatedshocks to the resource stock ε It , which are assumed to be i.i.d. standard normal.As in Clark (2010) and Nøstbakken (2006), the growth rate of the biomass is assumed to follow alogistic function and is presented in Equation 3.2. This function explicitly captures the fact that if thebiomass approaches its carrying capacity Imax, resources in the environment become scarce, reducingthe natural growth to zero2.G(It) = γIt(1− ItImax)(3.2)Figure 3.1 shows the previously mentioned logistic function features for the parameters γ = 0.8,Imax = 150:The second source of uncertainty is the resource price, which we assume follows the stochasticprocess:lnPt+1 = f (Pt)+g(Pt)εPt+1 (3.3)Where Pt is the unit fish price at year t, f (Pt) is the expected annual rate of change in the logarithmof the price, g(Pt) is the volatility of the unexpected price shocks εPt which are assumed to be i.i.d.standard normal. We assume that the price and biomass shocks are uncorrelated, that is E[ε It × εPt]= 0for all t. 3Consider an infinitely-lived value maximizing fishery, with the enough installed capacity for therange of harvests considered, and the right to harvest a particular fish specie. Then, the fishery’s annual2If the biomass becomes larger than the carrying capacity the natural growth becomes negative.3This assumption was initially made for computational convenience and can be easily relaxed, although we tested theindependence of the historical realizations of both stochastic processes finding that the correlation between them is 0.01,and not statistically different from zero.48cash flow from harvesting is equal to:pi(It ,Pt ,qt) = Pt ×qt − c(It ,qt) (3.4)c(It ,qt) is the operating cost function of harvesting qt given by the quadratic equation:c(It ,qt) =c0+ c1×qtIt+ c2×q2t i f qt > 0c3 i f qt = 0(3.5)where c0 is the fixed cost, c1 is the variable cost, c2 is the quadratic cost reflecting an increasingmarginal cost. The cost function parameter c3 reflects the fact that there is a fixed cost paid by thefishery to remaining open in years without harvest.The increasing marginal cost is included to capture expenses required for harvesting beyond thecurrent levels. Examples of these costs may be increasing the fleet capacity, finding new personal orinvesting in new technology. Function (3.5) is a simple way to include this realistic feature into themodeled cost function.The present value of the fishery’s future expected cash flows for a given harvesting policy qt =q(It ,Pt), assuming an infinitely lived representative fishery, is defined as:H (It ,Pt ,q(It ,Pt)) = Et[ ∞∑τ=t1(1+ r)τ−tpi (Iτ ,Pτ ,q(Iτ ,Pτ))](3.6)where r is the fishery’s risk-adjusted cost of capital. Equation 3.6 can be re-written as:H (It ,Pt ,q(It ,Pt)) =pi (It ,Pt ,q(It ,Pt))+1(1+ r)Et[∞∑τ=t+11(1+ r)τ−(t+1)pi (Iτ ,Pτ ,q(Iτ ,Pτ))](3.7)Therefore,H (It ,Pt ,q(It ,Pt)) =pi (It ,Pt ,q(It ,Pt))+1(1+ r)Et [H (It+1,Pt+1,q(It+1,Pt+1))](3.8)A value maximizing fishery will choose the optimal harvesting policy q∗(It ,Pt), that is, the harvest-ing policy that maximizes the value of the fishery, by solving the following Hamilton–Jacobi–Bellman(HJB) equation:V (It ,Pt) = maxq(It ,Pt)≥0{pi (It ,Pt ,q(It ,Pt))+11+ rEt[V (It+1,Pt+1)]}V (It ,Pt) = pi (It ,Pt ,q∗(It ,Pt))+11+ rEt[V (It+1,Pt+1)] (3.9)were V (It ,Pt) is the value of the fishery under the optimal policy q∗(It ,Pt). As the present value of the49Figure 3.2: International Pacific Halibut Commission Regulatory Regions. Source: InternationalPacific Halibut Commission (IPHC).cash flows is maximized over the set of feasible harvesting policies it is not dependent of this functionanymore.In Section 4.3.1 we present the model solution using data of the British Columbia halibut fishery,including estimation of the relevant parameters, the harvesting policy, and the fishery’s value.3.3 Parameter Estimation for the British Columbia Halibut FisheryCaseTo illustrate the implementation of the methodology proposed in this article we calibrate and solvethe model for the case of the British Columbia halibut. We use data from the International PacificHalibut Commission (IPHC), established in 1923 by a convention between Canada and the U.S. for thepreservation of the Pacific halibut fishery. The IPHC provides recommendations to these governmentson the total catch limit and monitors the resource over the regulatory areas presented in Figure 3.2.We focus on the area 2B corresponding to British Columbia.Our second source of data is the Department of Fisheries and Oceans of Canada (DFO), agencyresponsible for ”...sustainably manage fisheries and aquaculture and work with fishers, coastal andIndigenous communities to enable their continued prosperity from fish and seafood.”4 Specifically,we use the British Columbia halibut landing price data and financial reports published on their site.In the following subsections we present the estimations for the parameters of the BC halibutbiomass dynamic, price dynamic, cost function, and risk adjusted discount rate.4http://www.dfo-mpo.gc.ca/about-notre-sujet/org/mandate-mandat-eng.htm50Figure 3.3: British Columbia halibut stock assessment and landings, 1996-2017. Source: Inter-national Pacific Halibut Commission (IPHC).3.3.1 British Columbia Halibut Biomass Dynamic ParametersAlthough the biomass is not perfectly known, the stock assessment provided by Stewart and Hicks(2017) and Stewart and Webster (2017) is the closest proxy to its true magnitude. As detailed in thecited documents the biomass estimation is the result of a combination of several models which useshort and long term data. Figure 3.3 shows the time series for the biomass and the landings of halibutfor the British Columbia region, for the period 1996-2017.Panel A of Figure 3.3 shows that the biomass exhibited a strong decline between 1996 and 2000,period also characterized by high harvesting as Panel B of Figure 3.3 exhibits. By 2010 the biomasswas almost half of the 1996 level and harvesting was reduced to levels that remain controlled.Using this data we estimate the parameters of the biomass logistic growth function, and the volatil-ity of the random shocks. Combining Equations (3.1) and (3.2) we obtain the non-linear regression:It+1+qt = It(1+ γ(1− ItImax))+ ItσIε It+1 (3.10)Equation (3.10) is a non-linear function of the required parameters, so the estimation is done usingthe Nonlinear least-squares technique5, the results of this approach are presented in Table 3.1.Figure 3.4 illustrates the goodness of fit of the estimation by comparing the biomass natural his-torical growth rate (L.H.S. of Equation (3.10)) versus the growth (Expected value of the R.H.S. ofEquation (3.10) calculated using the estimated parameters.Figure 3.4 shows that the estimated parameters are effective in capturing the relation between thebiomass level and its growth, although there is a significant level of biological uncertainty captured byσI , which explains the overall difference between the fitted model and the data.5A technical description of the method can be found in Heer and Maussner (2009)51Table 3.1: Estimated Parameters for the Biomass Dynamic, 1996-2017The parameters are estimated using Nonlinear least-squares (Levenberg-Marquardt algorithm). The data covers from 1996to 2017 and is obtained from Stewart and Hicks (2017) and Stewart and Webster (2017). All coefficients are estimatedsimultaneously.γ 0.59(t-stat) (5.80)Imax 85.51(t-stat) (17.04)σI 0.11Adj. R2 0.69Figure 3.4: British Columbia Halibut Biomass Growth and the Non-Linear Least Squared ModelEstimation3.3.2 British Columbia Halibut Price Dynamic ParametersFrom the Department of Fisheries and Oceans of Canada (DFO) website6, we gather the halibut ex-vessel historical prices for British Columbia. The time series of prices covers from 1996 to 2017and is used to test multiple models for the dynamic of halibut prices, this is, we test for differentspecifications for the functions f (Pt) and g(Pt) in Equation 3.3, and determine which of them fits theavailable data better.The tested models for the dynamic of the halibut prices include mean reverting, autoregressiveand moving average time series specifications. We conclude that for the period studied the log-normalmodel fits the data the best:lnPt+1 = lnPt +νP+σPεPt (3.11)In the appendix we provide the regression statistics for the models tested, including the values ofthe Akaike information criterion (AIC) used to determine the performance of the models surveyed.As mentioned, we tested several alternative models, including one on which the price of the halibut6http://www.dfo-mpo.gc.ca52Figure 3.5: British Columbia Halibut Ex-Vessel Real Price and Logarithmic Returns, 1996-2017. Source: Fisheries and Oceans of Canada - Quantities and ValuesTable 3.2: Ex-Vessel Real Price Dynamic Parameters, 1996-2017The parameters are the mean and standard deviation obtained for the estimation of an ARIMA(0,1,0) model for the Loga-rithm of the British Columbia Halibut Ex-Vessel Price. The data covers from 1996 to 2017 provided by the DFO.νP 0.038(t-stat) (0.94)σP 0.154is determined by a negatively sloped demand curve, but from all these alternatives, the best statisticalfit is the selected log-normal model. From an economic perspective, the selected model implies thatfisheries are price takers, that is, the modeled fishery’s harvest does not affect the equilibrium price,as it is determined in a broader market, on which several alternatives goods and alternative producersparticipate. This market arrangement affects the problem of the fishery as it is possible to conjecturethat in scenarios of extremely high prices, it may be optimal to harvest a significant fraction of thebiomass, leading to the well known problems of the tragedy of the commons. Beyond this point, thispossibility will be allowed in the model for academic purposes, as one of our goals is to evaluatethe possibility of observing severe overfishing scenarios, so we can evaluate its consequences in thedynamic of the biomass.Figure 3.5 presents the time series of the real halibut prices (Panel A) and the distribution of thereal logarithmic price returns (Panel B). All prices are inflated using the CPI for the British Columbiaprovince and expressed in 2017 Canadian dollars.The estimated drift and volatility are presented in Table 3.2:From Table 3.2 is possible to notice that the estimated drift is not statistically different from zero,hence for the model calibration we set this parameter to zero. 77For convergence of the algorithm it is required that the discount rate used is higher than the drift of the price process.Since in the Appendix we analyze the solution of the problem with a real social discount rate of 1%, the drift of the priceprocess needed anyhow to be below 1%.53Table 3.3: British Columbia Halibut Fishery Revenues, 2007 and 2009The values are obtained from the reports prepared for the DFO-Pacific Region by Stuart Nelson of Nelson Bros FisheriesLtd. (Nelson (2009) and Nelson (2011)), and provide estimates of the financial performance for vessels operating in BritishColumbia for the years 2009 and 2007. These reports are done with a combination of data from the DFO and consultantcollected information through interviews/correspondence with fishermen and experts. The presented data corresponds to thegroup of vessels with the middle third of the individual landings. All values are expressed in 2017 CAD using the CPI forBritish Columbia.2007 (In 2017 CAD) 2009 (In 2017 CAD)Total Biomass [Mill. lb.] 53.69 62.78Landings [Mill. lb.] 2.88 2.14Vessel Price [CAD/lb.] $5.56 $5.99Gross Revenue [Mill. CAD] $16.03 $12.85Total Fishery Specific Expenses $4.75 $3.77Crew and Captain Shares $4.78 $3.85Total Vessel Expenses $1.28 $0.99Total Cost [Mill. CAD] $10.81 $8.62EBITDA [Mill. CAD] $5.23 $4.233.3.3 British Columbia Halibut Fishery Costs ParametersThe model’s cost function is presented in Equation 3.5 and includes a fixed operating cost, a linearharvesting cost which is related to the biomass through the fishery’s efficiency (catchability), and anincreasing marginal cost captured by the quadratic component. The parameters of this function areestimated using two surveys performed by Nelson Bros Fisheries Ltd. for the DFO (Nelson (2009) andNelson (2011)). The survey separate the total vessels operating in British Columbia in three groups,depending on its harvest, we use the median group as it represents the average vessel productionfunction. The surveys are summarized in Table B.3:Table B.3 presents two years of costs and revenues for the mid level efficient vessels in the BritishColumbia halibut fishery. During 2007 the fisheries registered higher harvest and lower costs, perunit harvested, in comparison to 2009. All dollar values are inflated using the British ColumbiaCPI and expressed in 2017 Canadian Dollars (CAD), making all future costs estimations and valuescomparable.The parameters of the cost function are determined solving an over-identified system of equationsfor the annual cost, that is, we solve Equation 3.5 by leaving one parameter free, in this case c2, andthen solve for the remaining two c0,c1, subject to c0 > 0, c1 > 0 and c2 > 0, using the two years ofavailable data.The set of feasible values for the parameter c2 is (0,0.6], that is, if c2 > 0.6 =⇒ c1 < 0. For thequadratic cost parameter we choose the median of the feasible values, that is c2 = 0.3, implying thatc1 = 54.87 and c0 = 5.37. Finally, we assume that if the fishery does not harvest it will only pay thefixed cost c0, therefore c3 = c0 = 5.37.This parametrization gives a balanced combination between the increasing marginal cost and the54linear component of the harvesting cost. As mentioned, there are several cost parameters that solvethe over-identified system of equations associated with the presented harvesting costs, so the maindifference among the those solutions is the trade off between the weight of the quadratic and linearcomponent of the cost, to generate the same total cost.We implement the model using the cost function parameters estimated for the mid level efficiencyvessels harvesting the British Columbia halibut. As we assume that there is a sole representativefishery harvesting the each year, we use these parameters for the whole annual harvest in the model.We also studied the model with alternative cost parameters, based on the high efficiency and lowefficiency fisheries of the British Columbia halibut, the numerical results for these paremetrizationsare available in the Appendix.Although we are able to provide a calibration of the cost function, it is clear that more data isrequired to achieve a proper implementation of the model. Clark et al. (2009) already pointed out thisissue, and unfortunately these surveys are not available for other years. Any effort to fully implementthe model will have to deal with the lack of information of the production costs, which will requirecollecting and standardizing additional information.3.3.4 Risk Adjusted Fishery Discount RateTo estimate the risk adjusted discount rate for fisheries we look at the historical returns for companiesclassified as Fisheries using the SIC industrial classification, which codes are:• 0912: Fisheries, Finfish• 0913: Fisheries, Shellfish• 0919: Miscellaneous Marine Products• 0921: Fish Hatcheries and PreservesUnfortunately not a significant number of firms are recorded on CRSP with the identified SICcodes. In Fama and French (1997) however, these firms are included in the macro-sector portfolio”Agriculture”. We use this portfolio definition to obtain a robust estimation of the sector beta and theexpected rate of return. The CRISP database is used to obtain the firm’s stock returns and the historicalrisk-premium is obtained from Kenneth R. French site8.For the returns of each firm registered in the ”Agriculture” portfolio, 60-months rolling betasare computed. The median beta for the Agriculture portfolio during the 1987-2016 period is 0.35.Combining this value with the historical risk premium and risk-free rate the estimated real rate ofreturn for a fishery company is 2.9%. The detailed calculation is presented in Table 3.4To get additional information about the appropriate risk-adjusted discount rate we also looked atthe few fisheries included in CRSP. Table 3.5 presents the estimated rolling-betas and nominal returns.8http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html55Table 3.4: Fishery’s risk adjusted rate of returnThe included beta is the annual average of the median 60-months rolling betas of the firms registered in the ”Agriculture”portfolio. The risk premium and risk-free rate are obtained from the historical excess of return for the Canadian stock andbond market. The Bank of Canada inflation target of 2% is used to obtain the real rate using the continuous compoundingFisher equation. Data from CRSP and Ken French website. RFishery = R f +(Rm−R f )βFisheryPanel A: Estimated Rates and Fishery’s Betaβ 0.349Rm−R f 0.055R f 0.030RNomFishery 0.049Panel B: Fishery’s Real Risk Adjusted Rate of ReturnRRealFishery = (1+RNomFishery)/(1+pi)−1 = 0.029Table 3.5: Fishery Betas, Available FirmsThe parameters are the average of the 60-months rolling betas for the firms in CRPS whose SIC code is 0912, 0913, 0919or 0921. The risk adjusted returns are computed using the included beta and the risk premium presented in Table 3.4Company Period Beta RFisheryMarine Harvest ASA Feb. 2014 - Jun. 2016 0.3503 0.0493Aquaculture Production Tech Ltd. Jun. 2007 - Mar. 2011 0.7470 0.0711Marine Nutritional Sys Inc. Nov. 1996 - Jun. 2007 0.8399 0.0762The range of nominal rates of returns for fisheries is [0.049,0.076]. Marine Harvest ASA hasthe most recent data, and its rate of return is consistent with the estimation presented in Table 3.4,therefore, this will be the primary risk adjusted real rate of discount used in the model.3.4 Numerical Results3.4.1 The Value-Function Iteration ApproachTo solve the Hamilton–Jacobi–Bellman equation for the fishery’s value V (It ,Pt), we follow the Value-Function Iteration Approach as presented in Heer and Maussner (2009). We start from Equation 3.9:V (It ,Pt) = maxq≥0{pi (It ,Pt ,q(It ,Pt))+11+ rEt [V (It+1,Pt+1) |It ,Pt ]}(3.12)where q(It ,Pt) is the extraction policy, and (It+1,Pt+1) is the state at year t +1 for the two stochasticvariables in the model, the resource biomass and price.The solution approach starts by defining a discrete state space for the biomass and the resourceprice, (In,Pm), where In ∈ {I1, I2, ..., IN} and Pm ∈ {P1,P2, ...,PM}. The optimal control is discretizedto the set q j ∈ {0,q1, ...,qJ}. The N×M matrix V = Vnm represents the value of the fishery for thestate (In,Pm).The biomass and the price stochastic shocks are denote by ZI and ZP respectively. As mentioned in56the model section, these shocks are assumed to be i.i.d. standard normal. The shocks discretization isa finite Markov chain ZIk ∈ {ZI1,ZI2, ....,ZIK} and ZPl ∈ {ZP1 ,ZP2 , ....,ZPL} for the biomass and the resourceprice respectively.For the biomass growth shocks λ Ik represents the probability of transition from the current shockof the biomass ZI0 to a shock ZIk in the next period. For the price shocks λPl represents the probabilityof transition from the current price shock ZP0 to a shock ZPl .Using this discretization of the state space, value function, harvest policy and stochastic shocks,Equation 3.12 can then be re-written as:Vn,m = maxq j∈{0,q2,...,qJ}{pi(In,Pm,q j)+11+ rK∑k=1L∑l=1λ Ik ×λPl ×V (In+∆In,Pm+∆Pm)}(3.13)where In+∆In and Pm+∆Pm are the state of the biomass and price in the next period. These values areestimated using the stochastic processes defined in Equations 3.1 and 3.11, and for a specific policyq j and stochastic shocks (ZIk, ZPl ) are:In+∆In = In+ γIn(1− In/Imax)−q j + InσIZIk (3.14)Pm+∆Pm = PmeνP+σPZPl (3.15)The solution algorithm follows Heer and Maussner (2009). It starts from a guess of the value-function V 0n,m and iterates over the defined state space. In each point of the two-dimensional state(In,Pm) the right-hand-side of Equation 3.13 is maximized using the stochastic optimal control q j. Ifthe optimized value of the current iteration is greater than the previous iteration value-function forthe state, the old value-function is replaced by the current iteration maximized value. The process isrepeated until no significant changes are made to the value-function in the latter iteration.To complement this short description we present a formal scheme of the solution algorithm in theAppendix. The following section presents the results of the application of the value-function iterationapproach for the British Columbia halibut fishery.3.4.2 Model Parameters, Grids Dimensions and LimitsAs previously mentioned the model is solved for the British Columbia halibut fishery. Since all thedata used in the parametrization is obtained with annual frequency, we solve the model using a one-year time step. The parameters used to solve the model are summarized in Table 3.6.The grids for the biomass, policies, and random shocks are constructed dividing a specified set inan equally-spaced discrete points. In the case of the halibut price, we use a log-linear grid to bettercapture the distribution of prices. The biomass grid boundaries are 0.19 and carrying capacity Imax. For9Given that the cost function is undefined if the biomass is zero, we choose this small value to represent the depletion of57Table 3.6: Estimated Parameters for the British Columbia Halibut FisheryThis table is a summary of the parameters estimated on the previous subsections. Details on each parameter estimation canbe found there.Panel A: Biomass Growth ParametersParameter Estimated Value DescriptionI0 57.82 2017 Biomass AssessmentImax 85.51 Non-Linear Least Squares Biomass Growth Estimationγ 0.59 Non-Linear Least Squares Biomass Growth EstimationσI 0.11 Non-Linear Least Squares Biomass Growth EstimationPanel B: Resource Price ParametersParameter Estimated Value DescriptionP0 7.75 2017 Halibut PriceνP 0.00 Real Halibut Log Price Model EstimationσP 0.15 Real Halibut Log Price Model EstimationPanel C: Cost Function ParametersParameter Estimated Value Descriptionc0 5.37 Annual Cost Function Estimationc1 54.87 Annual Cost Function Estimationc2 0.30 Annual Cost Function Estimationc3 5.37 Annual Cost Function EstimationTable 3.7: Grid Dimensions and Limits for Numerical SolutionThis table presents the limits and density of the discrete grids used in the value-function algorithm. Each grid used to solvethe problem is a discrete set of equally spaced points within the specified interval.Grid Dimension Interval UnitsBiomass Grid: In 75 [0.1,85.51] Million Pounds [Mill. lb.]Price Grid: Pm 75 [2.99,20.07] CAD per pound [CAD/lb.]Random Shock: Z j 15 [−2.33,2.33]Policy Grid: qi 90 [0,20] Million Pounds per Year [Mill. lb.]the price grid the boundaries are the 99% confidence interval, for a 10 year time horizon, constructedusing the historical price distribution. For the policy grid we use a boundary of 20 million poundsper year, which is high in comparison to the current 7.45 million pounds harvest limit. The specificdimensions and boundaries for these sets are presented in Table 3.7:In the following subsections we present results for the benchmark case and some sensitivity anal-ysis to the uncertainty parameters. In the Appendix we provide additional sensitivity analysis withrespect to costs and discount rates.the resource.58Figure 3.6: Value Function of the British Columbia Halibut Fishery3.4.3 Value Function and Harvesting Policies for the British Columbia HalibutFishery ParametrizationThe value of the British Columbia halibut fishery for different values of the biomass and the price,under the optimal harvesting policy, is shown in Figure 3.6.As the resource price increases, current revenues and the incentives to increase the harvest alsoincrease. But this will diminish the biomass level, reducing the future resources growth and increasingthe future marginal cost. This represents the main economic trade-off in the model and it can beobserved in Figure 3.6. The marginal increment in the value of the fishery is positive when the price orthe biomass increase. The marginal increment in the value over the state space is non-linear, however,an extra unit of biomass becomes more valuable in high price states in comparison to low price states,as in high biomass states an extra unit not only improves the the current and future profits in a highprice state, it also reduces the extraction cost.The optimal harvesting policy is chosen to maximize the value of the fishery, and their values areshown in Figure 3.7 for different values of the state variables.Figure 3.7 shows that the annual optimal harvesting goes from zero, in states of low biomass andprice, to 20 million pounds per year in states of high price and biomass10. The optimal harvestingpolicy is also a non-linear function of the state variables. For example, the harvesting policy in ahigh price state ($20 Canadian dollars per pound) goes from zero to 20 million pound per year as thebiomass increases, but if the price is low ($4 Canadian dollars per pound) harvesting goes from zeroto just 5.6 million pound per year.10The upper bound set at 20 million pounds per year is not really binding. As we show in the next subsection, startingfrom the current state, the probability of reaching it is less than 1%.59Figure 3.7: Optimal Harvesting Policy of the British Columbia Halibut FisheryThe model results indicate that for the current state of the British Columbia halibut fishery, that isa biomass of 57.8 million pounds and a halibut price of $7.75 Canadian dollars per pound, the valueof the resource is approximately $1.81 billion Canadian dollars, and the optimal harvesting policy is9.95 million pounds per year.Figure 3.7 also indicates that the fishery should optimally reduce the harvest to zero in some states,most of them characterized by low biomass and low fish prices. In the following section we computesimulations for the estimated parameters of the British Columbia halibut fishery, and show that it ishighly unlikely that the fishery would reach that situation, since it would optimally modify its harvestto avoid it.Simulations of the Biomass and Harvesting Policies for the British Columbia HalibutParametrizationTo illustrate how the halibut biomass will evolve if the optimal harvesting policy is implemented,simulations of the price and biomass are generated combining their respective distributions with theoptimal policy. We simulate 10,000 different paths over an horizon of 10 Years for the biomass andthe halibut price, all starting from the current state: I0 = 57.82 million pounds and P0 = 7.75 CAD perpound.Figure 3.8 presents two different paths for the simulated fish price, biomass, and harvesting policyover a 10 year horizon.Figure 3.8 shows a significant variability of the optimal harvest for the simulated paths. As thetwo states variables experience random shocks, the uncertainty faced by fisheries is significant, and theoptimal harvesting policy adjusts reflecting those changes. ”Path A” is characterized by positive price60Figure 3.8: Simulated Paths for the Price, Optimal Harvesting Policy, and Biomass for theBritish Columbia Halibut Fisheryshocks during most of the simulated years, consequently the fishery starts increasing its harvest untilyear 6 reducing the total biomass of the resource. Then the fishery decides to harvest a smaller amountof the resource even after a new positive price shock, allowing the biomass to recover, indicating aclear financial incentive for conservation. ”Path B” differs by exhibiting negative shocks to the pricefor most of the simulation. As a consequence, the harvest is reduced in several periods, allowing thebiomass to grow.Figure 3.9 presents the median, 1th and 99th percentiles of the simulated 10,000 different pathsover an horizon of 10 years.Panel A of Figure 3.9 shows the median, and the 1th and 99th percentiles, of the optimal harvestpaths. The median harvest slightly decay during the 10 year simulation, and as shown in Panel Bof the same figure, the biomass median grows reaching a higher level in comparison to the initialstate. The 1th percentile of the biomass shows that the there are several paths on which the biomassdecreases, but it always remains away from depletion being above 35 million pounds in 10 years with99% probability. The 99th percent percentile illustrates that in paths of biomass growth will approach61Figure 3.9: Median, 1th and 99th Percentiles of the Simulated Harvesting Policy and Biomassfor the British Columbia Halibut Fisheryits carrying capacity (Imax).These simulations exemplify the results of the model. First, we observe a significant amountof uncertainty and a harvesting policy which adjusts promptly. Second, we notice that the biomasswill increase in most of the simulated paths and it will not reach levels close to extinction with 99%probability, presenting support for the intuition that conservation is economically optimal.3.4.4 Multiple Sources of Uncertainty and their Impact on the Simulated Biomassand Harvest DynamicTo asses the impact of uncertainty on our results we solved the valuation problem using differentassumptions about the volatility of the price and biomass processes. Our first case is the benchmarkcase with full uncertainty as in the previous section. In the second case we set the volatility of theprice process to zero and maintain the estimated volatility of the biomass process. In the third casewe set the volatility of the biomass process to zero and maintain the estimated volatility of the priceprocess. In the fourth and final case we set the volatilities of the two processes to zero.For the estimated parameters for the British Columbia halibut we find that the differences betweenthe first and the third case, that is between the benchmark case and the no biomass volatility case, arenegligible. We also find that the differences between the second and the fourth case, that is between thecase with only biomass volatility and no volatility, are negligible. This implies that for our parameters,only price volatility generates sizable differences between the cases. Therefore, in what follows wediscuss only the differences between the benchmark case and the case with only biomass uncertainty,so that these differences can only be attributed to price uncertainty.62Table 3.8: Value Function for Different Levels of Uncertainty at the Current StateThis table presents the numerical solution for the value function for models solved using only biomass uncertainty or priceand biomass uncertainty.(1) (2) (3)Model Value Function [Mill. CAD] Optimal Harvest [Mill. lb.] ∆VVBenchmark Case $1803.08 9.95 -Biomass Uncertainty Case $1164.43 10.30 -0.35We first look at the valuation effects. Column (1) of Table 3.8 shows that the value of the fisheryfalls from 1.8 billion Canadian dollars to 1.1 billion for the current state (biomass of 57.82 millionpounds, halibut price of $7.75 Canadian dollars); this is a drop of 35%. As we show bellow thissignificant difference comes from a non-optimal harvest policy if price uncertainty is not taken intoaccount. That is, the fishery, for a given biomass, will have the same harvesting policy for any levelof the price losing the opportunity to optimally react to changes in prices. In essence, in Real Optionsterms, assuming that there is no price volatility limits the flexibility of the fishery to adjust to changesin the state space.Column (2) of table Table 3.8 show that the harvest only changes form 9.95 million pounds in thebenchmark case to 10.30 million pounds in the case with biomass uncertainty. This is a 4% increasewhich is substantially smaller than the 35% decrease in value. This shows that the difference in valueis generated by the flexibility in the optimal policy in cases when the price deviates from the expectedvalue. This will become clear in the following simulation analysis.The data supports a world where there is both biomass and price uncertainty. We want to quantifythe effect of solving the model assuming that there is no price uncertainty in a world that has priceuncertainty. In addition to the benchmark case discussed in the previous section we simulate a fisherythat follows the optimal policy in the case of no price uncertainty but it is subject to shocks in thebiomass and price. Figure 3.10 shows the 1% and the 99% of the simulated harvest for these to cases.Even though the median values of the harvest in the two cases are relatively close, Figure 3.10shows that the 1th and 99th percentiles are significantly different. This implies that abstracting fromprice uncertainty leads to a harvesting policy which very stable and close to its median value, withoutreacting to extreme price changes.Panel A of Table 3.9 shows the numerical values of the harvest for the 1th and 99th percentile at 5and 10 years into the future. For example, for the benchmark case at 10 year there is a 1% probabilitythat the harvest rate will be below 3.6 million pounds, whereas this figure is 8.4 for the model withoutprice volatility. This shows that for the benchmark case the flexibility of the harvesting policy is muchhigher resulting in higher valuation of the fishery.Panel B of Table 3.9 shows that although the flexibility in the harvest is higher for the benchmarkcase, the effect on the biomass is much smaller. For example, for the benchmark case at 10 years thereis a 1% probability that the biomass will be below 35.3 million pounds, whereas this figure is 39.763Figure 3.10: Percentile 1th and 99th of the Simulated Harvesting Policy for the Benchmark Caseand the Only Biomass Uncertainty Case for the British Columbia Halibut FisheryTable 3.9: Simulations for Models with Different Levels of UncertaintyThis table presents the 1th and 99th percentiles at 5 and 10 years, for the harvest policies simulated. Each curve is generatedusing the optimal harvesting policy for the case with uncertainty in biomass and price, and the case with no price uncertainty(or just Biomass Uncertainty, denoted as “Biomass Case” in the table).Panel A: Simulated Harvest for Models with Different Levels of Uncertainty5 Years Simulation 10 Years Simulation 5 Years Simulation 10 Years SimulationModel 1th Percentile 1th Percentile 99th Percentile 99th PercentileBenchmark Case 4.257 3.596 16.462 17.038Biomass Case 8.681 8.418 11.246 11.313Panel B: Simulated Biomass for Models with Different Levels of Uncertainty5 Years Simulation 10 Years Simulation 5 Years Simulation 10 Years SimulationModel 1th Percentile 1th Percentile 99th Percentile 99th PercentileBenchmark Case 39.426 35.251 85.011 85.517Biomass Case 40.835 39.717 81.797 82.331million pounds for the model without price volatility.It is to be expected that price volatility should have a large effect on the harvesting policy, sincethe price process is totally exogenous. The biomass process is partially endogenous, since in additionto the biomass shocks, the fishery can react to changes in the biomass with its harvesting policy,consequently influencing the future dynamics of the biomass process.643.5 ConclusionThis article develops and implement an optimal stochastic control approach to value a renewablenatural resource, in particular a fishery, with two sources of uncertainty: the biomass and the price.The solution of the model is obtained by solving a Hamilton-Jacobi-Bellman equation for the valueof the Fishery using a value-function iteration approach. Overall, the results highlight the strong non-linear relation between the biomass and the resource price on the value of the fishery and the optimalharvesting policy.The solution is implemented using the estimated parameters for the British Columbia halibut fish-ery. The model results are used to simulate the dynamic of the studied fishery, finding that the optimalharvesting policy is sustainable. For negative shocks to the biomass growth we obtain reductions ofthe resource stock, but the simulations show that with more than 99% probability we will not observethe extinction of the resource. For the current state I0 = 57.82 million pounds, P0 = 7.75 CAD perpound, we found an optimal annual harvesting policy is 9.95 million pounds per year.We evaluate the impact of price uncertainty on the harvesting policy and compare it to the tradi-tional approach which assumes that prices follow a deterministic path. We find that price volatility hasa large effect on the value of the fishery and the harvesting policy. This is due to the fact that the priceprocess is totally exogenous so that price shocks cannot be offset by changes in the harvesting policy.The model solved for a realistic set of parameters suggests that an economically viable fisheryis feasible, that overfishing is indeed not optimal, even in the presence of fish price and biomassuncertainty. This highlights the value of conservation and confirms that current efforts to controloverfishing are indeed efficient from a social and a financial perspective.65Chapter 4Tax Loss Carry Forwards and EquityRisk4.1 IntroductionCorporate taxes are among the most studied of financial frictions. Corporate taxes are importantdeterminants of value and, accordingly, have been used to explain corporate decisions such as capitalstructure, dividend policy, real investment and risk management.1 In contrast to the wide range ofstudies documenting how corporate taxes affect corporate decisions and firm value, less is knownabout how corporate taxes are related to equity risk and return. The general consensus, starting withModigliani and Miller (1963), is that corporate taxes and tax shields reduce a firm’s equity risk. Westudy one particular component of corporate taxes - Tax Loss Carry Forwards (TLCFs) - and show thatboth empirically and theoretically, TLCFs are positively related to a firm’s risk and return. Empirically,firms with high TLCFs have higher future returns, risk betas, and volatilities. Moreover, these higherreturns are not fully explained by standard measures of risk.TLCFs arise because tax codes do not allow firms to generally realize negative taxes, i.e. NetOperating Losses (NOLs) do not automatically generate payments from the government to the firm.Instead, tax codes only allow NOLs to generate immediate refunds if the firm can apply the lossesto prior taxable income (Tax Loss Carry-backs). When this is not possible, NOLs may be carriedforward. Subsequent positive taxable income can be reduced by applying some or all of the TLCF asan offset while subsequent losses are added to the TLCF portfolio. Hence, TLCFs form a valuable butrisky corporate asset.Figure 4.1 shows how significant TLCFs have become over the past 20 years, having increasedfrom 1% to 5% of total book assets. Over the same time, the presence of TLCFs has become morewidespread; the percentage of firms reporting TLCF has increased from 30% to 75% of all firms1See Graham (2006) and Ravid (1988) for comprehensive surveys of the literature.66Figure 4.1: Tax Loss Carry Forwardin our CRSP-Compustat sample over this same period. The increase in TLCFs dominates cyclicalfactors and is not explained by two of the more significant legislated changes during this period; theEconomic Recovery Act of 1981 that reduced some corporate taxes, and the Tax Reform Act of 1986that reduced statutory tax rates.While TLCFs and the sources of their growth has been studied by others,2 our interest is in un-derstanding how this significant corporate asset affects equity returns and risk.3 Intuitively, a TLCFcreates a contingent tax savings; taxes are reduced in some states but not others. Accordingly, it wouldintuitively be expected that this non-linearity would affect risk. Given the rising importance of TLCFs,the lack of previous research linking TLCFs and risk is surprising.42It seems that the primary explanation of the growth in operating losses over this period is lower returns to assets. SeeAltshuler et al. (2009) for an in depth discussion of the growth in corporate tax losses and Denis and McKeon (2016) for arecent discussion of losses and their relationship to R&D and cash holdings.3In addition to being of theoretical interest to both asset pricing and corporate finance, we are motivated by the large andgrowing importance of TLCFs in the public finance literature. Auerbach (2006) shows that while the statutory corporate taxrate in the U.S. has fallen from 46% in 1983 to 35% in 2003, the average tax rate - the ratio of taxes paid to corporate income- has increased dramatically from 27% to 45% over the same period. Auerbach shows that, by far, the largest contributor tothe increase in the average tax rate is the asymmetric treatment of tax losses and the increase in NOLs over this period. Taxloss carry forwards also became an important issue in the 2016 Presidential election due to Donald Trump’s huge TLCFs,see Confessore and Applebaum (2016) for an account of the issue.4There is, however, a literature that considers personal taxes and returns. This literature starts with Brennan (1970).67Our task of deriving a general understanding of how TLCF, risk, and return are related is madedifficult by the fact that a firm’s TLCFs result from complex, path dependent tax minimization deci-sions. For instance, Cooper and Franks (1983) show how operating decisions, asset allocations, leaseor buy decisions and NOLs interact to determine value. Moreover, in any one year, non-operatingdeductions such as depreciation and interest payments, both of which are the result of endogenouscorporate decisions, affect a firm’s NOLs. Furthermore, firms can reduce taxable income by applyingan existing TLCF and/or using Investment Tax Credits (ITCs) to pay for the taxes owed. Since bothITCs and TLCFs have specific maturities, the decision to use one or the other at any point in time isitself a complex decision.The implications, therefore, of TLCFs for firm value, risk and return are, to some extent, historydependent and idiosyncratic. Still, some general features of the tax code emerge as important forequity risk. Our focus is on the convexity of the tax schedule and its implication for equity risk. Wefollow Majd and Myers (1985) and Green and Talmor (1985) by viewing a firm’s equity as a claimto pretax operating cash flows plus a short position in a call option on corporate taxes. The asset thatunderlies the implicit call sold to the tax authorities is the tax revenue that would be paid if tax shieldswere zero. The strike price of the option is the tax shield times the tax rate; the tax authorities cancollect taxes if they pay this amount. If corporate taxes are less than the tax shield, the option willexpire unexercised, while if the taxes are higher the tax authorities will exercise their option, collectingtaxes net of the exercise price.Green and Talmor (1985) recognized that being short a risky derivative makes the firm’s after taxequity safer than the underlying pretax cash flows. This intuition is similar to the 2nd proposition ofModigliani and Miller (1963), who show that interest tax shields make a firm safer. We add to thisinsight by showing that, while this is generally true, the risk reduction from additional tax shields isnon-monotonic and that the relationship between TLCFs and risk is typically positive.To see the intuition behind our results, consider a firm generating a distribution of future taxableincome and, for ease of exposition, assume that the lowest possible taxable income is greater thanzero. Suppose first that the firm has zero TLCFs and no other tax shields, so that, although the amountis uncertain, it pays some taxes with certainty. In this case the riskiness of the after tax cash flowsis equal to the riskiness of the pre tax cash flows since there are no TLCFs to shelter income. Nowconsider adding a low level of TLCFs, less than the minimum taxable income. In this case, the fullamount of the TLCFs will be used with certainty, providing the firm with a risk free tax saving thatreduces the total risk born by equity holders. As the size of the TLCFs increases from this low initiallevel, the risk free asset increases and total equity risk falls, as long as the tax shield is used withcertainty. Eventually, however, as the level of TLCF rises, a portion of the tax shield will only beused in high income states, and will be lost in low income states - some o the TLCFs become risky.This increases equity risk because the firm’s post-tax cash flow rises in good states. Thus, equity riskas a function of TLCFs is non-monotonic, decreasing at low levels of TLCFs, and increasing at highlevels of TLCFs. Now, suppose the firm has additional annual tax shields (i.e. interest or depreciation)68which will be used before TLCFs. In this case, the relationship between risk and TLCFs may bepurely positive because all of the TLCFs may end up unused.Our study has two main components. First, we theoretically study the relationship between TLCFsand return. In a simple one period binomial model we show that the relationship between risk andTLCFs is non-monotonic. We also show that if the firm has existing non-TLCF tax shields, then therelationship between TLCFs and risk may be strictly positive rather than non-monotonic. We thensolve a realistic, dynamic model of a firm, and calibrate it to the data. In this model, the relationshipbetween TLCFs an risk is positive and quantitatively important for risk.Second, we empirically examine the relationship between TLCFs and asset prices. We show thatTLCFs are positively related to standard measures of risk, like betas and volatility. We then showthat TLCFs are are also positively related to equity returns. Importantly, in our regression analysis ofreturn and TLCFs we find that TLCFs are able to explain future returns even when we condition onstandard measures of risk. Hence, studies that include standard measures of risk account for some butnot all of the risk generated by TLCFs.Additionally, we take advantage of a distinct policy change to add support to our results. The 1986Tax Reform Act reduced the statutory tax rate from 46% to 34%, effective for tax years after July 1,1987. Our theory shows that the theoretical impact of TLCFs on risk is increasing in the tax rate,hence a decrease in the tax rate will reduce the importance of TLCFs in explaining risk and return.Indeed, we find that the coefficient on TLCFs decreases in magnitude and significance after the taxreform, although it continues to be statistically significant.Our paper builds on the work of Green and Talmor (1985) who explicitly recognize the call optionstructure of the tax claim on the firm. They use this insight to study investment behavior by firms andthe debt-equity conflict of interest. Recently, Albertus et al. (2017) pick up on the study of asymmetrictaxation and investment decisions in an international context. Streitferdt (2010) also builds on theinsight of Green and Talmor (1985) to consider alternative more realistic stochastic process for thevalue of the underlying tax base but does not draw implications for risk.Our focus is instead on the implication on equity risk and return. We know of no other studythat has directly looked at the relationship between TLCF and equity risk.5 Others have indirectlylooked at the tax return relationship. Lev and Nissim (2004) consider the ratio of tax to book incomeas a measure of the quality of accounting information. They show that this ratio, which reflects taxdeductions including TLCFs, forecasts firm growth but is not significant in forecasting returns.The remainder of the paper is organized as follows. We present a theoretical analysis of therelationship of TLCFs and risk in Section 4.2. In this section the main intuition of our analysis isillustrated in a simple binomial model relating equity risk to TLCFs. We numerically explore a morerealistic model in Section 4.3. Section 4.4 provides empirical evidence on the TLCF/risk relationship5Somewhat relatedly, Schiller (2015) finds that firms with low average tax rates are safer and have lower expectedreturns. Since higher TLCFs could be associated with lower tax rates, this result may be in contrast to our study. Inunreported regressions, however, we find that the coefficient on average tax rate when added to our regressions is negative,but that the significance of TLCFs is little change.69that is strongly supportive of the simple theory. Section 4.5 concludes.4.2 Simple Binomial ModelConsider an all equity firm that at t0 owns a future stochastic cash flow Π1 ∈{Πu,Πd}, Πu > Πd .The corporate tax rate is τ , and the firm is in possession of a non-cash tax deduction of Φ. Φ can bethought of as a tax-loss carry forward, depreciation, or any other non cash tax deduction6.The value of the all equity firm at t0, VE , is equal to the value of the expected pretax cash flows,VΠ, minus the value of expected taxes, VT , i.e.VE =VΠ−VT (4.1)Accordingly, the risk of the equity, βE , is given byβE =VΠVΠ−VT βΠ−VTVΠ−VT βT (4.2)where βΠ is the beta of the pre-tax cash flows and βT is the beta of the tax payments.Green and Talmor (1985) and Majd and Myers (1985) show that the expected tax payment isequivalent to a call option. The underlying asset is the tax payment with full tax offset, τΠ, and theactual tax payments will be a call on this asset with an exercise price τΦ, i.e. the tax payment will bemax{τΠ− τΦ,0}.Since the firm is short the tax payment and, as we will show, β T > 0, the risk of equity is lower thanthe risk of the pretax cash flows as long as Φ> 0. Our theoretical contribution is to show that the riskreduction is non monotonic in Φ, first decreasing and then increasing. Hence, for many firms risk isincreasing in TLCFs.The relationship we will derive is graphically presented in Figure 4.2. Three cases are apparentin Figure 4.2: Case 1, 0≤Φ≤Πd ; Case 2, Πd <Φ<Πu; Case 3, Φ≥Πu.4.2.1 Case 1: 0≤Φ≤ΠdThis case applies to firms that have positive taxable income but little or no tax deductions. As a result,the available tax shields Φ are used with certainty making the tax savings risk-free. Hence, the valueof the tax payments is:VT = τVΠ− τVΦ (4.3)6Investment tax credits (ITCs) would play a similar role.70Figure 4.2: Firm Risk and Tax Loss Carry ForwardUsing Equation (4.3) in the value of the equity claim, Equation (4.1), gives:VE = (1− τ)VΠ+ τVΦIn terms of the risk of the equity, the after tax cash flow and pretax cash flow have the same beta whilethe value of the tax shield from Φ is riskless. That is, the firm has effectively sold an equity claim tothe government but has received a risk free bond in return resulting in the following equity risk:βE =(1− τ)VΠ(1− τ)VΠ+ τVΦβΠ (4.4)As Φ increases in this range, the value of the risk free bond, VΦ, increases and the overall equityrisk decreases.4.2.2 Case 2: Πd ≥Φ<ΠuIn this region the tax payment depends on the state:T =τ (Πu−Φ) if Πu0 if Πd (4.5)The t0 value of the tax payment VT is the value of the replicating portfolio, a levered long positionin the underlying tax claim, τVΠ.VT = ∆τVΠ−∆τ Πd(1+ r f )where ∆ is:∆=Πu−ΦΠu−Πd < 1 (4.6)71Using Equation (4.6) in Equation (4.1) gives the equity value:VE = (1−∆τ)VΠ+ ∆τΠd(1+ r f )(4.7)which implies that the firm risk will be :βE =(1−∆τ)VΠVΠ−VΦ βΠ (4.8)The tax deduction Φ affects βE through its impact on ∆ and VE = VΠ−VΦ. The net result can beshown to be strictly increasing in Φ in this range since∂βE∂Φ=τVΠβΠΠdV 2E (Πu−Πd)(1+ r f )(4.9)is positive.4.2.3 Case 3: Φ≥ΠuSince deductions are larger than the maximum taxable income the firm will not pay taxes with cer-tainty. Hence VT = 0 and:VE =VΠ (4.10)As a result, βE = βΠ for any level of Φ in this range.This simple model demonstrates an important new insight. Prior studies have shown that firmrisk is lower as a result of the asymmetric taxation of corporate earnings and losses. Essentially thegovernment shares in the corporate losses by not collecting taxes when business is bad. To this weadd an understanding of how this lower risk changes through the range of possible values ofΦ relativeto taxable income. For low levels of Φ risk is decreasing until Φ = Πd , at which point risk begins toincrease up to a point where the firm pays no taxes, after which firm risk is constant as Φ increases.7Next, suppose that the firm’s total tax shields are composed of two pieces: Φ=Φ0+ΦT LCF . HereΦ0 are non-TLCF tax shields available to all firms, such as depreciation or interest; ΦT LCF are TLCFswhich differ across firms. Also suppose that non-TLCF tax shields are used first; this designationis irrelevant in a one period setting but is true in a multi-period setting where many non-TLCF taxshields are available every year and disappear immediately if not used, but TLCFs can be carried tofuture years. In this case, if Πd < Φ0 < Πu, then the relationship between risk and ΦT LCF is strictlyincreasing.8 This can be seen by noting that the relationship between βE and Φ in Figure 4.2 remainsunchanged, however the point where ΦT LCF = 0 is now to the right of where Φ= 0.7In a multi-period setting risk could continue to change as Φ increases beyond Πu since the excess in the single periodwill be carried forward to the subsequent period. This is incorporated in our numerical model of Section 4.3.8Even if Φ0 <Πd , as long as Φ0 > 0, then a firm with ΦT LCF = 0 is less risky than a firm with ΦT LCF =Πu.72In reality the relationship of risk with tax deductions is much more complex. A multi-periodsetting implies that tax deductions not used in one period can be carried forward. Tax Loss CarryForwards compete with period deductions such as depreciation and interest as well as with investmenttax credits. The Tax Loss Carry Forward is made up of operating losses over various periods and eachof these has a finite maturity. In Section 4.3, we show that the relationship described in this section isquantitatively important in a dynamic, realistically calibrated model.4.3 Quantitative ModelThe one period model in Section 4.2 provides qualitative intuition for why the relationship betweenTLCFs and risk or return should be either non-monotonic, first decreasing and then increasing, orstrictly increasing if other tax shields are sufficiently important. In this section, we solve a dynamicmodel where the firm’s cash flows, tax shields, and TLCFs behave in a similar way to the real world.In this model, we show that the relationship between TLCFs and risk tends to be positive, and quanti-tatively important.Consider a multi-period, discrete time extension of the one period model. The firm owns capitalKt = 1 and its only capital expenditure is the replacement of depreciated capital It = δKt = δ . The firmproduces pre-tax cash flows (EBITDA) of Π(At), which is a function of an exogenous productivityshock At . The firm distributes all free cash flows to investors, hence dividends are equal to the pre-taxcash flow, minus its tax bill Tt , minus capital expenditure costs:Dt =Π(At)−Tt − ItThe firm’s value is equal to the present value of its dividends, discounted by an exogenously specifiedstochastic discount factor Mt+1.The firm pays taxes at a rate τ on taxable income Π(At) minus any tax shields Φt . We also assumethat the tax paid cannot be negative, thus the total tax paid is:Tt = τmax(0,Π(At)−Φt)We assume that the firm has three types of tax-shields. First, non-depreciation and non-TLCF taxshields Φ0. The real world analog of Φ0 are interest tax shields (although we abstract from financialleverage), R&D tax shields, and any other general tax-shields; we assume these are constant. Second,depreciation tax shieldsΦδt = δ , which are also constant in the model because depreciation is constant.Third, tax loss carry forwards ΦT LCFt = δ , which will be described below. The firm’s total tax shieldsare Φt =Φ0+Φδ +ΦT LCFt .Because TLCFs are treated as in the real world, ΦT LCFt becomes a state variable which declineswhen TLCFs are used or expire, and increases when the firm incurs losses. Because of the rate of timepreference, the firm always uses as much TLCFs as possible to reduce current tax liability. Define the730 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.0580.060.0620.0640.0660.0680.070.0720.074TLCF/VE[R−R f]  TS0=0TS0=0.5xEBITDAFigure 4.3: Expected return as a function of TLCFThis figure plots the expected return on the y-axis, against the amount of tax-loss carry forwards(TLCF) on the x-axis from the simple model. We compare a firm with no other tax shields (solid line)and existing tax shields (dashed line).firm’s tax liability, before using the TLCFs, as T˜t =Πt−Φ0−Φδ . If T˜t < 0, then the firm pays zero taxand no TLCFs are used; furthermore, the stock of TLCFs increases by −T˜t . If 0 < T˜t < ΦT LCFt , thenTLCFs fully reduce the firm’s tax liability to zero, and the amount of TLCFs remaining is ΦT LCFt − T˜t .If 0 <ΦT LCFt < T˜t , then all of the TLCFs are used and zero remain; in this case, the firm’s tax liabilityTt = T˜t −ΦT LCFt > 0. We also assume that TLCF’s expire at a rate δ τ so that:ΦT LCFt+1 = (1−δ τ)max(0,ΦT LCFt − (Πt −Φ0−Φδt ))We can now formally describe the firm’s value:V (At ,ΦT LCFt ) = Dt +Et [Mt+1V (At+1,ΦT LCFt+1 )] s.t.Kt = 1Dt =Π(At)−Tt − ItIt = δKtTt = τmax(0,Π(At)− (Φ0+Φδ +ΦT LCFt ))Φδt = δKtΦT LCFt+1 = (1−δ τ)max(0,ΦT LCFt − (Πt −Φ0−Φδ ))(4.11)This more realistic model preserves the basic insight of the simple binomial model. Figure 4.3plots the expected return against the amount of TLCF implied by our quantitative model, but if the74Table 4.1: CalibrationThis table presents the value for each of the parameters used in the model.Preferencesβ 0.9 Time Discount Factorγ 8 Risk AversionCash Flowsψ 0.14 EBITDA-to-Total AssetsAa(0.81 1.00 1.19)Realizations of aggregate component of EBITDA/TAPa 0.9 0.1 0.00.05 0.9 0.050.0 0.1 0.9 Tr. Prob. of aggregate component of EBITDA/TAAi(0.46 1.00 1.54)Realizations of idiosyncratic component of EBITDA/TAPi 0.8 0.1 0.10.1 0.8 0.10.1 0.1 0.8 Tr. Prob. of idiosyncratic component of EBITDA/TATaxes and tax shieldsτ 0.35 Corporate tax rateδ 0.046 Depreciation tax shields-to-Total AssetsΦ0 0.023 Interest tax shields-to-Total Assetsδ τ 0.05 Expiration rate of TLCFfirm lives for a single period only.9 Note that if the firm has no pre-existing tax shields (solid line),then the expected return is non-monotonic in TLCF. The expected return first decreases, as additionaltax shields imply a safe cash flow (tax refund) relative to a zero-tax shield firm. The expected returnincreases for high levels of TLCF because the TLCF will be used in the good state of the world, whencash flows are already high, but will be lost in the bad state of the world, when cash flows are low. Onthe other hand, when there are enough pre-existing tax shields (dashed line), then the expected returncan be strictly increasing in TLCF.4.3.1 CalibrationThis section describes our choices of the model’s parameters. The model is solved annually.The actualparameters are listed in Table 4.1, and the target moments for both model and data appear in Table 4.2.The productivity shock At = Aat Ait consists of an aggregate and an idiosyncratic component, whichare uncorrelated; the stochastic discount factor depends on the aggregate component only. Both theaggregate component Aat and the idiosyncratic component Ait are 3-state Markov chains. We choose theparameters of the aggregate shock to roughly match the volatility and autocorrelation of the aggregatecomponent of EBITDA/TA. We choose the parameters of the idiosyncratic shock to roughly matchthe mean and volatility of our key variable, TLCF/EBITDA; as can be seen in Table 4.2, this choice9To create this figure, we assumed that there are three equally likely states. The stochastic discount factor is Mt+1 =(1.2,1.0,0.8), the pre-tax cash flow is Π(Kt ,At) = (0.5,1.0,1.5), and the tax rate is τ = 0.3.75also implies that the volatility and autocorrelation of the idiosyncratic component of EBITDA/TA areclose to the data.10We assume that the stochastic discount factor takes the form Mt+1 = β(Aat+1Aat)−γwith β = 0.9 andγ = 8.0. These numbers are chosen to target a risk free rate of 1.5% and a market return Sharpe ratioof 0.4. Although this is a partial equilibrium model and the SDF is exogenously specified, if aggregateproductivity growth Aat+1Aatwas equal to consumption growth, then this SDF would be consistent withone implied by a representative agent with CRRA utility where β and γ would correspond to timepreference and risk aversion, respectively.We assume that EBITDA is linear in capital multiplied by productivity, Π(At) = ψAtKt , whereKt = 1. We setψ = 0.14 to match the average EBITDA/TA, δ = 0.046 to match the average Depreciation-to-EBITDA ratio, and Φ0 = 0.023 to match the average Interest-to-EBITDA ratio. We set the TLCFdepreciation rate δ τ = 0.05 because the U.S. tax code allows a firm to keep TLCF for 20 years beforethey expire. We set the corporate tax rate τ = 35%, matching the statutory tax rate in the U.S between1993 and 2017.We simulate the model for 1,000 years and 200 firms, we then repeat this procedure 100 times tocompute model implied moments. Panel A of Table 4.2 reports target moments for the data and themodel counter-parts.4.3.2 Model resultsThe target moments, as well as some additional moments, for both model and data are presented inPanel A of Table 4.2. We first compute each moment, for each firm, using its time-series data; wethen compute the average and median of each moment across all firms. For the model, we report theaverage only, but median and average are fairly close for most quantities.The model fits the target moments (columns 1-2, 4, 6-9, 12-13) very well.11 Note that we do nottarget individual firms’ mean equity return or equity return volatility, but both are reasonably close tothe data (columns 10-11). We also do not target the volatility and autocorrelation of the idiosyncraticcomponent of EBITDA/TA (the idiosyncratic component is used to target the mean and volatility ofTLCF/EBITDA), nevertheless, these two moments are close to their data counterparts (columns 3 and5). We also solved a model where we target the volatility and autocorrelation of the idiosyncraticcomponent of EBITDA/TA; in this case, the average TLCF/EBITDA ratio is somewhat too high (0.2910We use the EBITDA-to-Total assets ratio instead of just EBITDA because in the data EBITDA is non-stationary andtakes on negative values, therefore we scale it by a non-negative, co-integrated series. Note that Total assets is slowermoving that EBITDA, thus EBITDA-to-Total assets still captures the key variation in EBITDA. We separate the volatility ofEBITDA-to-Total assets into aggregate and idiosyncratic components by the following procedure. We define the aggregatecomponent each year as the sum of all EBITDA that year, divided by the sum of all Total assets that year; we computethe volatility and auto-correlation of the aggregate component for 1962-2015. We then divide each firms EBITDA-to-Totalassets by the aggregate component and define this as the idiosyncratic component. For each firm, we compute the volatilityand autocorrelation of the idiosyncratic component and report the median, and the average weighted by the firm’s numberof annual observations.11We have nine free parameters(β ,γ,ψ,Aa,Pa,Ai,Pi,δ ,and Φ0), and nine target moments.76Table 4.2: Model ResultsThis table reports results from the model and compares them to the data. The procedure for computingthe aggregate and idiosyncratic components of EBITDA/TA is described in footnote 10. For the othermoments, we compute each statistic for each firm individually using its time series data, and thenreport either the median, or the average across all firms. For the model, we report the average only.The reported statistics are: the EBITDA-to-total assets ratio; the volatilities of the systematic and ag-gregate components of EBITDA/TA; the autocorrelations of the systematic and aggregate componentsof EBITDA/TA; depreciation, interest expenses, and TLCF each as a share of EBITDA; the volatilityof TLCF/EBITDA; the average excess stock return; the volatility of the excess stock return; the riskfree rate; and the Sharpe Ratio. Panels B (model) and C (data) report the results of Fama and MacBeth(1973) regressions of future (1 year and 5 year) realized stock returns, volatilities, and market betason firm characteristics. The key characteristic in our results is the ratio of TLCF-to-Total assets; eachfirm’s size (market value) is also used as a control. Volatilities are computed based on monthly returnsin the data. In the model, the one year volatility is defined as | Rit+1−Et [Rit+1] |, and the five yearvolatility is computed using annual returns; both are divided by√12 to convert to monthly.Panel A: Model and data accounting momentsCash Flows Tax Shields ReturnsETA σ(EaTAa)σ(E iTAi)ρ(EaTAa)ρ(E iTAi)DEPREINTET LCFE σ( T LCFE)E[Ri,e] σ [Ri,e] R f SRmData (Avg.) 0.138 0.139 0.64 0.88 0.60 0.319 0.177 0.236 2.210 10.8 49.4 1.5 0.40Data (Med.) 0.140 0.139 0.53 0.88 0.61 0.298 0.133 0.087 0.327 9.1 56.6 1.5 0.40Model 0.140 0.134 0.44 0.89 0.69 0.329 0.164 0.108 0.316 12.2 36.9 1.5 0.38Panel B: TLCF and equity risk, modelRt+1,t+k σt+1,t+k βMKTt+1,t+kk = 1y k = 5y k = 1y k = 5y k = 1y k = 5yUnivariateT LCFTA 0.277 0.750 0.369 0.178 0.274 0.532BivariateT LCFTA 0.024 0.046 0.121 0.062 0.018 0.027ME -0.067 -0.177 -0.091 -0.037 -0.093 -0.127Panel C: TLCF and equity risk, dataRt+1,t+k σt+1,t+k βMKTt+1,t+kk = 1y k = 5y k = 1y k = 5y k = 1y k = 5yUnivariateT LCFTA 0.06 0.22 0.05 0.05 0.16 0.19t-stat (2.47) (3.03) (5.79) (6.05) (3.99) (4.17)BivariateT LCFTA 0.06 0.21 0.05 0.05 0.15 0.18t-stat (2.56) (3.03) (5.82) (6.10) (3.96) (4.21)ME -0.00 -0.10 -0.00 -0.02 -0.02 -0.06t-stat (-1.18) (-2.32) (-7.97) (-8.63) (-2.81) (-3.47)compared to a median of 0.087 and a mean of 0.236), and the volatility is too high (0.66 comparedto a median of 0.327), nevertheless the key result - a positive relationship between TLCF and risk -remains unchanged.In Panel B of Table 4.2 we report results from a Fama MacBeth regression of future realized equityreturns, equity return volatilities, and market betas on the TLCF-to-Total Assets ratio. These regres-sions are done at 1 year, and 5 year horizons. Focusing first on the univariate results, all coefficientsare positive, implying that firms with more TLCFs tend to be riskier. Panel C reports analogous re-gressions using data from CRSP/Compustat; Section 4.4 presents many more similar regressions with77additional controls, but univariate and bivariate regressions are presented here for ease of comparisonwith the model. As in the model, there is a positive relationship between TLCF/TA and measures ofequity risk.Next, moving onto the bivariate regression. While in the data, there are multiple firm characteris-tics we can control for, in the model the only firm characteristic other than TLCF is the firm’s value orsize. Firms in the model may be valuable for one of two reasons: first firms with higher idiosyncraticproductivity Ai are more valuable because they have higher expected pre-tax cash flows, second firmsthat have more TLCFs are also more valuable because they are expected to pay less taxes. We redo thesame regressions, but adding firm size as a control. As in the data, firm size is negatively associatedwith risk,12 however, the coefficients on TLCFs are still positive.4.4 Empirical EvidenceThe model in Section 4.3 suggests that we should see a positive relationship between TLCFs andmeasures of equity risk. In this section we study the empirical support for these implications. Inparticular, we examine the relationship between TLCF and standard measures of risk (betas, volatility,realized return), 12 and 60 months ahead. Our empirical analysis uses both portfolio sorts and Famaand MacBeth (1973) regressions. Since our return regressions condition on standard risk factors, thereturn regressions provide evidence of the extent to which priced TLCF risk is or is not capturedin standard risk measures. As controls in the Fama and MacBeth (1973) regressions, we use size,book-to-market, profitability, EBITDA, interest tax credit, average tax rate, depreciation, leverage,and investment-to-assets. We also include controls for market, SMB, and HML betas.To illustrate our regression analysis, consider our return regressions. Firm characteristics at yeart are used to forecast the firm return from January to December in year t + 1 (k = 12), or Januaryto December in year t+5 (k = 60). Backward looking variables are computed with the same timewindow (k) as the forward looking returns. For each year in the sample, the following cross-sectionalspecification is estimated:Rit,t+k = αt + γtT LCFTAit+ψ ′t Xit + εitWhere:Rit,t+k =k∑n=1(rit+k− r ft+k)is the realized return in the following k periods (i.e., 12 or 60 months), and Xit represent the year-firmcharacteristics. We also use this approach to investigate the risk/TLCF regressions.12In this model, all firms, small and large, have the same risk in their pre-tax cash flows because all load in the sameway on the aggregate shock Aa. However, even when there are no TLCFs (δ τ = 1.0), small firms are riskier because theirnon-TLCF tax shields are higher than their cash flows, thus these non-TLCF tax shields can only be used in good statesof the world. In the presence of TLCFs (δ τ < 1.0), smaller firms will also have more TLCFs, therefore it is important tocontrol for size before concluding that TLCFs affect risk positively.78Table 4.3: TLCF Summary StatisticsThis table presents summary statistics for TLCF/TA [millions of dollars] available from Compustat.Statistics are presented by decade. N indicates the number of firms with positive TLCF, mean, standarddeviation, and percentiles are computed over the firms with positive TLCF for the period.N Mean SD 10th 50th 90th1971-1980 2,954 $11.06 $46.68 $0.25 $2.13 $19.161981-1990 10,261 $24.09 $107.04 $0.50 $3.97 $39.501991-2000 13,294 $55.61 $222.69 $1.10 $12.02 $109.002001-2010 14,946 $235.34 $871.46 $3.81 $54.43 $464.002011-2015 8,920 $837.18 $15,486.14 $6.40 $106.09 $881.80We begin our analysis in Section 4.4.1 with a description of the data.4.4.1 DataWe use the merged CRSP-Compustat database from WRDS to combine financial and stock price in-formation. The selected firm-year sample covers the period from 1971 to 2015. As seen in Figure 4.1,prior to 1971, very few firms had TLCFs, and TLCFs were relatively small in dollar value. FollowingFama and French (1992) we exclude firms in the financial industry, firms that are in our sample forless than two years, and firms not incorporated in the U.S.Our focus is on TLCF as reported in the Compustat data base and defined as13 ”The portionof prior and current year losses, applied as a reduction of taxable income in the next succeedingyear or years. When available and applicable, this item is usually reported in the notes to financialstatements.” This measure includes the current Tax Loss Carry Forwards, TLCFs of both domesticand foreign consolidated subsidiaries, and TLCFs incurred prior to acquisition of a consolidated sub-sidiary.Table 4.3 reports summary statistics for TLCFs. All statistics are in millions of dollars. Thegrowing economic importance of this variable is apparent in both the increase in the number of firmswith positive TLCF, and the increase in the size of the mean TLCF over time. Table 4.4 reportssummary statistics and correlations for some of the variables used in our analysis. All variables aredefined in this section appendix.4.4.2 TLCF and riskIn this section, we test for a relationship between TLCFs and equity risk. We measure equity risk inseveral ways. Naturally, we consider the market beta (βMkt). Additionally, since the risk amplificationis essentially due to option leverage, high TLCF firms should have a higher beta with respect to the13Standard and Poor’s (2017). ”Xpressfeed Reference Data”. Wharton Research Data Services (WRDS) atwrds.wharton.upenn.edu79Table 4.4: Summary StatisticsThis table presents summary statistics for the equal weighted average, value weighted average, andstandard deviation of the statistic for this period. We report the time-series average of each of thesecomputations.Panel A: Summary statisticsMEAvgMEBEMET LCFTAPROFTAEBIT DATADEPRTAINTTAITCTAEEW [x] 1.00 0.87 0.32 0.03 0.09 0.04 0.02 0.02EVW [x] 1.00 0.67 0.03 0.11 0.16 0.04 0.02 0.04σ [x] 5.27 1.93 1.17 0.25 0.21 0.04 0.02 0.03Panel B: CorrelationsBEMET LCFTAPROFTAEBIT DATADEPRTAINTTAITCTAMEAvgME -0.03 -0.04 0.06 0.06 0.01 -0.01 0.14BEME -0.09 -0.09 -0.08 0.01 0.07 0.09T LCFTA -0.49 -0.51 0.11 0.09 -0.14PROFTA 0.91 -0.16 -0.25 0.12EBIT DATA 0.07 -0.13 0.14DEPRTA 0.09 0.12INTTA 0.01stochastic discount factor and anything that the SDF loads on, regardless of whether the true model isthe CAPM or not. Therefore, the same relationship should be present in volatility, and other standardrisk measures, such as βSMB, and βHML. Finally, we consider average realized returns. In all cases, therisk measures are forward looking, thus we are testing whether current TLCF is related to future risk.We begin by looking a the risk of various TLCF to Total Assets portfolios. Specifically, we formone portfolio made of all firms with zero TLCF, labelled P0. This portfolio makes up 60% of ouroverall sample. The remaining 40% of our firms are split into equally sized portfolios, P1,P2, and P3,ranked in order of increasing TLCF-to-Total Assets. The results of this sort for various risk measuresare presented in Table 4.5. The TLCF portfolios are all monotonically increasing in risk as measuredby volatility, market beta, and SMB beta; however, there does not appear to be a relationship withHML beta. The relationship between TLCF and average return is not monotonic - first falling andthen rising - though the overall relationship is positive as with the other measures of risk.Portfolio sorts are suggestive of a positive univariate relationship between TLCF/TA and risk.Next, we use Fama and MacBeth (1973)regressions to confirm that this relationship is not jointlydriven by an omitted variable. Table 4.6 reports the result of a Fama-MacBeth regressions where thedependent variable is the market beta over 12 and 60 month horizons. TLCF/TA has strong uncondi-tional predictive power for 12 month ahead market betas with most controls, but becomes insignificantwhen past volatility is included. On the other hand, when forecasting 60 months CAPM betas, TL-CF/TA is always significant, for any controls we have included.Table 4.7 reports the result of a Fama-MacBeth regressions where the dependent variable is thevolatility of returns over 12 and 60 month horizons. TLCF/TA predicts volatility positively for both80Table 4.5: Portfolio Sorts on TLCF and Standard Risk MeasuresThis table reports results from sorting firms into four portfolios based on TLCF/TA at t. Portfolio 0contains all the firms with zero TLCF/TA; all other firms are sorted into portfolios 1, 2, and 3 such thateach portfolio contains 1/3 of positive TLCF/TA firms. For each portfolio, we report forward lookingstatistics over the subsequent 12 months. The statistics are average return Avg(Rt+1,t+12), volatilityσ(Rt+1,t+12), market beta βMKTt+1,t+12, SMB beta β SMBt+1,t+12, and HML beta βHMLt+1,t+12, all computed usingmonthly returns.P0 P1 P2 P3Avg(Rt,t+12) 1.33 1.19 1.36 1.63σ(Rt,t+12) 3.53 3.85 4.83 6.39βMKTt,t+12 1.07 1.18 1.27 1.40β SMBt,t+12 1.28 1.42 1.70 1.97βHMLt,t+12 -0.70 -0.37 -0.36 -0.65Table 4.6: TLCF and Future Market BetaThis table reports the results of Fama and MacBeth (1973) regressions of future realized market betaon firm characteristics. The key characteristic is the ratio of TLCF to Total Assets. The controls aresize, book-to-market, profitability, past market, SMB, and HML betas, past stock return, and pastvolatility. We use annual accounting variables from Compustat 1971-2015. Accounting variablesin year t are used to forecast the market beta of monthly returns from January to December in yeart +1 (k = 12) or in from January in year t +1 to December in year t +5 (k = 60). Backward lookingvariables are computed with the same k as the forward looking returns.k = 12 k = 60T LCFTA 0.16 0.14 0.09 −0.00 0.02 0.19 0.16 0.15 0.08 0.07t-stat (3.99) (3.33) (2.43) (−0.03) (0.55) (4.17) (3.90) (3.48) (3.00) (3.16)ME −0.07 −0.02 −0.06 −0.02t-stat (−2.94) (−1.32) (−3.64) (−1.91)BE/ME −0.10 −0.09 −0.09 −0.08t-stat (−3.89) (−4.53) (−4.20) (−4.57)PROF/ME −0.01 −0.00 −0.01 −0.00t-stat (−1.35) (−0.14) (−2.48) (−1.39)INV/TA 0.06 0.10 0.06 0.09t-stat (0.41) (0.85) (0.74) (1.22)βMKTt−k,t 0.13 0.10 0.10 0.07t-stat (8.28) (7.72) (7.33) (6.65)β SMBt−k,t 0.04 0.03 0.04 0.02t-stat (2.04) (2.51) (3.22) (3.27)βHMLt−k,t −0.04 −0.03 −0.04 −0.02t-stat (−2.19) (−2.43) (−3.06) (−3.04)E[Rt−k,t ] −0.04 −0.06 −0.04 −0.07t-stat (−0.78) (−1.27) (−1.27) (−2.26)σ [Rt−k,t ] 2.33 1.27 1.85 1.11t-stat (6.80) (4.46) (8.39) (5.73)R2 0.01 0.02 0.05 0.06 0.09 0.01 0.04 0.09 0.09 0.1481Table 4.7: TLCF and Future VolatilityThis table reports the results of Fama and MacBeth (1973) regressions of future realized stock returnvolatility on firm characteristics. The key characteristic in the ratio of TLCF to Total Assets. Thecontrols are size, book-to-market, profitability, past market, SMB, and HML betas, past stock return,and past volatility. We use annual accounting variables from Compustat 1971-2015. Accountingvariables in year t are used to forecast the volatility of monthly returns from January to Decemberin year t + 1 (k = 12) or from January in year t + 1 to December in year t + 5 (k = 60). Backwardlooking variables are computed with the same k as the forward looking returns.k = 12 k = 60T LCFTA 0.05 0.05 0.05 0.03 0.02 0.05 0.05 0.05 0.03 0.03t-stat (5.79) (5.73) (5.97) (5.11) (4.83) (6.05) (6.10) (6.13) (5.58) (5.51)ME −0.02 −0.01 −0.02 −0.01t-stat (−8.16) (−7.96) (−8.78) (−9.24)BE/ME 0.01 0.00 0.01 0.00t-stat (4.60) (3.15) (2.77) (1.27)PROF/ME −0.00 −0.00 −0.00 −0.00t-stat (−5.08) (−3.08) (−3.99) (−2.90)INV/TA 0.02 0.01 0.02 0.01t-stat (1.75) (0.91) (2.57) (1.86)βMKTt−k,t 0.00 −0.00 0.00 −0.00t-stat (3.01) (−4.50) (2.68) (−4.56)β SMBt−k,t 0.00 −0.00 0.01 0.00t-stat (1.46) (−0.72) (3.11) (0.31)βHMLt−k,t −0.00 −0.00 −0.00 −0.00t-stat (−1.23) (−1.15) (−1.14) (−0.83)E[Rt−k,t ] −0.04 −0.04 −0.04 −0.04t-stat (−11.54) (−11.60) (−15.23) (−15.41)σ [Rt−k,t ] 0.52 0.52 0.51 0.51t-stat (25.00) (25.00) (31.99) (31.34)R2 0.08 0.11 0.13 0.30 0.32 0.08 0.12 0.15 0.32 0.35the 12 and 60 month horizons. The relationship is even stronger than for the CAPM beta - it is notsensitive to controls, with most t-statistics ranging between 5 and 6 and the lowest being 4.78.Tables 4.8 and 4.9 examine SMB and HML betas, respectively. TLCF is positively and signifi-cantly related to SMB betas for 12 and 60 month horizons. On the other hand, TLCF is not signifi-cantly related to HML beta.Finally, we consider the relationship between current TLCF/TA and average realized future stockreturn. Table 4.10 reports results from Fama-MacBeth regressions, showing a positive relationshipbetween TLCFs and the realized stock return. TLCF enters positively and significantly in all modelsthat predict future returns for both the 12 and 60 month horizons, with t-statistics across specifiedcations ranging from 2.23 and 3.66. The predictive power of TLCF is little changed when Size andBook-to-Market, both of which enter significantly, are also included. It is also unaffected by includingpast betas or past volatility. It is interesting to note that existing measures of risk, either based on firmcharacteristics or (backward looking) loadings on factors do not drive away the significance of TLCF.82Table 4.8: TLCF and Future SMB BetaThis table reports the results of Fama and MacBeth (1973) regressions of future realized SMB betaon firm characteristics. The key characteristic is the ratio of TLCF to Total Assets. The controls aresize, book-to-market, profitability, past market, SMB, and HML betas, past stock return, and pastvolatility. We use annual accounting variables from Compustat 1971-2015. Accounting variables inyear t are used to forecast the SMB beta of monthly returns from January to December in year t + 1(k = 12) or from January in year t+1 to December in year t+5 (k = 60). Backward looking variablesare computed with the same k as the forward looking returns.k = 12 k = 60T LCFTA 0.57 0.54 0.43 0.22 0.23 0.52 0.49 0.44 0.23 0.22t-stat (2.88) (2.82) (2.70) (1.93) (1.98) (4.16) (4.14) (3.97) (3.67) (3.70)ME −0.37 −0.23 −0.38 −0.25t-stat (−7.15) (−7.90) (−7.10) (−7.99)BE/ME 0.03 0.01 −0.00 −0.02t-stat (0.86) (0.17) (−0.19) (−1.14)PROF/ME −0.02 −0.01 −0.02 −0.01t-stat (−2.79) (−1.19) (−3.26) (−1.86)INV/TA −0.33 −0.37 −0.29 −0.28t-stat (−1.43) (−1.66) (−2.61) (−2.69)βMKTt−k,t 0.09 0.04 0.09 0.03t-stat (2.44) (1.05) (4.42) (2.01)β SMBt−k,t 0.11 0.06 0.11 0.06t-stat (3.01) (2.61) (4.60) (4.83)βHMLt−k,t −0.03 −0.01 −0.02 −0.01t-stat (−0.98) (−0.57) (−1.68) (−1.14)E[Rt−k,t ] −0.32 −0.30 −0.32 −0.30t-stat (−3.79) (−3.73) (−6.41) (−6.25)σ [Rt−k,t ] 5.11 3.91 4.79 3.76t-stat (10.55) (8.60) (12.05) (9.77)R2 0.01 0.04 0.06 0.08 0.11 0.02 0.06 0.10 0.15 0.18This could be consistent either with mispricing - the market prices high TLCF firms too low relativeto their true risk leading to high positive returns, or with the market pricing being correct but thesemeasures of risk being incomplete.We also ran unreported regressions that included firm fixed effects, time fixed effects, and industryfixed effects. In all cases the TLCF coefficients have the same sign and similar significance as reportedabove, indicating that the forecasting power of TLCF is not related to unobserved firm, industry or timecharacteristics. Results from regressions including the Fama and French (2015) 4 factor model betas,and Hou et al. (2015) 4 factor model betas were also essentially the same as those reported above.Similar results were found when we standardized TLCF by size, book asset value, book debt plussize, or revenues rather than total assets.In summary, consistent with the model presented in Section 4.3, equity risk as measured by real-ized returns, volatility, market beta, and SMB beta, is positively and significantly related to TLCF inthe cross-section of firms.83Table 4.9: TLCF and Future HML BetaThis table reports the results of Fama and MacBeth (1973) regressions of future realized HML betaon firm characteristics. The key characteristic is the ratio of TLCF to total assets. The controls aresize, book-to-market, profitability, past market, SMB, and HML betas, past stock return, and pastvolatility. We use annual accounting variables from Compustat 1971-2015. Accounting variables inyear t are used to forecast the HML beta of monthly returns from January to December in year t +1(k = 12) or from January in year t+1 to December in year t+5 (k = 60). Backward looking variablesare computed with the same k as the forward looking returns.k = 12 k = 60T LCFTA −0.00 0.05 0.04 0.05 0.07 −0.03 −0.01 −0.03 −0.02 −0.01t-stat (−0.01) (0.63) (0.41) (0.54) (0.86) (−0.58) (−0.14) (−0.78) (−0.77) (−0.60)ME 0.01 0.02 −0.00 0.01t-stat (0.20) (0.81) (−0.10) (0.52)BE/ME 0.40 0.33 0.29 0.24t-stat (9.24) (7.53) (13.67) (10.56)PROF/ME 0.00 0.00 0.00 0.01t-stat (0.21) (0.46) (0.56) (1.66)INV/TA 0.28 0.27 0.25 0.23t-stat (0.98) (1.07) (1.39) (1.33)βMKTt−k,t −0.09 −0.07 −0.06 −0.04t-stat (−3.38) (−2.34) (−3.16) (−2.79)β SMBt−k,t 0.04 0.02 0.02 0.01t-stat (1.19) (0.97) (0.83) (0.78)βHMLt−k,t 0.11 0.09 0.09 0.07t-stat (4.11) (4.62) (4.25) (4.63)E[Rt−k,t ] −0.27 −0.16 −0.16 −0.08t-stat (−3.09) (−1.92) (−2.70) (−1.46)σ [Rt−k,t ] −0.55 −0.21 −0.58 −0.31t-stat (−0.86) (−0.38) (−1.17) (−0.77)R2 0.01 0.04 0.05 0.06 0.10 0.01 0.06 0.08 0.09 0.144.4.3 1986 Tax Reform ActThe Tax Reform Act of 1986 provides a clean test of our model. In our theory, the firm sells a calloption written on tax revenues; i.e., the tax rate times taxable income. If the tax rate deceases, the valueof this option, and the option leverage that is central to our theory, will both decrease. As describedby Guenther (1994), the government “in September 1986, reduced the statutory corporate income taxrate from 46 percent to 34 percent, effective for taxable years beginning on or after 1 July 1987. Thisrepresents a reduction of 26 percent of the pre-reform tax expense”.14Our theory predicts that such a change in tax rates will reduce the relationship between TLCF,risk and return. Indeed, Table 4.11 provides evidence of the predicted decrease in the TLCF/returnrelationship15. The slope from regressing 12-month ahead returns on TLCF is 0.08 in the full sample,but it falls from 0.18 in 1971-1986 to 0.02 in 1987-2015, though it remains significant in both samples.14The Omnibus Budget Reconciliation Act of 1993 increased the corporate tax rate to 35% on income above $18 million.15We also repeated the TLCF/risk measure analysis and find similar results84Table 4.10: TLCF and Future ReturnThis table reports the results of Fama-MacBeth regressions of future realized stock returns on firmcharacteristics. The key characteristic is the ratio of TLCF to Total Assets. The controls are size,book-to-market, profitability, past market, SMB, and HML betas, past stock return, and past volatility.We use annual accounting variables from Compustat 1971-2015. Accounting variables in year t areused to forecast the sum of log monthly returns from January to December in year t + 1 (k = 12)or from January in year t + 1 to December in year t + 5 (k = 60). Backward looking variables arecomputed with the same k as the forward looking returns.k = 12 k = 60T LCFTA 0.06 0.07 0.07 0.07 0.08 0.22 0.23 0.21 0.16 0.17t-stat (2.47) (2.95) (2.96) (3.47) (3.49) (3.03) (3.32) (3.27) (3.34) (3.66)ME −0.01 −0.01 −0.08 −0.05t-stat (−0.72) (−1.37) (−2.17) (−1.83)BE/ME 0.06 0.05 0.16 0.12t-stat (5.25) (4.92) (8.70) (7.37)PROF/ME −0.00 −0.00 −0.01 −0.01t-stat (−0.14) (−0.61) (−2.31) (−1.62)INV/TA −0.13 −0.15 −0.24 −0.24t-stat (−1.88) (−2.43) (−1.30) (−1.49)βMKTt−k,t −0.01 −0.01 −0.03 −0.04t-stat (−1.23) (−1.58) (−1.62) (−3.10)β SMBt−k,t −0.00 −0.01 0.02 0.00t-stat (−0.55) (−0.87) (0.90) (0.09)βHMLt−k,t −0.00 −0.00 0.00 −0.00t-stat (−0.30) (−0.43) (0.10) (−0.15)E[Rt−k,t ] −0.01 0.00 −0.23 −0.18t-stat (−0.62) (0.05) (−5.48) (−5.26)σ [Rt−k,t ] −0.02 −0.00 1.19 1.15t-stat (−0.12) (−0.03) (3.66) (3.94)R2 0.01 0.03 0.03 0.04 0.07 0.01 0.05 0.03 0.05 0.08For the 60-months ahead returns, the full sample slope is 0.17, but falls from 0.40 in the 1971-1986sample, to 0.02 and is only marginally significant in the 1987-2015 sample.4.5 ConclusionThis paper examines the implications of TLCFs for equity return moments. Although it has beenpreviously argued that the presence of tax shields reduces a firm’s risk, we show that this is notnecessarily the case. Empirically, we show a clear positive relationship between TLCFs and returns,volatility, and the market and SMB betas. Our theoretical model, calibrated to the data, reproducesthis relationship.Overall, our results suggest that TLCF and other tax management assets are important determi-nants of risk and return. A more complete understanding of the complex tax management task thatfirm’s faces will be the subject of future research.85Table 4.11: TLCF and Future returns, 1986 change in tax codeThis table reports the results of Fama MacBeth regressions of future realized stock return on firmcharacteristics. The key characteristic is the ratio of TLCF to Total Assets. The controls are size,book-to-market, profitability, past market returns, SMB, and HML betas, past stock return, and pastvolatility. We use annual accounting variables from Compustat 1971-2015. Accounting variables inyear t are used to forecast the firm returns from January to December in year t + 1 (k = 12) or fromJanuary year t+1 to December in year t+5 (k = 60). Backward looking variables are computed withthe same k as the forward looking returns.k = 12 k = 60Full Sample 1971-1986 1987-2015 Full Sample 1971-1986 1987-2015T LCFTA 0.08 0.18 0.02 0.17 0.40 0.02t-stat (3.49) (3.48) (2.15) (3.66) (4.42) (1.61)ME -0.01 -0.01 0.00 -0.05 -0.12 0.00t-stat (-1.37) (-1.66) (0.62) (-1.83) (-2.08) (0.58)BE/ME 0.05 0.04 0.05 0.12 0.14 0.10t-stat (4.92) (4.50) (3.50) (7.37) (8.86) (4.19)PROF -0.00 0.00 0.00 -0.01 -0.02 0.00t-stat (-0.61) (-0.09) (-1.07) (-1.62) (-2.36) (0.45)INV/TA -0.15 -0.16 -0.14 -0.24 -0.32 -0.19t-stat (-2.43) (-1.88) (-1.68) (-1.49) (-1.15) (-0.95)βMKTt−k,t -0.01 -0.02 0.00 -0.04 -0.04 -0.03t-stat (-1.58) (-2.01) (-0.45) (-3.10) (-1.91) (-2.44)β SMBt−k,t -0.01 0.00 -0.01 0.00 0.03 -0.02t-stat (-0.87) (0.35) (-1.38) (0.09) (1.97) (-1.09)βHMLt−k,t -0.00 0.00 -0.01 -0.00 0.00 -0.01t-stat (-0.43) (0.35) (-0.70) (-0.15) (0.25) (-0.33)E [Rt−k,t ] 0.00 0.05 -0.03 -0.18 -0.14 -0.21t-stat (0.05) (1.59) (-1.08) (-5.26) (-2.26) (-5.24)σ [Rt−k,t ] -0.00 -0.11 0.06 1.15 1.11 1.18t-stat (-0.03) (-0.46) (0.36) (3.94) (1.77) (4.45)R2 0.07 0.08 0.06 0.08 0.12 0.0686Chapter 5ConclusionIn this thesis I studied the impact of three legal institutions over asset prices, the decisions of firms andhouseholds, and the economic sustainability of regulated markets. The three legal institution studiedhere are the personal bankruptcy code, the regulation of the harvest of natural resources (fish), andthe tax code. These institutions directly define property rights, support contractual arrangements, anddictaminate the payment of taxes, key legal institutions in place for financial markets, with significantimplications for the decisions of the agents involved.In my study of the personal bankruptcy code I focused on how the magnitude of the homesteadexemption relates to the supply and demand for loans. As the homestead exemption specifies theamount of home equity that a household will be entitled to keep at bankruptcy, one might expect thata higher exemption will increase the moral hazard on the part of the borrowers, leading to higherdemand for loans, with higher delinquency ratios, while the lenders will respond with higher interestrates.My results show that the magnitude of the homestead exemption is significant to explain the totalamount of loans to households, its aggregate riskiness and the state level house prices. I find that stateswith a higher homestead exemption exhibit fewer secured loans granted, lower delinquency ratios onsecured and unsecured loans, lower interest rates, and higher house prices.To understand the economic mechanism behind these empirical results, I did a theoretical analysisusing an equilibrium model on which a set of households face idiosyncratic income risk and usesecured and unsecured loans to finance their consumption. The households have the option to filefor bankruptcy in a process that resembles the personal bankruptcy code. Loans are provided in themodel by a competitive lender that price default risk using the overall debt position of the households,and their assets holdings. Lenders are assumed to initially be unable to observe the riskiness of thehousehold’s income but can invest in a costly monitoring technology that eliminates this informationasymmetry.The model shows that the empirical results are consistent with the following economic channel.A more generous homestead exemption increases the household’s benefits after bankruptcy. Bene-87fits arise from the implicit insurance provided by the real estate, therefore the demand for housingincreases endogenously pushing house prices up. These bankruptcy benefits for the households aremirrored by a rise in the credit losses faced by the lender. As unsecured debt is partially or fullydischarged, the lender has incentives to increase monitoring, and price each loan accordingly to itsspecific credit risk. Although, monitoring benefits the low risk households as they no longer providesubsidies to the riskier households, eroding their pooling advantage as they are now subject to higherinterest rate as the exemption increases. This effect produces an aggregate reduction in the securedloans as now low risk households increase their demand for unsecured loans, and reduce their overallleverage, therefore, the overall debt. This mechanism is consistent with the empirical evidence indi-cating that higher exemptions lead to a lower fraction of secured loans issued, with lower rates anddelinquency, with higher overall house prices.The second legal institution studied in this work is the regulation of the harvest of natural re-sources, with special focus on fisheries and the potential of this institution to achieve a financially andecologically sustainable exploitation. My co-author and I constructed an optimal stochastic controlapproach model to value a fishery, with two sources of uncertainty: the biomass and the price. Thesolution of the model is obtained by solving a Hamilton-Jacobi-Bellman equation for the value of theFishery by using a value-function iteration approach. Overall, the results highlight the strong non-linear relation between the biomass and the resource price on the value of the fishery and the optimalharvesting policy.The solution is implemented using the estimated parameters for the British Columbia halibut fish-ery. The model results are used to simulate the dynamic of the studied fishery finding that the optimalharvesting policy is sustainable. For negative shocks to the biomass growth we obtain reductions ofthe resource stock, but the simulations show that with almost certainty the extinction of the resourcewill not occur.The model solved for a realistic set of parameters suggests that an economically viable fisheryis feasible, that overfishing is indeed not optimal, even in the presence of fish price and biomassuncertainty. This highlights the value of conservation and confirms that current efforts are indeedefficient from a social and a financial perspective, but can be improved.The third legal institution studied is the tax code. I focus on how the treatment of corporatelosses for tax shield benefit ties in with the firm’s equity risk and return. This research examinesthe implications of Tax Loss Carry Forwards (TLCFs) for equity return moments. Although it hasbeen previously argued that the presence of tax shields reduces a firm’s risk, we show that this is notnecessarily the case. Empirically, we show a clear positive relationship between TLCFs and returns,volatility, the market, High-Minus-Low (HML) and Small-Minus-Big (SMB) betas. Our theoreticalmodel, calibrated to the data, reproduces this relationship. Overall, our results suggest that TLCFsand other tax management assets are important determinants of risk and return. A more completeunderstanding of the complex tax management task that firm’s faces will be the subject of futureresearch.88To conclude, the results of this thesis show that the three legal institutions studied here have asignificant impact on the decisions of market agents and in the determination of asset prices, that theyare relevant not only for academics, but also for investors, households facing financial distress, lendersevaluating granting policies, and governmental institutions designing regulations, henceforth they havethe potential to help in the improvement of these legal institions directly related to the development offinancial credit markets, the extraction of endangered natural resources, and the understanding of theimpact of the tax code on the firm’s financial decisions and the choices of investors.5.1 Future ResearchThe first line of future research is related to my work on personal bankruptcy. My results show thatthe magnitude of the homestead exemption has implications on the real-estate market. I would liketo explore this in greater depth. Specifically, there is a positive effect on house prices driven by anincrease in the demand, however, it would be interesting to also incorporate the supply effect, notonly in construction, but also in the access to loans for development. Also, I have noticed that thepersonal bankruptcy code exhibits similar features internationally. With this in mind, I would like toexplore this problem using, for example, Canadian data, in order to understand whether the patternsand theoretical results are also relevant abroad.With relation to the sustainable harvesting of natural resources, a significant body of the fish-eries literature has concluded that the presence of overinvestment is behind the mentioned overfishingevidence (Clark (2010)). One interesting hypothesis that has yet to be explored is that there couldbe a relationship between the historical level of investment and the behavior of a firm adjusting itsharvesting policy in the presence of shocks in the biomass and fish prices to maximize its value.As my research shows, the optimal harvest policy requires a high degree of flexibility to respondto changes in price and biomass. This flexibility comes in the form of a high fishing capacity but at thecost of remaining unused at least part of the time. This channel could be even more important if theinvestment is highly irreversible. My co-author and I are already exploring this problem by developinga model of a firm harvesting a natural resource, which includes the real option for investment.The goal is to revisit the investment problem in the presence of multiple sources of uncertaintyand different levels of investment reversibility. The objective is to explore the new economic channelsthat may arise from these novel features, and compare the optimal capital investment policies with thetraditional capital accumulation benchmarks, revisiting the overinvestment conclusion.With respect to my research on Tax Loss Carry Forwards, an interesting problem related is therelation between TLCFs and the real option to invest. Following Auerbach and Poterba (1987), anhypothesis to explore is that when a firm that has has TLCFs invests in a new asset, the after-taxincome will most likely decrease. As the project initial losses will be carried forward until the firmachieves a positive taxable income, some investments will be discouraged by the presence of unusedtax benefits as they may be lost before used. My co-authors and I have preliminary empirical evidence89consistent with this hypothesis, indicating that the valuation of the real option to invest for differentlevels of TLCFs is indeed an interest extension of our work.90BibliographyS. Agarwal, C. Liu, and L. Mielnicki. Exemption laws and consumer delinquency and bankruptcybehavior: an empirical analysis of credit card data. The Quarterly Review of Economics andFinance, 43:273–289, 2003. → page 97J. F. Albertus, B. Glover, and O. Levine. Heads i win, tails you lose: asymmetric taxes and foreigninvestment. Working Paper, 2017. → page 69R. Altshuler, A. J. Auerbach, M. Cooper, and M. Knittel. Understanding U.S. Corporate Tax Losses.University of Chicago Press, 2009. → page 67B. W. Ambrose, J. Conklin, and J. Yoshida. Credit rationing, income exaggeration, and adverseselection in the mortgage market. The Journal of Finance, 71(6):2637–2686, 2016. → page 97K. Athreya. Fresh start or head start? uniform bankruptcy exemptions and welfare. Journal ofEconomic Dynamics and Control, 30(11):2051–79, 2006. → pages 10, 35A. Auclert, W. Dobbie, and P. Goldsmith. Macroeconomic effects of debt relief: Consumerbankruptcy protections in the great recession. National Bureau of Economic Research, (w25685),2019. → page 11A. J. Auerbach. Why have corporate tax revenues declined? another look. NBER Working PaperSeries, 12463, 2006. → page 67A. J. Auerbach and J. M. Poterba. The effects of taxation on capital accumulation. University ofChicago Press, 1987. → page 89T. Beck and R. Levine. Handbook of New Institutional Economics. Springer, 2005. → page 1J. Berkowitz and R. Hynes. Bankruptcy exemptions and the market for mortgage loans. The Journalof Law and Economics, 42(2):809–830, 1999. → pages 5, 6, 10H. Bester. Screening vs. rationing in credit markets with imperfect information. American EconomicReview, 75(4):850–855, 1985. → page 11M. Brennan. Taxes, market valuation, and corporate financial policy. National Tax Journal, 23:417–427, 1970. → page 67M. J. Brennan and E. S. Schwartz. Evaluating natural resource investments. Journal of Business,pages 135–157, 1985. → page 4791J. M. Burke, C. R. Taylor, and L. Wagman. Information acquisition in competitive markets: Anapplication to the us mortgage market. American Economic Journal: Microeconomics, 4(4):65–106, 2012. → page 97G. Cerqueiro, D. Hegde, M. Penas, and R. C. Seamans. Debtor rights, credit supply, and innovation.Management Science, 63(10):3311–3327, 2016. → page 7S. Chatterjee, D. Corbae, M. Nakajima, and J.-V. Rios-Rull. A quantitative theory of unsecuredconsumer credit with risk of default. Econometrica, 75(6):1525–1589, 2007. → page 10S. Chomsisengphet and R. Elul. Bankruptcy exemptions, credit history, and the mortgage market.Journal of Urban Economics, 59(1):171–188, 2006. → pages 10, 19C. W. Clark. Mathematical bioeconomics: the mathematics of conservation. John Wiley and Sons,2010. → pages 48, 89C. W. Clark and G. P. Kirkwood. On uncertain renewable resource stocks: optimal harvest policiesand the value of stock surveys. Journal of Environmental Economics and Management, 13(3):235–244, 1986. → page 46C. W. Clark and G. R. Munro. Capital theory and the economics of fisheries: implications for policy.Marine Resource Economics, 32(2):123–142, 2017. → page 119C. W. Clark, G. R. Munro, and B. Turris. Impacts of harvesting rights in Canadian Pacific fisheries.Fisheries and Oceans Canada, 2009. → pages 47, 55, 122N. Confessore and B. Applebaum. How a simple tax rule let donald trump turn a 960 million lossinto a plus. New York Times, 2016. → page 67I. Cooper and J. Franks. The interaction of financing and investment decisions when the firm hasunused tax credits. The Journal of Finance, 38(2):571–583, 1983. → page 68S. Corradin, R. Gropp, H. Huizinga, and L. Laeven. The effect of personal bankruptcy exemptions oninvestment in home equity. Journal of Financial Intermediation, 25:77–98, 2016. → page 10J. L. Davis, E. Fama, and K. French. Characteristics, covariances, and average returns: 1929 to 1997.The Journal of Finance, 55(1):389–406, 2000. → page 124G. Dell’Ariccia and R. Marquez. Information and bank credit allocation. Journal of FinancialEconomics, 72(1):185–214, 2004. → page 11G. Dell’Ariccia and R. Marquez. Lending booms and lending standards. The Journal of Finance, 61(5):2511–2546, 2006. → page 12D. J. Denis and S. B. McKeon. Operating losses and cash holdings. Working Paper, 2016. → page 67P. Dubey and J. Geanakoplos. Competitive pooling: Rothschild stiglitz reconsidered. The QuarterlyJournal of Economics, 117(4):1529–1570, 2002. → page 29S. Elias and A. Renauer. How to file for Chapter 7 Bankruptcy. Nolo Legal, 2001,2009,2016. →page 1492E. Fama and K. French. The cross-section of expected stock returns. The Journal of Finance, 47:427–465, 1992. → page 79E. Fama and K. French. A five-factor asset pricing model. Journal of Financial Economics, 116(1):1–22, 2015. → page 83E. Fama and J. MacBeth. Risk, return, and equilibrium: Empirical tests. Journal of PoliticalEconomy, 81(3):607–636, 1973. → pages 78, 80, 81, 82, 83, 84E. F. Fama and K. R. French. Industry costs of equity. Journal of Financial Economics, 43(2):153–193, 1997. → page 55FAO. Fisheries management 3: Managing fishing capacity. FAO Technical Guidelines forResponsible Fisheries, 2008. → page 45S. Fay, E. Hurst, and M. J. White. The household bankruptcy decision. American Economic Review,92(3):706–718, 2002. → page 97A. Ghent. Securitization and mortgage renegotiation: evidence from the great depression. TheReview of Financial Studies, 24(6):1814–1847, 2011. → page 6J. R. Graham. A review of taxes and corporate finance. Foundations and Trends in Finance, 1(7),573-691 2006. → page 66C. Grant. Evidence on the insurance effect of bankruptcy exemptions. Journal of Banking &Finance, 34(9):2247–2254, 2010. → page 9R. C. Green and E. Talmor. The structure and incentive effects of corporate tax liabilities. TheJournal of Finance, 1(7):1095–1114, 1985. → pages 68, 69, 70J. Greiff. Quicktake: Overfishing. Bloomberg News, 2017. → page 3R. Gropp, J. Scholz, and M. J. White. Personal bankruptcy and credit supply and demand. TheQuarterly Journal of Economics, 112(1):217–251, 1997. → page 9D. A. Guenther. Earnings management in response to corporate tax rate changes: Evidence from the1986 tax reform act. The Accounting Review, pages 230–243, 1994. → page 84B. Heer and A. Maussner. Dynamic general equilibrium modeling: computational methods andapplications. Springer Science and Business Media, 2009. → pages 51, 56, 57T. Hintermaier and W. Koeniger. Debt portfolios and homestead exemptions. American EconomicJournal: Macroeconomics, 8(4):103–141, 2016. → pages 10, 114K. Hou, C. Xue, and L. Zhang. Digesting anomalies: An investment approach. The Review ofFinancial Studies, 28(3):650–705, 2015. → page 83R. M. Hynes, A. Malani, and E. A. Posner. The political economy of property exemption laws. TheJournal of Law and Economics, 47(1):19–43, 2004. → pages 11, 97S. Indarte. The impact of debt relief generosity and liquid wealth on household bankruptcy.Available at SSRN 3378669, 2019. → page 1193K. Jeske, D. Krueger, and K. Mitman. Housing, mortgage bailout guarantees and the macroeconomy. Journal of Monetary Economics, 60(8):917–35, 2013. → pages 10, 35S. F. Kvamsdal, D. Poudel, and L. K. Sandal. Harvesting in a fishery with stochastic growth and amean-reverting price. Environmental and Resource Economics, 63(3):643–663, 2016. → pages47, 116L. Lefgren and F. McIntyre. Explaining the puzzle of cross-state differences in bankruptcy rates. TheJournal of Law and Economics, 52(2):367–393, 2009. → page 97B. Lev and D. Nissim. Taxable income, future earnings, and equity values. The Accounting Review,79(4):1039–1074, 2004. → page 69W. Li, M. J. White, and N. Zhu. Did bankruptcy reform cause mortgage defaults to rise? AmericanEconomic Journal: Economic Policy, 3(4):123–47, 2011. → page 97E. Y. Lin and M. J. White. Bankruptcy and the market for mortgage and home improvement loans.Journal of Urban Economics, 50(1):138–162, 2001. → pages 10, 19I. Livshits, J. MacGee, and M. Tertilt. Consumer bankruptcy: A fresh start. American EconomicReview, 97(1):402–418, 2007. → page 10E. Lyandres, L. Sun, and L. Zhang. The new issues puzzle: Testing the investment-basedexplanation. The Review of Financial Studies, 21(6):2825–2855, 2007. → page 125S. Majd and S. C. Myers. Valuing the government’ tax claim on risky corporate assets. NBERWorking Paper, (1553), 1985. → pages 68, 70A. Mian and A. Sufi. Household leverage and the recession of 2007–09. IMF Economic Review, 58(1):74–117, 2010. → pages 5, 97A. Mian and A. Sufi. House prices, home equity-based borrowing, and the us household leveragecrisis. American Economic Review, 101(5):2132–56, 2011. → pages 97, 98A. Mian, A. Sufi, and F. Trebbi. The political economy of the us mortgage default crisis. AmericanEconomic Review, 100(5):1967–98, 2010. → page 97A. Mian, A. Sufi, and F. Trebbi. Foreclosures, house prices, and the real economy. The Journal ofFinance, 70(6):2587–2634, 2015. → page 97H. Milde and J. G. Riley. Signaling in credit markets. The Quarterly Journal of Economics, 103(1):101–129, 1988. → page 29M. Miller. Who files for bankruptcy? state laws and the characteristics of bankrupt households.Working Paper, 2011. → page 97K. Mitman. Macroeconomic effects of bankruptcy and foreclosure policies. American EconomicReview, 106(8):2219–2255, 2016. → pages 7, 10, 35, 43F. Modigliani and M. H. Miller. Corporate income taxes and the cost of capital: a correction. TheAmerican Economic Review, 53(3):433–443, 1963. → pages 4, 66, 6894R. Morck, E. S. Schwartz, and D. Stangeland. The valuation of forestry resources under stochasticprices and inventories. Journal of Financial and Quantitative Analysis, 24(4):473–487, 1989. →page 46A. Murillas. Investment and development of fishing resources: a real options approach. InternationalInstitute of Fisheries Economics and Trade, 2001. → page 47S. Nelson. Pacific Commercial Fishing Fleet: Financial Profiles for 2007. Fisheries and OceansCanada (DFO), 2009. → pages 47, 54, 120S. Nelson. Pacific Commercial Fishing Fleet: Financial Profiles for 2009. Fisheries and OceansCanada (DFO), 2011. → pages 47, 54, 120L. Nøstbakken. Regime switching in a fishery with stochastic stock and price. Journal ofEnvironmental Economics and Management, 51(2):231–241, 2006. → pages 47, 48K. M. Pence. Foreclosing on opportunity: State laws and mortgage credit. Review of Economics andStatistics, 88(1):177–182, 2006. → page 10R. S. Pindyck. Uncertainty in the theory of renewable resource markets. The Review of EconomicStudies, 51(2):289–303, 1984. → pages 46, 47D. Poudel, L. K. Sandal, S. F. Kvamsdal, and S. I. Steinshamn. Fisheries management underirreversible investment: does stochasticity matter? Marine Resource Economics, 28(1):83–103,2013. → page 47A. Ravid. On interactions of production and financial decisions. Financial Management, 17(3):87–99, 1988. → page 66J. G. Riley. Informational equilibrium. Econometrica: Journal of the Econometric Society, pages331–359, 1979. → pages 29, 33A. Schiller. Corporate taxation and the cross-section of stock returns. Working paper, 2015. → page69G. Sethi, C. Costello, A. Fisher, M. Hanemann, and L. Karp. Fishery management under multipleuncertainty. Journal of Environmental Economics and Management, 50(2):300–318, 2005. →page 46F. Severino and M. Brown. Personal bankruptcy protection and household debt. Working Paper,2017. → pages 9, 10, 19I. Stewart and A. Hicks. Assessment of the Pacific halibut (Hippoglossus stenolepis) stock at the endof 2017. International Pacific Halibut Commission, 2017. → pages 51, 52I. Stewart and R. Webster. Overview of data sources for the Pacific halibut stock assessment, harveststrategy policy, and related analyses. International Pacific Halibut Commission, 2017. → pages51, 52J. E. Stiglitz and A. Weiss. Credit rationing in markets with imperfect information. AmericanEconomic Review, 71(3):393–410, 1981. → page 1195F. Streitferdt. The valuation of tax loss carryforwards. Working paper, 2010. → page 69M. J. White. Bankruptcy reform and credit cards. Journal of Economic Perspectives, 21(4):175–200,2007. → page 97M. J. White. Bankruptcy: Past puzzles, recent reforms, and the mortgage crisis. American Law andEconomics Review, 11(1):1–23, 2009. → page 97Y. Ye and N. Gutierrez. Ending fishery overexploitation by expanding from local successes toglobalized solutions. Nature Ecology & Evolution, 1(0179), 2017. → pages 3, 4596Appendix AAppendix to Chapter 2A.1 Complementary LiteratureSeveral papers have also studied the relation between the homestead exemption and bankruptcy rates.Fay et al. (2002) used the Panel Study of Income Dynamics, from 1984 to 1995, to show that thefinancial benefit from bankruptcy is positively related with the debt discharge. Hynes et al. (2004)showed that state exemptions are correlated with bankruptcy filing, suggesting that the examination ofthe impact of bankruptcy laws should not treat protection levels as exogenous variables. Agarwal et al.(2003), White (2007) and White (2009) found that in the cross-section, state exemptions are positivelycorrelated with higher delinquency in unsecured loans and bankruptcy rates.Lefgren and McIntyre (2009) used zip-code-level data of bankruptcy filings between 1999 and2001. They found that the homestead exemption (included as a High and Low dummy) does notexplain the variation in bankruptcy filings across states, as the exemption only affects a small fractionof bankruptcies.Miller (2011) constructed a data set of the 1,694 households that filed for bankruptcy in 2007.He showed that high homestead exemption levels encouraged households with higher asset to file forbankruptcy. Finally, Li et al. (2011) show that 2005 BAPCPA act had a positive effect in the primeand subprime mortgage default rates.My paper also relates to the literature on legal institutions and asset prices. Mian et al. (2010) andMian et al. (2015) study how the judicial requirement for foreclosures relate to real estate prices, find-ing that easier foreclosures enforcement led to a large decline in house prices, residential investment,and consumer demand from 2007 to 2009.Monitoring efforts in secured lenders have been explored in the literature. Burke et al. (2012)show that, for secured loans, if the lender increases its screening efforts, it ends up rejecting the riskyapplicants. Mian and Sufi (2010) and Mian and Sufi (2011) show that lending standards dramaticallyweakened after 2004, which ended in lenders allocating resources to increasingly risky borrowers.Ambrose et al. (2016) study the effect of adverse selection in the mortgage market had during the97Figure A.1: House Price Index State Average, The Zillow Home Value Index (ZHVI) and theFederal Housing Finance Agency (FHFA) House Price Index (HPI). Data from 1999 to2016.rise in leverage previous to the Great Recession, showing that risky lenders where likely to inflate thereported income to improve their access to loans.A.2 House Prices Trends 1999-2016With respect to the house prices, the median value of a residential house for the 1999-2016 period was$179,537, with a range from $104,300 at the 10th percentile to $290,500 at the 90th percentile. TheU.S. average cross-sectional house price are included in Figure A.1 illustrating the time trends of thismarket.Figure A.1 shows the general house price behavior observed during the last 27 years. From 1999to 2006 is characterized by a a sustained in house prices, which has been extensively discussed in theliterature, and directly related to the Great Recession, that finally produced the decay in the pricesobserved from 2007 to 2011 (Mian and Sufi (2011)). Sustained growth is again observed from 2011 to2016. As an opening illustration of the relation between the homestead exemption and house prices,Figure A.2 show the difference the house price average for states above and below the homesteadexemption median of each year.Figure A.2 shows that during the previous to the relation between high and low exemptions stateswas close, but it becomes positive and significant after the start of the great recession and remains untiltoday, indicating that high exemption states exhibited higher house prices, although they did exhibiteda decay in its level, after the start of the recession.A.3 U.S. Court data on Chapter 7U.S. Court data includes statistics for the non-business Chapter 7 filings from 2001 to 2016. Duringthat period there was a total of 13,659,782 cases (11% of the total number of households in the U.S.),highlighting the importance of the institution. With respect to the 2005 BACPAC act, is possible to98Figure A.2: House Price Index For States with High and Low Homestead Exemption, FederalHousing Finance Agency (FHFA) House Price Index (HPI). Data from 1999 to 2016.Table A.1: Non-Business Chapter 7 Filings Summary StatisticsThis table presents the state level summary the number of non-business Chapter 7 filings obtained from the U.S. BankruptcyCourts. This information is obtained for the 12-month period ending in December. Data is available from 2001 to 2016.year N Mean SD 10th 90th2001 50 20,455 21,207 2,185 46,6502002 50 21,564 21,657 2,015 49,0002003 50 22,944 22,214 2,162 52,7612004 50 22,178 21,026 2,166 53,3982005 50 32,368 31,755 3,158 84,1702006 50 6,957 6,543 640 17,1252007 50 9,934 10,222 975 25,2812008 50 14,174 16,586 1,183 35,9372009 50 20,033 25,321 1,472 48,2412010 50 21,845 30,081 1,577 48,1382011 50 19,003 26,539 1,363 41,5522012 50 16,198 21,567 1,200 35,3732013 50 14,008 17,263 1,097 31,7012014 50 11,889 13,634 933 26,6462015 50 10,261 11,090 849 23,7682016 50 9,386 9,803 879 22,167notice that there is a reduction on the average number of filings per year, a clear indicator of the morerestrictive process induced by the act. Table A.1 presents the Chapter 7 fillings per year, and TableA.2 presents the summary of the assets and debts of the non-business Chapter 7 filings from 2007 to2016.The data resumed in Table A.2 is reported by the U.S. Bankruptcy Courts as part of the BAPCPA,and provides state level aggregate statistics of the assets and liabilities of the non-business Chapter7 filed cases. Although the aggregate data loses part case heterogeneity, there are some aggregatefeatures that will be useful to understand which households are going through the process, as that 76%of the household’s assets are concentrated in real state, showing that this asset is the main wealth being99Table A.2: Non-Business Chapter 7 Assets and Liabilities Summary StatisticsThis table presents the state level summary of the assets and liabilities reported by individual debtors in non-business Chapter7 cases. This data is obtained from the U.S. Bankruptcy Courts website (BAPCPA Table 1A). Information is reported forthe 12-month period ending in December. Data is available from 2007 to 2016.N Mean Median SD 10th 90thCases (per State) 529 13,536 7,730 18,869 982 29,947Total Assets (Per Case) 529 $99,262 $90,679 $41,359 $56,575 $149,193Real Property (Per Case) 529 $75,126 $66,237 $37,318 $37,558 $121,010Personal Property (Per Case) 529 $24,171 $22,460 $13,595 $16,486 $30,714Total Liabilities (Per Case) 529 $192,500 $153,045 $376,399 $110,360 $243,849Secured Claims (Per Case) 529 $89,548 $78,767 $41,097 $47,224 $146,621Unsecured Priority Claims (Per Case) 529 $7,364 $2,873 $76,777 $1,900 $4,980Unsecured Non-Priority Claims (Per Case) 529 $81,154 $68,398 $108,060 $55,426 $113,809protected by the bankruptcy procedure. Is also noticeable that the unsecured non-priority1 liabilitiesconstitute 42% of the total household liabilities, showing that a significant amount of the household’sdebt may be discharge in bankruptcy.A.4 PSID data of households’ wealth portfolio and the magnitude ofthe homestead exemptionI include data from the Panel Study of Income Dynamics (PSID) of the University of Michigan tounderstand the U.S. households’ wealth portfolio. Unfortunately several states are represented by asmall number of households, making it difficult the use this data for inference over the cross-sectionaldifferences at state level. All information is collected from 1999 to to 2016. Table A.3 summarizes thePSID data at state level, to show the wealth profile across states, and how it relates to the magnitudeof the homestead exemption.Table A.3 highlights the relevance of the “House Value” in the household’s balance sheet, illus-trating the importance of real estate as a wealth accumulation device. This Table also shows that thereis a sizable, positive, home equity. This magnitude is fundamental to understand the financial benefitof filing for bankruptcy, as it will be the subject of protection of the homestead exemption.Table A.4 presents the PSID state average of the unsecured loans and Home Equity.Panel A of Table A.4 shows that the average home equity is positive, and that the unsecured debt isclose to $10,000 dollars, smaller is several cases than the home equity. This shows that the homesteadexemption will be extremely relevant for most of those households, as in the case of default on theunsecured debt, their housing value will be greater than their dischargeable debt, hence, if the homeequity is below the exemption, they will see their house liquidated.Panel B of Table A.4 complements the previous observation by showing that on average, 30.6%1The unsecured priority claims include tax obligations, alimony and child support, and are non discharged, so theyremain as part of the household obligations after bankruptcy100Table A.3: PSID State Level Average Wealth, Summary StatisticsThis table presents the state level mean of the wealth components and total debt surveyed in the PSID household panel data.The information is obtained every two years and represent the current level of the surveyed variable. Data is included from1999 to 2015.N Mean Median SD 10th 90thHouse Value 432 $113,116 $91,369 $66,254 $49,378 $253,390Remaining Mortgage 432 $48,841 $40,980 $25,773 $15,205 $95,595Other Real Estate 432 $22,632 $15,332 $23,913 $1,671 $71,375Vehicles 432 $11,954 $12,875 $4,413 $8,803 $18,182Business 432 $11,779 $21,268 $26,808 - $78,565Individual Retirement Account (IRA) 432 $26,749 $20,960 $24,783 $2,636 $57,238Stocks (non-IRA) 432 $29,019 $16,913 $46,314 $289 $62,201Transaction Accounts 432 $17,893 $13,723 $20,157 $4,325 $32,658Other Assets 432 $7,533 $4,927 $11,851 $140 $14,955Table A.4: PSID State Level Average Home Equity and Unsecured Debt, Summary StatisticsThis table presents the state level mean of the wealth components and total debt surveyed in the PSID household panel data.The information is obtained every two years and represent the current level of the surveyed variable. Data is included from1999 to 2015.Panel A: Home Equity and Unsecured DebtN Mean Median SD 10th 90thHome Equity 432 $64,275 $48,315 $46,606 $25,465 $125,768Unsecured Debt Value 432 $9,964 $9,170 $5,546 $4,400 $16,537Panel B: State Level Fraction of Households with Positive Home Equity, Positive Unsecured Debt, and Exempted HomeEquity and Positive Unsecured Debt.N Mean Median SD 10th 90thHome Equity and Unsecured Debt>0 432 30.6% 29.4% 11.1% 20.0% 40.7%Home Equity < Homested Exemption 432 28.8% 24.9% 20.9% 4.4% 60.4%Exempted Home Equity and Debt>0 432 17.3% 14.5% 13.3% 1.8% 35.0%of surveyed households exhibit positive home equity and positive debt, these are households who maydirectly benefit from the homestead exemption at bankruptcy. On average 28.8% of the householdshave their home equity fully protected by the state homestead exemption, while 17.3% of those fullyprotected have unsecured debt. These households will see their unsecured debt discharged in case offiling for personal bankruptcy.Although the PSID data is rich terms of the household information, there are several states inthe U.S. with less than 10 households surveyed each year, for example, Rhode Island has 3 surveyedhouseholds in 1999, and 7 in 2015. The reduced number of observations for some states makes itdifficult to draw robust inference for the cross-sectional effect of the homestead exemption over thehousehold debt and home equity. Acknowledging this difficulty, I ran preliminary tests for the stateaverage housing wealth and home equity, finding that a higher homestead exemption is related to101higher housing wealth and higher home equity.A.5 Final Period Optimal PoliciesAt t = 1 households is state j ∈ {(i,e),(i,u)} maximize:maxc j1,hj1,djB,djM ,Bj1,Mj1u(c j1)+φu(h j1)+βδu(p1hj1)As {d jB,d jM,B j1,M j1} are estimated by maximizing the cash-on-hand W j1 for each of the previouslydiscussed relevant cases, the household solves the maximization problem taking this account as given.This is equivalent to solve:maxc j1,hj1u(c j1)+φu(h j1)+βδu(p1hj1)subject to:c j1+ p1hj1 ≤W j1Then, dropping the indexes of consumption and housing for notation simplicity, the Lagrangian ofthe presented problem is:L =c(1−γ)(1− γ) +φh(1−γ)(1− γ) +βδ(ph)(1−γ)(1− γ) +λ (Wj1 − c− ph)The F.O.C. are:c−γ −λ = 0φh−γ +βδ p(ph)−γ −λ p = 0Re-arranging:h−γ[φp+βδ p−γ]= λ = h−γA(p)Then:hA(p)−1/γ = cReplacing in the budget constraint, the optimal policies as a function of the household wealth are:h j1 =W j1A(p1)−1/γ + p1c j1 =W j1 A(p1)−1/γA(p1)−1/γ + p1102A.6 Additional TablesTable A.5: Credit Card Loans and Homestead ExemptionThis table present the results for regressions for credit card loans to individuals obtained from the FFIEC database, andinclude the ratio of these loans to of total loans, the annual loan yield, and the delinquency ratio. The main control isthe logarithm of the homestead exemption, but the regressions also include the logarithm of the per-capita income, thepercentage of the population with high school diploma, the unemployment level, the percentage of households under povertylevel, the percentage of households lead by married couples, the percentage of households lead by a female, and the numberof households with children. Standard errors are heteroskedasticity-robust and clustered at the state level.(1) (2) (3)Credit Card Loans Credit Card Credit Card% of Total Loans Yield Delinquency Ratiolog(Homestead Exemption) 0.14 -0.91 -0.24(t-stat) (1.60) (-0.87) (-1.4)House Price Index -0.01 -0.01 0.00(t-stat) (-1.10) (-0.76) (0.03)log(Income) -2.64 3.57 0.05(t-stat) (-2.48) (1.44) (0.02)High School -0.00 0.12 0.02(t-stat) (-0.66) (0.35) (0.33)Unemployment 0.02 1.46 0.07(t-stat) (1.10) (1.34) (0.49)Under Poverty -4.90 7.96 3.40(t-stat) (-1.26) (0.99) (1.13)Married Couples -0.15 3.87 0.55(t-stat) (-2.00) (1.88) (1.35)Female Householder -0.19 2.61 0.55(t-stat) (-1.84) (1.22) (1.2)Families with Child -0.07 -1.00 -0.18(t-stat) (-1.60) (-1.38) (-0.69)Age -0.04 1.33 -0.06(t-stat) (-0.81) (0.5) (-0.16)Race -0.13 -0.28 0.35(t-stat) (-2.95) (-0.95) (2.8)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.53 0.37 0.28Observations 433 433 433Sample 2006-2016 2006-2016 2006-2016103Table A.6: House Price Index Summary StatisticsThis table presents the state level summary different house price indexes. The Zillow Home Value Index (ZHVI) is used inall the respective measures and correspond to a smoothed, seasonally adjusted measure of the median estimated home valueacross a given region and housing type. It is a dollar-denominated alternative to repeat-sales indexes. The Federal HousingFinance Agency (FHFA) House Price Index (HPI) is a broad measure of the movement of single-family house prices. TheHPI is a weighted, repeat-sales index, meaning that it measures average price changes in repeat sales or refinancing on thesame properties. This information is obtained by reviewing repeat mortgage transactions on single-family properties. HPIAll Transaction Index is 100 in 1980, HPI Purchase Only Index is 100 in 1991. Data is available from 1999 to 2016.N Mean Median SD 10th 90thZillow State ZHVI Median Value Per Sqft 729 $122.95 $102.00 $67.95 $68.00 $187.00Zillow State ZHVI - 1 bedroom 622 $123,454 $106,700 $64,765 $64,900 $204,700Zillow State ZHVI - All Houses 714 $179,537 $151,350 $87,711 $104,300 $290,500Zillow State ZHVI - Single Family Residence 714 $184,835 $153,200 $97,900 $103,800 $303,800FHFA HPI All-Transaction Index 816 314.43 288.07 104.23 190.24 459.07FHFA HPI Purchase Only Index 816 195.79 191.71 42.58 147.27 253.01Table A.7: House Prices and Homestead Exemption GroupsThis table present the results for regressions of the two house price indexes, the FHFA House Price Index (HPI) and theZillow Home Value Index (ZHVI) per Sq.Ft. but using instead of the homestead exemption magnitude as a the main controlcategorical variables for high vs. low homestead exemption, and low vs. mid vs. high homestead exemption. All regressionsalso include the house price index, the logarithm of the income per-capita, the percentage of the population with high schooldiploma, the unemployment rate, the percentage of households bellow poverty level, the percentage of households lead bymarried couples, the percentage of households lead by a female, the number of households with children, the median stateage, and the fraction of the state population of white race as the controls. Standard errors are heteroskedasticity-robust andclustered at the state level.(1) (2) (3) (4) (5) (6)FHFA House Price Index Zillow Home Value Index (ZHVI) per Sq.Ft.log(Homestead Exemption) 0.29 0.29(t-stat) (2.89) (2.89)High vs. Low Homestead Exemption 0.35 0.09(t-stat) (1.59) (1.17)Low vs. Mid Homestead Exemption 0.75 0.21(t-stat) (2.27) (2.07)Low vs. High Homestead Exemption 0.09 0.01(t-stat) (0.06) (0.20)Controls Yes Yes Yes Yes Yes YesYear-FE Yes Yes Yes Yes Yes YesObs. 12,612 15,806 15,806 6,267 7,726 7,726104Table A.8: U.S. Census New House Units Permits and Homestead Exemption CategoriesThe following table presents a test for U.S. Census permits to build new 1-unit houses, at state level. The main control isthe logarithm of the homestead exemption at state level. Regression include year and state fixed effects. Standard errors areheteroskedasticity-robust.U.S. Census New Unit Hoses Permits [100 Units](1) (2) (3) (4)Full Sample (1999-2016) 1999-2005 2006-2010 2011-2016log(Homestead Exemption) -2.81 -5.31 -1.85 -1.33(t-stat) (-1.92) (-1.55) (-3.03) (-2.76)Year FE Yes Yes Yes YesState FE Yes Yes Yes YesR-Squared 0.19 0.03 0.19 0.09N 697 328 164 205Table A.9: Construction and Land Development Loans and Homestead Exemption CategoriesThe following table presents a test for the FFIEC Construction and Land Development Loans as a fraction of total loans, atstate level. The main control is the logarithm of the homestead exemption at state level. Regression include year and statefixed effects. Standard errors are heteroskedasticity-robust.U.S. Census New Unit Hoses Permits [100 Units](1) (2) (3)Full Sample (2006-2016) 2006-2010 2011-2016log(Homestead Exemption) -0.55 -0.68 -0.26(t-stat) (-1.57) (-0.75) (-1.20)Year FE Yes Yes YesState FE Yes Yes YesR-Squared 0.79 0.91 0.97N 551 156 395105Table A.10: Household Secured Loans and Homestead Exemption CategoriesThis table present the estimation for the secured loans allocation as a fraction of the the total loans, the annual yield and thedelinquency ratio. The main control in this case is the homestead exemption categories low, mid and high (low categorysi dropped), and all regressions include the house price index, the logarithm of the income per-capita, the percentage ofthe population with high school diploma, the unemployment rate, the percentage of households bellow poverty level, thepercentage of households lead by married couples, the percentage of households lead by a female, the number of householdswith children, the median state age, and the fraction of the state population of white race as controls. Standard errors areheteroskedasticity-robust.(1) (2) (3)Family Real Estate Loans Family Real Estate Family Real Estate% of Total Loans Effective Rates Delinquency RatioMid Homestead Exemption 0.31 0.03 -0.15(t-stat) (0.71) (0.43) (-1.78)High Homestead Exemption -1.35 -0.03 -0.27(t-stat) (-2.05) (-1.39) (-3.01)House Price Index 0.00 0.00 0.01(t-stat) (0.55) (-2.63) (8.84)log(Income Per Capita) -0.06 -0.62 -1.25(t-stat) (-0.01) (-1.1) (-1.92)High School 0.13 0.01 0.00(t-stat) (2.32) (1.77) (-0.08)Unemployment 0.42 0.05 -0.03(t-stat) (3.47) (2.77) (-1.23)Bellow Poverty 4.42 0.72 0.45(t-stat) (2.56) (3.16) (1.5)Married Couples 1.00 0.09 0.03(t-stat) (2.72) (2.02) (0.6)Female Householder 0.85 0.05 0.13(t-stat) (2.17) (0.95) (2.38)Families with Child 0.18 0.03 0.03(t-stat) (0.91) (1.22) (1.57)Age 0.71 -0.01 -0.09(t-stat) (1.7) (-0.12) (-1.7)Race -0.62 -1.32 7.80(t-stat) (-0.05) (-0.85) (3.9)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.96 0.70 0.89Observations 510 510 510Sample Available 2006-2016 2006-2016 2006-2016106Table A.11: Household Secured Loans by Type and the Homestead ExemptionThis table present the estimation for the different type of loans that constitute the household secured loan portfolio, whichare 1-4 families real estate loans, multifamily (more than 5) real estate loans, and home equity loans. The main control isthe logarithm of the Homestead Exemptions, and all regressions include the house price index, the logarithm of the incomeper-capita, the percentage of the population with high school diploma, the unemployment rate, the percentage of householdsbellow poverty level, the percentage of households lead by married couples, the percentage of households lead by a female,the number of households with children, the median state age, and the fraction of the state population of white race ascontrols. Standard errors are heteroskedasticity-robust.(1) (2) (3) (4)Household Real Estate 1-4 Family RE Multifamily RE Home Equity% of Total Loans % of Total Loans % of Total Loans % of Total Loanslog(Homestead Exemption) -0.98 -1.26 0.16 0.13(t-stat) (-2.67) (-3.81) (1.19) (1.40)House Price Index 0.00 0.00 0.00 0.00(t-stat) (-0.17) (-0.16) (0.09) (-0.17)log(Income) -6.70 0.00 -2.19 -4.51(t-stat) (-1.08) (0.01) (-1.30) (-3.47)High School 0.17 0.15 0.02 0.00(t-stat) (2.45) (2.29) (1.01) (-0.03)Unemployment 0.55 0.50 0.05 0.00(t-stat) (3.6) (3.65) (0.98) (0.01)Bellow Poverty 4.00 4.96 -1.45 4.86(t-stat) (1.91) (2.44) (-2.23) (0.88)Married Couples 0.61 0.91 -0.92 -0.21(t-stat) (1.28) (1.88) (-1.3) (-1.94)Female Householder 0.17 0.64 -1.16 -0.36(t-stat) (0.31) (1.28) (-1.23) (-2.67)Families with Child 0.09 0.22 -1.02 -0.03(t-stat) (0.37) (0.87) (-1.54) (-0.61)Age 0.01 0.57 -0.33 -0.23(t-stat) (0.01) (1.21) (-1.52) (-2.57)Race -0.35 -0.22 -0.73 -0.06(t-stat) (-1.9) (-1.32) (-1.75) (-1.27)Year-FE Yes Yes Yes YesState-FE Yes Yes Yes YesAdj. R-Squared 0.94 0.96 0.86 0.95Observations 433 433 433 433Sample Available 2006-2016 2006-2016 2006-2016 2006-2016107Table A.12: Total Secured Loans and Homestead ExemptionThis table present the estimations for the total secured loans (FFIEC Real Estate Loans for households and commercial) atstate level. The L.H.S. variables is the median over all the commercial banks insured by the FFIEC of the real estate loanspercentage of the total loans, and the separated of this ratio into household secured loans and commercial secured loans. Themain control is the logarithm of the Homestead Exemptions. All regressions include the house price index, the logarithm ofthe income per-capita, the percentage of the population with high school diploma, the unemployment rate, the percentage ofhouseholds bellow poverty level, the percentage of households lead by married couples, the percentage of households leadby a female, the number of households with children, the median state age, and the fraction of the state population of whiterace as controls. Standard errors are heteroskedasticity-robust.(1) (2) (3)Total Secured Loans Household Secured Loans Commercial Secured Loans% of Total Loans % of Total Loans % of Total Loanslog(Homestead Exemption) -0.32 -0.98 0.89(t-stat) (-0.93) (-2.67) (2.3)House Price Index 0.01 0.00 0.00(t-stat) (1.66) (-0.17) (0.57)log(Income) 19.39 -6.70 14.85(t-stat) (2.92) (-1.08) (2.3)High School 0.10 0.17 -0.13(t-stat) (1.39) (2.45) (-1.45)Unemployment 0.35 0.55 -0.57(t-stat) (1.99) (3.6) (-3.01)Bellow Poverty 7.29 4.00 1.35(t-stat) (3.06) (1.91) (0.49)Married Couples 0.12 0.61 -1.20(t-stat) (0.25) (1.28) (-2.16)Female Householder 0.06 0.17 -0.79(t-stat) (0.09) (0.31) (-1.29)Families with Child 0.05 0.09 -0.26(t-stat) (0.27) (0.37) (-0.89)Age 0.65 0.01 -0.26(t-stat) (1.24) (0.01) (-0.44)Race 0.26 -0.35 0.42(t-stat) (1.2) (-1.9) (1.92)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.96 0.94 9.85Observations 433 433 433Sample Available 2006-2016 2006-2016 2006-2016108Table A.13: Commercial Loans and Homestead ExemptionThis table present the estimations for FFIEC Commercial Loans at state level. The L.H.S. variables is the median over allthe commercial banks insured by the FFIEC of the commercial real state and non-real estate loans as a percentage of thetotal loans. The main control is the logarithm of the Homestead Exemptions. All regressions include the house price index,the logarithm of the income per-capita, the percentage of the population with high school diploma, the unemployment rate,the percentage of households bellow poverty level, the percentage of households lead by married couples, the percentageof households lead by a female, the number of households with children, the median state age, and the fraction of the statepopulation of white race as controls. Standard errors are heteroskedasticity-robust.(1) (2) (3)Total Commercial Loans Commercial Real Estate Commercial non-RE% of Total Loans % of Total Loans % of Total Loanslog(Homestead Exemption) 0.89 0.78 0.11(t-stat) (2.30) (2.04) (0.71)House Price Index 0.00 0.01 -0.01(t-stat) (0.57) (1.59) (-2.50)log(Income) 14.85 21.58 -6.74(t-stat) (2.3) (2.99) (-2.20)High School -0.13 -0.07 -0.05(t-stat) (-1.45) (-0.87) (-1.50)Unemployment -0.57 -0.20 -0.37(t-stat) (-3.01) (-1.03) (-4.57)Bellow Poverty 1.35 3.77 -2.42(t-stat) (0.49) (1.5) (-1.55)Married Couples -1.20 -0.69 -0.51(t-stat) (-2.16) (-1.32) (-2.18)Female Householder -0.79 -0.47 -0.33(t-stat) (-1.29) (-0.72) (-1.15)Families with Child -0.26 -0.07 -0.20(t-stat) (-0.89) (-0.26) (-1.79)Age -0.26 0.41 -0.67(t-stat) (-0.44) (0.69) (-2.79)Race 0.42 0.55 -0.13(t-stat) (1.92) (2.26) (-1.50)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.94 0.94 0.93Observations 433 433 433Sample Available 2006-2016 2006-2016 2006-2016109Table A.14: Household Unsecured Loans and Homestead Exemption CategoriesThis table present the estimation for unsecured loans to households (FFIEC Individual Loans). The L.H.S. variables are theratio of household unsecured loans to total loans, the annual yield of the household unsecured loans, and the delinquencyratio. The main control in this case is the homestead exemption categories low, mid and high (low category si dropped),and all regressions include the house price index, the logarithm of the income per-capita, the percentage of the populationwith high school diploma, the unemployment rate, the percentage of households bellow poverty level, the percentage ofhouseholds lead by married couples, the percentage of households lead by a female, the number of households with children,the median state age, and the fraction of the state population of white race as controls. Standard errors are heteroskedasticity-robust.(1) (2) (3)Loans to Individuals Loans to Individuals Loans to Individuals% of Total Loans Effective Rates Delinquency RatioMid Homestead Exemption 0.03 -0.47 -0.59(t-stat) (0.48) (-0.82) (-2.01)High Homestead Exemption -0.14 -0.22 -0.36(t-stat) (-1.59) (-0.52) (-1.23)House Price Index 0.00 0.00 0.00(t-stat) (-2.94) (-1.09) (-0.35)Income Per Capita -1.61 9.78 -7.71(t-stat) (-2.48) (2.01) (-2.9)High School 0.01 0.02 -0.04(t-stat) (0.61) (1.02) (-1.3)Unemployment 0.01 0.10 0.02(t-stat) (0.36) (1.43) (0.26)Bellow Poverty 0.09 4.36 -4.92(t-stat) (0.26) (2.25) (-4.34)Married Couples -1.79 46.66 -8.77(t-stat) (-0.41) (1.35) (-0.51)Female Householder -0.01 0.71 0.07(t-stat) (-0.28) (1.86) (0.31)Families with Child 0.01 0.25 -0.05(t-stat) (0.36) (1.77) (-0.57)Age -0.04 0.61 0.04(t-stat) (-0.67) (2.68) (0.18)Race 0.01 0.10 -0.45(t-stat) (0.33) (0.97) (-4.76)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.51 0.91 0.77Observations 510 510 510Sample Available 2006-2016 2006-2016 2006-2016110Table A.15: Credit Card Loans and Homestead ExemptionThis table present the estimation for FFIEC Credit Card Loans to Individuals. The L.H.S. variables are the ratio of creditcard loans to individuals to total loans, the annual credit card yield, and the delinquency ratio. The main control is theratio Homestead Exemptions to House Prices. All regressions include the house price index, the logarithm of the incomeper-capita, the percentage of the population with high school diploma, the unemployment rate, the percentage of householdsbellow poverty level, the percentage of households lead by married couples, the percentage of households lead by a female,the number of households with children, the median state age, and the fraction of the state population of white race ascontrols. Standard errors are heteroskedasticity-robust.(1) (2) (3)Credit Card Loans Credit Card Loans Credit Card Loans% of Total Loans Yield Delinquency RatioHomestead ExemptionHouse Price Index 0.23 0.92 0.17(t-stat) (1.93) (0.93) (0.32)log(Income) -3.64 29.76 -0.83(t-stat) (-2.3) (1.32) (-0.26)High School -0.01 0.11 0.02(t-stat) (-1.18) (0.35) (0.32)Unemployment -0.01 1.44 0.05(t-stat) (-0.36) (1.27) (0.36)Bellow Poverty -0.94 6.94 3.40(t-stat) (-1.57) (0.93) (1.15)Married Couples -0.19 3.57 0.49(t-stat) (-1.72) (1.82) (1.21)Female Householder -0.21 2.27 0.47(t-stat) (-1.7) (1.11) (1.07)Families with Child -0.10 -1.13 -0.20(t-stat) (-1.7) (-1.55) (-0.74)Age -0.07 1.35 -0.10(t-stat) (-1.11) (0.51) (-0.24)Race -0.14 -0.37 0.30(t-stat) (-2.6) (-1.29) (2.42)Year-FE Yes Yes YesState-FE Yes Yes YesAdj. R-Squared 0.49 0.36 0.29Observations 450 450 450Sample Available 2006-2016 2006-2016 2006-2016111Table A.16: Loans Yield and Homestead ExemptionThis table present the results for regressions for Loans Yield obtained from the FFIEC, including the Family Real EstateLoans Yield, Individual Loans Yield, Credit Card Loans Yield, and the spread between them. The main control is thelogarithm of the Homestead Exemptions, but also I include regressions including a dummy variable for high exemption vs.low exemption, and low exemption vs. mid exemption vs. high exemption. Alls regressions include the per-capita Income,the percentage of the population with high school diploma, the unemployment level, the percentage of households bellowpoverty level, the percentage of households lead by married couples, the percentage of households lead by a female, and thenumber of households with children as controls, and standard errors are heteroskedasticity-robust and clustered at the statelevel.(1) (2) (3) (4) (5)Family Real Estate Individual Loans Credit Card Family R.E. - Ind. Family R.E. - C.C.Yield Yield Yield Yield Spread Yield Spreadlog(Homestead Exemption) -0.07 -0.21 -0.91 -0.14 -0.84(t-stat) (-1.41) (-0.90) (-0.87) (-0.61) (-0.80)House Price Index 0.01 0.00 -0.01 -0.01 -0.01(t-stat) (7.6) (-0.75) (-0.76) (-2.14) (-1.31)log(Income) -2.23 7.18 35.67 9.41 37.90(t-stat) (-2.91) (1.78) (1.44) (2.33) (1.53)High School 0.00 0.01 0.12 0.01 0.12(t-stat) (0.03) (0.52) (0.35) (0.5) (0.34)Unemployment -0.04 0.11 1.46 0.15 1.50(t-stat) (-1.47) (1.37) (1.34) (1.86) (1.38)Bellow Poverty 0.13 2.74 7.96 2.62 7.83(t-stat) (0.38) (1.96) (0.99) (1.85) (0.96)Married Couples -0.05 0.23 3.87 0.28 3.92(t-stat) (-0.84) (0.75) (1.88) (0.91) (1.91)Female Householder 0.03 0.54 2.61 0.51 2.58(t-stat) (0.44) (1.44) (1.22) (1.35) (1.21)Families with Child 0.04 0.15 -1.00 0.11 -1.04(t-stat) (1.6) (1.37) (-1.38) (0.97) (-1.42)Age -0.14 0.53 1.33 0.67 1.47(t-stat) (-2.32) (2.27) (0.5) (2.85) (0.56)Race 0.09 0.05 -0.28 -0.04 -36.62(t-stat) (3.54) (0.48) (-0.95) (-0.44) (-1.29)Year-FE Yes Yes Yes Yes YesState-FE Yes Yes Yes Yes YesAdj. R-Squared 0.98 0.47 0.36 0.83 0.41Observations 433 433 433 433 433Sample Available 2006-2016 2006-2016 2006-2016 2006-2016 2006-2016112Table A.17: Ratio Homestead Exemption over House Prices: 2011 - 2016This table presents the ratio of the state homestead exemption over the median house price value, reported by the FederalHousing Finance Agency (FHFA). The median price is calculated over a set of purchases of single- family homes andreported at state level.State 2010 2016Alabama 0.42 1.18Arizona 6.33 4.49Arkansas Unlimited UnlimitedCalifornia 2.05 1.51Colorado 3.88 3.49Connecticut 3.60 2.98Delaware 1.54 3.27Florida Unlimited UnlimitedGeorgia 0.72 1.16Idaho 4.03 3.03Illinois 1.31 0.82Indiana 1.77 1.62Iowa Unlimited UnlimitedKansas Unlimited UnlimitedKentucky 0.48 0.31Louisiana 1.04 1.18Maine 4.12 3.40Maryland 0.00 0.48Massachusetts 13.56 8.64Michigan 1.85 1.29Minnesota 11.68 13.27Mississippi 4.36 3.14Missouri 0.77 0.54Montana 18.94 16.01Nebraska 3.26 2.54Nevada 25.85 17.59New Hampshire 8.41 6.46New Jersey 0.00 0.00New Mexico 5.20 4.73New York 2.98 3.18North Carolina 2.55 2.13North Dakota 4.90 3.65Ohio 1.90 9.81Oklahoma Unlimited UnlimitedOregon 1.56 1.20Pennsylvania 1.61 1.39Rhode Island 8.31 11.78South Carolina 3.86 3.79South Dakota Unlimited UnlimitedTennessee 0.32 0.23Texas Unlimited UnlimitedUtah 1.35 1.49Vermont 9.39 4.01Virginia 0.24 0.21Washington 3.38 2.54West Virginia 3.26 2.06Wisconsin 6.32 5.43Wyoming 0.70 0.63113Table A.17 shows that in most of the states the homestead exemption is greater than the average priceof a single family house, highlighting that for most of the households the homestead exemption willbe relevant, although not as strong in the margin as in most cases the home equity will significantlybelow the exemption magnitude. This values are consistent with those reported in Hintermaier andKoeniger (2016). A second observation from this table shows that there is also historical variation inthis ratio, which is driven by changes in house prices, as the homestead exemption exhibits limitedchanges during the studied period.114Appendix BAppendix to Chapter 3B.1 Value-Function Algorithm SchemeIn this section we sketch the solution algorithm, describing the key steps, but abstracting from detailedcalculations. Broadly, we start from an initial value function and iterate over the policy space until amaximum is attained. The outcome of the process is the maximized value-function, and the optimalpolicy, for each point in our two-dimensional state space.Step 1: Initialize v0.To define the initial value of the value function, we use a coarse grid on the defined interval[I1, IN ]× [P1,PM], and compute the optimal value using our algorithm. Then, we use our desired grid,interpolate using the coarse grid, and the estimated value function, to obtain an initial value functionon the finer desired grid.Step 2: Compute a new value function v1, and the policy q1.For each (n,m) ∈ {(1,1) ,(1,2) , ..,(N,M)} repeat the following steps:Step 2.1: Initialize the policy q∗(In,Pm) = q1Step 2.2:Find the index i∗ that maximizes:wi∗ = pi(In,Pm,qi∗)+ e−r∆t∑k, jλ IkλPj vˆ0(In+G(In)−qi∗+ InσI√∆tZIk,PmeµP∆t+σP√∆tZPj)Where qi∗ is q∗(In,Pm) = qi∗ , and vˆ0 is the interpolated value function, for the next period state,computed using the initial value function v0. Piecewise Cubic Hermite Interpolating Polynomial areused to compute these values.Step 2.3: Replace v1 by the respective elements wi∗ , for each point in the state space (n,m).Step 3: Check for convergence. If:115max(n,m)∈{(1,1),...,(N,M)}| v1n,m− v0n,m |≤ ε tol ε tol > 0stop iterating, else, replace v0 with v1, and return to step 2.When the algorithm converges we have the optimal v and q for our problem.B.2 Price Dynamic Estimation for the British Columbia HalibutIn this section we describe the price dynamic models and estimations for the time series of ex-vesselprices for the British Columbia halibut. In particular, we start from the general stochastic process:lnPt+1 = f (Pt)+g(Pt)εPtWhere Pt is the unit fish price at year t, f (Pt) is the expected annual rate of change in the logarithmof the price, g(Pt) is the volatility of the unexpected price shocks εPt which are assumed to be i.i.d.standard normal.To identify which functional form of f (Pt) is consistent with the time series of halibut prices from1990 to 2016, we test 5 of the most used price stochastic dynamics in the literature. We test three timeseries models: the log-normal i.i.d. model or ARIMA(0,1,0) in the first difference, an ARIMA(1,1,0)or autoregressive of order 1, and a ARIMA(0,1,1) or moving average of order one. We use only firstorder lags as the first autocorrelation is the only statistically different from zero (Figure B.1 includesthe estimated autocorrelations (black bars) and the respective 95% confidence interval (gray bands)being the fist lag the only estimated autocorrelation significantly different from zero).Beside this time series models, we use two economic models, the first is a model of inverse demandon which the price dynamic is related to changes in the total harvest and an unobserved stochasticprocess that affects the demand for the halibut. Second, we test the mean reverting price modelpresented in Kvamsdal et al. (2016). Notice that in the last two models the price dynamics is nottotally exogenous since it depends on the harvest. Formally the models to test are:1. ARIMA(0,1,0): lnPt+1 = lnPt +νP+σPεPt2. ARIMA(1,1,0): lnPt+1 = α+ρ lnPt +σPεPt3. ARIMA(0,1,1): lnPt+1 = α+θσPεPt−1+σPεPt4. Inverse Demand: Pt = eα+σPεPt q−γt =⇒ lnPt+1 = α− γ lnqt +σPεPt5. Mean-Reverting: lnPt+1 = α+ lnPt +βP P0Pt +βhqtPt+σPεPtThe economic implications of the models impose restrictions on some of the parameters. Specifi-cally, for the inverse demand model the estimated γ has to be positive. βP also has to be positive as itis the speed of reversion from the price current price to the selected reference level P0.116Figure B.1: Autocorrelation for the Logarithm of the British Columbia Halibut Price, 1996-2017. Source: DFOThe results from the time series estimations are presented in Table B.1:117Table B.1: Price Dynamic Estimation: Multiple ModelsThis table presents the results for testing three time series specifications plus two economic models for the price dynamic.The data for the halibut ex-vessel historical prices for British Columbia is obtained from the Department of Fisheries andOceans of Canada (DFO) website http://www.dfo-mpo.gc.ca, for the period 1990 to 2016.(1) (2) (3) (4) (5)ARIMA(0,1,0) ARIMA(1,1,0) ARIMA(0,1,1) Inverse Demand Mean RevertingνP 0.035(z-stat) (0.94)ρP 0.865(z-stat) (6.44)θP 0.729(z-stat) (3.42)γP 0.685(z-stat) (5.33)βP -0.706(z-stat) (-1.53)βh 0.071(z-stat) (0.73)Wald χ2 - 41.50 11.67 14.32 28.44Log. Likelihood 8.79 8.62 4.69 13.36 7.77AIC -13.58 -11.24 -3.40 -8.11 -18.72Sample 1996-2017 1996-2017 1996-2017 1996-2017 1996-2017To select the best model for our halibut price data we use the Akaike information criterion (AIC)presented in Table B.1. The AIC takes into account the trade off between better fit and the numberof estimated parameters. The best model is identified by the lowest value of the AIC. Among theproposed models, the lowest AIC is measured for the Mean-Reverting model, but there are two keyissues that make the use of the AIC inappropriate in this case. The first and most important is that bothestimated coefficients of the explanatory variables are not significantly different from zero, hencethe proposed model is indeed failing to explain the dynamic of the halibut price for the selectedperiod. The second issue with the mean reverting model is that the estimated speed of reversion isnegative (althogh not significant), which we know is inconsistent with the technical requirements forconvergence of the stochastic process. We conclude that although this model exhibits a high AIC, it isnot adequate for the British Columbia halibut.From the remaining models, we notice that models (2), (3) and (4) exhibit significant coefficients,their ability to explain the time series does not compensate the increment in the number of parameters.Model 1, the log-normal i.i.d model, has the lowest AIC and therefore is the one that best fits theHalibut price time series.118Table B.2: Summary Statistics for the Differences in the Harvesting Policy: Benchmark Caseminus Social Discount CaseThis table presents summary statistics for the differences in the harvesting policy between the benchmark case and the socialdiscount case computed over the model state space, this is Biomass in the range [0.1,85.51] and the price in the range[2.99,20.07].Mean Median SD 10th 25th 75th 90thqBenchmarkt −qSocial Discountt 0.17 0.13 0.18 0.00 0.00 0.32 0.44B.3 Biomass and Harvest Dynamic for the British Columbia HalibutUsing a Social Discount RateAs fisheries are commonly regulated by governmental institutions and resources are publicly owned,it is useful to understand how the model results will change if a social discount rate is used (Clark andMunro (2017)).To fulfill this goal we solve a version of the model on which we replaced the private discountrate for a social real discount rate of 1%, directly increasing the relative weight of future cash flowswith respect to current cash flows, therefore the economic incentives for the conservation the resource.The model results indicate that the value of the fishery is higher with a social discount rate, which isexpected as the future cash flows are discounted at a lower rate, although the most interesting variationsin the models solutions are observed in the harvesting policy.To compare the harvesting policies of the benchmark case and the social discount case we com-puted the differences among them over the state space. We find that this quantity can be significantin several states, specially in those of mid-low biomass and high prices, pointing to a clear trade-offbetween current profits and sustainability. For example, if the halibut price is $11 Canadian dollarsand the biomass is 38 million pounds, the benchmark case fishery will harvest 12.4 million pounds peryear, while the social discount case fishery will harvest 11.6 million pounds per year, hence a differ-ence of 0.8 million pounds in the annual harvest. The summary statistics for the computed differencesin the harvesting policy across the full space state are resumed in Table B.2:Although Table B.2 shows that in 25% of the space state the benchmark case fishery harvests atleast 0.3 million pounds more than the social discount case fishery, these high magnitude differenceoccur in highly unlikely states, as the fishery will optimally avoid the reduction of the biomass tolevels on which the social discount case fishery harvest significantly less than in the benchmark case.Consequently, our simulation analysis shows that for the current state and estimated parameters, theeffects of these differences in the harvesting policies are not quantitatively important for the simulatedbiomass dynamic.119Table B.3: British Columbia Halibut Fishery Revenues, 2007 and 2009The values are obtained from the reports prepared for the DFO-Pacific Region by Stuart Nelson of Nelson Bros FisheriesLtd. (Nelson (2009) and Nelson (2011)), and provide estimates of the financial performance for vessels operating in BritishColumbia for the years 2009 and 2007. These reports are done with a combination of data from the DFO and consultantcollected information through interviews/correspondence with fishermen and experts. Group 1 is the group of vessels withthe highest third individual landings, Group 2 is the group of vessels with the middle third individual landings, and Group3 is the group of vessels with the lowest third individual landings. All values are expressed in 2017 CAD using the CPI forBritish Columbia.2007 (Expressed in 2017 CAD) 2009 (Expressed in 2017 CAD)Group 1 Group 3 Group 1 Group 3Total Biomass [Mill. lb.] 53.69 53.69 62.78 62.78Landings [Mill. lb.] 5.51 0.95 3.33 0.72Vessel Price [CAD/lb.] $5.56 $5.56 $5.99 $5.99Gross Revenue [Mill. CAD] $30.68 $5.29 $19.98 $4.30Total fishery specific expenses $8.43 $1.67 $5.63 $1.46Crew and captain shares $8.65 $1.37 $5.99 $0.86Total Vessel Expenses $1.28 $1.30 $1.23 $0.69Total Cost [Mill. CAD] $18.36 $4.34 $12.85 $3.02EBITDA [Mill. CAD] $12.32 $0.95 $7.13 $1.28B.4 Alternative Cost Function Parametrizations for the BritishColumbia Halibut and their Impact on the Simulated Biomass andHarvest DynamicThe model is solved using cost parameters estimated from the two surveys performed by NelsonBros Fisheries Ltd. for the DFO (Nelson (2009) and Nelson (2011)). The survey separates the totalvessels operating in British Columbia in three groups, depending on their harvest. The median groupis assumed to represent the average vessel production function, hence it is used in the benchmark caseincluded in the main text. In this Appendix we present the numerical results for the simulation of themodel solved using the cost function parameters of the group of high efficiency vessels, and the lowefficiency vessels, also included in the survey. The production costs for the high and low efficiencyvessels are included in Table B.3:Table B.3 presents two years of costs and revenues for the high and low efficiency vessels in theBritish Columbia halibut fishery. During 2007 the fisheries registered higher harvest and lower costs,per unit harvested, in comparison to 2009, but still the difference between these two groups is sizablewithin a year, and they also exhibit significant difference with the mid level efficiency group used inthe benchmark case.As mentioned, the parameters of the cost function are determined solving an over-identified systemof equations for the annual cost, that is, we solve Equation 3.5 by leaving one parameter free, in thiscase c2, and then solve for the remaining two c0,c1, subject to c0 > 0, c1 > 0 and c2 > 0, using the twoyears of available data.120Figure B.2: Median Simulated Biomass and Harvesting Policy for Different Cost FunctionParametrizations of the British Columbia Halibut FisheryAs in the mid level efficiency, for the quadratic cost parameter we choose the median of the feasiblevalues for the high and low efficiency vessels. The calibrated parameters for the high efficiency group{c0 = 8.39,c1 = 52.65,c2 = 0.15,c3 = c0 = 8.39}, and for the low efficiency group {c0 = 0.94,c1 =105.21,c2 = 1.70,c3 = c0 = 0.94}1. Notice that these groups have significant differences in theirproduction efficiency, reflected on the variations in the estimated parameters. We use these parametersto solve the model and simulate its impact on the dynamic of the harvest and biomass. The results arepresented in Figure B.2.Figure B.2 shows a clear impact of the cost function parameters in the model results, and conse-quently in the expected dynamic of the harvesting policy and the biomass. For the high efficiency ves-sels parameters the harvest is higher than the benchmark case, starting from over 16 millions poundsfor the current state. The harvesting decreases over time but it remains above mid level efficiency forthe full period simulated. The higher harvest generates a biomass of approximately 47 million poundsin 10 years, 22% lower than the median biomass of the benchmark case at the same date, hence thehigh efficiency vessels increase their annual harvesting reducing the long-run biomass, but with nototal depletion of the resource with 99% probability.Figure B.2 also includes the simulations for the low efficiency vessels parameters. In that case theharvest is lower than the benchmark case, starting from approximately 2 millions pounds for the cur-rent state. The harvesting increases over time but it remains in levels bellow the natural growth of thebiomass, so we observe a continuous growth of the resource until levels close to the carrying capac-ity are achieved. Therefore, the low efficiency vessels significantly decrease their annual harvesting,increasing the long-run biomass.The significant differences observed for the different cost parametrizations of the British Columbiahalibut fishery show how important these parameters are for the numerical solution of the model,1In both cases c3, the cost paid in case of no harvest, is assumed to be equal to fixed cost c0.121providing a wide range of potential results, going from significant growth to a decrease of the biomassof the resource. Although different, these outcomes share a significant feature, the resource is notdepleted in both scenario with 99% probability, pointing to a sustainable harvest even in cases onwhich the production is highly profitable.As Clark et al. (2009) already pointed, unfortunately these surveys are scarce and not availablefor multiple years, hence any implementation effort of the model will have to deal with the lack ofinformation for the production costs. This section shows how important theses parameters are for thenumerical results, so any additional effort in collecting and standardizing additional information willbe extremely useful and significant to improve the accuracy of the numerical results.B.5 Impact of an increase in the Biomass Volatility on the SimulatedBiomass and Harvest Dynamic for the British Columbia HalibutIn the main text of the paper we observed that for the estimated parameters, the effect of biomassvolatility was substantially smaller than the effect of price volatility. In this section we illustratehow an increase in the biomass volatility affects the optimal harvesting policy of the fishery, andconsequently the simulated biomass and harvest dynamic. To address this objective we solved a newcase denoted increased biomass volatility case, on which the annual biomass shock volatility is set toσˆI = 4×10.84% = 43.36% and assume no price volatility.We mentioned that the data supports a world where there is both biomass and price uncertainty, sowe simulate the model that assumes an increased biomass volatility but no price uncertainty in a worldthat has price uncertainty. This is, we simulate the fishery that follows the optimal policy in the caseof no price uncertainty with an increased biomass volatility, but it is subject to shocks in the biomassand price. We then compare the simulated harvest moments obtained for this new case with those ofthe biomass volatility case and the benchmark case. These results are presented in Figure B.3:Panel A of Figure B.3 shows the simulated harvest in a world where there is both biomass andprice uncertainty, obtained using the policy of the biomass volatility case, or the harvest policy ofthe increased biomass volatility case. As expected, an increment in the biomass volatility producesand overall reduction in the median harvest, and an increment in harvest flexibility is observed in thedifference between the 1th and 99th percentile in the 10 years horizon.Although the increment in the harvest flexibility driven by the a higher biomass volatility appearsto be sizable, Panel B of Figure B.3 shows that the flexibility in the optimal harvest is still higher insimulations generated using the harvest policy of the benchmark case, highlighting the high impact ofthe exogenous shock prices in the harvesting policy of the fishery.To conclude, the drastic increment in the biomass volatility indeed increased the flexibility in thesimulated harvest, but as mentioned, the biomass process is partially endogenous since in response tothe biomass shocks the fishery can adjust its harvesting, incorporating the increase in volatility to itspolicy to react properly to modified dynamics of the biomass process.122Figure B.3: Median, 1th and 99th Percentiles of the Simulated Harvest for the Biomass Volatil-ity Case, Increased Biomass Volatility Case, and the Benchmark Case, For the BritishColumbia Halibut Fishery.123Appendix CAppendix to Chapter 4C.1 Variable DefinitionsThe variable definitions for those included in all the regressions presented in this paper are explicitedbelow. Compustat variable names are denoted by their pneumonic between parenthesis.• Market Value: Stock price at the end of the fiscal year (prcc f ), multiplied by the number ofshares outstanding (csho).• Size: Total assets (at), plus the Market Value, minus the stockholders equity (seq).• Book Equity: Computed as defined in Davis, Fama, and French (2000) using the stockholdersequity (seq), common equity (ceq), the value of preferred stock (pstx), total assets (at) amongothers.• BEME: Book to Market, Book Equity as in Davis et al. (2000), market value is computed usingthe stock price at the end of the fiscal year (prcc f ) and the number of shares outstanding (csho).• PROF: Profitability, defined as Pretax Income (pi) over Book Equity.• EBITDA: (ebitda) over Total Assets (at).• ITC: Interest tax credits (itc) over total assets (at).• ATR: firm’s average tax rate, computed as the Total Tax Expenses (txc) over (ebitda).• DEPRE: Depreciation expenses (dp) over Total assets (at).• LEVm: Leverage calculated using the Market Value of the Firm, and defined as the Debt inCurrent Liabilities (dlc), if positive, plus the Long-Term Debt (dltt), over the market value plusthe value of the mentioned debt.124• AI: Investment-to-assets (Lyandres et al. (2007)) defined as the change in the total Property,Plant and Equipment (ppegt) in the last year, plus the change in the total Inventories (invt) inthe last year, over the total assest (at) in the last year.• TA A: Total assets cross-sectional mean, over firm total assets (at).125

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0380616/manifest

Comment

Related Items