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Essays in open-economy macroeconomics Pang, Ke 2008

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Essays in Open-Economy Macroeconomics by Ke Pang B.A., Peking University, 2001 M.A., Memorial University, 2002 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in The Faculty of Graduate Studies (Economics) The University Of British Columbia (Vancouver) December, 2008 c© Ke Pang 2008 Abstract This dissertation addresses three issues in international macroeconomics. The first chapter examines optimal portfolio decisions in a monetary open- economy DSGE model. In a complete market environment, Engel and Mat- sumoto (2005) find that sticky price can generate equity home bias. How- ever, their result is sensitive to the structure of the financial market. In an incomplete market environment, we find “super home bias”in the equi- librium equity portfolio, which casts doubt on the ability of sticky price in describing the observed equity portfolios. We further show that introducing sticky wages helps to match the data. The second chapter analyzes the wel- fare impact of financial integration in a standard monetary open-economy model. Financial integration may have negative effects on welfare if integra- tion occurs in the presence of nominal price rigidities and constraints on the efficient use of monetary policy. The reason is that financial integration leads to excessive terms of trade volatilities. From a policy perspective, the model implies that developing economies that are experiencing financial integration may attempt to alleviate the welfare cost of integration by stabilizing the exchange rate. This prediction is consistent with the widespread reluctance to following freely floating exchange rates among these economies. On the other hand, for advanced economies that have the ability to operate efficient inflation targeting monetary policies, financial integration is always benefi- cial. Thus, the model accounts for the observed acceleration in cross-border asset trade among advanced economies in the early 1990s as it was mainly the industrial countries that switched to an inflation targeting regime at the time. The third chapter uses an open-economy neoclassical growth model to explain the saving and investment behavior of the U.S. and a group of other OECD countries. We find that while the model explains investment ii Abstract quite well, it tends to overpredict U.S saving and underpredict saving in the rest of the world. We show that the closed-economy version of the model also predicts saving accurately but that is only because it imposes equality between saving and investment. In effect, the model explains investment not saving behavior. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . x Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 Equity Home Bias and Nominal Rigidity . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Consumers . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Financial Sector . . . . . . . . . . . . . . . . . . . . . 10 1.2.4 Market Clearing . . . . . . . . . . . . . . . . . . . . . 10 1.2.5 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Portfolio Decisions . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Solution Method . . . . . . . . . . . . . . . . . . . . . 11 1.3.2 Risk Sharing . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.3 Flexible Price Case: κ = 0 . . . . . . . . . . . . . . . 14 1.3.4 Sticky Price Case: κ = 1 . . . . . . . . . . . . . . . . 15 1.4 A Model with Sticky Wage . . . . . . . . . . . . . . . . . . . 19 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 iv Table of Contents 2 International Financial Integration and Monetary Policy 28 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2.1 Consumers . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.3 Financial Sector . . . . . . . . . . . . . . . . . . . . . 39 2.2.4 Monetary Rules . . . . . . . . . . . . . . . . . . . . . 39 2.2.5 Market Clearing . . . . . . . . . . . . . . . . . . . . . 41 2.2.6 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 41 2.3 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.1 Optimal Portfolios . . . . . . . . . . . . . . . . . . . . 41 2.3.2 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4 Model Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.4.1 Exchange Rate, Terms of Trade, and Risk Sharing . . 46 2.4.2 Volatility of the Terms of Trade . . . . . . . . . . . . 47 2.4.3 Efficiency of the Terms of Trade . . . . . . . . . . . . 48 2.4.4 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5 Policy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.5.1 Exchange Rate Targeting Rules . . . . . . . . . . . . 54 2.5.2 Producer Price Targeting Rule . . . . . . . . . . . . . 56 2.5.3 Financial Integration and Monetary Policy . . . . . . 57 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3 Explaining Saving Behavior . . . . . . . . . . . . . . . . . . . 69 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3 Equilibrium and Solution . . . . . . . . . . . . . . . . . . . . 74 3.4 Data and Calibration . . . . . . . . . . . . . . . . . . . . . . 76 3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 v Table of Contents Appendices A Appendix for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . 100 A.1 First-Order Approximation . . . . . . . . . . . . . . . . . . . 100 A.2 Asset Returns, Exchange Rate, and Terms of Trade . . . . . 101 A.3 Log-linearized Sticky Wage Model . . . . . . . . . . . . . . . 103 B Appendix for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . 105 B.1 A Symmetric Steady State . . . . . . . . . . . . . . . . . . . 105 B.2 First-Order Approximation . . . . . . . . . . . . . . . . . . . 105 B.3 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . 107 B.4 Proof of E(L̂) + 12E(L̂ 2) = 0 +O(3) . . . . . . . . . . . . . 108 B.5 Computing the Consumption Equivalent Welfare Measure . . 109 C Statement of Co-Authorship . . . . . . . . . . . . . . . . . . . 111 vi List of Tables 1.1 Optimal Portfolio Holdings with Flexible Prices . . . . . . . . 14 1.2 Optimal Portfolio Holdings with Sticky Prices . . . . . . . . . 15 1.3 Share of Domestically Owned Home Equities with Sticky Prices and Flexible Wages . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Optimal Portfolio Holdings with Sticky Wages . . . . . . . . . 20 1.5 Share of Domestically Owned Home Equities with Sticky Prices and Sticky Wages . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 Targeting Regimes . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Second Moments and Welfare with Money Targeting Rules . 50 2.3 Second Moments and Welfare with Exchange Rate Targeting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4 Second Moments and Welfare with Price Targeting Rules . . 57 2.5 Average Inflation and Central Bank Characteristics . . . . . . 59 3.1 Steady State Values of the Exogenous Drivers . . . . . . . . . 77 vii List of Figures 1.1 Share of Domestically Owned Home Equities with Flexible Wage and Linear Disutility in Labor . . . . . . . . . . . . . . 24 1.2 Share of Domestically Owned Home Equities with Flexible Wage and Quadratic Disutility in Labor . . . . . . . . . . . . 25 1.3 Share of Domestically Owned Home Equities with StickyWage and Cut-off Value 0.9 . . . . . . . . . . . . . . . . . . . . . . . 26 1.4 Share of Domestically Owned Home Equities with StickyWage and Cut-off Value 0.75 . . . . . . . . . . . . . . . . . . . . . . 27 2.1 International Financial Integration: Industrial Group and De- veloping Countries Group, 1970-2004 . . . . . . . . . . . . . . 62 2.2 International Financial Integration: Explicit Inflation Target- ing Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.3 International Financial Integration: Implicit Inflation Target- ing Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.4 Second Moments and Welfare with Money Targeting Rules . 65 2.5 Exchange Rate Response Coefficients with Incomplete Markets 66 2.6 Consumption Equivalent Measures with Money Targeting Rules 67 2.7 Welfare Comparison . . . . . . . . . . . . . . . . . . . . . . . 68 3.1 U.S. Saving and Investment - Closed Economy . . . . . . . . 82 3.2 U.S. Saving and Investment - Benchmark . . . . . . . . . . . 83 3.3 U.S. Saving and Investment - Only TFP . . . . . . . . . . . . 84 3.4 U.S. Saving and Investment - All Except TFP . . . . . . . . . 85 3.5 U.S. Saving and Investment - Only Government Expenditure 86 3.6 U.S. Saving and Investment - Only Population Growth . . . . 87 viii List of Figures 3.7 U.S. Saving and Investment - Only Depreciation Rate . . . . 88 3.8 U.S. Saving and Investment - Only Capital Income Taxes . . 89 3.9 U.S. Saving and Investment - Only Labor Income Taxes . . . 90 3.10 Net Investment Rates vs TFPF Growth Rates - Benchmark . 91 3.11 Net Saving Rates vs TFPF Ratios - Benchmark . . . . . . . . 92 ix Acknowledgments I am extremely grateful to my supervisor, Prof. Michael B. Devereux for advice, guidance and encouragement. I am also greatly indebted to other members of my supervisory commit- tee, Profs. Amartya Lahiri, Henry Siu and Viktoria Hnatkovska for research direction and discussion. I would like to thank Profs. Paul Beaudry and Anji Redish for valuable suggestions and discussions at various stages of this dissertation. Sincere thanks are also extended to my colleagues, faculty and staff members at UBC for their support. I thank the seminar participants at Wilfrid Laurier University, Ryer- son University, Louisiana State University, West Virginia University, the SOEGW II conference, and the 2006, 2007 and 2008 meetings of the Cana- dian Economics Association for helpful comments. I am solely responsible for any error or misinterpretation. x Dedication To my parents and Jianfeng. xi Chapter 1 Equity Home Bias and Nominal Rigidity 1.1 Introduction Typical investors hold too little of their wealth in foreign assets relative to the predictions of standard financial and macroeconomic theory. According to French and Poterba (1991) [29] and Tesar and Werner (1995) [67], the percentages of aggregate stock-market wealth invested in domestic equities at the beginning of the 1990s were well above 90% for the US and Japan, and around 80% in the UK and Germany. Based on the portfolio data from Kraay et al (2005) [44], Kollmann (2005) [43] shows that the average locally owned capital share for 17 OECD coutries is 91% in 1997. More recently, Heathcote and Perri (2007) [38] report that foreign assets accounted for only around 25% of the total value of the assets owned by the U.S. residents over the period 1990-2004. This widespread lack of diversification across countries, named equity home bias, has become a major empirical puzzle in international finance. In a complete financial market environment, Engel and Matsumoto (2005) [24] find that the presence of nominal price rigidity can help explain the eq- uity home bias puzzle, because it generates a negative correlation between the labor income and the profit of domestic firms with respect to produc- tivity shocks. Within a similar open economy macro framework, this paper examines the impact of two additional frictions on the optimal equity port- folios. First, incomplete financial market. Second, nominal wage rigidity. We find that in an incomplete market environment, the labor income 1 Chapter 1. Equity Home Bias and Nominal Rigidity and the profit of domestic firms are negatively correlated in response to not only productivity shocks but also monetary shocks.1 Therefore, the equilibrium portfolios require an aggressive investment position in domestic equities. This “super home bias”result weakens the ability of sticky price alone in describing the observed equity holdings. Furthermore, introducing sticky wage can help match the data. The reason is that the labor income and the profit of domestic firms become positively correlated with respect to monetary shocks when wages are pre-set. Hence, it is optimal for households to hold some positive amount of foreign equities. With incomplete financial markets and nominal rigidities in both the goods price and the wage rate, this model predicts home bias for a wide range of parameterization that are often used in the macro literature. There is a large literature that seeks resolutions to the equity home bias puzzle.2 Potential explanations range from barriers to international capital movements to frictions that justify the observed portfolios as optimal risk management decisions. This paper builds on one thread of the study that focuses on the importance of hedging against non-traded labor income risk. Baxter and Jermann (1997) [4] show that returns to human capital are positively correlated with returns to domestic equities but not with returns to foreign equities. As the labor income risk is non-diversifiable and the labor income accounts for more than half of the total income, investors should take large short positions in domestic assets. The implied equity portfolios are more foreign-weighted than what a classical endowment economy, such as Lucas (1982) [50], would predict. Indeed, as long as non-traded labor income is more correlated with the domestic stock market than with the foreign stock market, the puzzle becomes even worse. In the flexible price case of our model, we corroborate the above results and show that they are identical in the sense that there is perfect pooling (i.e. each country receives half of the world output) eventually. Jermann (2002) [41] characterizes optimal international portfolios in a 1We assume money supply shocks in this paper. However, results are identical if assume money demand shocks. 2See Lewis (1999) [49] for a comprehensive survey on this literature. 2 Chapter 1. Equity Home Bias and Nominal Rigidity multi-country general equilibrium model with endogenous labor - leisure choice and with preferences that are nonseparable over consumption and leisure. The return on human capital and the return on domestic equity are still positively correlated. However, with consumption and leisure being substitutes, consumption is highly valued in periods when work effort is high. Therefore, a domestic claim provides the right hedge. Heathcote and Perri (2007) [38] studies a two-goods general equilibrium model with investment. In their framework, each country specializes in production of a final good that uses both local and imported intermediate inputs. Following a positive domestic productivity shock, home output and demand for labor increase. Home investment goes up as well, which reduces the dividend paid on home equities. Thus, the labor income is negatively correlated with the return to domestic equities. Home bias arises because domestic stocks make a good hedge against non-diversifiable labor income risk. The empirical evidence on the correlation of returns to human capital and domestic equities is mixed. Baxter and Jermann (1997) [4] use annual OECD data for Japan, Germany, UK, and US from 1960 to 1993, and find that human capital returns are highly correlated with domestic capital re- turns. However, Bottazzi, Pesenti, and van Wincoop (1996) [7] use slightly different measures based on annual OECD data from 1970 to 1992, and find that human capital returns are negatively correlated with domestic capi- tal returns for most OECD countries except US. Therefore, it is not clear whether home bias is puzzling or not by just looking at the unconditional correlation. As discussed above, what important here is the conditional cor- relation between returns to human capital and returns to domestic capital. Gali (1999) [32] and Gali and Rabanal (2004) [33] find that the conditional correlation between labour hours and productivity is negative in response to technology shocks, while the unconditional correlation is positive. These results are further confirmed by Francis and Ramey (2005a, 2005b) [27] [28] and Rotemberg (2003) [58]. This paper is also related to the research that focus on the importance of non-traded risk due to non-traded consumption goods.3 Kollmann (2005) 3Earlier papers in this literature see Stockman and Dellas (1989) [62], Tesar (1993) 3 Chapter 1. Equity Home Bias and Nominal Rigidity [43] generates portfolio home bias in an endowment economy with home bias in consumption and complete markets. Hnatkovska (2005) [39] shows that equity home bias can arise naturally in the presence of non-diversifiable non-traded consumption risk, consumption home bias, and incomplete as- set markets. She employs a numerical approximation method to solve for endogenous portfolio choices. This paper follows Devereux and Sutherland (2006a) [20] and uses a second-order approximation method to solve for the optimal portfolio composition. The paper is organized as follows. Section 1.2 presents the model. Sec- tion 1.3 describes the solution to the model and compares the equilibria under different market configurations. Section 1.4 analyzes the effect of sticky wage. Sections 1.5 concludes. 1.2 The Model The world is assumed to exist for a single period and to consist of two countries, which will be referred to as the home country and the foreign country. Each country is populated by agents who consume a basket of home and foreign produced goods. Each agent, using a linear technology in labor, is a monopoly producer of a particular differentiated product. The world population is normalized to have a measure of one. Home agents are indexed h ∈ [0, 12 ] and foreign agents are indexed f ∈ [12 , 1]. A fraction κ of agents in each country set prices before the realization of shocks. They are contracted to meet demand at pre-fixed prices. Other agents in the economy can set prices after shocks are realized. All prices are assumed to be set in the currency of producers. Thus, there is full exchange rate pass-through to prices paid by consumers. Agents supply homogeneous labor.4 Prior to the realization of shocks, they can trade in a range of financial assets. The financial market structure and the payoff [65], Pesenti and van Wincoop (1996) [55], Baxter, Jermann, and King (1998) [5], and Serrat (2001) [61]. 4We first look at the effect of nominal price rigidity. Nominal wage rigidity will be introduced later. 4 Chapter 1. Equity Home Bias and Nominal Rigidity to each asset are defined in Section 2.3. Each country faces two types of shocks: productivity and money supply shocks. The detailed structure of the home country is described below. The for- eign country has an identical structure. Where appropriate, foreign variables are denoted with an asterisk. 1.2.1 Consumers All agents in the home country have utility functions of the same form U = C1−ρ 1− ρ + χlog M P − η L 1+ψ 1 + ψ (1.1) where C is the consumption index, defined across all home and foreign goods, M denotes the end-of-period nominal money holding, P is the consumer price index (CPI), L is the labor supply, ρ (ρ ≥ 0) is the coefficient of relative risk aversion, χ is the coefficient of real balance, η is the coefficient of labor supply, and ψ (ψ ≥ 0) is the elasticity of labor supply. There are two stages to the household decision problem. Before shocks are realized, households choose portfolio positions out of available assets to maximize expected utility, E [ U(C, MP , L) ] , subject to n∑ k=1 αk = 0 (1.2) where αk represents the real holding of asset k, and n is the total number of assets. All real variables in this paper are defined in terms of home consumption basket. Each country starts with zero net wealth. After shocks are realized, households choose consumption, labor sup- ply, and money balances, in order to maximize ex-post utility, U(C, MP , L), subject to M + PC = M0 + PHYH + P n∑ k=1 αkrk + T (1.3) where M0 is the initial nominal money holding, PH is the aggregate price 5 Chapter 1. Equity Home Bias and Nominal Rigidity of home produced goods, rk is the real aggregate rate of return on asset k, and T is a lump-sum government transfer. YH is the world demand for aggregate home produced goods YH = 1 2 ( PH P )−θ (C + C∗) (1.4) where θ is the elasticity of substitution between home and foreign goods. Firms’ revenues are used to pay wages and profits PHYH = wL+Π (1.5) where w and Π denote the wage and the profit (dividend), respectively. Here, home agents first receive all profits from domestic firms. Then, if an international equity market exists, claims to home profits may be trans- ferred to foreign consumers via trade in equity shares.5 Moreover, we define Y as the home aggregate real production income PY = PHYH (1.6) Combined with the government budget constraint M −M0 = T (1.7) we can rewrite home household’s budget constraint (1.3) in real terms C = Y + n∑ k=1 αkrk (1.8) M is an i.i.d. stochastic money supply shock with E(logM) = 0, V ar(logM) = σ2M , and logM ∈ [−, ]. 5Alternatively, it can be assumed that profits proceed directly to shareholders. There is no fundamental difference between the two modeling approaches. 6 Chapter 1. Equity Home Bias and Nominal Rigidity The consumption index C for home agents is defined as C = ( 1 2 ) 1 θ−1 ( C θ−1 θ H + C θ−1 θ F ) θ θ−1 (1.9) CH and CF are indices of home and foreign produced goods CH = [( 1 2 ) 1 φ ∫ 1 2 0 CH(h) φ−1 φ dh ] φ φ−1 (1.10) CF = [( 1 2 ) 1 φ ∫ 1 1 2 CF (f) φ−1 φ df ] φ φ−1 (1.11) where φ (φ > 1) is the elasticity of substitution between individual home (or foreign) goods. The aggregate consumer price index for home households is P = ( 1 2 ) 1 1−θ ( P 1−θH + P 1−θ F ) 1 1−θ (1.12) where PH and PF are the price indices for home and foreign produced goods, respectively PH = [ 2 ∫ 1 2 0 PH(h)1−φdh ] 1 1−φ , PF = [ 2 ∫ 1 1 2 PF (f)1−φdf ] 1 1−φ (1.13) The law of one price implies that PH(h) = P ∗H(h)S and PF (f) = P ∗ F (f)S for all h and f . An asterisk indicates that the price is in foreign currency and S is the nominal exchange rate defined as the domestic price of foreign currency. Because there is no home bias in consumption, purchasing power parity (PPP) holds, i.e. P = SP ∗. Given prices and the total consumption C, home consumers’ optimal demands for home and foreign goods are CH = 1 2 ( PH P )−θ C, CF = 1 2 ( PF P )−θ C (1.14) 7 Chapter 1. Equity Home Bias and Nominal Rigidity CH(h) = 2 [ PH(h) PH ]−φ CH , CF (f) = 2 [ PF (f) PF ]−φ CF (1.15) The remaining first order conditions are E ( r1C −ρ) = E (rnC−ρ) E ( r2C −ρ) = E (rnC−ρ) ... (1.16) E ( rn−1C−ρ ) = E ( rnC −ρ) ηLψ = wC−ρ P (1.17) χ M = C−ρ P (1.18) Equation (1.16) indicates that portfolio choices are optimal only when the expected returns on all assets are equalized in terms of utility. Equations (1.17) and (1.18) are the standard intra-temporal labor-leisure choice func- tion and the money demand function. 1.2.2 Firms Firms engage in monopolistic competition. Each produces specific goods indexed by h with a linear technology in labor YH(h) = AL(h). A is an i.i.d. stochastic technology shock with E(logA) = 0, V ar(logA) = σ2A, and logA ∈ [−, ]. By assumption, a fraction κ of firms have to set prices in advance and the rest can set prices after shocks are realized. The profit maximization problem of a pre-set price firm i is Max E{D(i) [ Ppre,H(i)− w A ] [ Ypre,H(i) + Y ∗pre,H(i) ] } where D(i) is the stochastic discount factor for firm i, Ypre,H(i) and Y ∗pre,H(i) are the demand for good i from the home and foreign markets Ypre,H(i) = [ Ppre,H(i) PH ]−φ (PH P )−θ C (1.19) 8 Chapter 1. Equity Home Bias and Nominal Rigidity Y ∗pre,H(i) = [ P ∗pre,H(i) P ∗H ]−φ ( P ∗H P ∗ )−θ C∗ (1.20) Because firms of each type are all alike, they will set identical prices in equilibrium. Hence, the optimal pre-set price of home goods is Ppre,H = φ φ− 1 E [ DwAXH ] E [DXH ] (1.21) XH represents the demand for home produced goods XH = P φ H ( PH P )−θ (C + C∗) where we have applied the law of one price and PPP in CPI. The profit maximization problem of a flexible price firm j is Max D(j) [ Pflx,H(j)− w A ] [ Yflx,H(j) + Y ∗flx,H(j) ] whereD(j) is the stochastic discount factor for firm j, Yflx,H(j) and Y ∗flx,H(j) are the demand for good j from the home and foreign markets Yflx,H(j) = [ Pflx,H(j) PH ]−φ (PH P )−θ C (1.22) Y ∗flx,H(j) = [ P ∗flx,H(j) P ∗H ]−φ ( P ∗H P ∗ )−θ C∗ (1.23) The optimal flexible price of home goods is Pflx,H = φ φ− 1 w A (1.24) The price index for home produced goods can be rewritten as PH = [ κP 1−φpre,H + (1− κ)P 1−φflx,H ] 1 1−φ (1.25) 9 Chapter 1. Equity Home Bias and Nominal Rigidity 1.2.3 Financial Sector This paper examines two different asset market configurations: (1) Bond and Equity Economy (FBE), in which home and foreign nominal bonds and equities can be traded internationally; (2) Equity Economy (FE), in which only home and foreign equities are allowed for trade. Whether each financial market is complete depends on the nature of the rest of the model. Nominal bonds represent a claim on a unit of currency. Equities repre- sent a claim on aggregate profits. The real aggregate rate of return on each asset is defined as following rB = 1 qBP (1.26) rB∗ = Q qB∗P ∗ (1.27) rE = Π qEP (1.28) rE∗ = QΠ∗ qE∗P ∗ (1.29) where qk is the real price of asset k and Q is the real exchange rate, i.e. Q = SP ∗ P . 1.2.4 Market Clearing The goods market clearing condition is AL = 1 2 ( PH P )−θ (C + C∗) (1.30) The asset market clearing condition is αk = −α∗k, k = 1, 2, · · · , n (1.31) 1.2.5 Equilibrium The equilibrium comprises a set of prices, P , P ∗, PH , P ∗F , Ppre,H , P ∗ pre,F , Pflx,H , P ∗flx,F , w, w ∗, rk, S, and a set of quantities C, C∗, L, L∗, Π, Π∗, 10 Chapter 1. Equity Home Bias and Nominal Rigidity YH , Y ∗F , Y , Y ∗, αk, α∗k, M , M ∗, which solves a system of equations (1.4)- (1.6), (1.12), (1.16)-(1.18), (1.21), (1.24)-(1.25), (1.30), and their foreign counterparts, as well as (1.8), (1.26)-(1.29), and (1.31), given productivity and money supply shocks, A, A∗, M , and M∗.6 1.3 Portfolio Decisions 1.3.1 Solution Method Using the method developed by Devereux and Sutherland (2006a) [20], the equilibrium portfolio choices are solved to a second-order accuracy. The second-order approximation of home portfolio selection equations (1.16) around the non-stochastic steady state are given by7 E[(r̂1 − r̂n) + 12(r̂ 2 1 − r̂2n)− ρĈ(r̂1 − r̂n)] = 0 +O(3) E[(r̂2 − r̂n) + 12(r̂ 2 2 − r̂2n)− ρĈ(r̂2 − r̂n)] = 0 +O(3) ... (1.32) E[(r̂n−1 − r̂n) + 12(r̂ 2 n−1 − r̂2n)− ρĈ(r̂n−1 − r̂n)] = 0 +O(3) Because shocks are symmetrically distributed in the interval [−, ], O(n) represents residuals of an equation approximated to order n− 1. Foreign agents face a set of portfolio selection equations similar to (1.16) E ( r1 QC∗ρ ) = E ( rn QC∗ρ ) E ( r2 QC∗ρ ) = E ( rn QC∗ρ ) ... (1.33) E ( rn−1 QC∗ρ ) = E ( rn QC∗ρ ) 6By Walras’ Law, there is one equation redundant in the system. The foreign agent’s budget constraint is dropped. 7Hereafter, x̂ = log(X)− log(X̄). 11 Chapter 1. Equity Home Bias and Nominal Rigidity whose second-order approximation is given by E[(r̂1 − r̂n) + 12(r̂ 2 1 − r̂2n)− ρĈ∗(r̂1 − r̂n)] = 0 +O(3) E[(r̂2 − r̂n) + 12(r̂ 2 2 − r̂2n)− ρĈ∗(r̂2 − r̂n)] = 0 +O(3) ... (1.34) E[(r̂n−1 − r̂n) + 12(r̂ 2 n−1 − r̂2n)− ρĈ∗(r̂n−1 − r̂n)] = 0 +O(3) Note that PPP has been applied here. By subtracting equations (1.32) from (1.34), the set of equations to solve for equilibrium portfolios is obtained E[ρ(Ĉ − Ĉ∗)r̂x] = 0 +O(3) (1.35) It is written in a vector form with r̂′x = [r̂1 − r̂n, r̂2 − r̂n, · · · , r̂n−1 − r̂n]. Condition (1.35) contains only the second moments of endogenous vari- ables, indicating that solving the portfolio choice to a second-order accuracy only requires the first-order solution of the non-portfolio part of the model. This is because second-order accurate second moments can be computed from first-order solutions for realized variables. Finally, firms’ discount fac- tors do not appear in equation (1.35) or any other equilibrium condition up to the first-order. Hence, they do not affect the solution of optimal portfolio choices. The log-linearization of the model is presented in Appendix A.1. 1.3.2 Risk Sharing Use the log-linearized home CPI, P̂ = 1 2 (P̂H + P̂ ∗F + Ŝ) +O( 2) (1.36) we can express home real GDP as Ŷ = 1− θ 2 (P̂H − P̂ ∗F − Ŝ) + 1 2 (Ĉ + Ĉ∗) +O(2) 12 Chapter 1. Equity Home Bias and Nominal Rigidity = 1− θ 2 τ̂ + 1 2 (Ĉ + Ĉ∗) +O(2) (1.37) where τ is the home country’s terms of trade — defined as the price of exports relative to the price of imports. Because there is no aggregate un- certainty at the world level, country-specific income risks all come from the terms of trade fluctuations. Moreover, the log-linearized home budget constraint is Ĉ = Ŷ + α̃′r̂x +O(2) (1.38) where α̃ = ᾱ Ȳ . Hence, the consumption difference between home and foreign countries can be written as 1 2 (Ĉ − Ĉ∗) = 1− θ 2 τ̂ + α̃′r̂x +O(2) (1.39) Clearly, households’ consumption risks originate from uncertainties in their real income, which are further caused by variations in the terms of trade. For instance, home country’s terms of trade deteriorate, owing to certain fundamental shocks, τ̂ < 0. Home goods become cheaper relative to foreign goods. Given that home and foreign goods are substitutes, the world demand shifts towards home goods. Home output increases, ŶH > 0, which is called the expenditure switching effect. However, home goods are sold at a relatively lower price and foreign goods cost relatively more. Whether home GDP rises or falls in real terms depends on the strength of this substi- tution across countries. If the expenditure switching effect is strong enough (θ > 1), home real GDP increases. The exact opposite takes place in the foreign country. As a result, the portfolio decision is essentially about how to optimally hedge against the terms of trade fluctuations. Agents can di- versify away at least part of the consumption risks by trading assets across borders — as long as the returns on these assets are somehow correlated with the terms of trade. Now it is possible to state the optimal portfolio choices under each finan- cial market configuration. The model is entirely symmetric, which implies 13 Chapter 1. Equity Home Bias and Nominal Rigidity that in the FB economy, agents in both countries will have bond hold- ings that sum to zero, and in the FBE economy, their equity holdings and bond holdings will separately sum to zero. Thus, for the home country, we have α̃FE,E∗ + α̃FE,E = 0 in the FE economy, and α̃FE,B∗ + α̃FE,B = 0, α̃FE,E∗ + α̃FE,E = 0 in the FBE economy. As the aim is to understand the effect of nominal price rigidity on the equilibrium equity holdings, we will focus on the two extremes, in which goods prices are either completely flexible (κ = 0) or completely sticky (κ = 1). Any intermediate case with 0 < κ < 1 can be easily inferred from these two scenarios. 1.3.3 Flexible Price Case: κ = 0 Table 1.1 describes the optimal portfolio holdings in the FE and FBE economies when goods prices are fully flexible. The equilibrium asset hold- ings are identical between the two economies. In this case, the excess return of foreign equities relative to home equities is r̂E∗ − r̂E = (θ− 1)τ̂ +O(2).8 As long as equities can be traded internationally, households achieve perfect consumption risk sharing. Table 1.1: Optimal Portfolio Holdings with Flexible Prices FE α̃FE,E∗ = 12 FBE α̃FBE,B∗ = 0 α̃FBE,E∗ = 12 Here, money is neutral. Money supply shocks have no real effect on the economy, as changes in the prices and the exchange rate cancel out com- pletely. The terms of trade respond only to productivity shocks. There is no need to trade nominal bonds. With the optimal equity positions, households essentially receive half of each country’s output, which corresponds to the “full diversification”prediction by Lucas (1982) [50]. 8Detailed derivation see Appendix A.2. 14 Chapter 1. Equity Home Bias and Nominal Rigidity The share of domestically owned home equities is given by δE = 1− ᾱE∗qE = 1− α̃E∗ Π̄/P̄ Ȳ = 1− α̃E∗1−ζ . ζ is the share of labor income in total output at the non- stochastic steady state. When prices are fully flexible, δE = 1−2ζ2(1−ζ) . As labor income generally accounts for about two thirds of the total income, δE = −12 < 0. In other words, home households should not only diversify their portfolios and hold foreign equities, but indeed take a short position in their domestic equities. This reproduces the well-known Baxter and Jermann (1997) [4] result that households should aggressively invest in foreign equities to hedge their non-tradable labor income from productivity shocks, because the labor income and the profit of domestic firms are highly correlated. 1.3.4 Sticky Price Case: κ = 1 Table 1.2 describes the optimal portfolio holdings in the FE and FBE economies when goods prices are all pre-set. The two economies accomplish Table 1.2: Optimal Portfolio Holdings with Sticky Prices FE α̃FE,E∗ = 12 (θ−1)(ζ−1){[θ(1+ψ)+ρ(θ−1)]ζ+(1−θ)}σ2M ζ2(ψ+1)2[1+ρ(θ−1)]σ2 A +[θζ(ψ+1)+(1−θ)]{[θ(ψ+1)+ρ(θ−1)]ζ+(1−θ)}σ2 M FBE α̃FBE,B∗ = 1−θ2 α̃FBE,E∗ = 0 different degrees of consumption risk sharing. To understand the intuition behind the above optimal portfolios, we need to find out how the economy responds to various shocks in autarky. As all prices are pre-set and output is demand-determined, productivity shocks have no effect on firm revenue. The only changes occur are associ- ated with the allocation between labor income and profit. For example, if home firms experience a positive productivity shock, they need less labor to produce the same quantity of goods. Labor income decreases, but firm profit increases at the same time. If home agents hold one hundred percent of their own firms, their income as well as consumption are unaffected. In other words, the default equity position, or a complete home bias in equities, 15 Chapter 1. Equity Home Bias and Nominal Rigidity provides a perfect hedge against productivity shocks. Hence, money supply shocks are the only source of income uncertainties left in the economy. FBE Economy With fixed goods prices, the terms of trade move in the opposite direction of the exchange rate up to first-order. The excess return of foreign bonds relative to home bonds can be expressed as r̂B∗ − r̂B = −τ̂ +O(2). House- holds can fully insure themselves against money supply shocks by holding the right amount of nominal bonds (α̃FBE,B∗ = 1−θ2 ). For instance, if home experiences a positive money supply shock, home currency would depreci- ate, causing home terms of trade to deteriorate. Home real GDP increases when θ > 1. Home households should lend in the home currency denomi- nated bond and should borrow in the foreign currency denominated bond, α̃FBE,B∗ < 0. In this way, the gain in terms of real production income is balanced by a negative payment from bond holdings (when home currency depreciates). In short, home and foreign nominal bonds provide a perfect hedge against money supply shocks. As long as they are allowed for trade, the financial market is complete. Here, we confirm the Engel and Matsumoto (2005) [24] result that in the presence of sticky prices, the returns to workers and those to firm owners become negatively correlated in response to productivity shocks, leading to a home bias in investors’ portfolios. However, this result also relies on the fact that consumption risk sharing is perfect. It may no longer be true when the financial market is incomplete. FE Economy Generally speaking, home and foreign equities alone cannot fully hedge against productivity and money supply shocks at the same time. The port- folio decisions become a lot more complicated as only two individual assets are available to deal with four competing hedging tasks. The exact equity holdings depend on the relative size between the two types of shocks and on 16 Chapter 1. Equity Home Bias and Nominal Rigidity the value of structural parameters. Following the literature, we set the share of labor income equal to two thirds (ζ = 23). Let the shocks be one percent of their steady state level (σ2A = σ 2 M = 0.0001). Figure 1.1 shows five subsets of the share of domes- tically owned home equities (δE) when the disutility of labor is assumed to be linear (ψ = 0) and the relative risk aversion coefficient (ρ) and the elasticity of substitution between home and foreign goods (θ) are both set to be within the range of [0, 5]. The first thing to note is that when θ > 1, home households take a long position in domestic equities (δE > 1). The intuition is as following. Productivity shocks are hedged perfectly if households hold one hundred percent of their domestic equities. Therefore, how to hedge against money supply shocks using home and foreign equities in the FE economy determines the equilibrium portfolios. In response to a positive home money supply shock, home currency de- preciates. Demand for home goods goes up. The demand for labor and the wage rate increases at home, so is the firm’s revenue when θ > 1. Given ζ = 23 , the increase in labor cost is so significant that the dividend moves in the opposite direction to the firm’s revenue. Hence, it is optimal for home households to aggressively invest in their domestic equities (δE > 1) or take a short position in foreign equities (α̃FE,E∗ < 0). In this way, the gain in terms of real production income is balanced by a negative payment from equity holdings. Now let us look at the case when θ < 1. Again, suppose the home country experiences a positive money supply shock, home currency depreci- ates. Home goods become relatively cheaper than foreign goods. Demand for home goods goes up, and so are the demand for labor and the wage rate at home. If θ < 1, the expenditure switching effect is weak relative to the change in price. Thus, home real GDP decreases. The dividend on home equities drops too. It is optimal for home households to invest in foreign equities. Moreover, the smaller the expenditure switching effect (θ) is, the higher the share of foreign equities in home households’ portfolios. Figure 1.2 repeats the above exercise, but assumes the disutility of labor 17 Chapter 1. Equity Home Bias and Nominal Rigidity is in a quadratic form (ψ = 1). It is easy to see that the results are not sensitive to this modification. The elasticity of substitution between home and foreign goods (θ) is a key parameter that determines the equilibrium equity holdings. It has a wide range of estimates in the international economics literature, ranging from 1.2 to 21.4 as reviewed by Obstfeld and Rogoff (2000a) [53]. The number often used in the macroeconomics study is between 1 and 2, following Backus, Kehoe and Kydland (1994) [3] and Chari, Kehoe and McGrattan (2002) [10]. A value smaller than unity is seldom used except Stockman and Tesar (1995) [63] set the elasticity of substitution between traded and non-traded goods equal to 0.44 and Heathcote and Perri (2002) [37] set the elasticity of substitution between intermediate goods equal to 0.9. Table 1.3 describes the equilibrium share of domestically owned home equities in the FE economy with ζ = 23 , σ 2 A = σ 2 M = 0.0001 and ρ = 1.5. Table 1.3: Share of Domestically Owned Home Equities with Sticky Prices and Flexible Wages δFE,E θ = 0.44 θ = 0.9 θ = 1.5 ψ = 0 0.7445 0.9624 1.1957 ψ = 1 0.8284 0.9805 1.0818 Following the most typical calibration in the macro literature, we find that the labor income and the return on domestic equities are negatively correlated with respect to both the productivity shocks and the money sup- ply shocks. Therefore, the optimal portfolios involve a substantial short position in foreign equities (see the last column in Table 1.3). This “super home bias”result casts doubt on the ability of sticky price in characterizing the observed equity portfolios. Wage adjustments are likely to have strong implications for the correla- tion between the returns to workers and the returns to firm owners. In fact, there are more extensive empirical evidence for sluggish wages than that for 18 Chapter 1. Equity Home Bias and Nominal Rigidity sticky prices.9 We are going to examine the effect of nominal wage rigidity in the next section. 1.4 A Model with Sticky Wage Following Obstfeld and Rogoff (2000b) [52], each worker acts like a mo- nopolistic supplier of a distinctive variety of labor services. Workers set wages (in their domestic currency) before shocks are realized.10 Each firm uses workers of every type and the elasticity of substitution among varieties of labor is given by µ. The other parts of the model are kept same as before. The production function for aggregate home firms is YH = AL = A [ 2 1 µ ∫ 1 2 0 l(z) µ−1 µ dz ] µ µ−1 (1.40) which implies that their demand for agent z’s labor is l(z) = [ w(z) w ]−µ L (1.41) Before shocks are realized, agent z sets his wage to maximize his expected utility E [ U(c(z), m(z) P , l(z)) ] subject to m(z) + Pc(z) = m0(z) + w(z)l(z) + pi(z) + P n∑ k=1 αk(z)rk + t(z) 9See, for example, Altonji and Devereux (2000) [1],Fehr and Goette (2005) [26], and Goette et al (2007) [34]. 10Because the real marginal consumption value of wage is not equal to the marginal disutility of working when wages are pre-set, only sufficiently small shocks are considered here to avoid a further discussion of voluntary participation constraint. This concern also applies to sticky goods prices, as firms may have to operate under negative profits if a big negative productivity shock hits the economy. 19 Chapter 1. Equity Home Bias and Nominal Rigidity In a symmetric equilibrium, all agents will choose the same wage rate w = ηµ µ− 1 E [ L1+ψ ] E [ L PCρ ] (1.42) The wage equation (1.42) takes the place of the intratemporal labor- leisure choice equation (1.17) in the original set of equilibrium conditions. Table 1.4 describes the optimal portfolio holdings in the FE and FBE economies in the presence of nominal wage rigidities. Table 1.4: Optimal Portfolio Holdings with Sticky Wages κ = 0 : FE α̃FE,E∗ = 12 FBE α̃FBE,B∗ = 0 α̃FBE,E∗ = 12 κ = 1 : FE α̃FE,E∗ = 12 (θ−1)2(ζ−1)2σ2M ζ2[1+ρ(θ−1)]σ2A+(θ−1)2(ζ−1)2σ2M FBE α̃FBE,B∗ = 1−θ2 α̃FBE,E∗ = 0 Sticky Wage and Flexible Price Case When wages are fixed but goods prices are flexible, the excess return of foreign equities relative to home equities is r̂E∗ − r̂E = (θ − 1)τ̂ + O(2).11 Therefore, the portfolio decisions are identical to the case where both wages and prices are flexible. Consumption risk sharing is perfect so long as home and foreign equities are allowed for trade.12 11Detailed derivation see Appendix A.3 12One thing different here is that money has real effect on the economy now. In response to a positive home money supply shock, home currency depreciates but home goods prices are not adjusted due to fixed wage rates. Home terms of trade deteriorate and home real GDP becomes relatively higher than foreign real GDP. Although the equilibrium asset positions are not affected by this additional friction, the welfare changes. In fact, the welfare is lower because the two countries produce at different levels when they are 20 Chapter 1. Equity Home Bias and Nominal Rigidity Sticky Wage and Sticky Price Case As shown in Appendix A.3, the excess return of foreign bonds relative to home bonds can be expressed as r̂B∗ − r̂B = −τ̂ +O(2). Therefore, the presence of nominal wage rigidity has no effect on the optimal portfolios in the FBE economy. Households will still hold one hundred percent of their domestic equities to hedge against the productivity shocks, and borrow (lend) in foreign (home) nominal bonds to hedge against the money supply shocks when θ > 1. In the FE economy, home and foreign equities cannot simultaneously hedge against the productivity shocks and the money supply shocks. The consumption risk sharing is imperfect in this case. Once again, let ζ = 23 and σ2A = σ 2 M = 0.0001. Table 1.5 describes the equilibrium share of domestically owned home equities when ρ = 1.5. Table 1.5: Share of Domestically Owned Home Equities with Sticky Prices and Sticky Wages θ = 0.44 θ = 0.9 θ = 1.5 δFE,E 0.5067 0.9956 0.9483 For θ > 1, we no longer have the “super home bias”result as in the case with flexible wages. Recall that with fixed goods prices, households’ default equity positions provide a perfect hedge against the productivity shocks. What is important is how home and foreign equities are used to hedge against the money supply shocks. In response to a positive home money supply shock, home currency depreciates. Demand for home goods goes up, so are the demand for labor and the firm’s revenue (when θ > 1). Remember that nominal wages are fixed. So even the labor income accounts for two thirds of the total income, the increase in labor cost is not big enough to reduce home firms’ profits. The dividend on home equities is positively correlated with the labor income. Hence, it is optimal for home households equally productive. 21 Chapter 1. Equity Home Bias and Nominal Rigidity to diversify their portfolios and invest in foreign equities (α̃FE,E∗ > 0). In this way, the gain in terms of real production income is balanced by a negative payment from equity holdings. Figure 1.3 shows five subsets of the share of domestically owned home equities (δE) when the relative risk aversion coefficient (ρ) and the elasticity of substitution between home and foreign goods (θ) are both set to be within the range of [0, 5]. For most values of θ ∈ [0.8, 2], the model with sticky wages and sticky goods prices infers optimal equity portfolios that match the data quite well. With incomplete financial markets, the model predicts home bias for a wide range of parameterization, especially when the cut-off value for home bias is set to be 0.75 in stead of 0.9 (see Figure 1.4). 1.5 Conclusion This paper analyzes the optimal portfolio decisions in a monetary open economy macro framework with a particular attention to the completeness of financial markets and the presence of nominal rigidities in goods prices and in wages. With complete financial markets and sticky prices, the model generates a complete home bias in equities because the return to human capital and the return to domestic firms are negatively correlated with respect to pro- ductivity shocks. However, this result is sensitive to the configuration of financial markets. With incomplete financial markets, the model produces a “super home bias”result. As the return to human capital and the return to domestic firms are negatively correlated with respect to both the productiv- ity shocks and the monetary shocks, the optimal portfolios actually require households to take a short position in foreign equities rather than diversify their asset holdings. Therefore, sticky prices alone cannot fully explain the observed portfolios. Introducing sticky wages will help match the data because the return to human capital and the return to domestic firms become positively corre- lated with respect to monetary shocks in this case. In fact, the model with incomplete financial markets and nominal rigidities in both goods prices and 22 Chapter 1. Equity Home Bias and Nominal Rigidity wages predicts equity home bias for a wide range of parameterization used in the macro literature. An interesting direction for future research is to conduct welfare analysis for models incorporating endogenous portfolio choices, especially those with incomplete financial markets. Portfolio decisions can be very complicated as a limited set of assets often need to deal with many competing hedging tasks in these environments. Such models may have intriguing policy implications. After all, the real world is far from having perfect risk sharing. 23 Chapter 1. Equity Home Bias and Nominal Rigidity Figure 1.1: Share of Domestically Owned Home Equities with Flexible Wage and Linear Disutility in Labor 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Elasticity of Substitution Between Home and Foreign Goods R el at iv e R is k A ve rs io n C oe ffi ci en t 1<=δ e 0.9<=δ e <1 0.5<=δ e <0.9 0<=δ e <0.5 δ e <0 24 Chapter 1. Equity Home Bias and Nominal Rigidity Figure 1.2: Share of Domestically Owned Home Equities with Flexible Wage and Quadratic Disutility in Labor 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Elasticity of Substitution Between Home and Foreign Goods R el at iv e R is k A ve rs io n C oe ffi ci en t 1<=δ e 0.9<=δ e <1 0.5<=δ e <0.9 0<=δ e <0.5 δ e <0 25 Chapter 1. Equity Home Bias and Nominal Rigidity Figure 1.3: Share of Domestically Owned Home Equities with Sticky Wage and Cut-off Value 0.9 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Elasticity of Substitution Between Home and Foreign Goods R el at iv e R is k A ve rs io n C oe ffi ci en t 1<=δ e 0.9<=δ e <1 0.5<=δ e <0.9 0<=δ e <0.5 δ e <0 26 Chapter 1. Equity Home Bias and Nominal Rigidity Figure 1.4: Share of Domestically Owned Home Equities with Sticky Wage and Cut-off Value 0.75 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Elasticity of Substitution Between Home and Foreign Goods R el at iv e R is k A ve rs io n C oe ffi ci en t 1<=δ e 0.75<=δ e <1 0.5<=δ e <0.75 0<=δ e <0.5 δ e <0 27 Chapter 2 International Financial Integration and Monetary Policy 2.1 Introduction Cross-country gross asset positions have increased dramatically in the past few decades. As shown in Lane and Milesi-Ferretti (2006) [46], the ratio of the sum of foreign assets and liabilities to GDP (IFIGDP) has increased from 45 percent to over 300 percent in industrial countries and from 40 percent to 150 percent in developing countries (between 1970 and 2004).13 During the 1970s and 1980s, the increase in cross-border asset trade was fairly stable, and the two country groups had similar trends in international financial integration. IFIGDP reached 100 percent in 1987 for both groups. However, since the early 1990s, an acceleration of cross-border asset trade has taken place in industrial countries, while developing countries have failed to pick up the pace. Clearly, the early 1990s is a decisive period to focus on for explaining the observed cross-section and time-series differences in the evolution of financial integration. New Zealand adopted the first inflation targeting regime in 1990, quickly followed by other developed countries. According to Rose (2006) [57], Good- friend (2003) [35], Ito and Mishkin (2004) [40], and Wyplosz (2006), all 13See Figure 2.1. The industrial countries include Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United King- dom, and United States. 28 Chapter 2. International Financial Integration and Monetary Policy the twenty three industrial countries classified by Lane and Milesi-Ferretti (2006) [46] target inflation explicitly or implicitly. Therefore, the entire in- dustrial country group essentially has adopted the same monetary strategy since the early 1990s, which is exactly the time when the acceleration in cross-border asset trade began. Is this just a coincidence? Figure 2.2 shows that there is sharp trend change in international financial integration for the eight explicit inflation targeting countries around the year they adopted the policy: New Zealand 1990, Canada 1991, UK 1992, Australia 1993, Sweden 1993, Switzerland 2000, Norway 2001, Iceland 2001. The twelve Euro zone countries target inflation jointly. Figure 2.2 clearly shows that the trend in international financial integration starts to change after 1996, when the Euro zone countries get ready for the formal launch of Euro. Denmark implements a fixed exchange rate policy vis-a-vis the Euro. Hence, similar change is ob- served in Denmark as well. The United States has been implicitly targeting inflation since early 1990s. The only exception is Japan. It is not clear the trend in international financial integration has surged in Japan. Given the decade long deflation, Japan is probably the only industrial country that does not target inflation in any way. Therefore, all the evidences indicate that the link between the acceleration of cross-border asset trade and the introduction of inflation targeting is not random. According to the De Facto Classification of Exchange Rate Regime and Monetary Policy Framework published by IMF (2006), only 17 out of 122 developing countries classified by Lane and Milesi-Ferretti (2006) [46] have adopted an inflation targeting regime.14 Most of these countries started to adopt such a regime after the 1997 Asian Financial Crisis. The majority of developing countries still use exchange rates as a nominal anchor when implementing monetary policies. This phenomenon is well-known and has been termed “fear of floating”.15 Overall the industrial country group and the developing country group 14The developing countries that adopt an inflation targeting regime are Brazil, Chile, Colombia, Czech Republic, Hungary, Israel, Korea, Mexico, Peru, Philippines, Poland, South Africa, Thailand, Indonesia, Romania, Slovak Republic, and Turkey. 15See Calvo and Reinhart (2002) [9], Reinhart and Rogoff (2002) [56], and Levy-Yeyati and Sturzenegger (2003) [47]. 29 Chapter 2. International Financial Integration and Monetary Policy participate at very different levels in international financial markets. The two groups also adopt very different monetary strategies. This paper ex- amines the interaction between financial integration and monetary policy by addressing following three questions: (1) Is financial integration always welfare-improving? (2) Is there a case for fixed exchange rate regimes to be favorable as financial openness increases? (3) Does the monetary policy regime have an impact on the desirability of financial integration? In a simple two-country monetary general equilibrium model with nom- inal price rigidity,16 this paper explores a number of financial market struc- tures, in which agents optimally choose portfolio positions that comprise familiar assets (such as nominal bonds and equities). Conditional on the range of assets and other aspects of the model, the financial market can be in autarky, incomplete, or complete. By contrasting the financial au- tarky with the complete or incomplete financial market, this paper unifies the analysis of full and partial financial integrations. Moreover, four simple monetary rules are examined: a money targeting rule, a unilateral exchange rate peg, a bilateral exchange rate peg, and a producer price targeting rule. The money targeting rule simply involves a constant money supply, repre- senting a passive floating exchange rate regime and corresponding to the policy recommended by Friedman (1953) [30]. The producer price targeting rule, which represents an active floating exchange rate regime, corresponds approximately to inflation targeting. By analyzing the choice of financial integration (given the rule of monetary policy) and the choice of monetary policy (given the structure of financial market), this paper also reveals the interaction between monetary policy and financial globalization. The main finding of this paper is that in a sticky price world with a passive floating exchange rate regime, financial integration reduces welfare. The reason is that financial integration leads to an increase in the terms of trade volatility, which is already excessive from a welfare standpoint, in the 16This type of model, which is often referred to as the new open economy macroe- conomics (NOEM) framework, has become a standard tool of policy analysis in open economy macroeconomics. See Obstfeld and Rogoff (1995, 2000) [51, 52], Corsetti and Pesenti (2001, 2005) [16, 17], Devereux and Engel (2003) [18], and others. For a survey of the NOEM literature, see Lane (2001) [45]. 30 Chapter 2. International Financial Integration and Monetary Policy presence of nominal price rigidities and constraints on the efficient use of monetary policy. Active monetary policy certainly has a role in improving welfare. Pegging exchange rates eliminate the excessive terms of trade ad- justment. Hence, fixed exchange rate regimes become more appealing than a money targeting rule to a country that has some access to international asset markets. Nonetheless, a producer price targeting rule removes the sticky price distortion and replicates the flexible price equilibrium. This ac- tive floating exchange rate policy, combined with perfect consumption risk sharing, brings the economy to the first-best. Thus, by targeting inflation, countries will benefit the most from financial globalization. This paper suggests that the preferred depth of financial integration varies across countries that have different monetary regimes. Countries with a passive floating exchange rate choose to stay in the financial autarky. Countries with a fixed exchange rate are indifferent to financial openness. Only those countries that can successfully target inflation will gain from financial integration. As a result, inflation targeting countries should be the most financially open economies in the world. It was mainly the industrial countries that switched to an inflation targeting regime in the early 1990s. Hence, this paper accounts for the observed acceleration in cross-border asset trade among these countries. This paper also justifies the observed slow progress of developing countries in the process of financial globalization, as most developing countries implement a de facto fixed exchange rate regime. In order to implement efficient inflation targeting, countries need to meet several initial conditions, such as having a central bank that has enough in- dependence, accountability, and transparency, having well developed domes- tic financial markets and sufficient financial stability, and having adequate research and statistic resources in forecasting inflation. While industrial countries seem to have no problem fitting into an inflation targeting regime, developing countries may find it significantly challenging. In addition, fi- nancial and monetary shocks are believed to be much larger in developing countries. It is rational for developing countries to adopt fixed exchange rate regimes first to alleviate the welfare cost of financial integration before they are ready to adopt inflation targeting. Accordingly, this paper provides 31 Chapter 2. International Financial Integration and Monetary Policy a new explanation for “fear of floating”.17 This paper compliments the literature that examines the impact of fi- nancial integration by paying particular attention to the interaction between financial globalization and monetary policies that are popular in practice. A large literature in international finance analyzes the size of gains from fi- nancial integration.18 As models in this literature are frictionless other than imperfect risk sharing, they all imply positive gains from financial integra- tion. Some find huge gains, while some find rather small benefits. However, in an environment with more than one distortion, financial integration may not always be beneficial. In a multi-country model with endogenous growth, Devereux and Smith (1994) [22] shows that increased international risk shar- ing discourages precautionary saving, which reduces the growth rate. Hence, welfare in complete financial markets is actually lower than that in finan- cial autarky. Tille (2005) [68] also finds that integration is not universally beneficial in a model similar to ours. As he assumes a unity elasticity of substitution between home and foreign goods, the attention is focused on the degree of exchange rate pass-through. Instead, this paper solves for a general elasticity of substitution between home and foreign goods, which is a critical parameter that determines the welfare impact of integration. We find loss from integration when this elasticity is greater than unity, a case that is more empirically relevant and indicates that terms of trade play a key role in welfare evaluations. Engel (2001) [23] studies how the degree of exchange rate pass-through and the degree of risk sharing affect the choice between fixed and floating exchange rate regimes. However, he does not compare welfare between different asset market structures. All the above authors overlook the interaction between financial integration and mone- tary policy. They also ignore the issue of partial financial integration for tractability reasons. This paper is also related to the literature regarding the analysis of en- 17Factors that have been emphasized in the “fear of floating”literature include liability dollarization, lack of central bank credibility, exchange rate pass-through effect, concern about sudden stop, and the mercantilist view. 18See for example Backus, Kehoe, and Kydland (1993) [2], Cole and Obstfeld (1991) [14], Lewis (1996) [48], Tesar (1995) [66], and van Wincoop (1999) [69]. 32 Chapter 2. International Financial Integration and Monetary Policy dogenous portfolio choices in dynamic general equilibrium models with com- plex asset markets.19 Devereux and Sutherland (2007) [21] are the first to analyze monetary policy when international portfolio decisions are endoge- nous. While they explore the impact of monetary policy on country asset positions in both complete and incomplete financial market environments, they limit their examination to a producer price targeting rule and to the impact of the stance of monetary policy on equilibrium asset holdings. They do not compute welfare and do not study other types of monetary policies. They also do not link policy analysis with the observed trend in cross-border asset trade. The paper proceeds as follows. Section 2.2 describes the structure of the model. Section 2.3 presents the solution method for optimal portfolio choice and welfare. Section 2.4 discusses the impact of financial integration. Section 2.5 analyzes the welfare of alternative money supply rules. The paper concludes with a brief summary and with suggestions for subsequent research. 2.2 The Model The world is assumed to exist for a single-period and to consist of two countries, which will be referred to as the home country and the foreign country. Each country is populated by agents who consume a basket of home and foreign produced goods. Each agent, using a linear technology in labor, is a monopoly producer of a particular differentiated product. The world population is normalized to have a measure of one. Home agents are indexed h ∈ [0, 12 ] and foreign agents are indexed f ∈ [12 , 1]. Agents in each country set prices before the realization of shocks and the setting of monetary policies. They are contracted to meet demand at pre- fixed prices. All prices are assumed to be set in the currency of producers. 19A list of related papers are authored by Devereux and Sutherland (2006a, 2006b) [19, 20], Engel and Matsumoto (2005) [24], Evans and Hnatkovska (2005) [25], and Kollmann (2005) [43]. 33 Chapter 2. International Financial Integration and Monetary Policy Thus, there is full exchange rate pass-through to prices paid by consumers. Agents supply homogeneous labor. Prior to the realization of shocks, they can trade in a range of financial assets. The financial market structure and the payoff to each asset are defined in Section 2.2.3. The timing between asset trade and monetary policy does not affect the welfare of each scenario considered in this paper. Each country faces two types of shocks: produc- tivity and money demand shocks. A production subsidy is introduced to precisely offset the friction of imperfect competition. Therefore, only two types of distortions remain: nominal price rigidity and incomplete consump- tion risk sharing. The detailed structure of the home country is described below. The for- eign country has an identical structure. Where appropriate, foreign variables are denoted with an asterisk. 2.2.1 Consumers All agents in the home country have utility functions of the same form U = C1−ρ 1− ρ + χlog M P − η L 1+ψ 1 + ψ (2.1) where C is the consumption index, defined across all home and foreign goods, M denotes the end-of-period nominal money holding, P is the consumer price index (CPI), L is the labor supply, ρ (ρ > 0) is the coefficient of relative risk aversion, η is the coefficient of labor supply, ψ (ψ ≥ 0) is the elasticity of labor supply, and χ is an i.i.d. stochastic money demand shock, with E(logχ) = 0, V ar(logχ) = σ2χ, and logχ ∈ [−, ]. There are two stages to the household decision problem. Before shocks are realized, households choose portfolio positions out of available assets to maximize expected utility, E [ U(C, MP , L) ] , subject to n∑ k=1 αk = 0 (2.2) where αk represents the real holding of asset k, and n is the total number 34 Chapter 2. International Financial Integration and Monetary Policy of assets. All real variables in this paper are defined in terms of home consumption basket. Each country starts with zero net foreign asset. After shocks are realized, households choose consumption, labor sup- ply, and money balances, in order to maximize ex-post utility, U(C, MP , L), subject to M + PC = M0 + (1 + γ)PHYH + P n∑ k=1 αkrk + T (2.3) where M0 is the initial nominal money holding, γ is the rate of production subsidy, PH is the aggregate price of home produced goods, rk is the real ag- gregate rate of return on asset k, and T is a lump-sum government transfer. YH is the world demand for aggregate home produced goods YH = 1 2 ( PH P )−θ (C + C∗) (2.4) where θ is the elasticity of substitution between home and foreign goods. Although empirical works suggest a wide range of estimations for this elas- ticity, most researchers agree that a greater than unity elasticity is more empirically relevant. Firms’ revenues are used to pay wages and profits (1 + γ)PHYH = wL+Π (2.5) where w and Π denote the wage and the profit (dividend), respectively. Here, home agents first receive all profits from domestic firms. Then, if an international equity market exists, claims to home profits may be trans- ferred to foreign consumers via trade in equity shares.20 Moreover, we define Y as the disposable home aggregate real production 20Alternatively, it can be assumed that profits proceed directly to shareholders. There is no fundamental difference between the two modeling approaches. However, all firms have to be domestically owned in the financial autarky. It is easier to compare various financial market structures by assuming all profits are received by domestic agents first. 35 Chapter 2. International Financial Integration and Monetary Policy income PY = PHYH (2.6) Combined with the government budget constraint M −M0 = γPHYH + T (2.7) we can rewrite home household’s budget constraint (2.3) in real terms C = Y + n∑ k=1 αkrk (2.8) The consumption index C for home agents is defined as C = ( 1 2 ) 1 θ−1 ( C θ−1 θ H + C θ−1 θ F ) θ θ−1 (2.9) CH and CF are indices of home and foreign produced goods CH = [( 1 2 ) 1 φ ∫ 1 2 0 CH(h) φ−1 φ dh ] φ φ−1 (2.10) CF = [( 1 2 ) 1 φ ∫ 1 1 2 CF (f) φ−1 φ df ] φ φ−1 (2.11) where φ (φ > 1) is the elasticity of substitution between individual home (or foreign) goods. The aggregate consumer price index for home households is P = ( 1 2 ) 1 1−θ ( P 1−θH + P 1−θ F ) 1 1−θ (2.12) where PH and PF are the price indices for home and foreign produced goods, 36 Chapter 2. International Financial Integration and Monetary Policy respectively PH = [ 2 ∫ 1 2 0 PH(h)1−φdh ] 1 1−φ , PF = [ 2 ∫ 1 1 2 PF (f)1−φdf ] 1 1−φ (2.13) The law of one price implies that PH(h) = P ∗H(h)S and PF (f) = P ∗ F (f)S for all h and f . An asterisk indicates that the price is in foreign currency and S is the nominal exchange rate defined as the domestic price of foreign currency. Because there is no home bias in consumption, purchasing power parity (PPP) holds, i.e. P = SP ∗. Given prices and the total consumption C, home consumers’ optimal demands for home and foreign goods are CH = 1 2 ( PH P )−θ C, CF = 1 2 ( PF P )−θ C (2.14) CH(h) = 2 [ PH(h) PH ]−φ CH , CF (f) = 2 [ PF (f) PF ]−φ CF (2.15) The remaining first order conditions are E ( r1C −ρ) = E (rnC−ρ) E ( r2C −ρ) = E (rnC−ρ) ... (2.16) E ( rn−1C−ρ ) = E ( rnC −ρ) ηLψ = wC−ρ P (2.17) χ M = C−ρ P (2.18) Equation (2.16) indicates that portfolio choices are optimal only when the expected returns on all assets are equalized in terms of utility. Equations (2.17) and (2.18) are the standard intra-temporal labor-leisure choice func- tion and the money demand function. 37 Chapter 2. International Financial Integration and Monetary Policy 2.2.2 Firms Firms engage in monopolistic competition. Each produces specific goods indexed by h with a linear technology in labor YH(h) = AL(h). A is an i.i.d. stochastic technology shock with E(logA) = 0, V ar(logA) = σ2A, and logA ∈ [−, ]. The profit maximization problem of a firm h is Max E{D(h) [ (1 + γ)PH(h)− w A ] [YH(h) + Y ∗H(h)]} where YH(h) and Y ∗H(h) are the demand for goods h from the home and foreign markets YH(h) = [ PH(h) PH ]−φ (PH P )−θ C (2.19) Y ∗H(h) = [ P ∗H(h) P ∗H ]−φ ( P ∗H P ∗ )−θ C∗ (2.20) Because firms are all alike, they will set identical prices in equilibrium. Hence, the optimal price of home goods is PH = φ (φ− 1)(1 + γ) E [ DwAXH ] E [DXH ] (2.21) XH represents the demand for home produced goods XH = P φ H ( PH P )−θ (C + C∗) where we have applied the law of one price and PPP in CPI. When γ = 1φ−1 , the distortion created by monopoly is completely offset and the average output is at its first-best level. D is the stochastic discount factor for home firms. In the financial au- tarky and with complete financial markets, D = C −ρ P . Under incomplete financial markets, it would be natural to assume that firms will evaluate profits at their shareholders’ discount rate. However, this would require 38 Chapter 2. International Financial Integration and Monetary Policy knowing the portfolio holdings in the first place, as home and foreign agents’ discount factors are different (if consumption risk sharing is imperfect). This issue turns out to be irrelevant to the solution of portfolio choices, given the order of accuracy considered in this paper. It may become a concern for solving welfare. This point will be discussed below. 2.2.3 Financial Sector This paper examines four different asset market configurations: (1) Fi- nancial Autarky (FA), in which no assets can be traded across countries; (2) Bond Economy (FB), in which home and foreign nominal bonds are allowed for trade; (3) Equity Economy (FE), in which home and foreign equities can be traded; (4) Bond and Equity Economy (FBE), in which both nominal bonds and equities are allowed for trade. As long as the returns on different assets are not fully correlated, trading assets can increase the degree of in- ternational risk sharing. Whether the financial market is complete depends on its structure and on the nature of the rest of the model. Nominal bonds represent a claim on a unit of currency. Equities repre- sent a claim on aggregate profits. The real aggregate rate of return on each asset is defined as following rB = 1 qBP (2.22) rB∗ = Q qB∗P ∗ (2.23) rE = Π qEP (2.24) rE∗ = QΠ∗ qE∗P ∗ (2.25) where qk is the real price of asset k and Q is the real exchange rate, i.e. Q = SP ∗ P . 2.2.4 Monetary Rules We consider four different policies: a money targeting rule (MT), a uni- 39 Chapter 2. International Financial Integration and Monetary Policy lateral (or one-sided) exchange rate targeting rule (UERT), a bilateral (or cooperative) exchange rate targeting rule (BERT), and a producer price tar- geting rule (PPT). In each regime, the money supply is targeted on some easily observable variables, such as exchange rate and price index. With a constant money supply, the exchange rate will respond endoge- nously to domestic and foreign disturbances. Hence, the money targeting rule represents a passive floating exchange rate regime. The unilateral peg involves one country (w.o.l.g., the home country) adjusting its money sup- ply to achieve a fixed exchange rate target. Under the bilateral peg, both countries target the same level of exchange rate. When the home currency depreciates, the home money supply contracts and the foreign money supply expands at the same time. The producer price targeting rule stabilizes the domestic producer price level, which eliminates the relative price distortion when some prices cannot be adjusted in the short-run. Such a policy repre- sents a type of active floating exchange rate regime. Because all prices are assumed to be pre-fixed, the price targeting is defined in terms of stabiliz- ing the prices that producers would choose if prices were fully flexible. The policy equations are in the following form M = M̄ ( S S̄ )−δs (PXH P̄H )−δp (2.26) M∗ = M̄∗ ( S S̄ )δ∗s (P ∗XF P̄ ∗F )−δ∗p (2.27) where S̄, P̄H and P̄ ∗F are the target levels of exchange rate and home and foreign producer prices. “Flexible”prices are given by PXH = φ (φ− 1)(1 + γ) w A P ∗XF = φ (φ− 1)(1 + γ) w∗ A∗ (2.28) Table 2.1 summarizes all the regimes. Hereafter, x̂ = log(x)− log(x̄), where x̄ is the non-stochastic steady state value of variable x. 40 Chapter 2. International Financial Integration and Monetary Policy Table 2.1: Targeting Regimes Regime Targets Policy Parameters Money M̂ = M̂∗ = 0 δs = δ∗s = δp = δ∗p = 0 Unilateral Exchange Rate Ŝ = 0 δs →∞, δ∗s = δp = δ∗p = 0 Bilateral Exchange Rate Ŝ = 0 δs = δ∗s →∞, δp = δ∗p = 0 Producer Price P̂XH = P̂ ∗X F = 0 δs = δ ∗ s = 0, δp = δ ∗ p →∞ 2.2.5 Market Clearing The goods market clearing condition is AL = 1 2 ( PH P )−θ (C + C∗) (2.29) The asset market clearing condition is αk = −α∗k, k = 1, 2, · · · , n (2.30) 2.2.6 Equilibrium The equilibrium comprises a set of prices, P , P ∗, PH , P ∗F , w, w ∗, rk, S, and a set of quantities C, C∗, L, L∗, Π, Π∗, YH , Y ∗F , Y , Y ∗, αk, α∗k, M , M ∗, which solves a system of equations (2.4)-(2.6), (2.12), (2.16)-(2.18), (2.21), (2.29), and their foreign counterparts, as well as (2.8), (2.22)-(2.27), and (2.30), given productivity and money demand shocks, A, A∗, χ, and χ∗.21 2.3 Solution Method 2.3.1 Optimal Portfolios Using the method developed in Devereux and Sutherland (2006a) [20], the equilibrium portfolio choices are solved to a second-order accuracy. From 21By Walras’ Law, there is one equation redundant in the system. The foreign agent’s budget constraint is dropped. 41 Chapter 2. International Financial Integration and Monetary Policy the second-order approximations of home and foreign portfolio selection equations around the non-stochastic steady state,22, we obtained the set of equations to solve for equilibrium portfolios E[ρ(Ĉ − Ĉ∗)r̂x] = 0 +O(3) (2.31) It is written in a vector form with r̂′x = [r̂1 − r̂n, r̂2 − r̂n, · · · , r̂n−1 − r̂n]. Condition (2.31) contains only the second moments of endogenous vari- ables, indicating that the optimal portfolio allocation is generally indeter- minate in a first-order approximation of a model. Moreover, it shows that solving the portfolio choice to a second-order accuracy only requires the first-order solution of the non-portfolio part of the model. This is because second-order accurate second moments can be computed from first-order so- lutions for realized variables. Finally, firms’ discount factors do not appear in equation (2.31) or any other equilibrium condition up to the first-order. Hence, they do not affect the solution of optimal portfolio choices. The log-linearization of the model is presented in Appendix B.2. 2.3.2 Welfare It is not possible to derive an exact analytical expression for welfare in this model. A second-order accurate solution for welfare is necessary.23 It requires solving the model as a second-order approximation around the non-stochastic steady state. A second-order approximation of the welfare measure is given by Ũ = E [ C̄1−ρ ( Ĉ + 1− ρ 2 Ĉ2 ) − ηL̄1+ψ ( L̂+ 1 + ψ 2 L̂2 )] +O(3) (2.32) where Ũ is the deviation of welfare from the non-stochastic equilibrium. C̄ and L̄ are the steady state values of consumption and labor supply. Welfare 22The non-stochastic symmetric steady state is described in Appendix B.1. More details about the portfolio solution method can be found in Chapter 1 of this thesis. 23This has been well addressed in the literature. For example, see Collard and Juillard (2001) [15], Kim and Kim (2003) [42], Schmitt-Grohe and Uribe (2004) [59]. 42 Chapter 2. International Financial Integration and Monetary Policy is increasing in the expected level of consumption but is decreasing in the variance of consumption, in the expected level of labor and in the variance of labor. Equilibrium conditions that are log-linear are ready to use. The budget constraint, the consumer price index, the pre-fixed price, and the real pro- duction income equations require second-order approximations. They are given by Ĉ = Ŷ + α̃r̂x + λC +O(3) (2.33) Ĉ∗ = Ŷ ∗ − α̃r̂x + λC∗ +O(3) (2.34) P̂ = 1 2 (P̂H + P̂ ∗F + Ŝ) + λP +O( 3) (2.35) P̂ ∗ = 1 2 (P̂H + P̂ ∗F − Ŝ) + λP ∗ +O(3) (2.36) Ŷ = (1− θ)(P̂H − P̂ ) + 12(Ĉ + Ĉ ∗) + λY +O(3) (2.37) Ŷ ∗ = (1− θ)(P̂ ∗F − P̂ ∗) + 1 2 (Ĉ + Ĉ∗) + λY ∗ +O(3) (2.38) L̂ = −Â− θ(P̂H − P̂ ) + 12(Ĉ + Ĉ ∗) + λL +O(3) (2.39) L̂∗ = −Â∗ − θ(P̂ ∗F − P̂ ∗) + 1 2 (Ĉ + Ĉ∗) + λL∗ +O(3) (2.40) where α̃ = ᾱ Ȳ . λ summarize all the second-order terms.24 λP = λP ∗ = 1− θ 8 (P̂H − P̂ ∗F − Ŝ)2 (2.41) λY = λY ∗ = 1 8 (Ĉ − Ĉ∗)2 = λL = λL∗ (2.42) λC = − [α̃B∗,0(r̂B∗ − r̂B) + α̃E∗,0(r̂E∗ − r̂E)] Ŷ + 1 2 α̃B∗,0(r̂2B∗ − r̂2B) + 1 2 α̃E∗,0(r̂2E∗ − r̂2E) −1 2 [α̃B∗,0(r̂B∗ − r̂B) + α̃E∗,0(r̂E∗ − r̂E)]2 + 1 2 α̂B∗,0(r̂B∗ − r̂B) + 12 α̂E∗,0(r̂E∗ − r̂E) (2.43) 24This solution technique has been employed in a series of papers. For instance, Suther- land (2004) [64] and Senay and Sutherland (2005) [60]. 43 Chapter 2. International Financial Integration and Monetary Policy λC∗ = [α̃B∗,0(r̂B∗ − r̂B) + α̃E∗,0(r̂E∗ − r̂E)] Ŷ ∗ −1 2 α̃B∗,0(r̂2B∗ − r̂2B)− 1 2 α̃E∗,0(r̂2E∗ − r̂2E) −1 2 [α̃B∗,0(r̂B∗ − r̂B) + α̃E∗,0(r̂E∗ − r̂E)]2 −1 2 α̂B∗,0(r̂B∗ − r̂B)− 12 α̂E∗,0(r̂E∗ − r̂E) (2.44) A country’s terms of trade are defined as the price of its exports in terms of its imports, i.e. τ = 1/τ∗ = PHSP ∗F . Hence, E(λP ) and E(λP ∗) correspond to the variance of terms of trade. E(λY ), E(λY ∗), E(λL), and E(λL∗) indicate the degree of consumption risk sharing across countries. Moreover, α̂B∗,0 = α̂E∗,0 = 0 in a single-period model. The exact form of λC and λC∗ depends on the asset market structure. E(λC) and E(λC∗) represent the variance and covariance between production income and financial income. Firms’ discount factors drop out in the first-order approximation of the model. Hence, they have no influence on the optimal portfolio decisions. However, the discount factors appear in the second-order approximation of the model through the pricing function. In order to compute welfare appropriately, it is important to specify the discount factors clearly. If the financial market is complete, the marginal utility of one unit of currency is equalized between home and foreign agents. Thus, it does not matter whether the discount factors follow the home or the foreign owners or a combination of them. If there is no financial market at all, the discount factors follow the domestic agents automatically. Therefore, the only case that needs to be approached with caution is where financial markets exist but are incomplete. If firms are held by both the home and the foreign agents and assumed to evaluate profits at their shareholders’ discount rate, it becomes quite complicated to solve the model, especially in a multiple- period or infinite-horizon dynamic environment. However, in the single- period model, we can show that the results are robust to this assumption.25 For simplicity, the discount factors are assumed to always follow the domestic owners. That is, D = C −ρ P . As a result, second-order approximations of the 25Results are available upon request. 44 Chapter 2. International Financial Integration and Monetary Policy pre-fixed prices are given by P̂H = E(ψL̂+ P̂ + ρĈ − Â) + λPH +O(3) (2.45) P̂ ∗F = E(ψL̂ ∗ + P̂ ∗ + ρĈ∗ − Â∗) + λP ∗F +O(3) (2.46) where λPH and λP ∗F represent the risk premium that home and foreign firms build into their pre-fixed prices λPH = 1 2 E [ (ψL̂+ P̂ + Ŷ − Â)2 − (Ŷ − ρĈ)2 ] (2.47) λP ∗F = 1 2 E [ (ψL̂∗ + P̂ ∗ + Ŷ ∗ − Â∗)2 − (Ŷ ∗ − ρĈ∗)2 ] (2.48) Equations (2.33)-(2.48) plus other log-linear equilibrium conditions al- low us to express the approximated welfare (2.32) in terms of λ. The ex- pectations of these second-order terms contain only the second moments of variables in the model. Because second-order accurate second moments can be computed from first-order solutions for the realized values of en- dogenous variables, analytical solutions for welfare can be easily obtained. In addition, home and foreign countries have symmetric structures and are subject to i.i.d. shocks with zero means. Thus, the two countries are ex-ante identical and have same expected utilities. 2.4 Model Solution This section abstracts from policy issues and only looks at the solution under a money targeting rule. Section 2.5 will give a complete analysis of monetary policy. We start with discussing the relationship between the exchange rate, the terms of trade, and the risk sharing condition. Then, we show that there are two key aspects of the terms of trade in determining the welfare. One is the volatility of the terms of trade and the other is the efficiency of the terms of trade adjustment. By efficiency, we mean whether the terms of trade move in the right direction to achieve efficient relative price adjustments with respect to country-specific shocks. More importantly, both the volatility and the efficiency of the terms of trade depend on the 45 Chapter 2. International Financial Integration and Monetary Policy financial market structure. 2.4.1 Exchange Rate, Terms of Trade, and Risk Sharing From the PPP and the money demand equations, we can write the ex- change rate as26 Ŝ = (M̂ − M̂∗)− (χ̂− χ̂∗)− ρ(Ĉ − Ĉ∗) (2.49) In this model, people hold money because real balances are a part of the utility function. The role of money can be rationalized as capturing the benefits of saving time when conducting transactions. The exchange rate is basically the relative price of two countries’ currencies; it is factored accord- ing to the relative money supply and demand in each country. Money supply is given by the monetary policy rule that is adopted by each country. Money demand shocks are indeed preference shocks, which are meant to capture the technology innovations that alter the usefulness of money balances. Other things being equal, the more that agents consume, the more demand for real balances. It is easy to see that higher money supply makes a currency depreciate, while higher money demand makes a currency appreciate. Home terms of trade in log-linear form are given by τ̂ = P̂H − P̂ ∗F − Ŝ (2.50) Combined with the log-linearized home CPI and the log-linearized aggregate demand for home produced goods, home real GDP can be written as Ŷ = 1− θ 2 τ̂ + 1 2 (Ĉ + Ĉ∗) +O(2) (2.51) Together with the log-linearized home budget constraint, Ĉ = Ŷ + α̃′r̂x +O(2) (2.52) 26With money targeting rules, M̂ = M̂∗ = 0. 46 Chapter 2. International Financial Integration and Monetary Policy the consumption difference between home and foreign can be expressed as 1 2 (Ĉ − Ĉ∗) = 1− θ 2 τ̂ + α̃′r̂x +O(2) (2.53) Clearly, households’ consumption risks originate from real income risks, which indeed all come from the terms of trade fluctuations because there is no aggregate uncertainty at the world level. Agents can diversify away at least part of the consumption risks by trading assets across borders — as long as the returns on these assets are somehow correlated with the terms of trade. 2.4.2 Volatility of the Terms of Trade The exchange rate equation (2.49), the terms of trade equation (2.50), and the consumption difference equation (2.53) are crucial for us to un- derstand how the terms of trade would adjust in the process of financial integration. Suppose that home terms of trade deteriorate owing to certain fundamental shocks, τ̂ < 0. Home goods become cheaper relative to foreign goods. Given that home and foreign goods are substitutes, the world de- mand shifts towards home goods. Home output increases, which is called the expenditure switching effect. However, home goods are sold at a rel- atively lower price and foreign goods cost relatively more. Whether home GDP rises or falls in real terms depends on the strength of this substitu- tion across countries. If the expenditure switching effect is strong enough (when θ > 1), home real GDP increases. In the lack of consumption risk sharing, home agents consume more relative to foreign agents. As shown in equation (2.49), home currency appreciates in this case, flattening the initial deterioration in home terms of trade. The income effect of the initial terms of trade movement triggers an additional exchange rate adjustment that stabilizes the terms of trade. Once international asset markets open, the cross-country consumption difference diminishes and even disappears, if the market is complete. Hence, the higher the degree of consumption risk sharing, the smaller the damping effect from the exchange rate. As a result, 47 Chapter 2. International Financial Integration and Monetary Policy financial integration increases the terms of trade volatility when θ > 1.27 Moreover, this result does not hinge on the degree of nominal price rigidity in the economy.28 Proposition 1When θ > 1, terms of trade become more volatile as financial markets liberalize. Proof: See Appendix B.3 and the above discussion. 2.4.3 Efficiency of the Terms of Trade Efficient terms of trade adjustment should respond only to productivity shocks. In particular, a country’s terms of trade should deteriorate if the country experiences a positive productivity shock relative to another coun- try. The reason is straightforward: shocks to productivity are real shocks; they affect the comparative advantage of each country in producing substi- tutable goods. It is efficient to allow the country that has a better technology to produce more. This country’s terms of trade have to worsen, in order that the demand for its goods increases. In contrast, shocks to money demand are nominal shocks. Any response of the terms of trade with respect to money demand shocks represents a cost to efficiency. The real allocation of consumption and labor must be suboptimal if two countries, with the same technology and preference, produce at different levels. In all sticky price environments, terms of trade adjust through exchange rates. If a country’s currency depreciates regarding a positive productivity shock, the efficiency of world production will increase. Nevertheless, if a country’s currency appreciates regarding a positive productivity shock or if the value of a currency changes in any way regarding a money demand shock, the efficiency of world production will decrease. 27The result will be reversed if θ < 1. 28Preliminary empirical results confirm that the volatility of terms of trade does response positively to the degree of international financial integration for most G7 countries, after controlling for trade openness, GDP volatility, and the volatility of commodity prices. 48 Chapter 2. International Financial Integration and Monetary Policy 2.4.4 Welfare The general solution is very complicated and can only be addressed nu- merically. Here, we focus on a simplified version of the model, in which utility is logarithmic in consumption and linear in labor, i.e. ρ = 1 and ψ = 0. This special case has interpretable analytical expressions and allows us to discuss the important and intuitive features of the model. Relaxing the above simplifying assumptions will not change the results qualitatively. When ρ = 1 and ψ = 0, we can show that E(L̂)+ 12E(L̂ 2) = 0+O(3).29 In this case, welfare only depends on the expected level of consumption. It also indicates that welfare is not affected by monopolistic distortion, regard- less of the existence of production subsidy. When all prices are sticky, each country’s welfare is given by Ũ = E(Ĉ) = Ũ∗ = E(Ĉ∗) = −1 2 (λPH + λP ∗F )− E(λP ) +O(3) (2.54) λPH and λP ∗F are the risk premiums included in the pre-fixed prices. Other things being equal, a higher level of risk faced by producers makes them charge a higher price ex-ante, which means a lower level of expected out- put and a lower level of expected consumption. Therefore, the pricing risk premium has a negative effect on welfare. λP stems from the non-log-linearity of CPI and E(λP ) = 1−θ8 V ar(τ̂). When θ > 1, CPI is concave regarding the price of home and foreign goods. Any volatility in the relative price of home and foreign goods reduces the expected cost of the consumption basket. Intuitively speaking, when home and foreign goods are substitutable with each other, agents can spend less by switching expenditure towards a set of goods that is cheaper ex-post. Therefore, the volatility of terms of trade affects welfare positively. However, the volatility of terms of trade also affects the risk of setting prices in advance. Such risks are caused by the fact that firms cannot freely adjust their prices after knowing the state of the economy. Given the struc- 29Proof see Appendix B.4. 49 Chapter 2. International Financial Integration and Monetary Policy ture of the economy, firms know in advance how the exchange rate would respond to different shocks, ex-post. If the exchange rate facilitates effi- cient adjustment in production, the risk of the inability to change prices after shocks are realized is smaller. Firms will charge a lower price, ex-ante, leading to an increase in expected consumption. On the other hand, if the exchange rate causes inefficient adjustment in production, the pricing risk is higher. Firms will charge a higher price, ex-ante, leading to a reduction in expected consumption. As asset markets liberalize, the volatility of the ex- change rate goes up. Welfare will fall if financial integration causes excessive adjustments in terms of trade. Financial Autarky v.s. Complete Markets When all prices are sticky, output is demand-determined. Productivity shocks have no effect on firm revenue. The only changes occur are associated with the allocation between labor income and profit. If home agents hold one hundred percent of their own firms, their income as well as consumption are independent of productivity shocks. In other words, the default equity po- sition, or a complete home bias in equities, provides a perfect hedge against productivity shocks. Money demand shocks are the only source of income risks. As Home and foreign nominal bonds provide a perfect hedge against money demand shocks, the financial market is complete in the bond and in the bond equity economies. Table 2.2 summarizes the key second moments and welfare results in the financial autarky and in the complete market. Table 2.2: Second Moments and Welfare with Money Targeting Rules Financial Autarky Bond and Bond Equity Economy V ar(Ŝ) 2 θ2 σ2χ 2σ 2 χ λPH = λP ∗F 1 2σ 2 χ + 1 2σ 2 A θ 2σ 2 χ + 1 2σ 2 A E(λP ) 1−θ4θ2 σ 2 χ 1−θ 4 σ 2 χ Ũ = E(Ĉ) −2θ2−θ+1 4θ2 σ2χ − 12σ2A −1+θ4 σ2χ − 12σ2A 50 Chapter 2. International Financial Integration and Monetary Policy Because productivity shocks receive perfect hedging in both the financial autarky and the complete market, exchange rates react solely to money demand shocks. Any induced adjustment on real allocations is inefficient. Increased exchange rate volatility simply means bigger distortion and higher pricing risk. Let σ2A = σ 2 χ = 0.0001. Figure 2.4 shows that the pricing risk is clearly higher under the complete market when θ > 1. Although the variance of consumption is reduced due to enhanced consumption risk sharing, financial integration is still costly because it leads to a lower level of consumption. As the first-moment effect dominates the second-moment effect, welfare is lower under the complete market. Proposition 2 With complete nominal price rigidity and money targeting rules, perfect international consumption risk sharing reduces welfare when θ > 1. Proof: From the last row of Table 2.2, ŨFB/FBE−ŨFA = (θ 2+1)(1−θ) 4θ2 σ2χ < 0 if θ > 1. Incomplete Market When all prices are sticky, international risk sharing is generally incom- plete in the equity economy. The exchange rate responds to both productiv- ity and money demand shocks. Portfolio diversification may raise or reduce welfare depending on deeper parameters in the model, especially the steady state labor income share ζ. In particular, we find a hump-shape relationship between the value of ζ and welfare in the equity economy. When ζ = 0, each equity has a payoff equal to the GDP of the corre- sponding country. Agents are indeed trading two state-contingent assets. Agents can perfectly hedge against money demand shocks by holding half of each country’s equities. In this case, markets are complete, and the exchange rate responds to money demand shocks only. Thus, the equity economy yields the same welfare as the complete market. This result holds for any θ. 51 Chapter 2. International Financial Integration and Monetary Policy When ζ > 0, money demand shocks affect both a firm’s revenue and its labor cost. In response to a positive home demand shock, both the firm’s revenue and the wage rate decrease in the home country. If ζ is small, the dividend on equity moves in the same direction as the firm’s revenue. Hence, it is optimal for home households to hold some foreign equities, i.e. α̃FE,E∗ > 0. On the other hand, if ζ is big, the reduction in wages is so significant that the dividend on equity moves in the opposite direction to the firm’s revenue. Hence, it is optimal for home households to take a short position in foreign equities, i.e. α̃FE,E∗ < 0. Once households start trading equities, exchange rates (or terms of trade) are influenced by productivity shocks. In this case, productivity shocks will have real income effects on the economy. As ζ increases, the welfare first rises and then falls. The intuition to this hump-shape relationship lies in how the terms of trade respond to different shocks. Up to first-order, the exchange rate in the equity economy is given by ŜFE = s1(Â− Â∗) + s2(χ̂− χ̂∗) (2.55) s1 = 2ζα̃FE,E∗ (1− ζ)[θ + 2α̃FE,E∗(1− θ)] (2.56) s2 = 2ζα̃FE,E∗ − 1 + ζ (1− ζ)[θ + 2α̃FE,E∗(1− θ)] (2.57) where α̃FE,E∗ = (1−θ)(1−ζ)[(1−θ)(1−ζ)+θζ]σ2χ 2{θζ2σ2A+(1−θ+θζ)[(1−θ)(1−ζ)+θζ]σ2χ} . Figure 2.5 plots the re- sponse coefficient of the exchange rate to each type of shock against the value of labor income share. We assume productivity and money demand shocks are equally volatile and that the elasticity of substitution between home and foreign goods is equal to 1.5, following Backus, Kehoe, and Kydland (1993) [2]. Similar results hold for any θ > 1. With respect to a positive home demand shock, home currency always appreciates. While with respect to a positive home productivity shock, home households experience a loss from their portfolio holdings, if α̃FE,E∗ > 0. 52 Chapter 2. International Financial Integration and Monetary Policy In this case, home currency depreciates. On the contrary, home currency appreciates if α̃FE,E∗ < 0. It is already known that any terms of trade adjustment due to monetary shocks cause inefficient movement in production. Therefore, the smaller the absolute value of s2, the less there is of real distortion. Moreover, when all prices are sticky, nominal exchange rates act as a relative price adjuster to real shocks. However, it is beneficial only if the exchange rate moves in the right direction. For example, if the home country experiences a positive productivity shock, a depreciation of home currency will help lower the relative price of home goods and shift world demand towards home produced goods. World production thus becomes more efficient. In contrast, world production is definitely more distorted if home currency appreciates; this is the case when ζ is greater than a certain level. International consumption risk sharing is usually imperfect in an equity economy, but it still trims down some of the income effect on exchange rates. Terms of trade are more volatile in the equity economy than that in the financial autarky. Whether portfolio diversification is welfare improving depends on the parameterization of the model, particularly on the value of ζ. If ζ is big enough, the exchange rate reacts inefficiently to both pro- ductivity and money demand shocks. Hence, increased international risk sharing makes people worse off. Instead, the exchange rate reacts efficiently to productivity shocks if ζ is small. There exists potential gain from di- versification. The net effect between efficient and inefficient terms of trade adjustments determines whether people will be better off. Proposition 3 With complete nominal price rigidity and money targeting rules, imperfect international risk sharing may either raise or reduce welfare, as a condition of the value of structural parameters in the model. Proof: See the above discussion. This paper illustrates the welfare effect by computing the consumption equivalent measure. This shows how much consumption would have to be given up under segmented markets to lead to the welfare level observed un- 53 Chapter 2. International Financial Integration and Monetary Policy der complete markets. Appendix B.5 gives the details of the derivations. Figure 2.6 plots the consumption equivalent measure (under each market configuration) against the value of the labor income share. As discussed, welfare is lower in the complete market than that in the financial autarky. The rank of incomplete market relies on the value of ζ. In the macroeco- nomics literature, the labor income share is normally set equal to two thirds, which implies that the equity economy generates a welfare lower than both the financial autarky and the complete market. 2.5 Policy Analysis Financial integration may reduce welfare because increased consumption risk sharing can cause excessive terms of trade volatility in the presence of nominal price rigidity. This quite surprising result suggests that active monetary policy may help to improve welfare as asset markets liberalize. 2.5.1 Exchange Rate Targeting Rules If the nominal exchange rate is fixed, there will be no idiosyncratic in- come risk. Hence, welfare with each type of exchange rate targeting rule is independent of the financial market structure. Nevertheless, a cooper- ative peg welfare dominates a one-sided peg due to the difference in the induced aggregate money supply, which affects the aggregate demand for goods. When all prices are sticky, output is demand-determined. The out- put volatility depends on the volatilities of relative price and aggregate de- mand. The bigger the output volatility, the higher the pricing risk faced by producers. Although the terms of trade are fully stabilized with a one- sided peg, the aggregate money supply varies so much that the pricing risk is indeed the same as that under a money targeting rule in the financial autarky. For a cooperative peg, there are not only no terms of trade adjust- ment, but no aggregate money supply change. As shown in Table 2.3, row 3, the pricing risk is smaller under a bilateral peg, i.e. λUERTPH > λ BERT PH . Undoubtedly, the cooperative peg dominates the unilateral peg, as can be 54 Chapter 2. International Financial Integration and Monetary Policy seen from the last row of Table 2.3, i.e. ŨBERT > ŨUERT . Table 2.3: Second Moments and Welfare with Exchange Rate Targeting Rules One-sided Peg Cooperative Peg V ar(Ŝ) 0 0 λPH = λP ∗F 1 2σ 2 χ + 1 2σ 2 A 1 4σ 2 χ + 1 2σ 2 A E(λP ) 0 0 Ũ = E(Ĉ) −12σ2χ − 12σ2A −14σ2χ − 12σ2A For any positive θ, the cooperative peg also dominates the money tar- geting rule in both the financial autarky and the complete markets, i.e. ŨBERT > ŨMT . The ranking between the money targeting rule and the unilateral peg depends on the structure of the financial markets and the value of θ. Consider the case θ > 1. In the financial autarky, the money targeting rule dominates the unilateral peg, i.e. ŨMTFA > Ũ UERT . Although the two policies have the same level of pricing risks, the money targeting rule allows some terms of trade volatility, which helps to lower the average cost of a consumption basket consisting of all home and foreign produced goods. When the financial market is complete, the terms of trade become too volatile and the pricing risk is much higher under a money targeting rule. In this case, the money targeting rule is dominated by the unilateral peg, i.e. ŨUERT > ŨMTFB/FBE . Similar results hold for the incomplete market with standard calibration. Proposition 4 Welfare of an exchange rate targeting rule is independent of the financial market structure. A cooperative peg always dominates a unilateral peg and also dominates a money targeting rule for all θ > 0. A unilateral peg is dominated by a money targeting rule in the financial autarky but dominates a money targeting rule in an open financial market when θ > 1. Proof: From the last rows of Table 2.2 and Table 2.3, ŨBERT − ŨUERT = 1 4σ 2 χ > 0; Ũ BERT − ŨMTFA = θ 2−θ+1 4θ2 > 0, ∀ θ > 0; ŨBERT − ŨMTFB/FBE = 55 Chapter 2. International Financial Integration and Monetary Policy θ 4 > 0, ∀ θ > 0; ŨUERT − ŨMTFA = 1−θ4θ2 < 0 if θ > 1; ŨUERT − ŨMTFB/FBE = θ−1 4 > 0, if θ > 1. In a non-coordinated game between home and foreign monetary author- ities, both authorities will choose not to intervene in the financial autarky, if the alternative policy is to operate a one-sided peg. However, when there is some international risk sharing, a passive floating exchange rate regime admits too many inefficient terms of trade adjustment. Each countries is better off by pegging its currency to the other. Once both countries do so, they in fact end up with a bilateral peg without any coordination. There- fore, financial market structures do matter for the choice of exchange rate regimes. Financial integration will be beneficial if countries are allowed to adjust their policies, even within a set of restricted exchange rate targeting rules. Moreover, stabilizing excessive terms of trade volatility can improve welfare, providing a new angle on the analysis of fixed vs floating exchange rate regimes. 2.5.2 Producer Price Targeting Rule An active floating exchange rate regime, such as the producer price tar- geting rule, will eventually dominate the money targeting rule and the fixed exchange rate regimes. With a producer price targeting rule, prices are still one hundred percent pre-fixed, but they are set at a level that is optimal, even after shocks are realized. In other words, firms will stick to the prices they have chosen even when they are allowed to readjust the prices after the state of the economy is revealed. As shown in Table 2.4, row 3, there is no pricing risk at all, i.e. λPPTPH = λ PPT P ∗F = 0. Hence, a price targeting rule actually replicates the flexible price equilibrium. The only difference com- pared to a flexible price environment is that the relative price modification is made through nominal exchange rates rather than by prices themselves. There is no fundamental difference on real allocations or on any other aspect. Furthermore, markets are complete in the equity economy, if monetary au- thorities target producer prices directly. Therefore, the welfare of a producer 56 Chapter 2. International Financial Integration and Monetary Policy price targeting rule only depends on whether asset markets exist. As long as some assets (nominal bonds or/and equities) are available for trade, interna- tional consumption risk sharing is perfect. In brief, producer price targeting and financial integration bring the economy to the first-best. As shown in the last row of Table 2.4, financial integration is always welfare improving once the sticky price distortion is removed, i.e. ŨPPTFB/FE/FBE > Ũ PPT FA . Table 2.4: Second Moments and Welfare with Price Targeting Rules Financial Autarky Bond, Equity, and Bond Equity Economy V ar(Ŝ) 2 θ2 σ2A 2σ 2 A λPH = λP ∗F 0 0 E(λP ) 1−θ4θ2 σ 2 A 1−θ 4 σ 2 A Ũ = E(Ĉ) θ−1 4θ2 σ2A θ−1 4 σ 2 A Let σ2A = σ 2 χ = 0.0001 and θ = 1.5. Figure 2.7 plots the consumption equivalent measure of each targeting rule under each market configuration against the value of labor income share. Now it is possible to state the following proposition. Proposition 5 A producer price targeting rule dominates the money tar- geting and the exchange rate targeting rules in each financial market config- uration. With either bonds or equities available for trade, a producer price targeting rule delivers the first-best outcome. Proof: From the last row of Table 2.4, ŨPPTFB/FE/FBE−ŨPPTFA = (θ−1) 2(θ+1) 4θ2 > 0, ∀ θ > 0.30 2.5.3 Financial Integration and Monetary Policy The producer price targeting rule generates the highest welfare in each fi- 30The proof for the first part of Proposition 5 is a bit tedious as it depends on the value of θ and the size of both shocks. However, for any θ > 1 2 , ŨPPT > ŨMT/UERT/BERT holds for any size of the shocks and in any type of financial market. 57 Chapter 2. International Financial Integration and Monetary Policy nancial environment. Therefore, given the process of financial integration, it should be the choice of monetary policy for all countries. However, inflation targeting is quite a sophisticated policy to conduct in practice. It requires a mandate to pursue an inflation objective, the accountability of the central bank, macroeconomic and financial stability, and well-functioning domes- tic asset markets (especially the bond market). Deep and liquid markets contribute to the effective execution of the policy operation in the sense that there will be appropriate market-based monetary instruments and that the transmission mechanism is clear. The central bank should also be able to give credible inflation forecasting in order to carry out such a policy. Industrial countries seem to have no problem in qualifying for all these con- ditions. It may be hard for developing countries to meet even some of these conditions. Table 2.5 is constructed based on the Central Bank Studies Survey by Fry et al (2000) [31]. This survey is conducted for 93 central banks in 1998 and is revised in 1999. The data for the average inflation between 1997 - 1998 are drawn from Table A.1 of Fry et al (2000) [31], and the data for the indices of independence, accountability, and transparency are obtained from Table A.5-A.7. These scores represent percentages of the maximum. There are twenty two industrial countries and seventy one developing coun- tries in this dataset.31 According to Rose (2006)[57], Australia, Canada, New Zealand, Sweden, and United Kingdom are explicit inflation targeters by 1999. As we have discussed at the beginning of this paper, the other seventeen industrial countries target inflation implicitly. At the same time, six developing countries, Chile, Czech Republic, Israel, Korea, Mexico, and Poland, implement inflation targeting. Among the industrial countries, the explicit inflation targeters experience lower inflation than the implicit targeters. Their central banks also have higher degrees of independence, accountability, and transparency. Similar patterns hold in the developing countries, except that the central banks which target inflation seem to have a slightly lower score of accountability than those which do not. However, the difference is tiny (less than 1%) 31Use the classification of Lane and Milesi-Ferretti (2006) [46]. 58 Chapter 2. International Financial Integration and Monetary Policy Table 2.5: Average Inflation and Central Bank Characteristics Average Index Index Index Country Group Inflation of of of (1997-1998) Independence Accountability Transparency Industrial 0.0196 0.8400 0.7143 0.7457 explicit - inflation targeter 0.0131 0.8553 0.9333 0.8771 implicit - inflation targeter 0.0216 0.8355 0.6458 0.7047 Developing 0.2721 0.7030 0.7171 0.5401 inflation targeter 0.1007 0.8297 0.7083 0.7713 non-inflation targeter 0.2880 0.6913 0.7179 0.5188 compared to the differences observed in other categories. These empirical evidences support the view that, in order to carry out efficient inflation targeting, it is necessary for all countries to build up thier institutional infrastructures. For developing countries, this process may take some time. Fry et al (2000) [31] reports scores for financial stability (Table A.8) as well. Not surprisingly, industrial countries are more stable than developing countries; inflation targeters are more stable than non-inflation targeters. Considering the fact that financial and monetary shocks are larger and more frequent in developing countries, it may be rational for developing countries to target the exchange rate first. Such a policy is easy to formulate, and it eliminates the excessive terms of trade adjustment. Hence, it is more favorable than a passive floating exchange rate regime to a country that has some access to international asset markets. Once the above prerequisites are met (at least to some extent), developing countries can proceed by pursuing the optimal inflation targeting rule. Therefore, financial integration and the lack of readiness for complex policy actions could be the reasons why most developing countries do not float the way they announce. Given the nature of monetary policy, what is the choice of financial inte- gration? Countries with a money targeting rule are better off in the financial autarky. Countries with exchange rate targeting rules are indifferent to the asset market structures. Only countries with an inflation targeting rule 59 Chapter 2. International Financial Integration and Monetary Policy gain from financial integration. Thus, the most financially open economies should be those who can successfully target inflation. This paper provides an explanation for the acceleration of cross-border asset trade observed in industrial countries during the early 1990s because most industrial countries started an inflation targeting regime around that time. This model also ra- tionalizes the developing countries’ slow progress in the process of financial globalization because most developing countries are implementing a de facto fixed exchange rate regime. 2.6 Conclusion This paper analyzes the welfare impact of financial integration in a stan- dard monetary open economy model with nominal price rigidity. Results show that terms of trade become more volatile when international consump- tion risk sharing increases. Financial integration may reduce welfare if the integration leads to excessive terms of trade adjustment. This can happen when financial market segmentation is not the only distortion in the econ- omy. The existence of nominal price rigidity allows monetary shocks to affect the terms of trade, which is at a cost to efficiency. A fixed exchange rate regime is indeed more favorable than a passive floating exchange rate regime because fixed exchange rates eliminate the ex- cessive terms of trade volatility. Hence, this model implies that developing economies that are experiencing financial integration may attempt to alle- viate the welfare cost of integration by stabilizing the exchange rate. This prediction is consistent with the widespread reluctance to following freely floating exchange rates among these economies, a phenomenon that has been well documented in the “fear of floating”literature. On the other hand, for advanced economies that have the ability to operate efficient, inflation tar- geting monetary policies, financial globalization is always beneficial. The model thus predicts that advanced economies that have introduced inflation targeting as a monetary policy rule should experience a deeper level of finan- cial globalization. Most industrial countries started an inflation targeting regime in the early 1990s, which explains the acceleration of cross-border 60 Chapter 2. International Financial Integration and Monetary Policy asset trade in industrial countries since then. Given that most develop- ing countries still conduct a de facto fixed exchange rate regime, the slow progress of developing countries in the process of financial globalization is not surprising. An interesting direction for future research is to test the empirical impli- cations suggested by this model. Testable hypotheses have been developed about the impact of international consumption risk sharing on terms of trade volatility and about the interaction between monetary policy and fi- nancial integration. First, financial integration increases the terms of trade volatility, which is independent of whether there is nominal price rigidity and of how welfare changes. Second, inflation targeting countries are more financially open and integrated. Last but not least, the coexistence of fi- nancial globalization and lack of institutional infrastructure and financial stability may be the reasons why developing countries prefer not to float their currencies. 61 Chapter 2. International Financial Integration and Monetary Policy Figure 2.1: International Financial Integration: Industrial Group and De- veloping Countries Group, 1970-2004             Note: Ratio of sum of foreign assets and liabilities to GDP, 1970-2004.           Source: Lane and Milesi-Ferretti (2006) 62 Chapter 2. International Financial Integration and Monetary Policy F ig ur e 2. 2: In te rn at io na l F in an ci al In te gr at io n: E xp lic it In fla ti on T ar ge ti ng C ou nt ri es 19 70 19 80 19 90 20 00 20 10 0 0. 51 1. 52 2. 5 Ne w Ze al an d Ti m e IFIGDP NZ 19 70 19 80 19 90 20 00 20 10 0. 51 1. 52 2. 5 Ca na da Ti m e IFIGDP CA 19 70 19 80 19 90 20 00 20 10 12345678 Un ite d Ki ng do m Ti m e IFIGDP UK 19 70 19 80 19 90 20 00 20 10 0 0. 51 1. 52 2. 5 Au st ra lia Ti m e IFIGDP AU 19 70 19 80 19 90 20 00 20 10 012345 Sw ed en Ti m e IFIGDP SE 19 70 19 80 19 90 20 00 20 10 024681012 Sw itz er lan d Ti m e IFIGDP CH 19 70 19 80 19 90 20 00 20 10 0. 51 1. 52 2. 53 3. 5 No rw ay Ti m e IFIGDP NO 19 70 19 80 19 90 20 00 20 10 0 0. 51 1. 52 2. 53 3. 54 Ic el an d Ti m e IFIGDP IS 63 Chapter 2. International Financial Integration and Monetary Policy F ig ur e 2. 3: In te rn at io na l F in an ci al In te gr at io n: Im pl ic it In fla ti on T ar ge ti ng C ou nt ri es 19 70 19 75 19 80 19 85 19 90 19 95 20 00 20 05 00.511.52 Un ite d S tat es Tim e IFIGDP US 19 70 19 75 19 80 19 85 19 90 19 95 20 00 20 05 00.20.40.60.811.21.4 Ja pa n Tim e IFIGDP JP 19 70 19 75 19 80 19 85 19 90 19 95 20 00 20 05 012345 De nm ark Tim e IFIGDP DK 19 70 19 75 19 80 19 85 19 90 19 95 20 00 20 05 0.511.522.533.544.5 Eu ro Zo ne Tim e IFIGDP EU RO 64 Chapter 2. International Financial Integration and Monetary Policy F ig ur e 2. 4: Se co nd M om en ts an d W el fa re w it h M on ey T ar ge ti ng R ul es 0. 5 1 1. 5 2 − 8 − 6 − 4 − 2024 x 10 − 5 Co ns um pt ion  E qu iva len t M ea su re θ ω fin an cia l a ut ar ky co m ple te  m ar ke t 0. 5 1 1. 5 2 0. 6 0. 81 1. 2 1. 4 1. 6 x 10 − 4 Pr ici ng  R isk θ Lph 0. 5 1 1. 5 2 − 1. 6 − 1. 4 − 1. 2 − 1 − 0. 8 x 10 − 4 Ex pe cte d Le ve l o f C on su m pt ion θ EC 0. 5 1 1. 5 2 567891011 x 10 − 5 Va ria nc e of  C on su m pt ion θ VC 0. 5 1 1. 5 2 − 1. 8 − 1. 6 − 1. 4 − 1. 2 − 1 − 0. 8 x 10 − 4 Ex pe cte d Le ve l o f L ab or θ EL 0. 5 1 1. 5 2 1. 52 2. 53 3. 54 4. 5 x 10 − 4 Va ria nc e of  L ab or θ VL 65 Chapter 2. International Financial Integration and Monetary Policy Figure 2.5: Exchange Rate Response Coefficients with Incomplete Markets 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 Steady State Labor Income Share E xc ha ng e R at e C oe ffi ci en ts s1, w.r.t. productivity shocks s2, w.r.t monetary shocks 66 Chapter 2. International Financial Integration and Monetary Policy Figure 2.6: Consumption Equivalent Measures with Money Targeting Rules 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −0.5 0 0.5 1 1.5 2 2.5 x 10 −5 Steady State Labor Income Share C on su m pt io n E qu iv al en t M ea su re incomplete market financial autarky complete market 67 Chapter 2. International Financial Integration and Monetary Policy Figure 2.7: Welfare Comparison 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −2 0 2 4 6 8 10 12 14 x 10 −5 Steady State Share of Labor Income C on su m pt io n E qu iv al en t M ea su re money targeting − financial autarky money targeting − incomplete markets money targeting − complete markets unilateral peg bilateral peg producer price targeting − financial autarky producer price targeting − complete markets 68 Chapter 3 Explaining Saving Behavior 3.1 Introduction There has been some recent work on explaining the evolution of saving rates in Japan and the U.S. (see in particular Imrohoroglu et al (2006, 2008) [11, 12]). This work finds that when the observed time-series pattern of total factor productivity (TFP) is fed as an exogenous driving process into the standard neoclassical growth model, it generates a time series pattern of saving which matches the data in these countries reasonably well. Moreover, the model does an even better job of explaining saving rates once the list of exogenous driving processes is augmented to include population growth, government consumption, depreciation, and factor income tax shocks. In this paper we show that the ability of these models to explain saving rates is due to the assumption that the model economy is closed to inter- national goods and factor trade. This assumption forces saving to equal investment every period. We demonstrate that the model actually does a relatively good job of explaining investment rates in these countries. The reason they also appear to do well in explaining saving is due to the closed economy assumption that saving equals investment and the data fact that national saving and domestic investment rates are not very different. The main question of this paper is “Can a model in which saving behavior is dictated by the logic of the standard neoclassical growth model explain the time series and cross-sectional pattern of saving observed in the data?”We construct a model of the world economy comprised of two regions – the US and a group of OECD countries (called the rest of the world (ROW)).32 The 32The group of OECD countries are Austria, Canada, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Netherlands, Norway, Portugal, 69 Chapter 3. Explaining Saving Behavior model is the standard one-sector neoclassical growth model with complete markets, production, and investment. Exogenous drivers include measured TFP, population growth, government consumption, depreciation, and taxes on capital and labor incomes. We find that a closed-economy version of the model does an excellent job of reproducing investment as well as saving rates in the U.S. In the two-region version on the other hand, the model continues to match the U.S. investment rate but it fails to reproduce the path of US saving rates either in levels or in its time series pattern. The model is similarly unable to predict saving in the rest of the world. Therefore, the answer to our central question is “no, the neoclassical model with TFP movements cannot explain saving behavior.” The model explains investment not saving. The key intuition for our findings is that, in an open economy environ- ment, the presence of international consumption risk sharing delinks saving from investment. Basically, investment decisions are based on the future return on capital. Hence, it is the growth rate of TFP in each country that drives the evolution of investment. On this margin, there is not much dif- ference between a closed-economy version and an open-economy version of the neoclassical growth model. That is why both versions of the model can predict investment quite well. However, saving decisions rely on the risk sharing structure. When there exists some international risk sharing, the more productive country will run a current account surplus. In other words, this country will save more than its own investment. Thus, it is the rela- tive level of TFP between the two countries that determines the behavior of saving. Given that the U.S. is consistently more productive than the ROW in the data, it is unsurprising to find that the model overpredicts the U.S. saving and underpredicts saving in the ROW. We conclude that explaining saving, especially the large cross-sectional and time series variations in them, remains a challenge for the profession.33 Spain, Sweden, Switzerland, and United Kingdom. 33The literature on explaining the differences in saving rates between the U.S. and Japan goes back to the mid 1980’s. A representative though not exhaustive sample of this work is Braun et al (2004) [8], Christiano (1989) [13], Hayashi (1989) [36], Parker (1999) [54], and Summers et al (1987) [6]. 70 Chapter 3. Explaining Saving Behavior The next section lays out the baseline model. Section 3.3 defines the equi- librium, presents the stationary form of the model, and states the algorithm. Section 3.4 describes the data and the calibration strategy. Section 3.5 re- ports results of the basic data accounting exercise wherein we simulate the model under each of the exogenous drivers individually and also all of them together in order to assess the relative importance of each factor. The last section concludes. 3.2 The Model We consider the basic one good, two-country open economy model. We label the two countries Home and Foreign. At every date t, Home and Foreign are inhabited by Nt and N∗t identical agents. The lifetime welfare of each agent at Home is given by: U = ∞∑ t=0 βtu (ct, 1− ht) (3.1) where u (ct, 1− ht) = logct + αlog(1− ht), α > 0 (3.2) c is consumption and h denotes the fraction of time devoted to work. Pref- erences are identical across countries so there is an identical utility function for Foreign residents. Output of the single good in both countries is produced using an identical production technology which uses capital and labor: Yt = Kθt (atNtht) 1−θ (3.3) where θ is the income share of capital, Kt is aggregate physical capital, Nt is total population, and at denotes labor augmenting productivity. There is a corresponding production technology for output abroad which takes as inputsK∗t and a∗tN∗t h∗t . Note that per capita output at Home can be written 71 Chapter 3. Explaining Saving Behavior as yt = kθt (atht) 1−θ (3.4) where yt = Yt/Nt and kt = Kt/Nt. In terms of notational convention, throughout the paper we shall denote all Foreign variables with stars. Variables with capital letters denote aggre- gate variables, lower case letters denote per capita variables (z = ZN ), and lower case letters with tildes on top denote variables per efficiency units of labor (z̃ = ZaNh). Capital accumulates at Home according to Kt+1 = (1− δt)Kt +Xt (3.5) It = Xt + φKt ( Xt Kt − ψ )2 (3.6) where It denotes gross investment. Thus, we are allowing for adjustment costs in the capital accumulation process whenever φ > 0. Similarly, for Foreign we have: K∗t+1 = (1− δ∗t )K∗t +X∗t (3.7) I∗t = X ∗ t + φK ∗ t ( X∗t K∗t − ψ∗ )2 (3.8) There is a government in each country which consumes Gt and G∗t in period t Gt = gtYt (3.9) where gt is the government consumption as a share of total output. A corresponding equation holds for Foreign. The aggregate resource constraint for the world dictates that total pri- vate consumption plus total investment plus total public consumption in 72 Chapter 3. Explaining Saving Behavior Home and Foreign must equal total world output. Hence, Ct + It + C∗t + I ∗ t = (1− gt)Yt + (1− g∗t )Y ∗t (3.10) Moreover, the aggregate government budget constraint is given by gtYt + g∗t Y ∗ t = τh,twtHt + τk,t (rt − δt)Kt +τ∗h,tw ∗ tH ∗ t + τ ∗ k,t (r ∗ t − δ∗t )K∗t + Tt (3.11) where wt is the real wage. rt is the rate of return on capital. δt is the depreciation rate. τh,t and τk,t are tax rates on labor and capital incomes respectively. There is no international factor trade. We set up the problem as a planning problem. In particular, the social planner maximizes: V = ∞∑ t=0 βt [Ntu (ct, 1− ht) +N∗t u (c∗t , 1− h∗t )] (3.12) subject to equations (3.2)-(3.3), (3.5) - (3.6) and their foreign counterparts, (3.10), and (3.11). We choose to set up the problem in this way because the planning problem provides the frictionless paradigm. This corresponds to the case of complete markets which is the benchmark model in the lit- erature.34 Note that the social planner pays factors at their competitive market rates, takes the tax regime in each country as given, and keeps equa- tion (3.11) balanced with a lump sum tax Tt in every period. Finally, the net saving rate is defined as savt = (1− gt)Yt − Ct − δtKt Yt − δtKt (3.13) 34Note that we could have instead set up the decentralized problem with firms in each country choosing inputs, households choosing labor supply and their portfolio allocation between domestic capital, domestic real bonds and foreign real bonds, and governments financing their consumption needs through the given tax regimes. That decentralized problem would induce identical allocations to the planning problem we analyze here. 73 Chapter 3. Explaining Saving Behavior with the net investment rate defined as invt = Xt + φ ( Xt Kt − ψ )2 − δtKt Yt − δtKt (3.14) 3.3 Equilibrium and Solution Equilibrium Given the fiscal policy {Gt, G∗t , τh,t, τ∗h,t, τk,t, τ∗k,t}∞t=0, the equilibrium com- prises allocations {Ct, C∗t ,Ht,H∗t , Xt, X∗t ,Kt+1,K∗t+1}∞t=0 such that follow- ing conditions are satisfied: • the international risk sharing equation • home and foreign intratemporal Euler equations which describe the labor leisure choice in each country • home and foreign intertemporal Euler equations which characterize the investment decision in each country • home and foreign capital accumulation equations • the world resource constraint Stationary Representation The model has a unique steady state if written in terms of per efficiency units. Sa,thtc̃t = h∗t c̃ ∗ t (3.15) αhtc̃t 1− ht = (1− θ)(1− τh,t)(k̃t) θ (3.16) αh∗t c̃∗t 1− h∗t = (1− θ)(1− τ∗h,t)(k̃∗t )θ (3.17) 74 Chapter 3. Explaining Saving Behavior γtht+1c̃t+1 βhtc̃t [ 1 + 2φ ( x̃t k̃t − ψ )] = 1 + (1− τk,t+1) [ θ(k̃t+1)θ−1 − δt+1 ] + φ ( x̃t+1 k̃t+1 − ψ )[ x̃t+1 k̃t+1 + ψ + 2(1− δt+1) ] (3.18) γ∗t h∗t+1c̃∗t+1 βh∗t c̃∗t [ 1 + 2φ ( x̃∗t k̃∗t − ψ∗ )] = 1 + (1− τ∗k,t+1) [ θ(k̃∗t+1) θ−1 − δ∗t+1 ] + φ ( x̃∗t+1 k̃∗t+1 − ψ∗ )[ x̃∗t+1 k̃∗t+1 + ψ∗ + 2(1− δ∗t+1) ] (3.19) γn,tγtht+1k̃t+1 = ht [ (1− δt)k̃t + x̃t ] (3.20) γ∗n,tγ ∗ t h ∗ t+1k̃ ∗ t+1 = h ∗ t [ (1− δ∗t )k̃∗t + x̃∗t ] (3.21) Sn,tSa,tht [ (1− gt)(k̃t)θ − c̃t − x̃t − φk̃t ( x̃t k̃t − ψ )2] + h∗t (1− g∗t )(k̃∗t )θ − c̃∗t − x̃∗t − φk̃∗t ( x̃∗t k̃∗t − ψ∗ )2 = 0 (3.22) γn,t is the population growth rate, γn,t = Nt+1 Nt . γt is the TFP factor (TFPF) growth rate, γt = at+1 at . Following the literature, the adjustment cost is specified such that there is no cost occurred at the steady state. Hence, ψ = γ̄nγ̄−1+ δ̄. Note that variables denoted with bars represent the corresponding steady state value. To be consistent with balanced growth, the population growth rates and the TFPF growth rates have to be equal across countries in the steady state (γ̄n = γ̄∗n and γ̄ = γ̄∗). In addition, we assume δ̄ = δ̄∗, which implies that ψ = ψ∗. Sa,t is the relative TFPF between home and foreign, Sa,t = ata∗t . Sn,t is the relative population size between the two countries, Sn,t = NtN∗t . Once Sa,0 and Sn,0 are given, the entire series of Sa,t and Sn,t can be derived recursively from the sequences of {γt, γn,t}∞t=0 Sa,t = γt γ∗t Sa,t−1 (3.23) 75 Chapter 3. Explaining Saving Behavior Sn,t = γn,t γ∗n,t Sn,t−1 (3.24) Algorithm Our strategy is to compute the transition dynamics of an open econ- omy given the initial capital-output ratio in each country. We obtain our solution by numerically solving a system of non-linear equations. The base- line two-country model has eight endogenous variables with eight associated equilibrium conditions at each date. We allow 200 periods for the economy to converge to the steady state. We stack all the equations together and solve the resulting system. Thus, the stacked system has 1, 600 equations and 1, 600 unknowns. The sparsity of the Jocobian matrix makes solving such a huge nonlinear system practical. The Newton-Raphson algorithm is much more efficient and stable than the more commonly used shooting method to solve such models. This is especially true in our two-country context where there are more than one state variable. 3.4 Data and Calibration The data for exogenous driving forces35 are from Imrohoroglu et al (2008). The sample period is 1960-2004. Hence, the economy converges to the steady state in 2159.36 The depreciation rates are assumed to be the same across countries. The steady state values for these exogenous driving forces, which are also the values for 2005-2159, are set to be the followings (see Table 3.1). To be consistent with balanced growth, ψ = ψ∗ = 0.0786. 35 { γt, γ ∗ t , γn,t, γ ∗ n,t, gt, g ∗, δt, τh,t, τ∗h,t, τk,t, τ ∗ k,t }2004 t=1960 36Imrohoroglu et al (2008) also examine an open economy model with international trade of risk-free bond. They conclude that the model can still predict saving and investment rates reasonably well. However, that is because they assume an unrealistically small size for the ROW relative to the U.S. In other words, although they look at a two-country world, one region (the ROW) is so small that it has very limited effect on the big country (the U.S.). Therefore, their exercise does not differentiate from the closed-economy case very much. Once the actual relative size between the ROW and the U.S. is fed in, the results become similar to ours. 76 Chapter 3. Explaining Saving Behavior Table 3.1: Steady State Values of the Exogenous Drivers US ROW γ̄ 1.0184 1.0184 γ̄n 1.01 1.01 ḡ 0.16 0.18 δ̄ 0.05 0.05 τ̄k 0.42 0.34 τ̄h 0.29 0.38 In order to show that the standard neoclassical growth model explains investment rather than saving, we keep the calibration as close as possible to Imrohoroglu et al (2008). The model has four invariant parameters. The labor disutility scale parameter α is set to 1.4480 so that the steady state fraction of time spent working equals to one thirds in the U.S. The subjective discount factor β is set to 0.9759 so that the steady state capital output ratio is 3.2 in the U.S. The capital share of output θ is set to 0.4, which is the average capital share in the U.S. for the period 1960-2004. Furthermore, the adjustment cost parameter φ is set to 2 to match the volatility of investment in the U.S. The initial capital output ratio for the U.S. is set to 3.5, while the initial capital stock of the ROW is set to be 1.55 times that in the U.S. The steady state population ratio between the U.S. and the ROW S̄n is set to 0.55, which matches the actual relative size of population between the two countries in 2004. The steady state TFPF ratio between the U.S. and the ROW S̄a is set to 0.9383 so that the steady state consumption output ratio is 0.5884 in the U.S. This assures that there is no current account deficit at the steady state. Moreover, the initial relative TFPF between the U.S. and the ROW Sa,1960 is set to 1.5922 to be consistent with the exogenous series for TFPF growth rates {γt, γ∗t }2159t=1960 and the fact that the steady state is reached in 2159 according to equation (3.23). Similarly, the initial relative population between the U.S. and the ROW Sn,1960 is set to 0.3955 to satisfy equation (3.24) given {γn,t, γ∗n,t}2159t=1960. 77 Chapter 3. Explaining Saving Behavior 3.5 Results We now show our basic quantitative results. We shall treat the U.S. as the home country and the ROW as the foreign country in all our sim- ulations. We report eight sets of results: (1) the benchmark case with all shocks; (2) only TFP shocks in which all the other exogenous driving forces are set to their steady state values; (3) all except TFP shocks; (4) only government expenditure shocks; (5) only demographic shocks; (6) only de- preciation shocks; (7) only capital income tax shocks; (8) only labor income tax shocks. We start by studying the closed economy case for the U.S. This is done by making the two countries symmetric, i.e. U.S. vs U.S.. We apply the U.S. time series for exogenous variables to both countries in the model. This implies that the relative levels of all the exogenous variables is unity throughout the simulation. Alternatively, we can assume the U.S. is huge compared to the ROW. If we set S̄n = 10000 and adjust the corresponding Sn,1960, the results will be identical. These two approaches effectively makes the model a closed economy. Figure 3.1 plots the model generated U.S. net saving to net GDP ratio and net investment to net GDP ratio with respect to the data. The star line represents the data, while the solid line represents the model prediction. clearly, the closed economy version does a good job of explaining both the saving and the investment rates for the U.S. Thus, the model replicates the principal findings of Imrohoroglu et al (2008). However, it is hard to tell which one is fitted better, given the fact that saving and investment are not very different in the data. Next we study the open economy case by reverting to the two-country model. Here we use the region specific time series for the exogenous vari- ables for the U.S. and the ROW. Figure 3.2 plots the benchmark net saving rate and the net investment rate with respect to the data when all the ex- ogenous variables are used. Figure 3.3 plots the net saving rate and the net investment rate with respect to the data when we only use the TFP series as exogenous drivers. In this and the following counterfactual experiments, the other exogenous variables are held constant at their mean levels during 78 Chapter 3. Explaining Saving Behavior the sample period which are also their assumed steady state levels. Fig- ure 3.4 plots the net saving rate and the net investment rate with respect to the data when all exogenous variables except the TFP series are used. Figure 3.5 plots the net saving rate and the net investment rate with re- spect to the data when only government expenditures vary across countries and over time. Figure 3.6 plots the demographically driven net saving rate and net investment rate with respect to the data. Figure 3.7 plots the net saving rate and the net investment rate with respect to the data when only depreciation rate series are used. Figure 3.8 plots the net saving rate and the net investment rate with respect to the data driven by capital income taxes. Finally, Figure 3.9 plots the net saving rate and the net investment rate with respect to the data driven by labor income taxes. The above simulations tell a similar story. In all the experiments, the predicted investment rate is close to that in the data. This is true for both the U.S. and the ROW. In addition, TFP explains most of the dynamics of the model, which is consistent with the previous literature. Saving, on the other hand, is a different story. The model tends to overpredict saving for the U.S. and underpredict saving for the ROW in all the simulations. In effect the observed saving behavior is unexplained by the model. We interpret these results as saying that the neoclassical model does a good job of predicting investment behavior. It is far less accurate in predicting saving behavior. The intuition is as following. Investment deci- sions are based on the future return on capital. Hence, the higher the TFP growth rate, the more incentives for investing. There is not much interna- tional factor entering into this decision. Figure 3.10 plots the two countries’ benchmark net investment rates with respect to their corresponding TFPF growth rate. We can see that the U.S. TFPF growth rate is slightly trend- ing up over the sample period. The model also predicts the U.S. investment going up. For the ROW, the TFPF growth rate first rises in 1960s, but de- scends since the early 1970s. Thus, the model predicts the ROW investment climbing up first, then crawling down. In the presence of international consumption risk sharing, it is efficient to let the more productive country produce more and share its output with 79 Chapter 3. Explaining Saving Behavior the less productive country. Alternatively speaking, the country with a higher TFP level should become a net exporter. Figure 3.11 plots the two countries’ benchmark net saving rates with respect to their TFPF ratios. Clearly, each country’s saving rate is highly correlated with its TFP level relative to that of the other country. The correlation coefficient is 0.975 for the U.S. and 0.9 for the ROW. Both are significant at any conventional level of significance. As the U.S. is more productive than the ROW (especially in 1960s and early 1970s), the model overpredicts the U.S. saving rate and generates huge current account surplus for the U.S. in 1960s.37 On the flip side, the model underpredicts the ROW saving rate and generates huge current account deficit for the ROW. Therefore, the model fails to predict saving is highlighted by the fact that when saving and investment become delinked from each other in an open economy environment, the model underperforms on the saving margin while its investment prediction remains relatively unchanged. The reason the closed economy neoclassical model is able to explain saving is that it imposes an identity between saving and investment. As the model predicts investment accurately and because the gap between saving and investment is relatively small in the data, the model generated saving tracks the saving data reasonably well. 3.6 Conclusion The closed economy neoclassical growth model has proved to be a wor- thy workhorse model for understanding and explaining a number of issues in macroeconomics. However, the model has trouble explaining some fea- tures of open economies. One example of this is is the current account. The standard version of the open economy neoclassical model has difficulty in 37Notice that the series for TFPF ratios is backed out from the actual series for TFPF growth rates and the calibrated steady state level of TFPF ratio. The resulting relative TFPF has exactly the same pattern as the actual TFPF ratio, but smaller values. In the data, U.S. is much more productive than the ROW throughout the sample period. Hence, the model would have generated even larger current account surplus for the U.S., if we fit in the actual TFPF ratio. 80 Chapter 3. Explaining Saving Behavior explaining the observed behavior of the current account. In this paper we have shown that this difficulty is the mirror image of the fact that while the model can predict investment behavior reasonably accurately, it does not explain saving. Hence, its current account predictions are often inaccurate. We have illustrated this fact using the example of the U.S. We show that while the investment predictions of the closed and open economy versions of the neoclassical model are similar and, crucially, very close to the data, the saving predictions are not. In particular, the open economy version of the model tends to overpredict the U.S. saving and underpredict saving in the ROW. The closed economy version of the model does well in explaining saving only because it imposes equality between saving and investment and the fact that saving and investment are relatively close in the data. Effec- tively, the closed economy model explains investment rather than saving. We consider the observed saving behavior a puzzle and we hope to address the saving puzzle in future work. 81 Chapter 3. Explaining Saving Behavior F ig ur e 3. 1: U .S . Sa vi ng an d In ve st m en t - C lo se d E co no m y 19 60 19 70 19 80 19 90 20 00 20 10 0 0. 050. 1 0. 150. 2 0. 250. 3 0. 350. 4 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 0 0. 050. 1 0. 150. 2 0. 250. 3 0. 350. 4 U. S.  In ve stm en t U. S.  In ve stm en t D at a 82 Chapter 3. Explaining Saving Behavior F ig ur e 3. 2: U .S . Sa vi ng an d In ve st m en t - B en ch m ar k 19 60 19 70 19 80 19 90 20 00 20 10 0 0. 1 0. 2 0. 3 0. 4 19 60 19 70 19 80 19 90 20 00 20 10 0 0. 1 0. 2 0. 3 0. 4 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 25 − 0. 15 − 0. 05 0. 05 0. 15 0. 25 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 25 − 0. 15 − 0. 05 0. 05 0. 15 0. 25 U. S.  S av ing U. S.  S av ing  D at a U. S.  In ve stm en t U. S.  In ve stm en t D at a RO W  S av ing RO W  S av ing  D at a RO W  In ve stm en t RO W  In ve stm en t D at a 83 Chapter 3. Explaining Saving Behavior F ig ur e 3. 3: U .S . Sa vi ng an d In ve st m en t - O nl y T F P 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 84 Chapter 3. Explaining Saving Behavior F ig ur e 3. 4: U .S . Sa vi ng an d In ve st m en t - A ll E xc ep t T F P 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 85 Chapter 3. Explaining Saving Behavior F ig ur e 3. 5: U .S . Sa vi ng an d In ve st m en t - O nl y G ov er nm en t E xp en di tu re 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 86 Chapter 3. Explaining Saving Behavior F ig ur e 3. 6: U .S . Sa vi ng an d In ve st m en t - O nl y P op ul at io n G ro w th 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 87 Chapter 3. Explaining Saving Behavior F ig ur e 3. 7: U .S . Sa vi ng an d In ve st m en t - O nl y D ep re ci at io n R at e 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 88 Chapter 3. Explaining Saving Behavior F ig ur e 3. 8: U .S . Sa vi ng an d In ve st m en t - O nl y C ap it al In co m e T ax es 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 89 Chapter 3. Explaining Saving Behavior F ig ur e 3. 9: U .S . Sa vi ng an d In ve st m en t - O nl y L ab or In co m e T ax es 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  S av ing U. S.  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 0. 05 0. 05 0. 15 0. 25 0. 35 0. 45 0. 55 U. S.  In ve stm en t U. S.  In ve stm en t D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  S av ing RO W  S av ing  D at a 19 60 19 70 19 80 19 90 20 00 20 10 − 1 − 0. 8 − 0. 6 − 0. 4 − 0. 20 0. 2 0. 4 RO W  In ve stm en t RO W  In ve stm en t D at a 90 Chapter 3. Explaining Saving Behavior F ig ur e 3. 10 : N et In ve st m en t R at es vs T F P F G ro w th R at es - B en ch m ar k 19 60 19 70 19 80 19 90 20 00 20 10 0. 02 0. 04 0. 06 0. 080. 1 0. 12 0. 14 0. 16 0. 18 19 60 19 70 19 80 19 90 20 00 20 10 0. 94 0. 96 0. 981 1. 02 1. 04 1. 06 1. 081. 1 1. 12 U. S.  In ve stm en t RO W  In ve stm en t U. S.  T FP F Gr ow th  R at e RO W  T FP F Gr ow th  R at e 91 Chapter 3. 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First-order approximations of the other equilibrium condi- tions are given by P̂pre,H = 0 +O(2) (A.8) P̂ ∗pre,F = 0 +O( 2) (A.9) P̂H = κP̂pre,H + (1− κ)P̂flx,H +O(2) (A.10) P̂ ∗F = κP̂ ∗ pre,F + (1− κ)P̂ ∗flx,F +O(2) (A.11) P̂ = 1 2 (P̂H + P̂ ∗F + Ŝ) +O( 2) (A.12) 100 Appendix A. Appendix for Chapter 1 P̂ ∗ = 1 2 (P̂H + P̂ ∗F − Ŝ) +O(2) (A.13) Π̂ = 1 1− ζ [ P̂ + Ŷ − ζ(ŵ + L̂) ] +O(2) (A.14) Π̂∗ = 1 1− ζ [ P̂ ∗ + Ŷ ∗ − ζ(ŵ∗ + L̂∗) ] +O(2) (A.15) Ŷ = (1− θ)(P̂H − P̂ ) + 12(Ĉ + Ĉ ∗) +O(2) (A.16) Ŷ ∗ = (1− θ)(P̂ ∗F − P̂ ∗) + 1 2 (Ĉ + Ĉ∗) +O(2) (A.17) L̂ = −Â− θ(P̂H − P̂ ) + 12(Ĉ + Ĉ ∗) +O(2) (A.18) L̂∗ = −Â∗ − θ(P̂ ∗F − P̂ ∗) + 1 2 (Ĉ + Ĉ∗) +O(2) (A.19) Ĉ = Ŷ + α̃′r̂x +O(2) (A.20) r̂B = −P̂ +O(2) (A.21) r̂B∗ = Q̂− P̂ ∗ +O(2) (A.22) r̂E = Π̂− P̂ +O(2) (A.23) r̂E∗ = Q̂+ Π̂∗ − P̂ ∗ +O(2) (A.24) ζ is the share of labor income at the non-stochastic steady state, ζ = w̄L̄ Π̄+w̄L̄ . r̂x is the vector of relative returns between each asset and the reference asset n, r̂′x = [r̂1 − r̂n, r̂2 − r̂n, · · · , r̂n−1 − r̂n]. A.2 Asset Returns, Exchange Rate, and Terms of Trade From equations (A.1)-(A.4), (A.12)-(A.19), and (A.21)-(A.24), the ex- cess return on foreign bonds and foreign equities can be written as r̂B∗ − r̂B = Ŝ +O(2) (A.25) r̂E∗ − r̂E = Π̂∗ − Π̂ + Ŝ +O(2) = 1 1− ζ {−ζŜ + [θ − 1− θζ(ψ + 1)]τ̂ + ζ(M̂ − M̂ ∗) −ζ(ψ + 1)(Â− Â∗)}+O(2) (A.26) 101 Appendix A. Appendix for Chapter 1 Flexible Price Case: κ = 0 When goods prices are fully flexible, P̂H = ŵ − Â (A.27) P̂ ∗F = ŵ ∗ − Â∗ (A.28) Substitute equations (A.27)-(A.28) into the definition of the terms of trade and equation (A.26), we have r̂E∗ − r̂E = (θ − 1)τ̂ +O(2) (A.29) It is easy to see that achieving perfect consumption risk sharing up to first- order (ĉ − ĉ∗ = 0 + O(2)) requires households hold half of foreign equities (α̃E∗ = 12). In this case, Ŝ = M̂ − M̂∗ +O(2) (A.30) τ̂ = − 1 + ψ 1 + ψθ (Â− Â∗) +O(2) (A.31) Sticky Price Case: κ = 1 When goods prices are all pre-set, P̂H = 0 +O(2) = P̂ ∗F (A.32) which implies that τ̂ = −Ŝ +O(2). From equation (A.26), we have r̂E∗ − r̂E = 11− ζ {[θ − 1 + ζ − θζ(ψ + 1)]τ̂ + ζ(M̂ − M̂ ∗) −ζ(ψ + 1)(Â− Â∗)}+O(2) (A.33) There is complete risk sharing in the FBE economy. Hence, the exchange rate as well as the terms of trade respond only to money supply shocks up to first-order (Ŝ = M̂ − M̂∗ + O(2)). However, the consumption risk sharing 102 Appendix A. Appendix for Chapter 1 is generally incomplete in the FE economy. In this case, the exchange rate and the terms of trade will react to both the productivity shocks and the money supply shocks. A.3 Log-linearized Sticky Wage Model As wages are chosen in advance of production and consumption, log- linearized wage equations will substitute for the labor-leisure choice func- tions (A.1)-(A.2) in the set of log-linearized equilibrium conditions ŵ = 0 +O(2) (A.34) ŵ∗ = 0 +O(2) (A.35) From equations (A.3)-(A.4), (A.12)-(A.19), A.21)-(A.24), and (A.34)- (A.35), the excess return on foreign bonds and foreign equities can be written as r̂B∗ − r̂B = Ŝ +O(2) (A.36) r̂E∗ − r̂E = Π̂∗ − Π̂ + Ŝ +O(2) = 1 1− ζ {−ζŜ + [θ(1− ζ)− 1]τ̂ − ζ(Â− Â ∗)}+O(2) (A.37) Flexible Price Case: κ = 0 When goods prices are fully flexible, P̂H = −Â (A.38) P̂ ∗F = −Â∗ (A.39) Substitute equations (A.38)-(A.39) into the definition of the terms of 103 Appendix A. Appendix for Chapter 1 trade and equation (A.37), we have r̂E∗ − r̂E = (θ − 1)τ̂ +O(2) (A.40) Similar to the case with flexible wages, achieving perfect consumption risk sharing up to first-order (ĉ− ĉ∗ = 0 + O(2)) requires households hold half of foreign equities (α̃E∗ = 12). Here, Ŝ = M̂ − M̂∗ +O(2) (A.41) τ̂ = −(M̂ − M̂∗)− (Â− Â∗) +O(2) (A.42) When goods prices are flexible, the portfolio choices are the same whether wages are fixed or not. However, it is interesting to see that the terms of trade respond not only to the productivity shocks, but also the money supply shocks due to sticky wages. This clearly will affect the welfare. Sticky Price Case: κ = 1 When goods prices are all pre-set, we have τ̂ = −Ŝ + O(2). Thus, the FBE economy generates the same results as before and both the exchange rate and the terms of trade respond only to money supply shocks up to first-order (Ŝ = M̂ − M̂∗ +O(2)). While from equation (A.37), we know r̂E∗ − r̂E = (θ − 1)τ̂ − ζ1− ζ (Â− Â ∗) (A.43) In general, the consumption risk sharing is going to be imperfect in the FE economy. 104 Appendix B Appendix for Chapter 2 B.1 A Symmetric Steady State In a non-stochastic steady state, there is no shock, Ā = Ā∗ = χ̄ = χ̄∗ = 1. Note steady state values are marked by overbars. Since returns on all assets are equal, asset holdings are indeterminate in a non-stochastic steady state. However, asset positions are often well defined in a stochastic environment. Devereux and Sutherland (2006a) [20] prove that the solution of their method corresponds to a stochastic equilibrium portfolio allocation that is arbitrarily close to the non-stochastic equilibrium. All the prices are equal and the steady state exchange rate S̄ = 1. The steady state values of other variables are Ȳ = Ȳ ∗ = L̄ = L̄∗ = C̄ = C̄∗ = (η)− 1 ρ+ψ (B.1) where we have applied γ = 1φ−1 given the production subsidy exactly offsets the distortion due to monopoly power. B.2 First-Order Approximation The system consists of equations (2.5), (2.6), (2.12), (2.16)-(2.18), (2.21), (2.29), and their foreign counterparts, as well as (2.8), (2.22)-(2.27), and (2.30). Some of the equilibrium conditions are log-linear in themselves, such as the wage equations, the money demand and supply equations, the virtual price of each country’s goods, and the asset market clearing condition. ŵ = P̂ + ρĈ + ψL̂ (B.2) 105 Appendix B. Appendix for Chapter 2 ŵ∗ = P̂ ∗ + ρĈ∗ + ψL̂∗ (B.3) M̂ = χ̂+ P̂ + ρĈ (B.4) M̂∗ = χ̂∗ + P̂ ∗ + ρĈ∗ (B.5) M̂ = −δsŜ − δpP̂XH (B.6) M̂∗ = δ∗s Ŝ − δpP̂ ∗XF (B.7) P̂XH = ŵ − Â (B.8) P̂ ∗XF = ŵ ∗ − Â∗ (B.9) α̃ = −α̃∗ (B.10) where α̃ = ᾱ Ȳ . First-order approximations of the other equilibrium condi- tions are given by P̂H = 0 +O(2) (B.11) P̂ ∗F = 0 +O( 2) (B.12) P̂ = 1 2 (P̂H + P̂ ∗F + Ŝ) +O( 2) (B.13) P̂ ∗ = 1 2 (P̂H + P̂ ∗F − Ŝ) +O(2) (B.14) Π̂ = 1 1− ζ [ P̂ + Ŷ − ζ(ŵ + L̂) ] +O(2) (B.15) Π̂∗ = 1 1− ζ [ P̂ ∗ + Ŷ ∗ − ζ(ŵ∗ + L̂∗) ] +O(2) (B.16) Ŷ = (1− θ)(P̂H − P̂ ) + 12(Ĉ + Ĉ ∗) +O(2) (B.17) Ŷ ∗ = (1− θ)(P̂ ∗F − P̂ ∗) + 1 2 (Ĉ + Ĉ∗) +O(2) (B.18) L̂ = −Â− θ(P̂H − P̂ ) + 12(Ĉ + Ĉ ∗) +O(2) (B.19) L̂∗ = −Â∗ − θ(P̂ ∗F − P̂ ∗) + 1 2 (Ĉ + Ĉ∗) +O(2) (B.20) Ĉ = Ŷ + α̃′r̂x +O(2) (B.21) r̂B = −P̂ +O(2) (B.22) r̂B∗ = Q̂− P̂ ∗ +O(2) (B.23) r̂E = Π̂− P̂ +O(2) (B.24) 106 Appendix B. Appendix for Chapter 2 r̂E∗ = Q̂+ Π̂∗ − P̂ ∗ +O(2) (B.25) ζ is the share of labor income at the non-stochastic steady state, ζ = w̄L̄ Π̄+w̄L̄ . r̂x is the vector of relative returns between each asset and the reference asset n, r̂′x = [r̂1 − r̂n, r̂2 − r̂n, · · · , r̂n−1 − r̂n]. B.3 Proof of Proposition 1 Here, we focus on the case with all flexible prices and the case with all sticky prices. In addition, we just compare the financial autarky with the complete financial markets. Intermediate cases, such as only a fraction of firms can set prices freely and the international risk sharing is imperfect, can be inferred easily from the extreme cases shown below. Sticky Price Case From equations (2.50), (B.11)-(B.12), we have τ̂ = −Ŝ +O(2) (B.26) Substitute equation (2.53) into (2.49) and use (B.26), we get τ̂ = χ̂− χ̂∗ 1 + ρ(θ − 1) financial autarky (B.27) = χ̂− χ̂∗ complete financial markets (B.28) Thus, the volatility of the terms of trade are given by V ar(τ̂) = 2σ2χ [1 + ρ(θ − 1)]2 financial autarky (B.29) = 2σ2χ complete financial markets (B.30) As ρ > 0, the terms of trade are more volatile under complete financial markets than that under financial autarky when θ > 1. 107 Appendix B. Appendix for Chapter 2 Flexible Price Case In this case, P̂H = ŵ − Â and P̂ ∗F = ŵ∗ − Â∗. Combined with the wage equations (B.2)-(B.3) and the labor demand equations (B.19)-(B.20), we have τ̂ = − (1 + ψ)(Â− Â ∗) 1 + ρ(θ − 1) + ψθ financial autarky (B.31) = −Â− Â∗ complete financial markets (B.32) Thus, the volatility of the terms of trade are given by V ar(τ̂) = 2(1 + ψ)2σ2A [1 + ρ(θ − 1) + ψθ]2 financial autarky (B.33) = 2σ2A complete financial markets(B.34) As ρ > 0 and ψ ≥ 0, the terms of trade are more volatile under complete financial markets than that under financial autarky when θ > 1. B.4 Proof of E(L̂) + 12E(L̂ 2) = 0 +O(3) When ρ = 1 and ψ = 0, equations (2.45), (2.46), (B.4), and (B.5) imply that P̂H = E(M̂) + λPH +O( 3), P̂ ∗F = E(M̂ ∗) + λP ∗F +O( 3)(B.35) Combined with (2.35) and (2.36), we can show that E(Ĉ + Ĉ∗) = −(λPH + λP ∗F )− 2E(λP ) +O(3) (B.36) Furthermore, equations (2.33), (2.34), (2.37), and (2.38) indicate λY = (1− θ)λP − 12(λC + λC∗) +O( 3) (B.37) 108 Appendix B. Appendix for Chapter 2 Substitute (B.36) and (B.37) into equations (2.39) and (2.40), we have E(L̂+ L̂∗) = −(λPH + λP ∗F )− E(λC + λC∗) +O(3) (B.38) Moreover, substitute (B.11), (B.12), (B.13), (B.14), (B.17), (B.18), (B.21), and its foreign counterpart into equations (2.43), (2.44), (2.47), and (2.48), we get λC + λC∗ = −α̃r̂x(θ − 1)Ŝ − (α̃r̂x)2 +O(3) (B.39) λPH = 1 2 E [ ( 1 2 Ŝ + Ĉ − Â)2 − 2α̃r̂x(12 Ŝ + Ĉ − Â) ] +O(3) (B.40) λP ∗F = 1 2 E [ (−1 2 Ŝ + Ĉ∗ − Â∗)2 + 2α̃r̂x(−12 Ŝ + Ĉ ∗ − Â∗) ] +O(3) (B.41) Note that α̃r̂x = 1−θ2 Ŝ+ 1 2(Ĉ− Ĉ∗) up to first order. Finally, with equations (B.19) and (B.20), we can show that E(L̂+ L̂∗) + 1 2 E(L̂2 + L̂∗2) = α̃E [ r̂x(Ĉ − Ĉ∗) ] +O(3) (B.42) Recall the equilibrium portfolio equation (2.31), it is obvious that the right hand side of (B.42) equals zero. In other words, expected changes in the first and second moments of labor exactly offset each other. Given the two countries are ex-ante symmetric, we know E(L̂)+ 12E(L̂ 2) = 0 up to a second- order accuracy. Therefore, when ρ = 1 and ψ = 0, each country’s utility is simply represented by their expected level of consumption, i.e. Ũ = E(Ĉ). B.5 Computing the Consumption Equivalent Welfare Measure This section gives the details of the derivation of the consumption equiv- alent measure ω. Consider the money targeting rule in the complete market as the reference scenario, denoted by r, and an alternative scenario, denoted 109 Appendix B. Appendix for Chapter 2 by s. The expected utility in case r is given by U r = (Cr)1−ρ 1− ρ − η (Lr)1+ψ 1 + ψ (B.43) where Cr and Lr are the corresponding consumption and labor supply. Sim- ilarly, the expected utility in case s is given by U s = (Cs)1−ρ 1− ρ − η (Ls)1+ψ 1 + ψ (B.44) ω is defined as the fraction of consumption that an agent in scenario s would be willing to give up in order to make her indifferent between this and the reference scenario r. Thus, ω can be derived from the following equality [(1− ω)Cs]1−ρ 1− ρ − η (Ls)1+ψ 1 + ψ = (Cr)1−ρ 1− ρ − η (Lr)1+ψ 1 + ψ (B.45) Let Vc denote the utility of consumption and Vl denote the disutility of labor, i.e. Vc = C 1−ρ 1−ρ , Vl = η L1+ψ 1+ψ . Note U = Vc − Vl. Equation (B.45) can be rewritten as (1− ω)1−ρV sc = U r + V sl (B.46) When ρ 6= 1, we have ω = 1− ( U r + V sl V sc ) 1 1−ρ (B.47) When ρ = 1, it is even easier ω = 1− exp (U r − U s) (B.48) Given that we compute utility accurately up to second-order, i.e. U = Ū+Ũ , we restrict attention to an approximation of ω that is accurate up to second order and omits all terms of order higher than two. 110 Appendix C Statement of Co-Authorship The third chapter in this thesis reports the results of a joint research with Profs. Michael B. Devereux and Amartya Lahiri. The author took central roles in all stages of the research, such as iden- tifying the research question, developing the model, acquiring the data set, and conducting the numerical simulation. 111

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