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Three essays on asymmetric financial access Chu, Yin-Chen 2006

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Three Essays on Asymmetric Financial Access b y Y i n - C h e n C h u A D i s se r t a t i on S u b m i t t e d i n Pa r t i a l F u l f i l l m e n t o f the R e q u i r e m e n t s for the D e g r e e o f D o c t o r o f P h i l o s o p h y i n T h e F a c u l t y o f Gradua te S tudies , ( E c o n o m i c s ) T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a N o v e m b e r , 2 0 0 6 © Y i n - C h e n C h u , 2006 Abstract This dissertation consists of three essays on issues related to asymmetric financial access in two-country general equilibrium models with sticky prices. The form of asym-metric financial access is in terms of two groups of households: One group has full access to both bond and money markets, while the other is prohibited from bond trade or even monetary adjustments. The first essay is to examine effects of financial asymmetry on economic volatility. It finds that the effects depend on whether, in addition to restrictions on bond trade, you also have restrictions on monetary adjustments, among households who face financial limitation. If financially constrained households are prohibited from bond trade only, then inter-household monetary adjustments serve as a shock absorber and we have similar economic volatility under different degrees of financial asymmetry. If financially constrained households are prohibited from both bond trade and monetary adjustments, then we have positive correlation between degrees of economic volatility and financial imperfection. The second essay is to examine welfare effects of economic uncertainty under financial asymmetry. The welfare measure is defined as how much initial steady-state consumption a household is wil l ing to give up to negate effects of economic uncertainty. The essay finds that lower degrees of foreign financial openness increase welfare loss of financially unconstrained households but decrease welfare loss of financially constrained households. Moreover, welfare loss of both types of households is reduced with lower degrees of home financial openness. It also finds that i f financially constrained households are prohibited from both bond trade and monetary adjustments, then welfare loss of both types of households increases. The third essay is to examine welfare effects of exchange-rate regimes under financial asymmetry. It is assumed that governments fix their money supply at initial steady-state levels in the flexible exchange-rate regime, while coordinating their monetary policies to maintain the exchange rate level in the fixed exchange-rate regime. The welfare measure is defined as expected utili-ty excluding the term associated with real balances. The essay finds that under financial asymmetry, fixed nominal exchange rates are in many cases preferable to flexible nomi-nal exchange rates by both types of households. For financially unconstrained households, i i wealth effects associated with the monetary policies that aim to maintain the exchange rate level can dominate the welfare cost of fixed nominal exchange rates. For financially constrained households, they can not enjoy the benefit brought by expenditure switching effects due to their financial restriction, but need to bear the associated cost of higher economic variability. Therefore by reducing expenditure switching effects, the fixed exchange-rate regime can increase their welfare. in Table of Contents Abstract i i Table of Contents iv List of Tables ix List of Figures x i Acknowledgement x i i 1 Financial Asymmetry and Macroeconomic Volatility. 1 1.1 Introduction . 1 1.2 Model . 4 1.2.1 Households 5 1.2.2 Governments 8 1.2.3 Firms 8 1.2.4 Market-Clearing Conditions 11 1.2.5 Solution Methods 12 1.3 Money Supply Shock . 14 1.3.1 Restrictions on Bond Trade with Complete Producer-Currency Pricing .-. 14 1.3.2 Restrictions on Bond Trade with Complete Local-Currency Pricing 17 1.3.3 Restrictions on Bond Trade and Monetary Adjustments 19 1.4 Government Spending Shock 20 1.5 Conclusion 22 2 Welfare and Financial Asymmetry 24 2.1 Introduction 24 2.2 Model . 26 iv 2.2.1 Households .. 27 2.2.2 Governments 29 2.2.3 Firms 29 2.2.4 Economic Uncertainty . 30 2.2.5 Market-Clearing Conditions 31 2.3 Solution Method.. , 32 2.4 Simulation Result 34 2.4.1 Welfare Measures 34 2.4.2 Welfare Evaluation 36 2.4.3 Sensitivity Analyses. 38 2.4.4 Monetary Restrictions 39 2.5 Conclusion : 40 3 Financial Asymmetry and Different Exchange-Rate Regimes 42 3.1 Introduction 42 3.2 Model 44 3.2.1 Households 44 3.2.2 Governments 48 3 2.3 Firms 48 3.2.4 Market-Clearing Conditions 50 3.2.5 Model Equilibrium 51 3.3 Solution Method.. 52 3.4 Welfare Result 54 2.5 Conclusion.. 57 Bibliography . 59 A Appendices of Chapter 1 63 A . l Optimization Problem and First-Order Condition 63 A . 1.1 Households / , 63 A . 1.2 Households /'* 63 A . 1.3 Households j 64 v A . 1.4 Households / 65 A . 1.5 Firms x 66 A . 1.6 Firms x* 66 A . 1.7 Firms y . 67 A . 1.8 F i r m s / 68 A.2 Table 70 Table 1.1 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade with Complete P C P 70 Table 1.2 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade with Complete L C P 71 Table 1.3 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade and Monetary Adjustments with Complete P C P 72 Table 1.4 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade and Monetary Adjustments with Complete L C P 73 Table 1.5 Standard Errors under IID Random-Walk Home and Foreign Fiscal Disturbances -Restrictions on Bond Trade with Complete P C P 74 Table 1.6 Standard Errors under IID Random-Walk Home and Foreign Fiscal Disturbances -Restrictions on Bond Trade with Complete L C P 75 A.3 Figure... 76 Figure 1.1 Simulation Results o f (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Monetary Expansion -Restrictions on Bond Trade with Complete P C P 76 Figure 1.2 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under vi The Permanent Home Monetary Expansion -Restrictions on Bond Trade with Complete L C P . . 79 Figure 1.3 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Fiscal Expansion -Restrictions on Bond Trade with Complete P C P 82 Figure 1.4 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Fiscal Expansion -Restrictions on Bond Trade with Complete L C P 85 Appendices of Chapter 2 . 88 B . l Optimization Problem and First-Order Condition 88 B . l .1 Households/ '.. 88 B . l . 2 Households/*.... 89 B . l . 3 Households/.. 89 B . l . 4 Households / 90 B . l . 5 Firms z 91 B . l . 6 Firmsz : 91 B.2 Table 93 Table 2.1 Welfare Results of Home Households with . { n equaling .50, .25 and .05 93 Table 2.2 Welfare Results of Home Households with , n equaling .50, .25 and .05 , 94 Table 2.3 Welfare Results o f Home Households under Lower Price Rigidity with n equaling .50, .25 and .05 96 Table 2.4 Welfare Results of Home Households under Higher Elasticity of Consumption Demand with n equaling .50, .25 and .05 97 Table 2.5 Welfare Results o f Home Households under Lower Elasticity o f Labor Supply with n equaling .50, .25 and .05 98 Table 2.6 Welfare Results of Home Households under v i i Monetary Restrictions with n equaling .50, .25 and .05 99 C A p p e n d i c e s o f C h a p t e r 3 . 100 C . l Optimization Problem and First-Order Condition 100 C . l . l Households/ 100 C . l . 2 Households /*.... 100 C . l . 3 Households;..... 101 C . l . 4 Households / 101 C . l . 5 Firms z 102 C . l . 6 Firmsz* 102 C.2 Table 104 Table 3.1 Welfare Results of Financially Unconstrained Home Households / 104 Table 3.2 Welfare Results of ' Financially Unconstrained Foreign Households /'* 105 Table 3.3 Welfare Results of Financially Constrained Home Households j.... 106 Table 3.4 Welfare Results o f . Financially Constrained Foreign Households / 107 v m List of Tables Table 1.1 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade with Complete P C P 70 Table 1.2 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade with Complete L C P 71 Table 1.3 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade and Monetary Adjustments with Complete P C P 72 Table 1.4 Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances -Restrictions on Bond Trade and Monetary Adjustments with Complete L C P 73 Table 1.5 Standard Errors under IID Random-Walk Home and Foreign Fiscal Disturbances -Restrictions on Bond Trade with Complete P C P 74 Table 1.6 Standard Errors under IID Random-Walk Home and Foreign Fiscal Disturbances -Restrictions on Bond Trade with Complete L C P 75 Table 2.1 Welfare Results of Home Households with n equaling .50, .25 and .05 93 Table 2.2 Welfare Results of Home Households with n equaling .50, .25 and .05 94 Table 2.3 Welfare Results of Home Households under Lower Price Rigidity with n equaling .50, .25 and .05 96 Table 2.4 Welfare Results of Home Households under ix Higher Elasticity of Consumption Demand with n equaling .50, .25 and .05 97 Table 2.5 Welfare Results of Home Households under Lower Elasticity of Labor Supply with n equaling .50, .25 and .05 98 Table 2.6 Welfare Results of Home Households under Monetary Restrictions with n equaling .50, .25 and .05 99 Table 3.1 Welfare Results of Financially Unconstrained Home Households / 104 Table 3.2 Welfare Results of Financially Unconstrained Foreign Households /'* 105 Table 3.3 Welfare Results of Financially Constrained Home Households j 106 Table 3.4 Welfare Results of Financially Constrained Foreign Households/ . . . 107 x List of Figures Figure 1.1 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Monetary Expansion -Restrictions on Bond Trade with Complete P C P 76 Figure 1.2 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Monetary Expansion -Restrictions on Bond Trade with Complete L C P 79 Figure 1.3 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Fiscal Expansion -Restrictions on Bond Trade with Complete P C P 82 Figure 1.4 Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under The Permanent Home Fiscal Expansion-Restrictions on Bond Trade with Complete L C P . . . . . . 85 x i Aclmowledgement I am grateful to my supervisor, Professor Michael Devereux, for his research advice and guidance. I am extremely grateful to his encouragement and support when I encoun-ter research hindrance at various stages o f this dissertation. I am also grateful to other members of my supervisory committee, Professor Francisco Gonzalez, Professor Henry Siu and Professor Viktoria Hnatkovska for their research suggestions and discussions. I am responsible for all errors. xn Chapter 1 Financial Asymmetry and Macroeconomic Volatility 1.1 Introduction The literature about financial market imperfection on business cycle volatility has grown with a considerable volume in the last decade.' For a brief review of different approaches on the theoretical level, Mendoza (1994) adopts the traditional neo-classical model of savings and investment to examine different degrees of capital mobility and macroeconomic volatility. Razin and Rose (1994) also apply the neo-classical framework, but focus on different effects among idiosyncratic and global disturbances on the link between volatility and openness. Sutherland (1996) incorporates transaction costs o f bond markets into the model of new open economy macroeconomics introduced by Obstfeld and Rogoff (1995, 1996). In recent years, using asymmetric information of financial markets to explain volatility has drawn increasing attention. Related studies include Faia (2001), Aghion, Bacchetta and Banerjee (1999) and Cespedes, Chang and Velasco (2000). Among them, Faia and Cespedes et al. combine new open economy macroeconomics with the newly developed concept of financial accelerators.3 Despite the rich theoretical contents, a clear prediction for the effects of financial market imperfection on business cycle volatility is unfortunately absent. On the empirical level, moreover, even though studies such as Basu and Taylor (1999) document likely connections between openness and volatility based on stylized facts, it is still difficult to establish more systematic relations. Razin and Rose (1994) argue that the lack of empi-' For a survey of the literature see Buch (2002). 2 Henceforth N O E M refers to new open economy macroeconomics, and OR refers to Obstfeld and Rogoff. '' Asymmetric information of financial markets makes firms' net worth and their external finance premiums inversely related. If net worth is pro-cyclical, then external finance premiums will be counter-cyclical. Potentially they can enhance business cycle volatility. 1 rical evidence may be due to improper identification of idiosyncratic and global shocks. Mendoza (1994) suggests another explanation that economic structures have changed over time, and hence a stable link between openness and volatility does not exist. Given close interactions between financial openness and financial systems, more recent studies have tried to find the missing link by separating these two forces. Cecchetti and Krause (2001) and Easterly, Islam and Stiglitz (2000), for example, attribute the declining vola-tility in the past twenty years to financial deregulation. The ambiguous predictions of theoretical and empirical studies imply that the issue of financial imperfection and economic volatility remains as an essential field of research. This paper points out a new direction for the literature, by exploring the importance of money markets when financial access is not perfect. In the paper a two-country general equilibrium model is developed. A distinguishing feature of the model is that financial imperfection takes the form of two groups of households having asymmetric financial access, while most previous studies assume homogeneous financial limitation. The finan-cial homogeneity assumed in previous studies enables easier equilibrium derivation. But it overlooks monetary interactions between households that may have caused the weak correlation between volatility and openness. The model is built on the basic framework of new open economy macroeconomics introduced by Obstfeld and Rogoff. The OR model incorporates well established micro-foundations of aggregate demand and supply, imperfect competition with short-run price rigidity, and explicit welfare evaluation. These features make the OR model a powerful analytic framework for business cycle volatility and international macroeconomic poli-cies.4 In the OR model, home and foreign households are assumed to reside on a conti-nuum of interval. This paper follows this assumption and models financial asymmetry by dividing home and foreign households into two groups: One group has full access to both bond and money markets, while the other is prohibited from bond trade or even monetary adjustments. Changing the lengths for different types of households along the continuum 4 For a survey of the literature see Lane (2001). 2 of interval then allows us to examine economic volatility under different degrees o f home and foreign financial openness.5 Two additional modifications are applied to make the baseline model more realistic. First, it is assumed that short-run price rigidity takes the form of Calvo-staggering pricing following Calvo (1983). In the O R model, one-period-in-advance pricing has the counter-factual implication that price levels exhibit large and discrete jumps. B y adopting Calvo-staggering pricing the model permits smooth price adjustments that are more consistent with observations. The Calvo-staggering assumption means that in each period the oppor-tunity of adjusting its prices arrives stochastically to each firm. Provided independent decision making and a large number of firms, a fixed fraction gets to adjust prices each period and hence price levels gradually change over time. Second, some firms can charge different prices in different countries for the same commodity, a market segmentation commonly known as pricing-to-market. 6 Engel (1999) documents that P T M together with sticky prices account for a large proportion of real exchange rate fluctuations. Betts and Devereux (1996, 2000a) show that P T M enlarges the size of exchange rate move-ments when incorporated into the O R model. Gagnon and Knetter (1995), Goldberg and Knetter (1997) and Marston (1990) provide empirical evidence for P T M . According to their findings, P T M exists in many export countries with significant cross-country and cross-industry differences. The first important finding of the paper is that, with asymmetric financial access expansionary macroeconomic disturbances induce financially constrained households to raise their money balances, i f these households are prohibited from holding both foreign and domestic bonds. Under permanent monetary expansion, for example, higher income levels in the current period motivate households to transfer wealth into the future. If bond markets are not available, households w i l l be forced to take money balances as an inferior alternative for consumption smoothing. Hence inter-household monetary adjustments 5 If we want to make household types endogenous, we need a deeper model to incorporate economic and social factors that affect households' financial abilities. Because this is not the main purpose of the paper, I examine economic volatility taking different degrees of home and foreign financial openness as given. 6 Henceforth PTM refers to pricing-to-market. 3 from households without financial limitation to those who are financially constrained result.7 Second, the above inter-household monetary adjustments serve as a shock absorber to eliminate excess economic volatility originated from financial imperfection, resulting in similar economic dynamics under different degrees of financial asymmetry. Although households may be financially constrained, they are entitled with the same right to hold and to adjust money balances. This fact, together with the one that different households coexist, causes macroeconomic disturbances to be buffered by the adjustments o f money balances between them. The resulting economic dynamics of most variables hence exhi-bits small differences across various degrees of financial asymmetry unless in extreme cases. This finding may provide an explanation for the weak correlation between open-ness and volatility suggested by empirical studies. Third, i f financially constrained households are prohibited from not only bond trade but also monetary adjustments, then financial imperfection result in higher degrees of economic volatility compared to an economy with perfect financial markets. In this case, we have positive correlation between economic volatility and financial imperfection. The second and third findings imply that, the impacts of financial access on economic vola-tility depend on whether, in addition to restrictions on bond trade, you also have restric-tions on monetary adjustments, among the agents who face financial limitation. Financial imperfection presenting in bond markets only is insufficient to cause large differences of economic dynamics or any systematic relation with economic volatility. The rest of the chapter is organized as follows: Section 1.2 gives a brief description of the model. Section 1.3 and Section 1.4 analyze economic adjustments under money supply shocks and government spending shocks. Section 1.5 concludes. 1.2 Model 7 Note that inter-household monetary adjustments act as a way of consumption smoothing across both time and states. 4 In this section I briefly describe the model structure. The description focuses on the home country because of model symmetry. Readers can refer to Appendix A at the end of the dissertation for complete model equations. In each of the following subsections, I w i l l write down households, governments and firms' optimization problems first, followed by notation definitions. 1.2.1 Households Take a standard N O E M economy with two countries in the world. Assume that two types o f households reside in each country: Types / and /* have full access to the bond market, while types j and j* have no access.8 This financial asymmetry reflects in house-holds' budget constraints, such that only /' and /* can hold bonds. Note that j and j* can not borrow from or lend to domestic unconstrained households by bond trade either, and in this economy there is no government-issued asset. A [0, 1] interval represents the conti-nuum of households, where i,j, i* and j* belong to subintervals [0, ri], (n, .5], (.5, .5 + n] and (.5 + n*, 1], respectively. The values of n and n* are between 0 and .5, which are proportions of unconstrained home and foreign households. Larger values o f n or n* then stand for higher degrees of financial openness. In the original O R model, sizes of the home and foreign countries are not nece-^ ssarily the same. But in the current model, different country sizes affect the model results only in magnitudes rather than in signs. Therefore it is assumed that the two countries have the same size of .5 to simplify the underlying driving forces. The case of small open economies can be regarded as a special example of different country sizes, and hence the above argument applies. Also note that because the financial market is not perfect when n or n* is less than .5, Ricardian equivalence generally does not hold in this economy. Households earn wage income by labor supply, get equal dividends from domestic firms, pay taxes, choose consumption and money balances, and decide bond holdings i f applicable. Despite their different budget constraints, all households have the same C E S utility function that depends on consumption, labor supply and real balances. A typical household/'s utility-maximization problem takes the form: 8 Variables with an abstract mark denote foreign equivalents. 5 Max tf;=x/n-^c;** *^&T'---KM}, o--\ \-s Ps n subject to M\ + d,F; = M / _ , + + w,N; +17,- PtC\ - Prf. It gives first-order conditions with respect to bond holdings, money balances and labor supply as d,p,+i M' y - -TV;=(-^-C;"-P, . K P, with 0 < B < 1, a, K, s, x > 0 and // > 1. On the other hand, a typical household fs utility-maximization problem takes the form: Max Ii;= £ / r ' [ ^ - C / - +T 1-(^) I" £ ^ cr-1 1-^ Ps // subject to M / = M / _ , + w,W/ + 77, - ^ C / - 7^7/ It gives first-order conditions with respect to money balances and labor supply as MJ 1 .-i P -L- -1 7V /= ( -^-C / ^p . Note that i f households _/ get no dividend or less dividends than households / do, then the effects of economic disturbances on households fs consumption, labor supply and real balances wi l l be similar to the case of equal dividends, except with smaller magnitudes. In the above equations, the variable C, o f either household / or j is a consumption index defined by 6>-l 6 where 9>\; c,(z) and c,(z*) stand for consumption o f output produced by the home firm z and the foreign firm z* respectively. 9 The price index P, and consumption demand c,(z) and c,(z*) can be derived from C, such that 2 with p,(z) and p,(z*) standing for individual commodity prices. 1 0 The nominal discount bond Ft is denominated in the home currency. 1 1 Variables M,, Nh Tlh and T, denote the money balance, labor supply, the profit transfer and the tax payment. Variables w, and d, denote the wage rate and the bond price. In addition to bond trade, this paper also examines the case where households j and j* are further prohibited from adjusting money balances. When this complete financial restriction is applied, money balances and tax payments of households j and / are set at their initial steady-state levels over time. It is assumed that the initial steady-state values of tax payments are equal to 0 for both types of households in both countries. A typical household fs utility-maximization problem becomes: M a x u/=±/J-'[^cf^+^A--^Nn, 71 o--l Ps p 9 Pricing-to-market is permitted in this model, and hence a firm z may refer to either a firm x with local-currency pricing or a firm y with producer-currency pricing. 10 P, can be derived by solving the problem min Z = p /? (z)c (z)dz + | pi (z' )c (z* )dz , subject to [ £ c (z)" dz +1 c (z")" dz' j * " ' = 1. c,(z) and c,(z ) can be derived by solving the problem max Ci=[^-c(z)1' dz + | c ( z ' ) V z ' ] " " \ , subject to p,(z)ci (z)dz + |p , (z ' )c (z' )dz = Z . " We can assume that trading of bonds involve a small adjustment cost to ensure stationarity. But note that in this paper the economic predictions will not change with or without the adjustment cost. 7 subject to MJQ = MJ0 + w,Nj +I7l-PlC/ . A n d there is only one first-order condition taken with respect to labor supply as l w - i - i • Nf=(—±Cf*)'-i. 1.2.2 Governments The home government sets its spending, taxes and money supply according to the budget constraint G,-T<+ . •*/ . where lT,=nT;+(±-n)T/, Like other real composite variables government spending G, is measured in units of the consumption index. Therefore, government expenditure demand g,(z) and gt(z*) can be derived similar to household consumption demand as s , ( * ) = [ ^ r ' G , , •*/ . • Note that with two types of households, governments control total money supply but not individual money balances. This is very different from models with homogeneous agents where money balances are identical across households. When households are free to choose money balances over time, economic disturbances initiate inter-household monetary adjustments. It is shown later that these adjustments play an important role in stabilizing the economy. 1.2.3 Firms 8 Assume that there are two types of firms in each country. Types x and x* can price to markets by local-currency pricing, while types y and y can only use producer-currency pr ic ing. 1 2 For x and x*, they set one price for each country and these prices do not need to follow the law of one price. On the other hand, prices set by y and y are governed by the law o f one price and hence affected by exchange rates. Consequently, purchasing power parity generally does not hold in this economy. Similar to the continuum of households, firms locate on another [0, 1] interval with x, x*,y and_y* belonging to subintervals [0, u], (u, .5], (.5, .5 + u] and (.5 + u*, 1] respectively. The values of u or u* are between 0 and .5, which are proportions of home and foreign L C P firms. Larger values of u or u then stand for higher degrees of market segmentation. Firms produce differentiated products, engage in monopolistic competition, maxi-mize the present value of profits, and transfer profits back to domestic households evenly. It is assumed that firms' pricing decisions are subject to Calvo-staggering rigidity. In other words, the opportunity of adjusting its prices arrives stochastically to each firm in each period. Given independent decision making and a large number of firms, the final price set by firms in each type can be represented by their averaged price in each type. It is calculated as the sum of the final price in the previous period and the current target price, weighted by y and 1-y respectively. Other decision variables set by firms in each type are then calculated using these final prices. A typical firm x maximizes the discounted sum of its current and future profits by choosing one target price for each country in each period, given the probability y that any price chosen today remains to be the price tomorrow. Its profit-maximization problem takes the form: M a x v;x =Yjys"ps-n';, •1=1 subjectto I T : = p r ^ w + ^ r ^ w - ^ " . x's{z) = x'f(z) = [ ^ r 1 < +(1- n)C> + i G J , 1 2 Henceforth L C P refers to local-currency pricing and P C P refers to producer-currency pricing. 9 y / ( 2 ) = x ; / ( z ) = [ ^ r V c i " , + ( | - » ) c / + l G ; ] , *;(z)+x;*(z) = 4iv;\ It gives two first-order conditions with respect to p/x(z) and qlx(z) as 2 2 / l v = ^ r r ^ [ « ' c ; + ( - - « ' ) c f + ^ A 2 2 4 _ In the above equations, pt'x{z), q,'x(z), x,'(z) and x/*(z) are target prices.and target output chosen by the firm x for the home and foreign countries respectively. N/x is target labor demand of the firm x, A, is the technology level'and e, is the exchange rate. Final prices and other decision variables set by firms x are calculated as p;(z) = rp;_](z)+(\-r)P:(z) . q;(z) = rgUz)+(\-rHx(z) *, (z) = [ ^ h e [nc;+(I - » ) C / ' + x-ct ], x ; ( z ) = [^r[« c;' +(I-II*)c/ + ± G , * ] , i V ; = ^ [ x , ( z ) + x;(z)] n ; = p;(z)x,(z)+elq;(z)xl(z)-wlN;. A typical firm y has a similar profit-maximization problem but it only chooses one target price: Max v;y = Y^f-'p'-'n'/, 10 subject to n'/ = p'/{z)y's{z) + p't»{z)y';(z)-wXy, . ' y\ (z) = y'f (z) = [ ^ k 6 [ < + ( i - » ) C / + ± G J , e Z 2 2 X ( z ) + >•'(-) = .< A ; ' . • . T h e o n l y first-order c o n d i t i o n taken w i t h respect to p!y(z) becomes CO f " ' 1 1 (d-Dp'/iz^f'T'\P![nCs + ( ± - » ) C / + ^ G J + ( e s P; ) e Kc; '+ ( l - n * ) C / + | G ; ] " r 1 1 F i n a l prices and other d e c i s i o n variables set b y firms y are calculated as p^z) = YpU{z) + {\-y)pY{z) ' x = + 4 - «)c/+ ] e,P, 2 2 ^ = ^ r ( z ) + ^ ; ( z ) ] ^ ^ =Pi'(z)yl(z) + pj'(z)yt(z)-wlN^ 1.2.4 Market-Clearing Conditions There are six market-c lear ing condi t ions i n the m o d e l : nFt'=-nFf 11 -M,=nM'l+(--n)M/, X-M] =nM\f+{~n)M{ , . uN; +{--U)N* =nNi,+(--n)Ni u Nf + (--«* )Nf = ri N] + (--ri )N{ 2 2 ' C ; + G; = nC] + (- - n)Cf + ri C\ +(--ri )Cf + — G. + — G' ' 2 2 2 2 = „ [ ^ x , ( z ) + i M , ; ( 2 ) ] + ( I - . x ^ w + ^ / w ] . The first equation, is the bond market clearing condition. It states that total values of bonds held by home and foreign households must sum up to zero when evaluated in the home currency. The second and third equations are money market clearing conditions. They are part of the home and foreign government budget constraints and must hold all the time. The forth and fifth equations are labor market clearing conditions. Because in the model labor is assumed to be internationally immobile, total labor demand must equal total labor supply within each country. The last equation is the goods market clearing condition. Aggregate demand of household consumption C,w and government spending G," must equal aggregate output of the global economy Y,w. 1.2.5 Solution Methods After solving households' and firms' optimization problems, all optimal conditions are first-order log-linearized around a specific initial steady state. It is assumed that in this steady state the law of one price and purchasing power parity hold. A l l target prices and actual prices are equal when evaluated in the same currency. It is also assumed that in 1 2 this steady state home and foreign bond holdings, tax payments and government spending are equal to 0, and technology levels are equal to 1. Numerical results o f the linearized model are generated by Matlab simulation under monetary and fiscal disturbances. Literature on degrees of financial imperfection and market segmentation provides a wide range of estimates for u and n. Campbell and Mankiw (1989) test the permanent income hypothesis, and suggest about 50 percent of total income consumed by current-income consumers. Jappelli and Pagano (1989) document substantial deviations in the extent of financial imperfection from cross-country comparisons. Their estimates range from .1 to .7 for seven developed countries including the United Kingdoms, the United States and Japan. 1 3 1 4 1 5 For degrees of market segmentation, Gagnon and Knetter (1995) find stark differences in the extent of pricing-to-market across export countries, with esti-mates ranging from 0 to .9. Marston (1990) finds similar pricing-to-market diversities across industries, with estimates ranging from .3 to near 1. Despite the suggested ambi-guity, both studies have averaged degrees of market segmentation fall in the neighbor-hood of .5. It is also consistent with findings of Goldberg and Knetter (1997). In this paper, two cases of (n, ri), (.5, .5) and (.01, .01), are chosen to present in Figure 1.1 and Figure 1.2 under a once-and-for-all home monetary expansion, (n, ri) equaling (.5, .5) implies well developed financial markets without financial friction, while (n, ri) equaling (.01, .01) stands for a nearly closed economy. The difference between Figure 1.1 and Figure 1.2 is that the former assumes complete P C P and the latter assumes complete L C P . The reason of choosing these extreme values for (n, ri) is to allow easier understandings of underlying economic meanings. Cause without the restriction on mone-tary adjustments most other values of (n, ri) merely result in similar economic dynamics. This can be seen in Table 1.1 and Table 1.2, which.summarize standard errors of major l j Developing countries are excluded due to data limitation. 1 4 Because in this model money can serve as an inferior asset to smooth consumption, strictly speak-ing the complete liquidity constraints assumed by Campbell and Mankiw (1989) and Jappelli and Pagano (1989) are applicable only when financially constrained households are prohibited from both bond trade and monetary adjustments. 1 5 Generally speaking most households in the real world are only partially liquidity constrained, and hence Campbell and Mankiw (1989) and Jappelli and Pagano (1989) imply even higher population ratios under financial limitation. 13 economic variables for four sets of (n, ri) given different pricing behaviors. The simu-lation results are generated with identical and independent random-walk monetary distur-bances in both countries. This paper also examines economic volatility when financially constrained households are further prohibited from monetary adjustments. Because the graphical illustrations are difficult in some cases where economic dynamics exhibits large differences, the simulation results are presented by showing the standard errors o f major economic variables in Table 1.3 and Table 1.4. Again the results are generated with inde-pendent and identical random-walk monetary disturbances in both countries. Similar to monetary disturbances, economic dynamics under a once-and-for-all home fiscal expan-sion is presented in Figure 1.3 and Figure 1.4, where the former assumes complete P C P and the latter assumes complete L C P . Other parameters used by Matlab are as follows: The elasticity of consumption demand 6 is set to 11 to reproduce a wage-price markup of 10 percent. It is consistent with findings of Basu and Fernald (1997) and Burnside, Eichenbaum and Rebelo (1995). The elasticity of labor supply \l(u - 1) is set to 1 following Betts and Devereux (2000a, 2000b) and Christiano, Eichenbaum and Evans (1997), which gives /u a value of 2. The consumption elasticity of money demand for households / and /'* is 1/e given log utility. According to Mankiw and Summers (1986), this variable is very close to unity and hence e is set to 1. Finally, the elasticity of intertemporal substitution a and the discount factor /? are set to 1 and .96 respectively. These values are commonly used in quantitative real business cycle studies. 1 6 1.3 Money Supply Shock 1.3.1 Restrictions on Bond Trade with Complete Producer-Currency Pricing In this section I assume complete P C P in that all home and foreign firms set their prices in domestic currencies. Consider a pure and permanent home monetary expansion 1 6 Setting the elasticity of intertemporal substitution a to 1 provides a benchmark case of the model. But note that the economic predictions of this paper are not sensitive to the value of a. 14 adopted at period one, which permanently raises total money supply by . 1, while keeping government spending unchanged by reducing short-run taxes evenly across different households. Figure 1.1 summarizes simulation results o f major economic variables, with continuous lines representing the case o f (n, ri) equaling (.5, .5) and dashed lines repre-senting the case of (n, ri) equaling (.01, .01). Because consumption and labor supply of households / and /*, and prices and output of individual firms exhibit similar economic dynamics across different cases, these variables are excluded from the illustration. The case of («, ri) equaling (.5, .5) with complete P C P is close to the original O R model. A l l households have two alternatives to save as no financial limitation applies. They can hold bonds that generate interest revenues, or hold money that yields direct utility. In this economy home monetary expansion increases home households' money balances. Because there is only one type of households, each of them shares the same and constant amount of monetary increment over time. The home monetary expansion also increases the value of the exchange rate, which jumps immediately to its long-run level. This exchange rate depreciation raises home output and hence home labor supply relative to foreign output and foreign labor supply in the short run. It creates a wealth effect that increases home households' consumption and their bond holdings to smooth consumption. It also increases foreign households' consumption by making the foreign price of home output less expensive. Therefore the home country runs a current account surplus in the short run. In the long-run equilibrium, bond holdings and money balances of home house-holds increase, and consumption of all home and foreign households increases. 1 7 On the other hand i f asymmetric financial access presents, the only way households j can smooth consumption is.to increase their money balances further. A t the same time, households / must decrease their money balances by increasing their bond holdings to satisfy this extra money demand. Consequently, money moves from households without financial limitation to those who are financially constrained as the monetary expansion occurs. A s illustrated in Figure 1.1, bond holdings of households / are much higher when (n, ri) equals (.01, .01) than in the benchmark case of (n, ri) equaling (.5, .5) at period one. A n d because of the small population of households /, even they largely reduce their money balances, each household j only shares a tiny amount. Consumption smoothing of 1 7 Betts and Devereux (1996, 2000a, 2000b) and Obstfeld and Rogoff (1995, 1996). 15 households j is hence highly inefficient, which causes their period-one consumption to be higher compared to the benchmark case. However, this is not the case for households /, whose consumption is not affected by the financial asymmetry. The extra money demand of households j for the purpose of consumption smoothing also reduces exchange rate depreciation. This results in lower home output, lower home labor supply and the lower home wage rate compared to the benchmark case at period one. In the long run, money is inferior to bonds for value storing in the sense that it does not generate interest revenues. Therefore, consumption of households j decreases more rapidly and to a lower level than the benchmark case in the long-run equilibrium. Their money balances also decrease accordingly, and we find reversed monetary movements compared to the first period. The lower money demand o f households j causes the exchange rate to further depreciate in the long run. This makes home output, home labor supply and the home wage rate decrease less rapidly and to higher levels than the benchmark case in the long-run equilibrium. The current account of the home country is negative both at period one and in the long run. The first reason is the low population of households /. A n d the second reason is the small-er magnitude of exchange rate depreciation pointed out earlier that makes home output more expensive than the benchmark case. The underlying reasons for the resulting econo-mic dynamics of the foreign country are similar to those of the home country, and hence wi l l not repeat here. The particular adjustment pattern of money balances can be further explained by the different characteristics between bonds and money. When both financial instruments are feasible, households keep money because it yields direct utility from the utility function, and hold bonds because they smooth consumption more efficiently. This design empha-sizes the transaction motive of keeping money, compared to holding bonds as a major store of values. Once asymmetric financial access emerges, households without financial limitation wi l l continue to choose bonds for better consumption smoothing, while finan-cially constrained households must choose money as an inferior but the only way of value storing. The induced financial substitution of using money to replace bonds then results in the observed monetary movements. In this model, the facts that money balances do not generate interest revenues and are required when doing transactions make them close to saving accounts. The inter-household monetary adjustments then imply that financially 16 constrained households raise money balances or low-interest savings upon domestic monetary expansion. This contradicts the general impression that monetary expansion reduces the real value o f money, and hence induces the public to switch their portfolios into interest-bearing assets. In addition to Figure 1.1, Table 1.1 provides the simulation results with a more * complete set of n-n combinations. It summarizes standard errors of major economic vari-ables under independent and identical random-walk monetary disturbances in both coun-tries. The table shows that degrees of variability for most variables exhibit small diffe-rences across different (n, ri). Exceptions emerge mostly for bond holdings and money balances, or when the proportions of households /' and /* are reduced to very small values such as (.01, .01). This fact implies that inter-household monetary adjustments have very important effects on economic volatility. When the populations of households / and /* are above some reasonable levels, under monetary disturbances the extra money demand of households j or j* for consumption smoothing can be fulfilled efficiently by households i or i*. Inter-households monetary adjustments then serve as a shock absorber to eliminate excess variability in other variables. This is also why we observe large differences of standard errors across different (n, ri) for bond holdings and money balances but not other variables in Table 1.1. On the other hand, i f the populations of households i and /* are reduced to very small levels, then large amounts of total money demand from house-holds j o r / can no longer be fulfilled efficiently by households i or i*. Inter-households monetary adjustments are restricted, which also results in the large differences of stan-dard errors between (n, ri) equaling (.01, .01) and other cases. 1.3.2 Restrictions on Bond Trade with Complete Local-Currency Pricing Consider the same home monetary expansion as the one in the previous section, but now assume complete L C P in that all home and foreign firms set their prices in local currencies. Figure 1.2 summarizes simulation results of major economic variables, again with continuous lines representing the case of (n, ri) equaling (.5, .5) and dashed lines representing the case of (n,n ) equaling (.01, .01). To provide easier comparisons all vari-17 ables that have been shown in Figure 1.1 are included, even they have similar adjustment paths across different cases here. According to Figure 1.2, when (n, n) equals (.5, .5) the home monetary expansion raises home households' money balances evenly and constantly. The home monetary expansion depreciates the exchange rate, which jumps immediately to its long-run level. Note that the feature of P T M has made the exchange rate overshoot compared to the benchmark case in Figure 1.1. With complete L C P , once prices are set they wi l l not be changed by the exchange rate when output is imported into the other country. In other words, the foreign price of home output w i l l not be reduced by the exchange rate depre-ciation. And hence the expenditure switching effect of shifting world production from the foreign country to the home country is not observed here. Home labor supply decreases, and home output is lower both at period one and in the long-run equilibrium compared to the benchmark case in Figure 1.1. The extra money supply increases home households' consumption and bond holdings, but the magnitude of their bond holdings is small due to less home production. Consequently, the current account of the home country is negative both at period one and in the long-run equilibrium. The case of (n, n) equaling (.01, .01) has very similar economic dynamics to that of {n, n) equaling (.5, .5) except bond holdings and money balances. Under the restriction on bond trade, households j still need to smooth consumption by holding more money at period one even with complete L C P . Hence we still find higher bond holdings of house-holds /', as well as monetary movements from households i to households j upon the home monetary expansion. Nonetheless, because there is no expenditure switching effect with complete L C P , the magnitude of home output rise and the need of home consumption smoothing are limited. Therefore we only observe moderate adjustments in home house-holds' bond holdings and money balances. A n d these adjustments of bond and money are sufficient to eliminate excess variability in other variables, leaving their adjustment paths similar across different cases even with the small population of households /'. Table 1.2 provides consistent simulation results with the above findings. It shows that variability o f bond holdings and money balances is much lower compared to Table 1.1 where complete P C P is assumed. It also shows that variability of other variables exhi-bits little difference across different cases even when (n, n) equals (.01, .01). However, 18 these do not imply that inter-household monetary adjustments are minor in affecting economic volatility under complete L C P . In the next section I w i l l examine the case where financially constrained households are further prohibited from adjusting money balances to show the importance of inter-household monetary adjustments in stabilizing the economy. 1.3.3 Restrictions on Bond Trade and Monetary Adjustments In this section I modify the model by assuming money balances o f households j and j fixed at initial steady-state levels over time. In other words, financially constrained households are now prohibited from not only bond trade but also monetary adjustments. This extreme financial restriction helps us to understand the importance of inter-house-hold monetary adjustments in stabilizing the economy. Note that with the complete finan-cial limitation, economic volatility increases dramatically especially for the case o f (n, n) equaling (.01, .01). This creates difficulties for graphical illustrations and hence I only present the standard errors of major economic variables here. Table 1.3 and Table 1.4 summarize simulation results with complete P C P and complete L C P respectively. Stan-dard errors are generated under independently and identically distributed random-walk monetary disturbances in both countries. In Table 1.3, when (n, n) equals (.5, .5) the simulation results are the same as those in Table 1.1 for there is no financially constrained household in this case. But as the populations of financially constrained households increase in both countries, standard errors of all variables begin to deviate significantly across different cases. Moreover, financial imperfection and economic volatility generally have positive correlation, with higher degrees of financial imperfection resulting in higher standard errors. These two facts are in contrast to what the simulation results implied in Table 1.1, where the vari-ability degrees of most variables have no large difference across different (n, n) except (.01, .01), and there is no obvious relation between financial imperfection and economic volatility. The reason is that in Table 1.1 households j and j* still can use money to smoo-th consumption although they can not hold bonds. Hence different degrees of financial asymmetry only have limited effects on economy volatility. On the other hand, when households j and j* are prohibited from both bond trade and monetary adjustments, there 19 is no. way for them to smooth consumption upon monetary disturbances. Therefore, high-er populations of financially constrained households result in higher degrees o f economic volatility. This argument also applies on Table 1.2 and Table 1 .4 , where complete L C P is assumed. The previous section has discussed the reasons of complete L C P reducing the differences of economic volatility across different (n, ri), as shown in Table 1 .2. But with the restriction on monetary adjustments, again we observe larger degrees of variability in economic variables as well as positive correlation between financial imperfection and economic volatility, as shown in Table 1 .4 . The above argument suggests that inter-household monetary adjustments play a very important role in stabilizing the economy. The impacts of financial imperfection on economic volatility depend on whether you have restrictions on both bond trade and monetary adjustments among the agents who face financial limitation. In other words, financial imperfection presenting in bond markets only is insufficient to cause any large difference of economic dynamics or systematic relation with economic volatility. Many empirical studies have tried to explain the weak correlation between volatility and openness, but the real underlying reason is still unrevealed. The financial asymmetry modeled in this paper points out a new direction that may help to explain the weak corre-lation. Many financial markets are not fully open in the sense that some households can not trade bonds freely. But as long as these households are free to adjust money, inter-household monetary adjustments serve as a substitute to smooth consumption and el imi-nate excess economic volatility upon economic disturbances. Consequently, we observe no systematic relation between volatility and openness. 1.4 Government Spending Shock Consider a pure and permanent home fiscal expansion adopted at period one, which permanently raises government spending by . 1 , and keeps total money supply unchanged by increasing taxes evenly across different households. Figure 1.3 and Figure 1.4 summa-rize simulation results of major economic variables, with the former assuming complete P C P and the latter assuming complete L C P . Following the specification from previous sections, in these figures continuous lines represent the case o f (n, ri) equaling (.5, .5) 20 and dashed lines represent the case of (n, n) equaling (.01, .01). Note that consumption and labor supply of households / and /*, and prices and output of individual firms are excluded from the illustration because they exhibit similar economic dynamics across different cases. In the benchmark case of (n, n) equaling (.5, .5) with complete P C P , home fiscal expansion causes higher taxes that reduce home consumption and home money demand. The exchange rate depreciates accordingly, and the associated expenditure switching effect increases home production and labor supply while decreasing foreign production and labor supply. Because the tax burden is permanent but its effects on output are larger at the present than in the future, i f no financial imperfection presents home households w i l l raise bond holdings to compensate future consumption. Consequently, the home country runs a current account surplus upon the home fiscal expansion. When financial asymmetry emerges as in the case of (n, n) equaling (.01, .01), on the other hand, house-holds / m u s t acquire higher money balances to smooth consumption. This extra money demand reduces the exchange rate depreciation. It also induces monetary movements from households / to households j. Because the population of households i is small, each household j only shares a tiny amount of monetary increment. The inefficient consump-tion smoothing then results in higher consumption and lower labor supply of households j compared to the benchmark case. For households they increase bond holdings to substi-tute the decrease of their money balances, and there is effectively no difference in their consumption and labor supply compared to the benchmark case. The home output is lower due to lower total labor supply compared to the benchmark case, and the current account surplus of the home country reduces. The economic reasons behind the differences of Figure 1.4 from Figure 1.3 are similar to those of Figure 1.2 from Figure 1.1, where monetary disturbances are examined. With complete L C P there is no expenditure switching effect upon the home fiscal expan-sion. Hence even the populations of households / and /* are small, inter-household mone-tary adjustments are sufficient to absorb excess economic volatility originated from finan-cial imperfection. This is why we observe similar economic dynamics across different cases for most variables except bond holdings and money balances. 21 \ Table 1.5 and Table 1.6 provide more simulation results to support the above find-ings. Similar to previous sections, they summarize standard errors of major economic variables under independent and identical random-walk fiscal disturbances in both coun-tries, with complete PCP and complete LCP respectively. According to Table 1.5, vari-ability degrees of most variables have small differences across different (n, ri) except bond holdings, money balances, or when the two countries are nearly close economies as (n, n ) equals (.01, .01). If the pricing behavior changes to complete LCP, then variability degrees have even smaller deviations including (n, ri) equaling (.01, .01). Exceptions now are only bond holdings and money balances, but their magnitudes of deviations are also small. These results are consistent with the above argument that under complete LCP, a small extent of inter-household monetary adjustments is sufficient to offset excess economic volatility. Note that if financially constrained households are prohibited from monetary adjustments in addition to bond trade, we will observe significant differences of economic volatility across different cases, as well as positive correlation between finan-cial imperfection and economic volatility, even under complete LCP. The underlying reasons and economic implications are the same as those for monetary disturbances. 1.5 Conclusion In this paper a two-country sticky-price general equilibrium model is developed to examine the effects of financial imperfection on economic volatility. In the model finan-cial imperfection takes the form of two groups of households with only one group having access to the bond market. This specification of financial imperfection is different from previous studies but supported by empirical evidence. It turns out to have some expla-nation power on the empirically weak correlation between volatility and openness. When financially constrained households are prohibited from bond trade but not monetary adjustments, expansionary macroeconomic disturbances induce them to raise their money balances for consumption smoothing. Inter-household monetary adjustments from households without financial limitation to those financially constrained then serve as a shock absorber to eliminate excess economic volatility originated from financial asymmetry, resulting in the weak correlation suggested by empirical studies. This argu-'22 meht is further supported by the experiment that restricts both bond trade and monetary adjustments of financially constrained households. With this complete financial limitation, higher degrees of financial imperfection result in higher degrees o f economic volatility, and we observe positive correlation between volatility and openness. Hence the impacts of financial imperfection on economic volatility depend on whether you have restrictions on both bond trade and monetary adjustments. In other words, financial imperfection presenting in bond markets only is insufficient to cause large differences of economic dynamics or any systematic relation with economic volatility. Asymmetric financial access can cause important policy issues due to its effects on bond trade and monetary adjustments. In particular, the prediction o f the O R model that permanent monetary expansion evenly raises utility of home and foreign households may no longer hold under financial asymmetry. Its welfare effects are open for future research, and its welfare results can have important implications on welfare policies. 23 Chapter 2 Welfare and Financial Asymmetry 2.1 Introduction The welfare tradeoff between economic stability and economic efficiency has been an important issue in economics discussions. Al lowing an economic entity to function under smaller controls on its manufacture, financial or trade sector permits more efficient economic adjustments. On the one hand, it is welfare improving in the sense that any deviation from the optimal economic allocation can be corrected quickly. But on the other hand, the associated higher degree of economic variability and economic uncer-tainty may result in larger values of welfare loss. For the most classical example in existing literature, Lucas (1987) evaluates welfare as changes of steady-state consumption required to achieve the same expected utility. He shows that economic variability implied by business cycles tends to have small welfare effects. In addition to Lucas, many other economists also suggest that welfare loss asso-ciated with economic uncertainty is not significant. A n d hence governments should adopt the economic policies that aim to permit efficient economic adjustments. More recently, Bergin and Tchakarov (2003) apply second-order approximation on a two-country sticky-price general equilibrium model to examine welfare under monetary and technology shocks. They find that welfare effects of economic uncertainty are likely to be small for a wide range of cases. But when households exhibit habit persistence or when there is an international market for bonds in the currency of only one o f the two countries, welfare loss of economic uncertainty increases. In the latter case, the country whose currency serves as denomination tends to save more and have higher welfare while the other tends to save less and have lower welfare. This is because saving in interna-tional assets allows a country to hedge against exchange rate risk more efficiently i f it can save in terms of its own currency. 24 The findings of Bergin and Tchakarov (2003) imply that different types of financial asymmetry may play important roles in directing welfare results. Following Bergin and Tchakarov (2003), this paper uses a two-country sticky-price general equilibrium model to study welfare effects o f economic uncertainty. Different from the authors' concern about how welfare is changed'when there is cross-country inequality, this paper explores the feature of inter-household heterogeneity and its important impacts on welfare. In the paper, financial structures are generalized such that households in the same country face different financial limitations. These different financial limitations then alter households' . economic behaviors and cause asymmetric welfare effects upon economic disturbances. Compared to previous studies where economic agents in the same country are assumed to be homogeneous, this paper examines welfare by taking into account complicated inter-actions between different types of households. The model is built on the basic framework of new open economy macroeconomics introduced by Obstfeld and Rogoff. Similar to Chapter 1, this paper models financial asymmetry by dividing home and foreign households into two groups: One group has full access to both bond and money markets, while the other is prohibited from bond trade or even monetary adjustments. Changing the lengths for different types o f households along the continuum of interval then allows us to examine welfare under different degrees of home and foreign financial openness. The welfare measure adopted in this paper follows Bergin and Tchakarov (2003). First compute unconditional expectation of household utility under economic distur-bances. Then calculate how much consumption in the initial steady state the household is wil l ing to give up to negate effects of economic uncertainty. This consumption cost is the welfare measure. Using second-order Taylor expansion, moreover, we can enhance the accuracy of welfare evaluation. In addition to variances of consumption and labor supply, the welfare measure also captures welfare effects o f economic uncertainty through means of those variables. According to simulation results, this paper finds that lower degrees of foreign finan-cial openness cause welfare loss to increase for financially unconstrained home house-holds but to decrease for financially constrained home households. Moreover, it finds that lower degrees of home financial openness can cause welfare loss of both types of home 25 households to decrease. These findings are quite different from the general impression that financial restrictions reduce welfare, especially for households who have full access to both bonds and money. The reason is as follows: For households who have full access to both bonds and money, they smooth consumption mainly by adjusting bond holdings. Wi th lower degrees of home financial openness and hence fewer numbers of unconstrain-ed home households, consumption smoothing by bond trade becomes more efficient. This enhanced financial privilege then decreases welfare loss o f those remaining unconstrain-ed home households. For households who can not trade bonds, on the other hand, they smooth consumption only by adjusting money balances. Because lower degrees of home financial openness raise home money demand and the purchasing power o f home money, consumption smoothing by monetary adjustments becomes more efficient. Consequently, welfare loss of financially constrained home households also decreases. For the welfare effects associated with lower degrees of foreign financial openness the economic reasons are similar. This paper also examines monetary restrictions by further prohibiting finan-cially constrained households from monetary adjustments. It finds that not only these households experience larger welfare loss, but for households who have full access to both bonds and money welfare loss also increases. The experiment shows the importance o f money as a store of value for financially constrained households. It also shows the close interactions between different types of households under financial asymmetry. The rest of the chapter is organized as follows: Section 2.2 gives a brief description o f the model. Section 2.3 describes the solution method. Section 2.4 provides simulation results. Section 2.5 concludes. 2.2 Model In this section I briefly describe the model structure. The description focuses on the home country because of model symmetry. Readers can refer to Appendix B at the end of the dissertation for complete model equations. In each of the following subsections, I wi l l write down households, governments and firms' optimization problems first, followed by notation definitions. 26 2.2.1 Households The household structure in this model is identical to that of Chapter 1, and readers can refer to Section 1.2 for detailed model descriptions. Households earn wage income by labor supply, get equal dividends from domestic firms, pay taxes, choose consumption and money balances, and decide bond holdings i f applicable. Despite their different budget constraints, all households have the same C E S utility function that depends on consumption, labor supply and real balances. A typical household z's utility-maximization problem takes the form: M a x E,U; = E^r'V—C^ + - * - ( ^ ) ' - ' , subject to M\ + d,Ff + -erfFf = M / _ , + Ff_} + e,Ff-i +wtN\+ 77; - P,C; - Pjf - Df D , , r[c> (/<;•' Fo)\2 ' 2 P,Y, It gives first-order conditions with respect to bond holdings, money balances and labor supply as E i ^ c f - -f3^Cl+~i + T-£-(F;'-FO)\ = 0, 1 P, P,« P'V J with 0 < B < 1, cr, K, e, % > 0 and p > 1. On the other hand, a typical household / s utility-maximization problem takes the form: M a x Ep{=E^pr\—C{ " —Ni"], Ti, c r - 1 \-e Ps n Subject to Mf = Mf_, + w,Nf + 77; - PtCf - P,T/ . It gives first-order conditions with respect to money balances and labor supply as 27 £,|-^c/^-/civr ,|=o. In the above equations, the variable C, of either household / or j is a consumption index defined by 2 where 0>l; c,(z) and c,(z*) stand for consumption of output produced by the home firm z and the foreign firm z* respectively. The price index P, and consumption demand c, (z) and c,(z*) can be derived from C, such that i , i p.^pMtUz+lpXz'Vdz'y-e, i with pt(z) and pt(z*) standing for individual commodity prices. Variables F, and F* are nominal discount bonds denominated in home and foreign currencies respectively. Trading of bonds denominated in the currency of the other country is assumed to involve a small adjustment cost D,F to ensure stationarity in the foreign-asset position. For other variables, Mh N,, 17,, T, and Y, denote the money balance, labor supply, the profit transfer, the tax payment and total output of the home country. eh wt and d, denote the exchange rate, the wage rate and the bond price. In addition to bond trade, this paper also examines the case where households j and f are further prohibited from adjusting money balances. When this complete financial restriction is applied, money balances and tax payments of households j and j are set at their initial steady-state levels over time. It is assumed that the initial steady-state values o f tax payments are equal to 0 for both types of households in both countries. A typical household fs utility-maximization problem becomes: 28 M a x E,U{ = E,±/3-'[-^-cf° + - ^ - ( ^ ) ' - - ± N J / ] , subject to M Q = MQ + wtN'l +77* — P,Cf. A n d there is only one first-order condition taken with respect to labor supply as E,^cr°-KNr^=o. 2.2.2 Governments The home government sets its taxes and money supply according to the budget constraint M-M, 0 = T,+- •1-1 P, where IT ;=<+(1 -»)7;^ In this paper, economic disturbances are assumed to originate only from money markets and technology levels. Hence both home and foreign government spending are set at their initial steady-state values of 0 over time for simplicity. 2.2.3 Firms Similar to the continuum of households, firms locate on another [0, 1] interval with home firms z and foreign firms z belonging to subintervals [0, .5] and (.5, 1] respectively. Firms produce differentiated products, engage in monopolistic competition, maximize the expected present value o f profits, and transfer profits back to domestic households evenly. Following Bergin and Tchakarov (2003), it is assumed that firms' pricing decisions are subject to a quadratic adjustment cost. A typical firm z's profit-maximization problem takes the form: 29 Max E,V- =E^Bs-'nzs, subject to TI] = ps (z)ys (z) - wsNzs - D, p ys(z) = AsN;, DP_v[ps{z)-p,_x{z)f 2 P„-i(z) It gives one first-order condition with respect to pt(z) as E, jo - ^ <zye p / c ; + 0 A (z)-5-1 p°c: ^ A I A 2 A J In the above equations, pt(z), yt(z) and Nf are the price, output and labor demand of the firm z. A, is the technology level, and the quadratic adjustment cost of pricing deci-sions is defined by Df. 2.2 A Economic Uncertainty Economic disturbances in this economy are originated from money markets and technology levels. They are governed by the following money growth rules and techno-logy innovation processes: I n M , = lnM,_ , - e o ) + v, ln M * = ln M*_, + ^ (e,_1 - eo') + v* ln At = p ln A^ + w, ln A, - p ln + w* 3 where 30 In the above equations, sh st, u, and u, are independently distributed random variables from normal distribution. 2.2.5 Market-Clearing Conditions There are seven market-clearing conditions in the model: nF;=-riFf, nF'l'=-riF*'', ^Mt=nM\+{}--n)Mi, ^M]=riM\ + ( ! - „ * , . LN;=nN;+{L-n)N/, ±Nf =riN[+(\-n)Nf, c; = nc;+(±-n)c/+riq +(~ri)cf = \ ^ y t ( z ) + l - P ^ y , ( z ) = Y;. The first and second equations are bond market clearing conditions. They state that total values of international assets held by home and foreign households must sum up to zero, for both home- and foreign-currency denominated bonds. The third and fourth equations are money market clearing conditions. They are part o f the home and foreign government budget constraints and must hold all the time. The fifth and sixth equations are labor market clearing conditions. Because in the model labor is assumed to be internationally immobile, total labor demand must equal total labor supply within each country. The last equation is the goods market clearing condition, that aggregate demand of household consumption C,v must equal aggregate output of the global economy Y,w. 31 2.3 Solution Method After solving households' and firms' optimization problems, all optimal conditions are approximated by second-order Taylor expansion around a specific initial steady state. It is assumed that in this steady state all prices are equal when evaluated in the same currency. It is also assumed that in this steady state home and foreign bond holdings, tax payments and government spending are equal to 0, and technology levels are equal to 1. Different from standard first-order log linearization, second-order approximation captures welfare effects of economic uncertainty from not only the second moments but also the first moments of economic variables. It permits more accurate welfare evaluation and is suggested by many economists when analyzing welfare. To better understand the importance of second-order approximation, an example of a closed and static economy is provided below. Let C, P, N, M, Af, y, p, and w stand for the consumption index, the price index, labor supply, money demand, money endowment, output, the output price, and the wage rate respectively. And suppose households' and firms'optimization problems are Max EU = E[-l—C1-°+ln(—)-bN], 1 — a P subjectto M = Me + wN + 77 - PC, and Max K7I = E\py-wN], subjectto y = (^)~eC, with first-order Conditions of consumption, labor and the price derived as M = PCa, w = bPC, 9 E[wC] P~0-\ EC Assume further that the parameter a equals 1 and the variable M follows log-normal distribution. Then the above first-order conditions imply 32 1 = ^ - e x p - , [ £ c + i ] e x p [ 2 £ c +2a2c], tf — i , 2. . with Ec and ac standing for the mean and the standard error of consumption. According to the first-order condition of consumption, the variance pf consumption is affected by the variance of money demand. Moreover, the last equation shows that the mean of consumption is decided once the variance of consumption is given. Hence any disturbance in the money market not only directly changes the variance but also indi-rectly changes the mean of consumption. If these first-order conditions are first-order approximated, the above effects of economy uncertainty through the first moments of economic variables w i l l lose. Consequently, welfare evaluation wi l l bias. Numerical results of the model are generated by Matlab simulation. For the degrees of financial asymmetry, related literature provides a wide range of estimates for n and ri. Campbell and Mankiw (1989) test the permanent income hypothesis, and suggest about 50 percent of total income consumed by current-income consumers. Jappelli and Pagano (1989) document substantial deviations in the extent of financial asymmetry from cross-country comparisons. Their estimates range from .1 to .7 for seven developed countries including the United Kingdoms, the United States and Japan. In this paper, welfare is evaluated using several sets o f n-n combinations to examine how financial asymmetry affects welfare. Other parameters used by Matlab are as follows: The elasticity of consumption demand 0 is set to 11 to reproduce a wage-price markup o f 10 percent. It is consistent with findings of Basu and Fernald (1997) and Burnside, Eichenbaum and Rebelo (1995). The elasticity of labor supply \/(ju - 1) is set to 1 following Betts and Devereux (2000a, 2000b) and Christiano, Eichenbaum and Evans (1997), which gives /u. a value of 2. The interest elasticity and consumption elasticity of money demand are 1/e and Mae respec-tively. According to Bergin and Feenstra (2001) and Mankiw and Summers (1986), the former is about .25 and the latter is very close to 1. Therefore e is set to 4 and a is set to .25. The discount factor R is set to .96 by interpreting a period in the model as one year. Finally, monetary random processes s, and s* are assumed to follow normal distribution of mean 0 and standard deviation .03 with the degree of persistence X set to .99; technology random processes u, and u* are assumed to follow normal distribution of 33 mean 0 and standard deviation .01 with the degree of persistence p set to .9. These random processes are assumed to be uncorrelated with each other for simplicity. 2.4 Simulation Result 2.4.1 Welfare Measures The welfare measure adopted in this paper follows Bergin and Tchakarov (2003). First compute unconditional expectation of utility under economic disturbances for the type of households we want to examine. Then calculate how much consumption in the initial steady state this type of households is wi l l ing to give up to negate effects o f economic uncertainty. In other words, find out how much consumption deduction in the initial steady state gives this type of households the same expected utility as that under economic disturbances. This consumption cost is the welfare measure. Because the objective of this paper is to examine how financial asymmetry affects welfare, the above welfare measure is evaluated using several sets o f n-n combinations, as summarized in the next section. They help us to compare welfare loss across various degrees of financial openness for different types o f households. To derive the welfare measure, apply second-order Taylor expansion and uncon-ditional expectation on the utility function to get <T-1 -i G-\ E U, =Uo+ C V ~ £ ( & , ) C ^ F ( & , ) - /cNoE(W,).--(//-\)N~*V{%,), 2cr 2 where Co fr = N.z"° No Let If" and If denote shifts o f initial steady-state consumption that delivers the same expected utility, associated with the mean and variance parts respectively. Then it must hold that 34 cr-1 o-I U[(l + Um)Co,N0] = — [Q + Um)C0]° --No =Uo+ £ (& , ) - K N O E (W , ) , cr-1 CTM L/[(l + f / v ) C o , A r o ] = — [(l + f / v ) C o ] CT —No cr-1 // = UQ C 0 - V(%,)--(Ju-l)NoV(Nl). 2a 2 Solving the above equations gives us formulas of welfare measures If and If. It also gives us a formula of the welfare measure If, defined as the sum of If and If to capture total welfare effects of economic uncertainty. The formulas of If and If are cr U " ' = | l + ^ [ £ ( & 0 - * C o a NoE(N,)]^-\, a . c / v = j i - ^ [ ^ K ( & o + * ^ According to the formulas, welfare depends on means and variances of consump-tion and labor supply rates of changes. Take derivatives on the formulas with respect to the means and variances, we obtain the following equations: • ' _!_ fjjjm [ rr— \ 1 cr-1 JL -^^=\\+—[E(E,)-KCI° NoE{N,y}\ ={\ + UN'Y, [2.1] i dU"' L c r -1 °-i I _ 1 _ • a-\ _ i „_j dE(W,) = -fcC'0 ° No\\ + [ £ ( & , ) -KC ~ q ° NoE(W,)]\ dUv 1 , o - - l r l = -KC0° No{\ + Umy, [2.2] i l - ^ [ - F ( & , ) + / c ( / y - l ) C o - 7VoF(^,)] j (1 + C T ) * , - [2-3] dV$,) 2a\ 2a a 1 2a dUv 1 , . --—TT/< L ( T - 1 J = - - / r ( / / - l ) C o - Nl\\-^-—\-V$,)+K{p.-\)C, ° NoV{N,y] i CT-l 2 [ 2a a 35 I = ~KiM-iycl" No(\ + Uvy. [2.4] Because values of (1 + If") and (1 + If) are generally positive, Equation 2.1 and Equation 2.2 imply that If is positively correlated to the mean of the consumption rate of changes but negatively correlated to the mean of the labor supply rate o f changes. Moreover, Equation 2.3 and Equation 2.4 imply that If is negatively correlated to the variance of both consumption and labor supply rates of changes. 2.4.2 Welfare Evaluation Table 2.1 and Table 2.2 summarize welfare results using two sets of n-ri combi-nations. In Table 2.1, first it is assumed that there is no financial asymmetry in the home country by setting n to .5. Then it is assumed that only half of home households are able to smooth consumption through bond trade by setting n to .25. Finally, it is assumed that the proportion of home households with unrestricted financial access is reduced to n equaling .05. The degree of foreign financial openness is changed gradually in each case to generate welfare results for home households. Table 2.2 examines the opposite scena-rio, where n is fixed at .5, .25 and .05 while the degree of home financial openness is changed gradually in each case to generate welfare results for home households. Because economic reasons of welfare results for foreign households are similar to those for home households, the welfare analyses focus on home households only. According to Table 2.1, overall welfare loss If o f households i increases with lower degrees of foreign financial openness for n equaling either .5, .25 or .05, while overall welfare loss If o f households j decreases with lower degrees of foreign financial open-ness for n equaling either .25 or .05. The opposite welfare results for different types o f households are due to their different ways of consumption smoothing and the imperfect structures of financial markets. For households i, they have full access to both bond and money markets. When economic disturbances occur, they smooth consumption mainly by adjusting bond holdings through the international bond market. Hence the efficiency o f the international bond market is critical for them to hedge against risk. If the foreign country is more financially constrained in that less foreign households are allowed to trade bonds, consumption smoothing of households / wi l l be less efficient. Consequently, 36 the larger consumption and labor variances as well as the higher associated welfare loss of households /' result. For households j, however, the story is different. Given their financial limitation, the efficiency of the international bond market is minor for them to hedge against risk. Households j smooth consumption only by adjusting money balances, and hence any factor that affects the purchasing power of money wi l l directly affect their welfare. Take an expansionary home monetary disturbance for example, this type of economic uncer-tainty induces home households to save for the future. If the international bond market is more restricted due to lower degrees of foreign financial openness, the importance of home money wi l l increase. Home households wi l l tend to save by holding more money, which causes home money demand to rise. The higher home money demand stabilizes exchange rate depreciation, raises the purchasing power of home money, and in turns makes home money a better financial instrument for value storing. Consequently, the variances of consumption and labor supply as well as the associated welfare loss of households j decrease. In fact, even with other types of economic disturbances, lower degrees of foreign financial openness also reduce welfare loss of households j. The key reason is the more favorable financial environment created for this type of households, by raising the importance o f home money in consumption smoothing. Table 2.2 provides more welfare results that are consistent with the above argu-ments. In this table, overall welfare loss If o f both households / and j decreases with lower degrees of home financial openness for ri equaling either .5, .25 or .05. Recall that in this paper the degree of financial openness is defined as how many households who have full access to the bond market, rather than how severe financial restrictions are homogeneously imposed on every household. Therefore, although the welfare results of households /' may seem to be quite different from the general impression that financial restrictions reduce welfare, they have their economic reasons. Note that households / are those who have been endowed with the privilege of unrestricted financial access. Given the degree of foreign financial openness, lowering degrees of home financial openness only reduces the number of this type o f households. The financial privilege of the remain-ing households / is not only unchanged, but also enhanced due to the increasing pricing advantage over the international bond market. Consequently, welfare loss of the remain-37 ing households / decreases because of more efficient consumption smoothing. This argu-ment is justified by comparing welfare loss of households / across different degrees of foreign financial openness. A s ri changes from .5 to .25, for example, the same degree of home financial openness corresponds to larger welfare loss of households /'. It is because fewer foreign households of unrestricted financial access imply that the financial advan-tage of households / is relatively more limited. Only more restricted access to the bond market imposed on the home country, namely lower n, can regain the financial advantage for the remaining households / and reduce their welfare loss. For households j, the economic reasons are more straightforward. Lower degrees of home financial openness reduce their welfare loss by altering home money demand in a way similar to the case of lower degrees of foreign financial openness. Again take an expansionary home monetary disturbance for example. Lower degrees of home financial openness imply that more home households need to smooth consumption by holding money. The higher home money demand stabilizes exchange rate depreciation, raises the purchasing power of home money, and makes home money a better financial instrument for value storing. Consequently, the variances of consumption and labor supply as well as the associated welfare loss o f households j decrease. Lowering the degree of home financial openness seems to be welfare improving for both types of home households, but in fact the home government w i l l not use it as its welfare policy. The extreme case where welfare loss of both types o f home households is minimized by turning the home country into a closed economy w i l l not happen in this model. The reason is that lowering the degree of home financial openness creates more financially constrained home households. These households are worse off compared to when they are still financially unconstrained. Moreover, overall welfare loss increases with lower degrees of home financial openness. Hence the home government w i l l choose to maintain the openness o f the home country. 2.4.3 Sensitivity Analyses Table 2.3, Table 2.4 and Table 2.5 provide three sets of sensitivity analyses for the welfare results summarized in Table 2.1. In these tables n is fixed at .5, .25 and .05 with the degree of foreign financial openness being changed gradually. Table 2.3 decreases the 38 coefficient of the adjustment cost in firms' pricing decisions, Table 2.4 increases the elas-ticity of consumption demand, and Table 2.5 increases the elasticity of labor supply. The opposite scenario o f fixing ri at .5, .25 and .05 while changing the degree of home finan-cial openness are excluded. The function o f the pricing adjustment cost implies that firms tend to set higher prices on average. It is because a higher current price means that any adjustment in the future is a smaller percentage change. When the cost coefficient is reduced, firms' reac-tions to economic disturbances become more efficient and hence the overall price level decreases. Compared to Table 2.1, the welfare loss of both types of households is lower given the smaller cost coefficient, and the magnitude of welfare adjustments is larger for households j than that for households i. The reason behind the larger welfare adjustment of households j is that, this type of households only use money to smooth consumption and effects crucially depend on its real value. Because the lower price level raises the real value of home money, welfare loss of both types of home households decreases but more obviously for households / . The welfare results summarized in Table 2.4 and Table 2.5 are more intuitive. High-er elasticity of consumption demand permits higher flexibility in consumption decisions and hence lower volatility of composite consumption levels. Lower elasticity of labor supply causes lower flexibility in working decisions and hence lower volatility of labor supply levels. They both reduce overall welfare loss of households /' and households j compared to Table 2.1. 2.4.4 Monetary Restrictions In previous sections we have discussed welfare effects under different degrees of financial openness and parameter values. A l l the welfare analyses so far are based on the assumption that all households can hold and adjust money, although not all of them can trade bonds. It is found that when monetary adjustments are allowed between different types of households, the efficiency of using money to smooth consumption is critical to affect welfare of households j. Although welfare results can be changed by many factors, basically the main reason is that these factors alter this efficiency in some way. 39 ^ A n interesting question then rises: What happens i f monetary adjustments are shut down between different types of households? Note that money can serve as an alternative of bonds to smooth consumption only because the government allows it to adjust between different types of households. If monetary adjustments are prohibited, then financially constrained households wi l l have no way to smooth consumption upon economic distur-bances. Table 2.6 summarizes related welfare results by assuming that money balances of households j and households f are fixed at their initial steady-state levels over time. In this economy, financially constrained households can not smooth consumption by either bonds or money. The variances o f their consumption and labor supply inevitably increase, and their welfare loss is much higher compared to Table 2.1. For households /', although they still can smooth consumption by bond trade, they now embrace all the direct effects of monetary uncertainty. When the number of house-holds j increases as the degree of home financial openness decreases, households /' face increasing impacts from monetary disturbances. It is interesting to find that the variances of their consumption and labor supply also increase, and their welfare loss is also much higher compared to Table 2.1. The above findings not only show the importance of money as a store o f value for financially constrained households. They also show the close interactions between diffe-rent types of households under financial asymmetry. Hence welfare policies can not just consider different households separately, but must take into account these welfare inter-actions in order to obtain optimal welfare results. 2.5 Conclusion In this paper, a two-country sticky-price general equilibrium model is developed to examine welfare effects of economic uncertainty under financial asymmetry. The finan-cial asymmetry is defined as two .groups of households with different levels of financial privileges: One group is allowed to trade bonds and adjust money freely, while the other is prohibited from bond trade even with domestic households. This paper finds that the financial asymmetry alters households' economic behaviors, and changes the general impression that financial restrictions reduce welfare. According to the simulation results, 40 welfare loss of financially unconstrained households increases but welfare loss of finan-cially constrained households decreases with lower degrees o f foreign financial openness. Moreover, welfare loss of both types of households decreases with lower degrees o f home financial openness. The underlying reason is that the financial restrictions assumed in this model are not homogeneously imposed on every household. A n d hence when the degree of financial openness is changed, the financial asymmetry creates externalities between households that alter their welfare. The close interactions between different types of households can also be shown by examining monetary restrictions. If financially constrained households are further prohibited from monetary adjustments, not only their welfare loss w i l l increase but welfare loss o f financially unconstrained households w i l l also increase. The welfare effects of financial asymmetry studied in this paper can be used for policy analyses in future research. Because different types of households have different ways of consumption smoothing, they react differently upon economic disturbances and also interact closely with each other. These facts imply sophisticated welfare tradeoffs between different types of home households as well as households in different countries. They raise new considerations when we study domestic welfare policies and international macroeconomic coordination. 41 Chapter 3 Financial Asymmetry and Different Exchange-Rate Regimes 3.1 Introduction Exchange rate variability is an important feature of the real world, and also a major field of economics research. One reason for this issue to draw such high attention is that, exchange rate variability is believed closely relating to reduced gains from trade and hence welfare. Mundell (1968) suggests that an optimal exchange rate policy should be decided by cost-benefit analyses: On the one hand flexible exchange rates permit efficient economic adjustments, but on the Other hand they may also lower welfare because of their associated uncertainty. Based on Mundell 's theory, currency areas or free-trade areas and various exchange rate regulations have been designed trying to increase welfare by reducing exchange rate risk. One famous example is the European Union, which inte-grates 25 independent countries to enhance political, social as well as economic coope-ration. Mundell 's theory provides a theoretical guideline for exchange rate policies, and also serves as a theoretical support for exchange rate controls. Nonetheless, practically speaking precise cost-benefit analyses are difficult. This fact causes disputes on whether and how exchange rate regulations should perform to increase welfare. It also induces reconsiderations on whether currency areas are necessary to exist. In particular, many economists suggest that welfare loss associated with economic variability is not signi-ficant. A n d hence governments should adopt flexible exchange rates to permit efficient economic adjustments. For the most classical example, Lucas (1987) evaluates welfare as changes of steady-state consumption required to achieve the same expected utility. He shows that economic variability implied by business cycles tends to have small welfare effects. 42 More recently, Bergin and Tchakarov (2003) apply second-order approximation on a two-country sticky-price general equilibrium model to examine welfare under monetary and technology shocks. A s pointed out in Section 2.1, they find that welfare effects of economic variability are likely to be small for a wide range o f cases. But when house-holds exhibit habit persistence or when there is an international market for bonds in the currency of only one of the two countries, welfare loss of economic variability increases. The findings of Bergin and Tchakarov (2003) imply that different types of financial asymmetry may play important roles in directing welfare results, and hence in affecting optimal exchange rate policies. Lahir i , Singh and Vegh provide two related studies that analyze the issue of optimal exchange rate policies under financial asymmetry. Lahiri , Singh and Vegh (2004a) find that i f only some agents can participate in the financial market and there is no price rigi-dity, flexible exchange rates are optimal under monetary shocks and fixed exchange fates are optimal under real shocks. Because this result is opposite to the standard Mundellian prescription, the paper suggests that optimal exchange rate policies may depend on types of shocks as well as types of frictions. Moreover, Lahir i , Singh and Vegh (2004b) find that in a small open economy without price rigidity, policies targeting monetary aggre-gates welfare-dominate policies targeting the exchange rate. The paper thus suggests that fixed exchange rates are never optimal, and tends to support monetary policies imple-menting flexible exchange rates. In contrast to the above two studies, this chapter examines optimal exchange rate policies under financial asymmetry with price rigidity. The model is built on the basic framework of new open economy macroeconomics introduced by Obstfeld and Rogoff. Similar to Chapter 1 and Chapter 2, the paper models financial asymmetry by dividing home and foreign households into two groups: One group has full access to both bond and money markets, while the other is prohibited from bond trade and monetary adjust-ments. Changing the lengths for different types o f households along the continuum of interval then allows us to examine welfare under different degrees of home and foreign financial openness. The welfare measure adopted in this paper follows Devereux and Engel (2003) and Obstfeld and Rogoff (1995, 1996), defined as expected utility excluding the term asso-43 ciated w i t h real balances. It is assumed that i n the f lex ib le exchange-rate regime, both home and foreign governments fix their money supply at in i t i a l steady-state levels , w h i l e a l l o w i n g the exchange rate to m o v e freely. O n the other hand, i n the fixed exchange-rate regime, it is assumed that the home and foreign governments coordinate their monetary po l ic ies to mainta in the exchange rate l eve l . G i v e n country-specif ic r andom processes o f technology levels and one-period-in-advance pr ice r ig id i ty , this paper finds that fixed exchange rates are i n many cases preferable to f lex ib le exchange rates by a l l types o f households under f inancial asymmetry. In the fixed exchange-rate regime, a l l the changes o f money supply go to f inancia l ly unconstrained households. Hence for these households i f their number is relat ively smal l compared to the magnitude o f money supply changes, then the weal th effects associated w i t h the monetary po l ic ies that a i m to main ta in the exchange rate level can dominate the welfare cost o f fixed exchange rates. F o r financially constrained households, they can not enjoy the benefit brought by expenditure swi tch ing effects due to their financial restr ict ion, but need to bear the associated cost o f higher economic var iab i l i ty . Therefore b y reducing the expenditure swi tch ing effects, the fixed exchange rate regime can increase their welfare. The rest o f the chapter is organized as fo l l ows : Sec t ion 3.2 gives a b r i e f descr ipt ion o f the m o d e l . Sect ion 3.3 describes the solut ion method. Sect ion 3.4 p rovides welfare results. Sec t ion 3.5 concludes. 3.2 Model In this section I br ief ly describe the mode l structure. The descr ipt ion focuses o n the home country because o f mode l symmetry . Readers can refer to A p p e n d i x C at the end o f the dissertation for complete mode l equations. In each o f the f o l l o w i n g subsections, I w i l l wr i te d o w n households, governments and f i rms ' op t imiza t ion problems first, fo l lowed by notation defini t ions. 3.2.1 Households The household sector i n this mode l is s imi la r to those o f Chapter 1 and Chapter 2, and readers can refer to Sect ion 1.2 or Sect ion 2.2 for detailed mode l descriptions. The 44 only difference is that in addition to bond trade, households j and j* are also prohibited from adjusting money balances. Their money balances and tax payments are set at initial steady-state levels over time. It is assumed that the initial steady-state values of tax payments are equal to 0 for both types of households in both countries. The reason of controlling money balances of households j and j* is to clearly define them as liquidity constrained households. If this monetary restriction does not hold, there will be monetary adjustments between different types of households over time. The resulting effects of wealth redistribution are likely to be of second-order importance for the purpose of this paper, and ruling them out simplifies equilibrium derivation and welfare analyses. Households earn wage income by labor supply, get equal dividends from domestic firms, pay taxes, choose consumption and money balances, and decide bond holdings if applicable. For those households who have full financial access, there are complete bond markets and hence they trade state-contingent nominal bonds. It is assumed that these bonds are denominated in the home currency. Despite their different budget constraints, all households have the same C E S utility function that depends on consumption, labor supply and real balances. A typical household fs utility-maximization problem takes the form: Max E,U; =Elftp-t[-?-cf^ + -*-A'- - - A ^ L c r - l \-e Ps fi bjectto M ; + £ d{xt+,,xt)F\xM) = M:_x+F\xt) + w!N:+nl-PlCi-PlTl' su [3.1] It gives first-order conditions with respect to bond holdings, money balances and labor supply as d(xl+],x,)±q° = q { X i ^ X i ) p ± - C l + ^ , [3.2] i ^ = r n ' c ; » Di+1=/3-L-LTS [3.3] ' p (-•• a 1 - - — N;=(-^c;~°y-\ [3.4] K P 45 with0< 6 <],a,K,£,x>0,p>\, and E,D,+\ the inverse o f the gross nominal interest rate. On the other hand, a typical household fs utility-maximization problem takes the form: 00 - cr_1 v MJ % tN1s Max E,U, t l cr-1 \-£ Ps M subject to Ml = Mi + w,N/ + nzh, - PtC{. [3.5] It gives first-order conditions with respect to labor supply as 1 - - — i V / = ( - ^ C / " - r L l . [3.6] Recall that households j are prohibited from adjusting money balances, and hence their money balances and tax payments are set at initial steady-state levels over time with the latter equal to 0. In the above equations, the variable C, o f either household / or j is a consumption index defined by a geometric average of home and foreign consumption cyn cfm m {i — m) where m stands for the size o f the home country. Note that the home and foreign coun-tries have the same sizes that sum up to 1, and hence m is set to .5 in this paper. Variables . Cht and Cft are indexes over consumption of output produced in the home and foreign countries respectively, defined by _I ' — _L Chl=[m~>[ ch,(z)"dzY;\ , [3.8] « j _ i d j_ C , = [ ( l - m K lcfl{z) " dz'Y~x, [3.9] with X > 1. According to these consumption indexes, the elasticity of consumption substi-tution between goods produced within a country is X, while the elasticity o f consumption substitution between the home and foreign goods indexes is 1. The price index P, in the above equations is defined by p,=p:p;m, [3.io] 46 where m again stands for the size of the home country. Variables Pht and Pf, are price indexes of home and foreign output respectively, defined by 1 phl=[-[ph,(zt*dzrA, [3.ii] m i Pfl=[z-]—(Pfl^y~Adz'Y-". [3.12] 1 - m A" 1 The consumption and price indexes characterize the following consumption decisions, which are useful when we derive other equilibrium conditions: chl(z) = ^ -[P^-rChl, [3.13] m Ph, . 1 p„(z ) . cfl(z)=- P ^ r ' C , , [3.H] l-m Pft . • PhlChl = l'phl(z)ch,(z)dz = mP,C,, [3.15] PflCft = lpfl(z)cfl(z)dz =(\-m)PlCl. [3.16] In this paper there are complete bond markets, and hence households who have full financial access trade home-currency denominated state-contingent nominal bonds F(x), with any state realization x belonging to the state space X. The variable d(x,+\, x,) is the price o f the bond in the next period when x,+\ is realized, given the current state x,. A n d the variable q(x,+l, xt) is the probability of x , + ) to be realized in the next period, condi-tional on the current state x,. Chari, Kehoe and McGrattan (1997) show that complete bond markets imply the condition of complete risk sharing e p" c -1 -V- = r0(-^r)CT, [3.17] where the variable e, is the price o f the foreign currency in terms o f the home currency, and r0 is a constant depending on initial conditions/Assume that in the initial steady state the home and foreign countries are symmetric in every aspect, such that consumption is equal, purchasing power parity holds, and r 0 is equal to 1. Then under producer-currency pricing as purchasing power parity holds in all following periods after the initial steady state, the condition of complete risk sharing further implies 47 c;=c;. Note that i f firms are subject to producer-currency pricing, then consumption risk is completely shared due to the law of one price among financially unconstrained house-holds, even i f bond markets are not complete. But i f firms are subject to local-currency pricing, then the existence of complete bond markets becomes necessary for complete risk sharing to hold among financially unconstrained households. Hence the assumption of complete bond markets allows us to have perfect capital mobility in both cases, while simplifying equilibrium derivation and welfare analyses by ruling out dynamic effects of wealth redistribution, which are likely to be of second-order importance. For other variables, Mh N,, TIht and T, denote the money balance, labor supply, the profit transfer and the tax payment of the home country, w, denotes the wage rate. 3.2.2 Governments The home government sets its taxes and money supply according to the budget constraint M-M, , 0 = T+-P, where | M , = « M ; + < I - n ) M ; , In this paper, economic disturbances are assumed to originate from technology levels only. Hence both home and foreign government spending are set at their initial steady-state values of 0 over time for simplicity. 3.2.3 Firms Similar to the continuum of households, firms locate on another [0, 1 ] interval with home firms z and foreign firms z* belonging to subintervals [0, .5] and (.5, 1] respectively. Firms produce differentiated products, engage in monopolistic competition, maximize the 48 expected present value of profits, and transfer profits back to domestic households evenly. It is assumed that firms' pricing decisions are subject to one-period-in-advance rigidity, and hence prices are set before information of random technology levels is released. A typical firm z faces consumption demand on its product from two types of house-holds and two countries. Assume producer-currency pricing and let yh?(z) denote total consumption demand, using Equation 3.13, Equation 3.15 and their foreign equivalents it can be derived that yt,(*) = <(*) + (\~"K(z) + nci(z) + ( ! - „ * )c{ (z) • m Pln 2 2 = jT [nC, + (1 - n)Cf + n C] +(-\-n )Cf ]. "hi "hi . ^ Let phr(z), yhi(z) and N/,,2 represent the price, output and labor demand levels of the firm, and let D, and A, represent the discount factor and random technology level in the home country. Then the firm's profit-maximization problem takes the form: M a x E,_^,=E,_,D,nl, subject to 77;, = phl (z)yhl (z) - w,Nzhl, ( yhl(z) = yi{z) = ^ [ ^ Y x [ n C : + { \ - n ) C ! + n C i + (-L«*)Cf ], • "hi "hi ^ 2 yhl(z) = A,N:hl, which gives one first-order condition with respect to pht(z) as „ \wir ,\ .Cf . cf A . . C / ' , i -E, A-L[n + {--n)-J- + n - L - + ( - - n )- L -]C, ' CT x 14 2 c ; c ; v 2 • c; ' P M = -T7 V - • , A [3-18] The foreign price of the firm's output is affected by the exchange rate. Under producer-currency pricing the law of one price always holds and hence we have 49 K(*) = ^ ' . . [3-19] 3.2.4 Market-Clearing Conditions There are six market-clearing conditions in the model, i f we first exclude bond markets from the discussion: ±M-(±-n)Mi=nM',, [3.20] I M ; )Mf = n M \ , [3.21] \K=rN[+(\-n)Nj, [3.22] ±Nz'=riNl +{±-ri)Nf , [3.23] CI =nCht +{^-n)Ci + „*c£ +(~ri)C{, = i £ ^ £ l ^ ( z ) = y-, [3.24] C;=nC^+(±-n)Cji+riC^ + ( | - » * ) C j f = l ^ i ^ ( z * ) = y;. [3.25] The first and second equations are money market clearing conditions. They are part o f the home and foreign government budget constraints and must hold all the time. Because households j are prohibited from monetary adjustments, total money demand of house-holds / must equal total money supply of the home country minus total initial steady-state money balances of households j. Similarly, total money demand of households /* must equal total money supply of the foreign country minus total initial steady-state money * balances of households j . The third and forth equations are labor market clearing condi-tions. Because in the model labor is assumed to be internationally immobile, total labor demand must equal total labor supply within each country. The fifth and last equations are goods market clearing condition. Aggregate demand of household consumption C V and Cfl must equal aggregate output of the global economy Yh7 and YjT for home and foreign goods respectively. 50 For bond market clearing conditions, recall that there are complete bond markets and hence the number of equations depend on the size of the state space. Assume a finite number of state realizations, and then the set of bond market clearing conditions can be characterized as nF'(xl+]) = -nFr(xl+1) V x , + 1 e X . [3.26] It states that total values of state-contingent nominal bonds held by home and foreign households must sum up to zero when evaluated in the home currency. 3.2.5 Model Equilibrium To establish the system of equilibrium conditions, we first need to combine Equa-tion 3.5, Equation 3.15 and Equation 3.24. Equation 3.15 and Equation 3.24 imply that yhl(z) = 2 - k - [ < , +{\-n)Ci ^n-G^(-\-n)Ci ] phM) 2 2 • PL-^[nC;+(-\-n)C/ + nC; +(I-n*)C/.], PM  2 2 which together with Equation 3.5 gives us A = ^P-4~ i 7T 1 l<+4- '»)C/'+» C f +(I-„*)C I /]. [3.27] 4, phl(z) 2 2 We then need to combine Equation 3.22, Equation 3.15 and Equation 3.24, which give us nN!+(--n)Nf =-N* • ' 2 2 . 2 4 = ^-^-[nCt+(-\-n)Cl'+nC; + ( ! - „ * ) C / ' ] . [3.28] 2A ph,(z) 2 2 Also note that because all firms are identical within each country, Equation 3.11 and its foreign equivalent imply that / U z ) = / ; -PM = P*-51 Given exogenous values of M\,Mf,M\ andM^ , and properly defined random processes governing A, and A,*, we now have 17 functions depending on the state reali-zation: C ; , Cf, C\ , Cf', N;, Nf, N[, Nf' , Ph,, Pfu, Pft, Pft, Pt, Pf, w,, w, and et, determined by the 17 equilibrium conditions: Equations 2.3, 2.4, 2.6, 2.10, 2.18, 2.19, 2.27, 2.28 and their foreign equivalents, and Equation 2.17. 3.3 Solution Method Among the equilibrium conditions summarized in the previous section, the only dynamic component is the inverse of the gross nominal interest rate E,D,+\. Devereux and Engel (2003) show that, as long as log of nominal money supply in each country follows a random walk (with drift), this term is constant. Hence the solution of the model may be obtained by solving the equations for each period in isolation. The same assumption is made in the current analysis. In other words, for any economic agent the optimization problem is identical in every period although the model itself is infinite-horizon. We only need to take one representative period and calculate the solution of the system as i f in a static model. Numerical results of the model are computed by Matlab command fsolve, which solves nonlinear equations using a least-squares method given a particular starting point. For the system of equilibrium conditions in this paper, I define the starting point as a specific initial steady state where the home and foreign countries are symmetric in every aspect. It is assumed that in this steady state all prices are equal when evaluated in the same currency, and all types of households have the same money balances when evalu-ated in the same currency. It is also assumed that in this steady state home and foreign bond holdings, tax payments and government spending are equal to 0, and technology levels are equal to 1. For the random processes governing A, and A,*, assume that these technology levels are independently and identically distributed random variables following Bernoulli distri-bution. In each period, the home technology level takes one o f the two values: H for (1 + a)A0 and L for (1 - a)A0 with equal probability, where the constant A0 is its initial steady-state value and the coefficient a is between 0 and 1. The probability definition for the 52 foreign technology level is analogous, and these random processes imply that there are four states in this economy. The state space X hence consists of four elements each with probability .25: HH, HL, LH and LL, where the first and second letters o f each element denote values of the home and foreign technology levels respectively. For the values of M , ' , M ^ , A/,' a n d M „ , recall that households j and / are prohibited from adjusting money balances, and hence their money balances are always set at initial steady-state levels. On the other hand, money balances of households / and /* are directly determined by governments' decisions on money supply. When considering the flexible exchange-rate regime, I assume both home and foreign governments fix their money supply at initial steady-state levels, while allowing the exchange rate to move freely. This implies that money balances of households / and /"* are fixed at their initial steady-state levels as well . When considering the fixed exchange-rate regime, I assume the home and foreign governments coordinate their monetary policies to maintain the exchange rate level. Specifically they adjust their money supply with equal absolute amounts to stabi-lize the exchange rate, and then money balances of households / and i* are determined accordingly. This setting is natural given the symmetry of the two countries, and it allows us to understand the resulting welfare effects more clearly by simplifying underlying driving forces. , Other parameters used by Matlab are as follows: The elasticity of consumption ' substitution X is set to 11 to reproduce a wage-price markup of 10 percent. It is consistent with findings of Basu and Fernald (1997) and Burnside, Eichenbaum and Rebelo (1995). The elasticity of labor supply l/(u - 1) is set to 1 following Betts and Devereux (2000a, 2000b) and Christiano, Eichenbaum and Evans (1997), which gives pi a value of 2. The interest elasticity and consumption elasticity of money demand are lie and 1/tre respec-tively. According to Bergin and Feenstra (2001) and Mankiw and Summers (1986), the former is about .25 and the latter is very close to 1. Therefore e is set to 4 and a is set to .25. Finally, the inverse of the gross nominal interest rate EtD,+\ is set to .96, and the coefficient of technology random processes a is set to .05. The purpose of this paper is to examine welfare effects of different exchange-rate regimes under financial asymmetry. Hence for each exchange-rate regime, numerical results of consumption and labor supply are used to calculate expected utility under a full 53 set of n-ri combinations. Because utility associated with real balances is likely to be of minor importance, this term is excluded from calculation following Devereux and Engel (2003) and Obstfeld and Rogoff (1995, 1998). The formula of expected utility can be represented as — F II =—— F C a - - F NM c r - l fj. 3.4 Welfare Result Table 3.1 to Table 3.4 summarize welfare results using a full set o f n-ri combi-nations for households i,j, i* and j* respectively. In each table, the first number from each pair of welfare data is expected utility for the particular type of households under the flexible exchange-rate regime, while the second number is expected utility for the parti-cular type of households under the fixed exchange-rate regime, given the particular n-ri combination. Different n and ri represent different degrees of financial openness for the home and foreign countries respectively. When (n, ri) equals (.5, .5), there is no house-hold j and j* in the economy and hence the financial market is perfect. When n or ri gets smaller, the number of households./ or i decreases and the economy is of a lower degree o f financial openness. Upon country-specific real shocks, relative price levels between different countries need to adjust in order to bring real exchange rates to their equilibriums. A s a leading study in the case for flexible nominal exchange rates, Friedman (1953) points out that whether flexible nominal exchange rates are preferred at the presence of country-specific real shocks depends on the efficiency o f nominal price adjustments. If nominal prices are as flexible as nominal exchange rates, relative price levels between different countries can react to country-specific real shocks quickly through nominal price adjustments. Consequently the importance of nominal exchange-rate flexibility is reduced. Nonethe-less, nominal prices are usually sticky in the real world due to various types of adminis-trative actions of firms and governments. It usually takes a period of time with the cost of employment distortions before nominal prices can adjust properly. Hence flexible nomi-54 nal exchange rates are in many cases preferable to fixed nominal exchange rates to permit instant adjustments of relative price levels. The argument of Friedman (1953) is consistent with the findings of Devereux and Engel (2003). Devereux and Engel (2003) examine optimal monetary policies with one-period-in-advance price rigidity, for two different types o f pricing assumptions. They show that when firms are subject to producer-currency pricing, which is the one discuss-ed by Friedman (1953), the optimal monetary policy is one employing flexible nominal exchange rates. Wi th nominal exchange-rate flexibility, the optimal monetary policy even can replicate the equilibrium o f the economy as i f nominal prices are fully flexible. On the other hand, when firms are subject to local-currency pricing, there is no advantage to employ flexible nominal exchange rates because all nominal prices are set in consumers' currencies. Nominal exchange-rate flexibility only brings the cost of welfare loss from exchange rate risk, and hence the optimal monetary policy is one employing fixed nomi-nal exchange rates. This paper introduces another situation where fixed nominal exchange rates are preferable to flexible nominal exchange rates. Different from the argument of Friedman (1953), however, it suggests that the optimal choice of exchange-rate regimes depends on not only the efficiency o f nominal price adjustments, but also on financial structures of the economy. Go back to the welfare results summarized in Table 3.1 to Table 3.4. Note that under financial asymmetry, fixed nominal exchange rates are in many cases prefer-able to flexible nominal exchange rates by all types of households. A l so note that the welfare results are generally non-monotonic, which may be attributed to the absence o f real balances from the calculation of expected utility. When (n, ri) equals (.5, .5), the financial market is perfect. We get an ordinary economy with homogeneous households having full access to both bond and money markets. Given the country-specific technology random processes and one-period-in-advance price rigidity, the argument of Friedman (1953) applies: We need flexible nomi-nal exchange rates as substitutes for sticky nominal prices to permit instant adjustments of relative price levels. The welfare results show consistency that the values o f expected utility of households /' and /* are higher in the flexible exchange-rate regime than in the fixed exchange-rate regime when («, ri) equals (.5, .5). 55 When («, n) deviates from (.5, .5), on the other hand, financially unconstrained households can be better off with fixed nominal exchange rates than with flexible nomi-nal exchange rates. In the flexible exchange-rate regime, both home and foreign govern-ments fix their money supply at initial steady-state levels, while allowing the nominal exchange rate to move freely. This implies that money balances of households i and /* are fixed at their initial steady-state levels as well . But in the fixed exchange-rate regime, the home and foreign governments coordinate their monetary policies in order to maintain the exchange rate level. Because households j a n d / are prohibited from adjusting money balances, all the changes of money supply go to households i and /'*. If the number o f households i or i* is relatively small compared to the magnitude of money supply changes, then an increase o f home or foreign money supply for example wi l l cause a large amount of monetary increment for each household / or /'*. The associated wealth effects can domi-nate the welfare cost of fixed nominal exchange rates, bringing even higher values of expected utility for households i or i* than those with flexible nominal exchange rates. When («, n) deviates from (.5, .5), there are also some households in the economy not able to trade bonds and adjust money. These financially constrained households are actually current-income consumers, whose utility-maximization problems are static. Compared to financially unconstrained households, those who have full access to both bond and money markets, financially constrained households are more vulnerable to economic variability because they can not smooth consumption by either bond trade or monetary adjustments. Given the country-specific technology random processes and one-period-in-advance price rigidity, financially constrained households can be better off with fixed nominal exchange rates than with flexible nominal exchange rates. This is because in the flexible exchange-rate regime, expenditure switching effects upon economic distur-bances cause further output variability that requires subsequent consumption smoothing. For financially constrained households, they can not enjoy the benefit brought by expen-diture switching effects due to their financial restriction. A n d they need to bear the asso-ciated cost o f higher economic variability. Therefore by reducing expenditure switching effects, the fixed exchange rate regime can increase welfare for financially constrained households. 56 According to the welfare results, cases that the fixed exchange-rate regime is prefer-able to the flexible exchange-rate regime for households j and j* mostly occur when n or ri is reduced to some lower level. Recall that in this economy households / and /*. are those who bear all the changes of money supply to maintain the exchange rate level. When the number of households / or i* is small, each household / or /* shares a large amount of monetary adjustments, but the overall impact of wealth redistribution is less severe compared to an economy with a large number of households / or /*. Hence with the smaller effects of wealth redistribution from changes of money supply, the values of expected utility o f households/and j* are higher in the fixed exchange-rate regime than in the flexible exchange-rate regime. 3.5 Conclusion In this paper, a two-country sticky-price general equilibrium model is developed to examine welfare effects of different exchange-rate regimes under financial asymmetry. The financial asymmetry is defined as two groups of households with different degrees of financial access: One group is allowed to trade bonds and adjust money, while the other is prohibited from bond trade and monetary adjustments. Given the country-specific tech-nology random processes and one-period-in-advance price rigidity, this paper finds that fixed nominal exchange rates are in many cases preferable to flexible nominal exchange rates by all types o f households under financial asymmetry. For financially unconstrained households, the wealth effects associated with the monetary policies that aim to maintain the exchange rate level can dominate the welfare cost of fixed nominal exchange rates. For financially constrained households, they can not enjoy the benefit brought by expen-diture switching effects due to their financial restriction, but need to bear the associated cost of higher economic variability. Therefore by reducing expenditure switching effects, the fixed exchange rate regime can increase their welfare. The welfare results found in this paper imply that different types of monetary rules may be affecting the optimal choice o f exchange-rate regimes. In this paper, I assume the home and foreign governments adjust their money supply with equal absolute amounts to maintain the exchange rate level. 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Canadian Journal of Economics 28, 1135-1152. 62 Appendix A Appendices of Chapter 1 A . l Optimization Problem and First-Order Condition A. 1.1 Households/ Optimization Problem: Max L/; = 2 ^ - ' [ ^ c ; ^ + ^ ( ^ y - - - 7 v - ] O--I \-£ Ps jU Subjectto M;+d,F; =M'l_i+F;_]+w,N'l+ni-PlCil-PlTli First-Order Condition on Bond Holdings: •rc,. First-Order Condition on Money Balances: P, 1-d, First-order Condition on Labor Supply: N;=(-Equation o f Profit Sharing: -I7l=uI7;+(--u)I7; A. 1.2 Households / Optimization Problem: M a x 1 =fjr'\-^-ci^ + s=, cr-1 \-e Pl X t K 63 Subject to Mf + ^ - Ff = M'l, +—Ff_, + w] N[ + 77,* - Pf Ct - Pf e, e, First-Order Condition on Bond Holdings: CI =(/3^--p-rT°Cl+l First-Order Condition on Money Balances: M'' ' — -e , First-Order Condition on Labor Supply: l w -— —-NI =(--^c; -)*-• KP{ Equation of Profit Sharing: ^77,* = w*77,v" + (--w*)/7/ ' 2 ' ' 2 A. 1.3 Households/ Optimization Problem without Bond Trade: M a x Uf = £ ^ [ - 2 _ C / ^ +-^-(^-rc —NJ/] c r - l l-e Ps fi Subject to Mf =Mf_t + w,Nf +17,- PtCf - PfTf First-Order Condition on Money Balances without Bond Trade: MJ - •— P . -- --First-Order Condition on Labor Supply without Bond Trade: K P, Optimization Problem without Bond Trade and Monetary Adjustment: Max Uf = ±r'l—C^ +^L-A-<-*Nn C r - l \-E Ps fl 64 Subjectto Mf =Mf+wtNf +ni-P,Cf First-Order Condition on Labor Supply without Bond Trade and Monetary Adjustment: rc P, Equation of Profit Sharing: ln,=un;+{^-u)n> A. 1.4 Households j Optimization Problem without Bond Trade: M a x uf = £ / r ' [ - ^ - c ; - + ^ ( ^ r - y - e - - N y ] Subject to Mf = A/,{, + w, Nf' + 77,* - Pf Cf - Pf T/' First-Order Condition on Money Balances without Bond Trade: First-Order Condition on Labor Supply without Bond Trade: Nf'=(-^rC,r°r] KP, Optimization Problem without Bond Trade and Monetary Adjustment: M a x uf =Yp->[^C{^+^A-*--N{n ~ C r - 1 \-E Ps JU Subject to, M{ = Mf + w, Nf + 77,* - Pf Cf' First-Order Condition on Labor Supply without Bond Trade and Monetary Adjustment: N{ =(—^cf~°y~] kP< Equation of Profit Sharing: 65 A . 1.5 Firms x Optimization Problem: M a x v;x = Yjf~'f5s~'n\x S=l Subjectto n'sx = p'tx(z)x's(z) + esq'l\z)x'; (z)-wsN'; ' '• x ;(z) = [ ^ ^ n < + ( } - » ) C / + i G J . < ( z ) = [^r[« c; H\-n'yc{ 4-IGJ x;(z)+x;*(z) = 4 ^ First-Order Condition on Target Prices: 00 1 1 ( M M ^ ^ r ' - ' f ' ^ K + e - " ) ^ +^GJ Equation of Final Prices: A ( ^ ) = r J p ; - 1 (2 )+( i-r )A J r (2) ? ; ( z ) = 7 ? ; , (z )+( i-r ) g ; i (z) A. 1.6 Firms x* Optimization Problem: Max v;x =Y*y'-'p"n'f 66 Subject to nf = q' ( Z } x ; (z*) + p'f (z )x[' (z ) - w's N'f <(z ) = [ ^ 1 Y ' [ < + (1 -n)C's + i G J * : ^ ) = [ ^ ^ n < + ( | - » ) c / + | c ? ; ] x;(z" )+x; '(z*) = 4iv;/ First-Order Condition on Target Prices: . v = / ^ (0-\)qf {z'&f-'r—inq+^-^Cl + IG,] = ^ Z ^ > T ' ^ [ < + ( ^ - » ) C / + i G J ^ -Equation of Final Prices: pf (*) = ypUz)+Q-Y)p',x\z) q;\z) = rqi](z') + (l-r)q'/(z') A. 1.7 Firms v Optimization Problem: M a x V;y = Yjys- Bs-n: •y Subjectto 77.7 =Jp7(z)X;(z) + ^ ( z ) v ; * ( z ) - w v ^ ^ ' w = [ # r V c ; ' +d-«*)c/ +^GJ e,/, 2 2 67 y:(z) + y:'(z) = AsN'/ First-Order Condition on Target Prices: ( ^ - l ) ^ ( z ) | ] r ' / r ' | / f [ n C ; + ( ~ / i ) C / + ^ G J +ietp;)o[nc; +(!-»* )C/+^G;]| He,P;)e[nC; +(-\~n')C{ ^G]]-2 2 A Equation of Final Prices: P ; ( z ) = ^ , ( Z ) + ( i - 7 ) ^ ( z ) A . 1.8 Firms;;* Optimization Problem: M a x v;y' = Yjys"Ps"n'Z Subject to 17'/ = pf (z )y's(z* ) + p'f (z ) v f (z* ) - A ^ ' ) { ' ( o = [ ^ ] > ' c ; ' + ( | - » * ) c / +±G; ] V ; ( Z > X : ; ( Z > 4 A 7 " First-Order Condition on Target Prices: (0-l)p'/ { z ' ^ f - T { ( £ ) ' [ < + (-\-n)Cf +^G,] +P;e[n'Cfs ) C / + | G ; ] 68 \ e.. 2 2 +p;Vci"+(l-/i*)c/+l Equation of Final Prices: pf{z) = ypUz') + (\-y)p'Z{z*) 69 A.2 Table Table 1.1: Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances - Restrictions on Bond Trade with Complete P C P («, ri) =(•5,5) (n, n) =(•25,-5) («, n) =(.25,.25) (n, ri) =(-01,-01) F Bond Holding of Household i .1306 .2506 .1867 .2488 F1 Bond Holding of Household /* .1305 .1253 .1867 .2461 M\ Money Balance of Household / .0561 .0410 .0441 .0662 M' Money Balance of Household; na .0740 .0703 .0568 M' Money Balance of Household / .0797 .0796 .0673 .0822 M' Money Balance of Household j* na na .0935 .0803 C Consumption of Household / .0206 .0192 .0203 .0209 C Consumption of Household j na .0217 .0219 .0217 c Consumption of Household i .0265 .0264 .0251 .0251 C' Consumption of Household j* na na .0270 .0257 N' Labor Supply of Household i .0161 .0183 .0175 .0138 NJ Labor Supply of Household j na .0175 .0167 .0123 N' Labor Supply of Household /* .0225 .0239 .0233 .0201 NJ' Labor Supply of Household j na na .0231 .0186 e Exchange Rate .0930 .0898 .0895 .0906 w Home Wage Rate .0459 .0483 .0478 .0446 w Foreign Wage Rate .0611 .0624 .0616 .0615 P Home Price Index .0370 .0373 .0369 .0364 . P Foreign Price Index .0553 .0552 .0553 .0569 C Aggregate Home Consumption .0103 .0102 .0105 .0108 C Aggregate Foreign Consumption .0132 .0132 .0130 .0128 Y Aggregate Home Output .0105 .0082 .0077 .0051 Y' Aggregate Foreign Output .0112 .0107 .0106 .0087 -CA Home Current Account .0165 .0157 .0157 .0151 70 Table 1.2: Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances - Restrictions on Bond Trade with Complete L C P =(.5,.5) (n, n) =(.25,.5) («, «*) =(-25,.25) (n, n) =(-01,-01) F Bond Holding of Household / .0066 .0131 .0066 .0189 F' Bond Holding of Household /* .0066 .0065 .0066 .0189 M' Money Balance of Household ;' .0561 .0555 .0556 .0541 MJ Money Balance of Household j na .0566 .0566 .0561 M' Money Balance of Household /* .0797 .0796 .0792 .0784 M> Money Balance of Household f na na .0801 .0797 C Consumption of Household / .0215 .0216 .0215 .0215 C Consumption of Household j na .0218 .0216 .0216 c Consumption of Household i* .0271 .0268 .0270 .0271 C' Consumption of Household j* na na .0271 .0271 N' Labor Supply of Household / .0128 .0127 .0128 .0129 N1 Labor Supply of Household j na .0129 .0129 .0129 N' Labor Supply of Household /* .0191 .0191 .0190 .0191 Nf Labor Supply of Household/ na na .0191 .0191 e Exchange Rate .0957 .0956 i .0955 .0955 w Home Wage Rate .0436 .0434 . .0436 .0435 w Foreign Wage Rate .0608 .0609 .0607' .0608 P Home Price Index .0369 .0365 .0369 , .0369 P Foreign Price Index .0556 .0560 .0555 .0556 C Aggregate Home Consumption .0108 .0109 .0108 .0108 C Aggregate Foreign Consumption .0135 .0134 .0135 .0136 Y Aggregate Home Output .0050 .0049 .0050 .0049 •Y' Aggregate Foreign Output .0075 .0076 .0075 .0074 CA Home Current Account .0141 .0141 .0141 .0142 71 Table 1.3: Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances - Restrictions on Bond Trade and Monetary Adjustments with Complete PCP =(•5,5) (n, ri) =(.25,.5) («, ri) =(.25,25) (n, ri) =(.01,01) F' Bond Holding of Household i .1306 .3450 .3691 3.4218 F' Bond Holding of Household /'* .1306 .1725 .3694 3.4437 M' Money Balance of Household /' .0561 .1122 .1127 6.5820 MJ Money Balance of Household j na .0000 .0000 .0000 M' Money Balance of Household / .0797 .0797 .1589 11.1256 Mf Money Balance of Household j* na na .0000 .0000 C Consumption of Household i .0206 .0365 .0384 .....8179 C Consumption of Household j na .0690 .0657 1.4508 C Consumption of Household /* .0265 .0265 .0525 1.0785 C Consumption of Household j* na na .0681 1.5292 N' Labor Supply of Household / .0161 .0454 .0441 1.3168 NJ Labor Supply of Household j na .0264 .0260 .3502 N' Labor Supply of Household /* .0225 ' .0247 .0560 1.1555 N1' Labor Supply of Household j* na na .0366 .'3907 e Exchange Rate .0930 .1286 .1829 1.9930 w Home Wage Rate .0459 .1060 .1039 2.0981 w Foreign Wage Rate .0611 .0634 .1286 2.0998 P Home Price Index .0370 .0771 .0774 1.2055 P Foreign Price Index .0553 .0586 .1110 1.1219 C Aggregate Home Consumption .0103 .0247 .0242 .7145 C Aggregate Foreign Consumption .0132 .0132 .0280 .7562 Y Aggregate Home Output .0105 .0128 .0135 .1910 Y' Aggregate Foreign Output .0112 .0108 .0181 .1935 CA Home Current Account .0165 .0294 .0307 .8133 72 Table 1.4: Standard Errors under IID Random-Walk Home and Foreign Monetary Disturbances - Restrictions on Bond Trade and Monetary Adjustments with Complete L C P («,«*) («,«*) (n,n) ( («,«*) =(.5,.5). =(.25,.5) =(.25,.25) =(.01,.01) F' Bond Holding of Household / .0066 .0103 .0070 .1709 Fr Bond Holding of Household /'* .0066 .0051 .0070 .1688 M' Money Balance of Household /' .0561 .1122 .1124 2.7986 M> Money Balance of Household j na :oooo .0000 .0000 M: Money Balance of Household /* .0796 .0797 .1595 3.9767 M' Money Balance of Household j* na na .0000 .0000 C Consumption of Household i .0215 .0424 .0427 ' 1.0701 • C Consumption of Household j na .0432 .0438 1.0920 c Consumption of Household /"* .0271 .0260 .0546 1.3566 C Consumption of Household j* na na .0547 1.3537 N' Labor Supply of Household / ' .0128 .0253 .0253 ' .6286 N' Labor Supply of Household^ na .0254 .0260 .6451 N' Labor Supply of Household /"* .0191 .0196 .0382 .9597 Nf Labor Supply of Household j na na .0381 .9499 e Exchange Rate .0956 .1351 .1915 ' 4.7738 w Home Wage Rate .0436 .0874 .0877 2.1850 w Foreign Wage Rate :0608 .0605 .1216 3.0281 P Home Price Index .0369 .0746 .0744 1.8485 P Foreign Price Index .0555 .0571 .1107 2.7691 C Aggregate Home Consumption .0108 .0214 .0216 .5458 C Aggregate Foreign Consumption .0135 .0130 .0273 .6769 Y Aggregate Home Output .0050 .0101 .0099 .2456 Y Aggregate Foreign Output .0075 .0079 .0146 .3683 CA Home Current Account .0141 .0283 .0283 .7119 73 Table 1.5: Standard Errors under IID Random-Walk Home and Foreign Fiscal Disturbances - Restrictions on Bond Trade with Complete PCP («,«*) («,«*) («,«*) («,«*) =(.5,.5) =(.25,.5) =(-25,25) =(.01,.01) F' Bond Holding of Household /' .0445 .0572 .0485 .0583 Fr Bond Holding of Household ;'* .0445 .0286 .0485 .0584 M' Money Balance of Household / .0000 .0048 .0042 .0164 M' Money Balance of Household j na .0048 .0041 .0003 M' Money Balance of Household ;'* .0000 .0000 .0037 .0163 MJ Money Balance of Household;'* na na .0037 .0003 c Consumption of Household / .0097 .0101 .0096 .0099 c' Consumption of Household j na .0095 .0091 .0097 C Consumption of Household /'* .0138 .0133 .0145 .0138 c> Consumption of Household j* na na .0138 .0137 N' Labor Supply of Household i .0113 .0114 .0111 .0106 NJ Labor Supply of Household j na .0107 .0105 .0102 N' Labor Supply of Household /* .0147 .0143 .0149 .0143 N' Labor Supply of Household j* . na na .0140 .0141 e Exchange Rate .0235 .0233 .0228 .0235 vv Home Wage Rate .0118 .0111 .0110 .0102 w Foreign Wage Rate .0142 .0143 .0136 .0140 P Home Price Index .0103 .0098 .0095 .0097 P Foreign Price Index •.0132 .0133 .0133 .0136 C Aggregate Home Consumption .0048 .0049 .0047 .0049 C Aggregate Foreign Consumption .0069 .0067 .0071 .0069 Y Aggregate Home Output .0052 .0050 .0051 .0047 Y' Aggregate Foreign Output .0070 .0069 .0067 .0068 CA Home Current Account .0098 .0097 .0096 .0094 74 . Table 1.6: Standard Errors under IID Random-Walk Home and Foreign Fiscal Disturbances - Restrictions on Bond Trade with Complete L C P (/?,«*) («,«*) («,«*) (n,n) =(.5,.5) =(.25,.5) =(.25,.25) =(.01,.01) F' Bond Holding of Household / .0042 .0045 .0047 .0139 F' Bond Holding of Household /* .0042 .0023 .0047 .0139 M' Money Balance of Household ;' .0000 .0005 .0004 .0046 M' Money Balance of Household j na .0005 .0004 .0001 M' Money Balance of Household / .0000 .0000 .0004 .0047 Mf Money Balance of Household j* na na .0004 .0001 C Consumption of Household i .0097 ..0097 .0097 .0097 C' Consumption of Household j na .0097 .0097 .0097 C Consumption of Household /* .0134 .0135 .0134 .0135 d Consumption of Household j' na na .0134 .0134 N' Labor Supply of Household / .0099 .0099 .0099 .0099 NJ Labor Supply of Household j na .0099 .0099 .0099 N1' Labor Supply of Household /'* .0139 .0140 .0139 .0140 Nf Labor Supply of Household j* na na .0140 .0139 e Exchange Rate .0247 .0248 .0248 .0248 w Home Wage Rate .0099 .0099 .0099 .0099 w Foreign Wage Rate .0139 .0139 .0139 .0139 P Home Price Index .0097 .0096 .0097 .0097 P Foreign Price Index .0134 .0135 .0134 .0134 C Aggregate Home Consumption .0048 .0048 .0049 .0049 c Aggregate Foreign Consumption .0067 .0067 .0067 .0067 Y Aggregate Home Output .0049 .0050 .0050 .0050 y* Aggregate Foreign Output .0074 .0074 .0075 .0075 CA Home Current Account .0096 .0097 .0097 .0097 75 A.3 Figure Figure 1.1 ( 3 - 1 ) : Simulation Results of (n, ri) Equaling (.5, .5) and ( . 0 1 , . 0 1 ) under the Permanent Home Monetary Expansion - Restrictions on Bond Trade with Complete P C P 0.6000 0.0000 Fi Bond Holding of Household i Fi* - Bond Holding of Household i* 0.0000 0 2 4 6 10 12 14 16 18 20 0 2 4 6 10 12 14 16 18 20 Money Balance of Household i -0.1200 Mj - Money Balance of Household j 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 10 12 14 16 18 20 Mi* - Money Balance of Household i* Mj* Money Balance of Household j* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 10 12 14 16 18 20 The continuous lines represent the case of («, ri) equaling (.5, .5), and the dashed lines represent the case of («, « ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of («, ri) equaling (.5, .5), variables associated with them are replaced by those with households /' for clearer comparisons. 76 Figure11.1 (3-2): Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under the Permanent Home Monetary Expansion - Restrictions on Bond Trade with Complete P C P 0.0600 - Consumption of Household j Cf - Consumption of Household j* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Nj Labor Supply-of-Household j Nj* Labor Supply of Household j* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 0.1200 0.0900 0.0000 • Wage Rate of Home Country 0.0600 -0.0600 - Wage Rate pf Foreign Country 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10. 12 14 16 18 20 The continuous lines represent the case of («, n) equaling (.5, .5), and the dashed lines represent the case of («, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of (n, n) equaling (.5, .5), variables associated with them are replaced by those with households /' for clearer comparisons. 7 7 Figure 1.1 (3-3): Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under the Permanent Home Monetary Expansion - Restrictions on Bond Trade with Complete P C P - Price Index of Home Country Rice Index of Foreign Country 0.0450 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 • Aggregate Output of Home Country 0.0200 -0.0100 - Aggregate Output of Foreign Country 0.0200 -0.0300 10 12 14 16 18 20 0 2 4 6 8 . 10 12 14 16 18 20 0.0900 0.0750 0.0600 0.0450 0.0300 0.0150 0.0000 1 Exchange Rate CA • Current Account of Home Country 0.0100 -0.0200 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of («, n) equaling (.5, .5), and the dashed lines represent the case of (n, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of (n, n ) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 78 Figure 1.2 (3-1): Simulation Results of (n, ri) Equaling (.5, .5) and (.01, .01) under the Permanent Home Monetary Expansion - Restrictions on Bond Trade with Complete L C P Bond Holding of Household i 0.0600 Fi* Bond Holding of Household i* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 0.0000 Mi • Money Balance of Household i 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 1 Mj • Money Balance of Household j 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Mi* Money Balance of Household i -0.0040 Mj* Money Balance of Household j* 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of (n, ri) equaling (.5, .5), and the dashed lines represent the case of («, rt ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of («, ri) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 79 Figure 1.2 (3-2): Simulation Results of (n, ri) Equaling (.5, .5) and (.01, .01) under the Permanent Home Monetary Expansion - Restrictions on Bond Trade with Complete L C P 0.0700 0.0420 0.0280 0.0140 Q* • Consumption of Household j* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Nj Labor Supply of Household j Nj* Labor Supply of Household j* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 • Wage Rate of Home Country -0.0450 - Wage Rate of Foreign Country 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 . 16 18 20 The continuous lines represent the case of («, ri) equaling (.5, .5), and the dashed lines represent the case of («, « ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of («, ri) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 80 Figure 1.2 (3-3): Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under the Permanent Home Monetary Expansion - Restrictions on Bond Trade with Complete L C P 0.0900 Price Index of Home Country Price Index of Foreign Country 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 - Aggregate Output of Home Country Y* • Aggregate Output of Foreign Country 0 2 4 6 10 12 14 16 18 20 0 2 4 6 10 12 14 16 18 20 0.0000 Exchange Rate -0.0080 -0.0160 CA • Current Account of Home Country 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of («, n) equaling (.5, .5), and the dashed lines represent the case of («, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of (n, n) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 81 Figure 1.3 (3-1): Simulation Results of (n, ri) Equaling (.5, .5) and (.01, .01) under the Permanent Home Fiscal Expansion - Restrictions on Bond Trade with Complete P C P Fi Bond Holding of Household i 0.2500 0.2000 Fi* - Bond Holding of Household i -0.2000 -0.2500 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Mi • Money Balance of Household i Mj Money Balance of Household j 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16, 18 20 0.0750 Mi* Money Balance of Household i* Mj* Money Balance of Household j* 0 2 4 6 10 12 14 16 18 20 0 2 4 6 10 12 14 16 18 20 The continuous lines represent the case of (n, ri) equaling (.5, .5), and the dashed lines represent the case of («, ri) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of (n, ri) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 82 Figure 1.3 (3-2): Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under the Permanent Home Fiscal Expansion - Restrictions on Bond Trade with Complete P C P • Consumption of Household j • Consumption of Household j* 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 0.0200 0.0100 0.0000 Nj Labor Supply of Household j Nj* Labor Supply of Household j* 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 .14 16 18 20 0.0500 • Wage Rate of Home Country 0.0200 0.0000 w* • Wage Rate of Foreign Country 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of (n, n) equaling (.5, .5), and the dashed lines represent the case of («, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of (rt, n ) equaling (.5, .5), variables associated with them are replaced by those with households /' for clearer comparisons. 83 Figure 1.3 (3-3): Simulation Results of (n,ri) Equaling (.5, .5) and (.01, .01) under the Permanent Home Fiscal Expansion - Restrictions on Bond Trade with Complete P C P Price Index of Home Country -0.0150 Price Index of Foreign Country 0 2 4 6 8 10. 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 • Aggregate Output of Home Country Y* • Aggregate Output of Foreign-Country 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 0.0400 Exchange Rate CA - Current Account of Home Country 0.0400 0.0320 0 2. 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of («, ri) equaling (.5, .5), and the dashed lines represent the case of (n, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of («,.« ) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 84 Figure 1.4 (3-1): Simulation Results of (n, ri) Equaling (.5, .5) and (.01, .01) under the Permanent Home Fiscal Expansion - Restrictions on Bond Trade with Complete L C P Fi Bond Holding of Household i R* Bond Holding of Household i* 0 2 4 6 10 12 14 16 18 20 10 12 14 16 18 20 Mi - Money Balance of Household i Mj Money Balance of Household j 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 . 8 10 12 14 16 18 20 0.0050 0.0000 -0.0050 --o.oi oo ; -0.0150 '. -0.0200 -0.0250 — Mi* Money Balance of Household i* Mj* Money Balance of Household j * 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of («, ri) equaling (.5, .5), and the dashed lines represent the case of (n, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of («, ri) equaling (.5, .5), variables associated with them are replaced by those with households i for clearer comparisons. 85 Figure 1.4 (3-2): Simulation Results of (n, n) Equaling (.5, .5) and (.01, .01) under the Permanent Home Fiscal Expansion - Restrictions on Bond Trade with Complete LCP 0.0000 q Consumption of Household j q* Consumption of Household j* 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Nj - Labor Supply of Household j Nj* - Labor Supply of Household j* 0 2 4 6 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 • Wage Rate of Home Country • Wage Rate of Foreign Country 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 10 12 14 16 18 20 The continuous lines represent the case of («, n) equaling (.5, .5), and the dashed lines represent the case of («, n ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of («, n) equaling (.5, .5), variables associated with them are replaced by those with households ;' for clearer comparisons. 86 Figure 1.4 (3-3): S i m u l a t i o n Resul ts o f (n, n) E q u a l i n g (.5, .5) and (.01, .01) under the Permanent H o m e F i s c a l E x p a n s i o n - Restr ic t ions on B o n d Trade w i t h Comple te L C P Price Index of Home Country 0.0300 Price Index of Foreign Country 10 12 14 16 18 20 0 . 2 4 6 10 12 14 16 18 20 0.0300 0.0250 0.0200 0.0150 0.0100 0.0050 0.0000 1 • Aggregate Output of Home Country Y* • Aggregate Output of Foreign Country 0 2 4 6 8 10 12 14 16 18 20 10 12 14 16 18 20 Exchange Rate CA - Current Account of Home Country 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 The continuous lines represent the case of (/?, n) equaling (.5, .5), and the dashed lines represent the case of («, « ) equaling (.01, .01). The categories of the horizontal and vertical axes are time and the rate of changes from the initial steady state respectively. When households j are undefined as in the case of (n, n) equaling (.5, .5), variables associated with them are replaced by those with households / for clearer comparisons. 8 7 Appendix B Appendices of Chapter 2 B . l Optimization Problem and First-Order Condition B. l . l Households/ Optimization Problem: M a x .«=/ -cr-l l-e Ps Subject to M;+d,F; +erfFl*' =M\_,+FlL]+e,F;'i+wlN;+n;-plci-plT;-D! _ r [ e , ( ^ ' - F Q ] 2 ,F 2 PY First-Order Condition on Bond Holdings: (Ff-Fo) = 0 First-Order Condition on Money Balances: = 0 First-order Condition on Labor Supply: Equation of Aggregate Output: 88 B.l .2 Households i Optimization Problem: .Max E,U[ ^E^-'i-^-C^ + -*-(^L)'-*-H-N']"} a-I 1 - s Ps [j. Subject to M\ +i-Ff' +d-Ft'r Dl = M;_]+-Fr+rC +W*N; +nf -p;q -pji -D; ,, • r[e;\F; - F o ) f ' ' 2 PJ; First-Order Condition on Bond Holdings: First-Order Condition on Money Balances: * 1 /* First-Order Condition on Labor Supply: £f j ^ r C f ^ - l f ^ > , J = 0 Equation of Aggregate Output: B . l . 3 Households/ 89 Optimization Problem without Bond Trade: <T-1 Max Subject to Mf = M/_, + w,Nf + 77/ - PtCj - 7 ^ First-Order Condition on Money Balances without Bond Trade: \ •-. P -- MJ • 1 First-Order Condition on Labor Supply without Bond Trade: Optimization Problem without Bond Trade and Monetary Adjustment: co cr - l Max E,U{ = E^r'V—C^ + 7 ^ 0 ' ^ ~ — N{M] Tt c r - l \-s Ps p Subject to MJ0 = Mi + w,N/ + 77; - PtCf First-Order Condition on Labor Supply without Bond Trade and Monetary Adjustment: B.l.4 Households/ Optimization Problem without Bond Trade: Max E,Ui =E,2t/r-,[-?-CJ, ' +-^(^-)'"'-±N{ "] Tt C r - l \-E Ps p Subject to Mj = Mj'_} + w, Nj' + 77;" - PJCJ -PJT/ First-Order Condition on Money Balances without Bond Trade: f • ' p • Mf } First-Order Condition on Labor Supply without Bond Trade: 9 0 E,\^cr°-KNy-^ = o Optimization Problem without Bond Trade and Monetary Adjustment: . Max E,U{ -E^p-'i—Ci^ + ^ { ^ t s - - N { ^ ] f, CT-\ i-£ Px p. Subject to M[ = M{ + w,N{ + nf - Pfcf First-Order Condition on Labor Supply without Bond Trade and Monetary Adjustment: E^cf^-KNf^Y^ B . l . 5 Firmsz Optimization Problem: Max Ey; = £, J/?5~'77; Subject to 77; = ps (z)ys (z) - wsNzs - £>f ys{z) = AsN; D „ u [ A ( z ) - p , _ , ( z ) ] 2 2 T V . O ) First-Order Condition on Output Prices: Et ^i-0)p,(zy0p;(c:+G:)+0pxzyd-'pf(c:+G:)-^ p,-\ p, 2 p, i B . l . 6 Firmsz Optimization Problem: 91 M a x E,vf=E^Bs-'Tli .«=/ Subject to 111 = p] (z )ys (z ) - w] - Df (^^ * )=[^^n»c:+(|-»x:/+-|c?,+n c; H\-*yc{ +\GS] y s ( z ) = AsNf D P - __v[ps(z)-pUz)f S 2 pf(z') First-Order Condition on Output Prices: EAQ- 0)p, (z yep;\c:+G;>+eP\ (z )-*-' p;\c:+GD^ /Vi />, 2 p, \ 92 B.2 Table Table 2.1: Welfare Results of Home Households with n Equaling .50, .25 and .05 n = .50 / Household / n = .25 / Household i n = .25 / Household j n = .05 / Household / . n = .05 / Household j n If If If If' If If If' V If ir If If If' If V .50 -.5500 -.0377 -.5878 -.5472 -.0280 -.5752 -.5514 -.0633 -.6147 -.5374 -.0160 -.5534 -.5505 -.0610 -.6115 .45 -.5500 -.0383 -.5883 -.5473 -.0287 -.5760 -.5514 -.0631 -.6145 -.5380 -.0163 -.5543 -.5505 -.0610 -.6115 .40 ' -.5500 -.0390 -.5890 -.5475 -.0295 -.5770 -.5514 -.0629 -.6143 -.5388 -.0167 -.5554 -.5504 -.0610 -.6113 .35 -.5500 -.0398 -.5898 -.5478 -.0305 -.5783 -.5514 -.0627 -.6141 -.5396 -.0171 -.5567 -.5504 -.0609 -.6113 .30 -.5500 -.0409 -.5909 -.5480 -.0318 -.5798 -.5514 -.0625 -.6139 -.5405 -.0177 -.5582 -.5503 -.0609 -.6112 • .25 -.5501 -.0422 -.5923 -.5484 -.0334 -.5817 -.5513 -.0623 -.6136 -.5416 -.0184 -.5600 -.5503 -.0608 -.6112 .20 -.5501 -.0439 -.5941 -.5487 -.0354 -.5842 -.5513 -.0620 -.6133 -.5427 -.0195 -.5623 -.5503 -.0608 -.6111 .15 -.5502 -.0462 -.5964 -.5491 -.0383 -.5873 -.5512 -.0617 -.6129 -.5441 -.0212 -.5653 -.5503 -.0607 -.6110 .10 -.5502 -.0492 -.5994 -.5495 -.0422 -.5917 -.5511 -.0613 -.6124 -.5457 -.0243 -.5700 -.5503 -.0606 -.6109 .05 -.5502 -.0534 -.6036 -.5498 -.0484 -.5982 -.5508 -.0608 -.6116 -.5477 -.0310 -.5787 -.5503 -.0605 -.6107 If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part. If is the sum of If and If. When households j are undefined as in the case of n equaling .5, welfare measures associated with them are excluded. 93 Table 2.2 (2-1): Welfare Results of Home Households with n Equaling .50, .25 and .05 n = .50 / Household / . n = .50 / Household./ n = .25 / Household / «*.'= .25 / Household j n If If If If If If If If If If If If .50 -.5500 -.0377 -.5878 na na na -.5501 -.0422 -.5923 na na na .45 -.5498 -.0362 -.5860 -.5523 -.0643 -.6166 -.5498 -.0409 -.5907 -.5519 -.0628 -.6147 .40 -.5494 -.0344 -.5838 -.5521 -.0641 -.6162 -.5496 -.0394 -.5890 -.5518 -.0627 -.6145 .35 -.5488 -.0325 -.5813 -.5519 -.0639 -.6158 -.5493 -.0377 -.5870 -.5517 -.0626 -.6143 .30 -.5481 -.0304 -.5784 ' -.5516 -.0636 -.6152 -.5489 -.0357 -.5846 -.5515 -.0625 -.6140 .25 -.5472 -.0280 -.5752 -.5514 -.0633 -.6147 -.5484 -.0334 -.5817 -.5513 -.0623 -.6136 .20 -.5461 -.0254 -.5715 -.5511 -.0629 -.6140 -.5477 -.0306 -.5783 -.5511 -.0620 -.6132 .15 -.5445 -.0226 -.5671 -.5508 -.0624 -.6132 -.5467 -.0273 -.5739 -.5509 -.0618 -.6127 .10 -.5422 -.0195 -.5617 -.5505 -.0618 -.6123 -.5450 -.0233 -.5683 -.5506 -.0614 -.6120 .05 -.5374 -.0160 -.5534 -.5505 -.0610 -.6115 -.5416 • -.0184 -.5600 -.5503 -.0608 -.6112 If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part: If is the sum of If and If. . -94 Table 2.2 (2-2): Welfare Results of Home Households with ri Equaling .50, .25 and .05 (Continuous) n = .05 / Household / n = .05 / Household j n If If . If If If If .50 -.5502 -.0534 -.6036 na na . na .45 -.5502 -.0527 -.6029. -.5509 -.0608 -.6117 .40 -.5501 -.0520 -.6021 -.5509 -.0608 -.6117 .35 -.5501 -.0510 -.6011 -.5509 -.0608 -.6116 .30 -.5500 -.0499 -.5998 -.5508 -.0608 -.6116 .25 -.5498 -.0484 -.5982 -.5508 -.0608 -!6116 .20 -.5497 -.0463 -.5960 -.5508 -.0607 -.6115 .15 -.5494 -.0435 -.5929 -.5507 -.0607 -.6114 .10 -.5489 -.0390 -.5879 -.5506 -.0606 -.6112 .05 -.5477 -.0310 • -.5787 -.5503 -.0605 -.6107 If - denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part. if is the sum of If and If. ' "\ . 95 Table 2.3: Welfare Results of Home Households under Lower Price Rigidity with n Equaling .50, .25 and .05 n = .50 / Household / n = .25 / Household / n = .25 / Household j n = 05 / Household / n = .05 / Household j * n If If If If If If If If If If If If If If If .50 -.5119 -.0274 -.5394 -.5090 -.0202 -.5292 -.5138 -.0466 -.5605 -.4976 -.0110 -.5086 -.5132 -.0457 -.5589 .45 -.5119 -.0278 -.5397 -.5091 -.0207 -.5298 -.5138 -.0465 -.5604 -.4983 -.0112 -.5095 -.5131 -.0457 -.5588 .40 -.5119 -.0283 -.5402 -.5093 -.0212 -.5305 -.5138 -.0465 -.5603 -.4992 -.0115 -.5107 -.5131 -.0457 -.5588 .35 -.5119 -.0289 -.5408 -.5096 -.0220 -.5315 -.5138 -.0464 -.5602 -.5002 -.0118 -.5120 -.5130 -.0456 -.5587 .30 -.5120 -.0297 -.5417 -.5099 -.0229 -.5328 -.5138 -.0463 -.5601 -.5012 -.0123 -.5135 -.5130 -.0456 -.5586 .25- -.5121 -.0307 -.5428 -.5103 -.0241 -.5344 -.5138 -.0462 -.5600 -.5025 -.0128 -.5153 -.5130 -.0456 -.5586 .20 -.5122 -.0321 -.5443 -.5107 -.0257 -.5364 -.5138 -.0460 -.5599 -.5039 -.0137 -.5175 -.5129 -.0456 -.5585 .15 -.5123 -.0339 ; -.5462 -.5112 -.0279 -.5391 -.5138 -.0459 -.5597 -.5055 -.0150 -.5205 -.5129 -.0455 -.5584 .10 -.5125 -.0363 -.5488 -.5117 -.0310 -.5427 -.5137 -.0457 -.5594 -.5074 -.0173 -.5247 -.5129 -.0455 -.5584 .05 -.5127 -.0398 -.5525 -.5123 -.0359. -.5481 -.5135 -.0455 -.5590 -.5097 -.0225 -.5322 -.5129 -.0454 -.5583 . If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part. If is the sum of If and If. When households j are undefined as in the case of n equaling .5, welfare measures associated with them are excluded. 96 Table 2.4: Welfare Results of Home Households under Higher Elasticity of Consumption Demand with n Equaling .50, .25 and .05 n = 50 / Household / n = .25 / Household i n = .25 / Household j n = .05 / Household i n = .05 / Household j • n if" If If If if If ' If . v If If If If If if .50 -.5202 -.0291 -.5493 -.5165 -.0212 -.5377 -.5237 -.0498 -.5735 -.5019 -.0108 -.5127 -.5235 -.0484 -.5719 .45 -.5202 -.0295 -.5497 -.5168 -.0218 -.5386 -.5237 -.0497 -.5734 -.5031 -.0111 -.5142 -.5234 -.0484 -.5717 .40 -.5203 -.0300 -.5503 -.5172 -.0224 -.5396 -.5238 -.0496 -.5733 -.5044 -.0115 -.5159 -.5234 -.0484 -.5717 . .35 -.5204 -.0307 -.5511 -.5177 -.0233 -.5409 -.5238 -.0495 -.5732 -.5058 -.0120 -.5178 -.5233 -.0483 -.5716 .30 -.5206 -.0316 -.5522 -.5182 -.0243 -.5425 -.5238 -.0493 -.5731 -.5074 -.0125 -.5199 -.5233 -.0483 -.5716 .25 -.5209 -.0327 -.5536 -.5188 -.0256 -.5444 -.5238 -.0492 -.5730 -.5091 -.0132 -.5223 -.5232 -.0483 -.5715 .20 -.5212 -.034] ' -.5553 -.5194 -.0273 -.5467 -.5239 -.0490 -.5729 -.5110 -.0142 -.5252 -.5232 -.0483 -.5715 . .15 -.5215 -.0360 -.5575 -.5201 -.0296 -.5497 -.5239 -.0488 -.5727 -.5131 -.0157 -.5288 -.5232 -.0482 -.5714 .10 -.5219 -.0386 -.5605 -.5209 -.0329 -.5538 -.5238 -.0486 -.5724 -.5156 -.0183 -.5339 -.5232 -.0482 -.5714 .05 -.5224 -.0421 -.5645 -.5218 -.0380 -.5598 -.5237 -.0482 -.5719 -.5186 -.0238 -.5424 -.5232 -.0480 -.5713 If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part. If is the sum of If and If. When households j are undefined as in the case of n equaling .5, welfare measures associated with them are excluded. 97 Table 2.5: Welfare Results of Home Households under Lower Elasticity of Labor Supply with n Equaling .50, .25 and .05 n = .50 / Household i n .25 / Household i n = .25 / Household j n = .05 / Household i n = .05 / Household j n If If If 1 r V If If V if If If If If if If .50 -.5385 -.0320 -.5705 -.5333 -.0230 -.5563 -.5462 -.0552 -.6014 -.5097 -.0118 -.5215 -.5461 -.0537 -.5998 .45. -.5386 -.0324 -.5710 -.5339 -.0235 -.5574 -.5461 -.0551 -.6011 -.5118 -.0118 -.5236 -.5460 -.0537 -.5997 .40 -.5388 -.0330 -.5718 -.5345 -.0243 -.5588 -.5460 -.0550 -.6010 -.5141 -.0119 -.5260 -.5459 -.0537 -.5996 .35 -.5392 -.0337 -.5729 -.5353 -.0251 -.5605 -.5459 -.0548 -.6007 -.5166 -.0122 -.5288 -.5458 -.0537 -.5995 .30 -.5396 -.0347 -.5743 -.5362 -.0263 -.5625 -.5458 -.0547 -.6005 -.5192 -.0127 -.5319 -.5457 -.0536 -.5993 .25 -.5402 -.0359 -.5761 -.5372 -.0277 -.5649 -.5457 -.0545 -.6002 j -.5221 -.0134 -.5355 -.5457 -.0536 -.5993 .20 -.5409 -.0375 -.5784 -.5384 -.0296 -.5680 -.5456 -.0544 -.6000 -.5253 -.0145 -.5398 -.5456 -.0536 -.5992 .15 -.5416 -.0397 -.5813 -.5396 -.0323 -.5719 -.5455 -.0542 -.5997 -.5288 -.0163 -.5451 -.5456 -.0535 -.5991 .10 -.5426 -.0426 -.5851 -.5411 -.0360 -.5771 -.5455 -.0539 -.5994 -.5328 -.0192 -.5520 -.5456 -.0535 -.5991 .05 -.5437 -.0467 -.5904 -.5428 -.0419 -.5847 -.5454 -.0536 -.5990 -.5377 -.0255 -.5632 -.5456 -.0534 -.5990 If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. W denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part. If is the sum of If and If. When households j are undefined as in the case of n equaling .5, welfare measures associated with them are excluded. 9 8 Table 2.6: Welfare Results of Home Households under Monetary Restrictions with n Equaling .50, .45 and .40 n = .50 / Household / n = .45 / Household i n = .45 / Household j n = .40 / Household i n = .40 / Household j * n If If If If If If If If If If If If If' If If .50 -.5501 -mn -.5879 -.5832 -.0538 -.6370 -.5853 -.1046 -.6898 -.6162 -.0778 -.6940 -.6184 -.1514 -.7698 .45 -.5509 -.0392 -.5901 -.5834 -.0553 -.6386 -.5852 -.1032 -.6884 -.6164 -.0799 -.6962 -.6184 -.1495 -.7679 .40 -.5510 -.0404 -.5914 -.5835 -.0569 -.6404 -.5851 . -.1017 -.6868 -.6165 -.0822 -.6988 -.6183 -.1475 -.7658 .35 -.5511 -.0417 -.5928 -.5837 -.0588 -.6425 -.5849 -.1002 -.6851 -.6167 -.0849 -.7016 -.6182 -.1453 -.7635 .30 -.5512 -.0432 -.5944 -.5838 -.0609 -.6448 -.5848 -.0985 -.6833 -.6169 -.0880 -.7049 -.6180 -.1429 -.7610 .25 -.5513 -.0449 -.5963 -.5840 -.0634 -.6474 -.5846 -.0967 -.6813 -.6171 -.0915 -.7086 -.6179 -.1403 -.7582 .20 -.5514 -.0469 -.5984 -.5841 -.0663 -.6504 -.5844 -.0947 -.6791 -.6172 -.0957 -.7129 -.6177 -.1375 -.7552 .15 -.5515 -.0493 -.6007 -.5841 -.0697 -.6538 -.5842 -.0926 -.6768 -.6173 -.1006 -.7179 -.6175 -.1343 ,.7519 .10 -.5515 -.0521 -.6036 -.5842 -.0737 -.6579 -.5839 -.0902 -.6742 -.6174 -.1064 -.7238 -.6173 -.1309 -.7481 .05 -.5515 -.0554 -.6069 -.5842 -.0785 -.6627 -.5836 -.0877 -.6714 -.6174 -.1135 -.7308 -.6170 -.1270 -.7440 If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the mean part. If denotes the shift of initial steady-state consumption delivering the same expected utility associated with the variance part. If is the sum of If and V. . ' When households j are undefined as in the case of n equaling .5, welfare measures associated with them are excluded. 99 Appendix C Appendices of Chapter 3 C. 1 Optimization Problem and First-Order Condition C.l.l Households/ O p t i m i z a t i o n P r o b l e m : M a x E,U; = E.Yr'i—Cf + - - N ? ) Subject to M , ' + , x, )F' ( x , + 1 ) = M / _ , + F (x,) + w,N; + 77* - /JC/ -Firs t -Order C o n d i t i o n o n B o n d H o l d i n g s : 1 - 1 1 - 1 d(x,+„Xl)-C; ° =q{xM,xt)P—CM ° Firs t -Order C o n d i t i o n o n M o n e y Balances : M' - -- — PC'a ' P C a First-order C o n d i t i o n on L a b o r S u p p l y : 1 - 1 — ' K P, C.1.2 Households/ O p t i m i z a t i o n P r o b l e m : M a x E,U; = E^p-i^c^ +-JL(MLy'-< - -7v ;>] c r - 1 \-e Ps p 100 Subject to M\ + YJ D(X,+],XL)F'"(x,+1) xM<=X ei = M;_}+-F'\XI)+W'IN; +n; -p;q -PJ; E< First-Order Condition on Bond Holdings: 1 .-1 1 : .'. j ( x , + I , x , ) - r c ; ct=^(X,+1,X,)/5-^C;+1 -First-Order Condition on Money Balances: j _ M' 1 - . - 1 • — , p'C' a _ i - = r o - £ ( A + . ) * c ; - D ^ ^ B - ^ - j First-Order Condition on Labor Supply: K P C . l . 3 Households j Optimization Problem: Max E,Uj = E^r'i—Ct ° + - ^ ( ^ - ) ' -TI C r - l \-£ Ps H Subject to Ml =Mi+w,Nj +n;,-PlC/ First-Order Condition on Labor Supply: K P, • C . l . 4 Households/ Optimization Problem: Max E,U!• =E,Y,P"[—Ci ° ^ ^ ( ^ V " \ Ti CT - 1 1 - £ Px • M Subject to M{ = M{ + w, Nf + 77=" - Pjc{ 101 First-Order Condition on Labor Supply: KP, C.1.5 Firms z Optimization Problem: Max E,_yV-= E^D.n;, Subject to 77* = phl (z)yhl (z) - w,N*, yhl(z) = yt (z) = ^[^-V[nC, + (1 - ii)C/ + n C\ + (I- «* )C/" ] "hi "hi  1 l ' yhl(z) = A,N:hl D= pp^c'J:p,q° First-Order Condition on Output Prices: . x I V 2 }c\ c; ^2 ; c ; , J ' j C.1.6 Firms z* Optimization Problem: M a x E,_yj, =E,_]D,n; Subjectto 77; = p } , ( z ' ) y / / - ( z * ) - w | ^ v,(z*) = | r [ ^ ^ r [ < + ( l - « ) C / + « * C ; " + ( i - „ * ) C / " ] .if /' ^ ( z - ) = 4 ^ D,=ppuci_°p;cp 102 First-Order Condition on Output Prices: r f w ' - c ; ' i , c / '. ,1 • , c / ' w | - 1 £, ^ + (—w)—^ + « .+ ( — « )-^-]C; CT P/» ( z ) = — r~—: : : • r ^ - 1 .„ L c; , 1 , C 7 • J • , c / . „ ; - , - L c 2 'c : . 2 Jci 1 0 3 C.2 Table Table 3.1: Welfare Results of Financially Unconstrained Home Households / \^ n n \ .50 .40 .30 .20 .15 .10 .05 .01 ;50 -12.8792, -15.4458 -15.0733, -15.9481 -11.8055, -10.8160 -13.2814, -11.5190 -17.1220, -16.4275 -11.9068, -14.9313 -10.3143, -10.5455 ' -12.7093, -9.9839 .40 -12.1244, -13.4514 -17.0315, -15.0590 -14.2933, -13.0362 -14.0794, -15.5838 -13.3704, -12.7345 -13.1786, -13.9941 -11.2714, -11.8633 -12.7717, -11.6126 .30 -13.9102, -17.9424 -13.6980, -15.0515 -15.4796, -17.0480 -14.6518, --15.4157 -13.6172, -11.2750 -13.7300, -11.17il -14.8088, -10.1752 -12.8802, -8.7531 .20 -13.7645, -17.7887 -11.8424, -16.5284 -12.9052, -15.4339 -12.6691, -14.3610 -13:8049, -11.2387 -14.0894, -9.0688 -14.1083, -15.4816 -15.8844, -11.4573 .15 -12.2311, -12.9052 -18.3281, -16.9643 -14.5884, -11.1443 -12.9442, -12.4763 -17.0607, -12.4903 -12.6243, -11.8340 -14.9345, -10.2380 -13.3643, -10.5124 .10 -15.8832, -13.8091 -16.7244, -15.4061 -12.5050, -12.4653 -14.3271, -11.7346 -13.1162, -10.2035 -14.2803, -10.9647 -13/158, -11.1282 -14.7908, -14.0855 .05 -12.7723, -11.9833 -16.6253, -13.4537 -17.9751, -11.6601 -12.9009, -10.1174 -13.1116, -1 1.3532 -14:6689, -15.2033 -14.2363, -9.0063 -16.0855, -11.4884 .01 -11.7044, -10.5282 -14.5989, -11.0016 -12.1414, -8.5781 -14.4611, -10.8776 -12.7939, -12.1764 -14.3219, -13.5946 -11.9179, -11.0337 -15.3838, -10.2906 The first number from each pair of welfare data is expected utility under the flexible exchange-rate regime given the particular n-n* combination. The second number from each pair of welfare data is expected utility under the fixed exchange-rate regime given the particular n-n combination. 104 Table 3.2: Welfare Results of Financially Unconstrained Foreign Households /* N. n + \ ^ n \-.50 .40 .30 .20 .15 .10 .05 .01 .50 -12.8793, -15.4457 -15.0735, -15.9480 -11.8052, -10.8162 -13.2812, -11.5190 -17.1219, -16.4275 -11.9063, -14.9310 • -10.3121, -10.5444 -12.7078, -9.9818 .40 -12.1242, -13.4511 -17.0316, -15.0590 -14.2937, -13.0361 -14.0792, -15.5847 -13.3701, -12.7339 -13.1783, -13.9938 -11.2694, -11.8625 -12.7698, -11.6116. .30 -13.9102, -17.9424 -13.6977, -15.0514 -15.4796, -17.0481 -14.6518, -15.4155 -13.6171, -11.2744 -13.7296, -11.1704 -14.8075, -10.1733 -12.8783, -8.7500 .20 -13.7649, -17,7888 -11.8423, -16.5286 -12.9050, -15.4341 -12.6692, -14.3613 -13.8048, -11.2386 -14.0890, -9.0681 -14.1070, -15.4808 -15.8822, -11.4557 .15 -12.2314, -12.9056 -18.3283, -16.9646 -14.5888, -11.1445 -12.9443, -12.4764 -17.0606, -12.4904 -12.6237, -11.8341 -14.9332, -10.2366 -13.3616, -10.5087 .10 -15.8831, -13.8093 -16.7243, -15.4065 -12.5055, -12.4658 -14.3280, -11.7346 -13.1168, -10.2042 -14.2803, -10.9651 -13.2146, -11.1279 -14.7890, -14.0840 .05 -12.7732, -11.9842 -16.6257, -13.4549 -17.9756, -11.6613 -12.9027, -10.1193 -13.1132, -11.3544 -14.6695, -15.2038 -14.2364, -9.0055 -16.0846, -11.4877 • .01 -11.7058, -10.5299 -14.6002, -11.0030 -12.1442, -8.5822 -14.4630, -10.8804 -12.7967, . -12.1789 -14.3242, -13.5956 -11.9192, -11.0350 -15.3838, -10.2905 The first number from each pair of welfare data is expected utility under the flexible exchange-rate regime given the particular n-n combination. The second number from each pair of welfare data is expected utility under the fixed exchange-rate regime given the particular n-n combination. 105 Table 3.3: Welfare-Results of Financially Constrained Home Households j \ . n n \ .50 .40 .30 .20 .15 .10 .05 .01 .50 na -15.0755, -15.9500 -14.8002, -10.8198 -13.2825, -11.5189 -17.1242, -16.4306 -11.9206, -14.9379 -10.3180, -10.5516 -12.7247, -9.9907 .40 na -17.0354, -15.0597 -14.2997, -13.0354 -14.0807, -15.6205 -13.3869, -12.7377 -f3.1978, -14.0019 -11.2789, -11.8868 -12.7884, -11.6481 .30 na -13.6953, -15.0548 -15.4835, -17.0505 -14.6561, -15.4199 -13.6228, -11.2804 -13.7424, -11.1854 -14.8089, -10.1870 -12.9385, -8.8312 .20 na -11.8372, -16.5292 -12.9017, -15.4396 -12.6824, -14.3793 -13.8072, -11.2613 -14.1413, -9.1134 -14.1538, -15.4854 -15.8907, -11.6278 .15 na -18.3287, -16.9656 -14.5980, -11.1580 -12.9560, -12.5015 -17.0555, -12.5153 -12.6809, -11.9294 -14.9811, -10.4846 -13.4579, -10.5993 .10 na -16.7260, -15.4117 . -12.5120, -12.4897 -14.3406, -11.8287 -13.1332, -10.2029 . -14.3067, -11.1885 -13.3281, -11.4009 -14.9588, -14.3854 . .05 na -16.6181, -13.4467 -17.9846, -11.6740 -12.9201, -10.1743 -13.1718, -11.5081 -14.7495, -15.3100 -14.4566, -9.3911 -16.6187, -12.3615 .01 na -14.6055, -11.0197 -12.1591, -8.5941 -14.4978, -10.9656 -12.9079, -12.2703 -14.4614, -13.6792 -12.7277, -11.8259 -15.9862, -15.2335 The first number from each pair of welfare data is expected utility under the flexible exchange-rate regime given the particular n-ri combination. The. second number from each pair of welfare data is expected utility under the fixed exchange-rate regime given the particular n-ri combination. 106 Table 3.4: Welfare Results of Financially Constrained Foreign Households f \ ^ n * %. n \ .50 .40 .30 .20 .15 .10 .05 .01 .50 na na na na na na na na .40 -12.1299, -13.4560 -17.0315, -15.0595 -14.2960, -13.0339 -14.0764, -15.6133 -13.3855, -12.7354 -13.1901, -13.9993 -11.2757, -11.8783 -12.7786, -11.6376. .30 -13.9107, -17.9427 -13.7056, -15.0574 -15.4914, -17.0491 -14.6539, -15.4193 -13.6204, -11.2806 -13.7365, -11.1812 -14.8058, -10.1789 -12.9217,, -8.8110. .20 -13.7653, -17.7891 -11.8480, -16.5309 -12.9117, -15.4391 -12.6769, -14.3749 -13.8053, -11.2597 -14.1332, -9.1123 -14.1463, -15.4827 -15.8913, -11.6015 .15 -12.2363, -12.9103 -18.3311, -16.9676 -14.5969, -11.1670 -12.9595, -12.5025 -17.0578, -12.5136 -12.6762, -11.9238 -14.9782, -10.4713 -13.4540, -10.5900 .10 -15.8979, -13.8162 -16.7383, -15.4144 -12.5123, -12.4960 -14.3395, -11.8397 -13.1353, -10.2072 -14.3061, -11.1879 -13.3262, -11.3839 -14.9532, -14.3736 .05 -12.7850, -11.9929 -16.6291, -13.4410 -17.9887, -11.6811 -12.9278, -10.1863 -13.1752, -11.5216 -14.7633, -15.3115 -14.4572, -9.4000 v -16.6191, -12.3492 .01 -11.7322, -10.5420 -14.6127, -11.0347 -12.1650, -8.6052 -14.5152, -10.9783 -12.9210, -12.2801 -14.4664, -13.6819 -12.7357, -11.8298 -15.9854, -15.2317 The first number from each pair of welfare data is expected utility under the flexible exchange-rate regime given the particular n-n combination. The second number from each pair of welfare data is expected utility under the fixed exchange-rate regime given the particular n-n combination. 107 

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