Growth, Housing and Global Imbalances

Transcription

1 Growth, Housing and Global Imbalances Luis Franjo EPFL Luisa Lambertini EPFL September 13, 2016 Serhiy Stepanchuk EPFL PRELIMINARY AND INCOMPLETE. PLEASE, DO NOT CITE OR CIRCULATE. Abstract Existing literature has pointed out the negative correlation between house prices and current account balances from the 90s to the Great Recession. That was the case for the Unites States and Japan, one of the main trade partners of the United States. However, China, also one of the main trade partners of the United States, experienced large current account surpluses together with a boom in house prices during the 2000s. Existing models with housing and symmetric countries are not able to replicate this pattern. We investigate the relationship between current account balances and house prices in a two-country OLG model in which asymmetries across countries arise from differences in growth rates and the level of financial development. We carry out two experiments: in the first one, we calculate the transition after both economies become financially integrated and the foreign country is a fast growing and less financially developed economy (China); in the second case, we generate a recession in a foreign economy with the same level of financial development (Japan). Our model replicates the behavior of current account balances and housing prices in both cases, the United States and China case and the United States and Japan, before the Great Recession. In particular, it shows that when countries have these asymmetries, the correlation between housing prices and current account balances is positive in the less financially developed economy when both economies open to trade, similar to China s experience. Keywords: Growth, financial development, current account, housing prices. JEL classification numbers: E21, F41, G11. 1

2 1 Introduction The period between the mid 1990s and the Great Recession has been characterized by global imbalances, namely the emergence of large and persistent current account deficits in some countries financed by large and persistent current account surpluses in other countries. 1 At the same time countries with current account deficits experienced large housing booms followed by crushing busts after the crisis. 2 A large body of economic literature has emphasized the causal relationship between the global saving glut and the housing bubble in the United States see for example Bernanke (2101) and the availability of cheap funding for Greece, Ireland, Spain and Portugal after joining the euro zone and their large house market swings relative to stable or even falling house prices in Germany, the surplus country. The common theme in this literature is an (almost) exogenous fall in the world real interest rate and the focus is on the behavior of the housing market in deficit countries. Figure 1: Current Account (% GDP) in the United States (USA), Japan (JPN) and China (CHN). Constructed using data from Lane and Milesi-Ferretti (2007). The empirical evidence, however, is less uncontroversial. Prior to the Great Recession, the U.S. economy experienced large and persistent current account deficits, as shown in Figure 1, together with rising house prices, which are depicted in Figure 2. Over the same period Japan 1 See for example Obstfeld and Rogoff (2009) and?. 2 See for example André (2010). 2

3 Figure 2: Real House Prices in the United States (USA), Japan (JPN) and China (CHN). Constructed using data from the OECD, the Economist and Lane and Milesi-Ferretti (2007). and China, two of the largest trade partners of the United States, run large current account surpluses see Figure 1 accompanied by decreasing house prices in Japan but rapidly growing house prices in China. Rising house prices are not necessarily accompanied by current account deficits and current account surpluses do not imply falling house prices. Notice that Japan and China together account for a quarter to a third of the total trade of the United States. We want to emphasize two further facts. In Figure 3 we report the U.S. trade weight of China and Japan. During the period under consideration Japan started as one of the largest U.S. trading partner but China overtook Japan in Thus, the U.S. economy was shifting its trade pattern from Japan, a financially developed economy, to China, an economy with a substantially lower degree of financial development. Second, the United States were shifting trade weight from an economy in recession Japan (see Figure 5) to a fast-growing economy China. Our paper argues that asymmetries across countries in growth rates and the level of financial development are fundamental to explain the observed pattern of global imbalances and house price fluctuations. We develop a two-country model where the joint behavior of house prices and current account balances is explained by asymmetries across countries in growth rates and the level of financial development; this joint dynamics is also in accordance with the 3

4 Figure 3: Trade weights of the US for Japan (JPN) and China (CHN). Data from the BIS. Figure 4: Indices of financial markets heterogeneity in the US (USA), Japan (JPN) and China (CHN). The index is from Abiad et al. (2008). 4

5 Figure 5: Real GDP growth rate in the US (USA), Japan (JPN) and China (CHN). evidence presented above. We carry out two experiments with our model. In the first experiment we focus on the United States (domestic economy) and China (foreign economy). As in Coeurdacier et al. (2015), initially China grows faster but faces tighter borrowing constraints than the United States; at this point the two countries become financially integrated. The model predicts current account imbalances deficit for the financially developed economy and surpluses for the emerging one and an acceleration in the growth of house price early in the transition for China and later on for the United States. The key mechanism is the initial asymmetric response of the real interest rate an increase for the United States but a decrease for China which pushes saving and house price growth in opposite directions. In the second experiment we focus on the United States and Japan. The two countries are financially integrated and have a similar level of financial development when Japan experiences a recession. The model predicts decreasing housing prices and current account surpluses in the country in recession and current account deficits and increasing house prices in its trading partner. Our results are driven primarily by growth rate differentials across trading partners. House prices in the domestic economy are affected by these differentials. Our counterfactual exercises suggest that the growth rate differential is the main determinant of the joint behavior of the 5

6 current account and house prices, although the effect on the economy is mediated by financial development. After financial integration, differences in financial development alone cannot replicate the qualitative behavior of the data. In the case of the United States and Japan, the recession in Japan is the only difference between both countries and the model is able to replicate the negative correlation of current account balances and house prices in both economies. Also in this case, the recession in the foreign developed economy implies an increase in house prices in the domestic economy. Previous literature on the relationship between current account balances and house prices focuses primarily on the U.S. economy. A number of contributions are based on two-country models. Punzi (2013) develops a model following Iacoviello (2005) that differentiates between patient and impatient households in the domestic economy, and analyzes the business cycle properties after exogenous shocks to technology, housing preference and the Loan-to-Value (LTV) ratio. Ferrero (2015) also builds on Iacoviello (2005) and studies the response of the model to monetary policy and LTV shocks. These papers focus on domestic factors as the main drivers behind the joint behavior of the current account and house prices in the domestic economy. Our emphasis on foreign factors is novel; moreover we find them to be important determinants for the evolution of U.S. house prices.gete (2015) analyzes the effect of changes in house price expectations, U.S. population size and the LTV; it also studies the effects of an exogenous decrease in the interest rate as a proxy for a shock to the foreign discount factor. Our paper extends this analysis to a setup where asymmetries generate predictions consistent with the empirical evidence without the need of shocks. Small open economy models in the literature focus on the U.S. economy and study shocks to the interest rate and the downpayment requirement to buy a house. Adam et al. (2011) uses of Bayesian learning in a small open economy model with collateral constraints in order to broaden the effect of an exogenous decrease in the international interest rate. Kiyotaki et al. (2011) studies how interest rate and LTV shocks in a small open economy model with growth determine house prices with no focus on the evolution of the current account. Franjo (2015) studies the effect of a decrease in the international interest rate and in the downpayment requirement to buy a house in a small open economy model. This paper is a complement of the literature on global imbalances. Caballero et al. (2008) and Mendoza et al. (2009) study the coexistence of low interest rates and global imbalances in the world economy. They stress that a large amount of savings coming from emerging economies during the 90s depressed international interest rates XXXX what else?. Coeurdacier et al. (2015) studies the importance of credit constraints and growth rate differentials in the 6

7 global economy. The rest of the paper is organized as follows. The model economy is presented in Section 2. In Section 3 we explain our computational experiments; the model economy for each experiment is calibrated in Section 4. Simulations are performed and discussed in Section 5, and Section 6 concludes. 2 Model We build a two-country model. Each country is populated by overlapping generations of individuals who live for three periods: young (y), middle-aged (m), and old (o). Young and middle-aged individuals inelastically supply one unit of labor; old individuals are retired. We assume that labor is not mobile across countries while capital is. There are two sectors in each country: consumption and capital goods sector, and housing sector. We consider the consumption and capital goods sector as a tradable sector while housing is a non-tradable sector. The countries differ in two dimensions: the degree of financial development and the growth rate of productivity. Financial development is captured by a borrowing limit, which we model as the maximum loan-to-value ratio at which houses can be purchased. Life-time income is bell-shaped so that young individuals are constrained by the borrowing limit. Both countries have the same preferences and technology. 2.1 Production Production: Consumption and Capital Goods We define Kt i and L i t as the amount of capital and labor, respectively, employed in the production of consumption and capital goods at time t in country i. Firms choose labor L i t and capital Kt i that maximize their profits. Output by this sector is produced using a Cobb- Douglas production technology: Y i t = (Z i tl i t) 1 α ( K i t) α, where 0 < α < 1 is the capital share and Z i t country i. is country-specific productivity at time t in We define the total labor employed in production, L i t, as the sum of labor supplied by the young (L i y,t) and the middle-aged (L i m,t) individuals: 7

8 L i t = εl i y,t + L i m,t, where ε < 1 stands for the relative productivity of young workers. Capital follows the standard law of motion: K i t+1 = (1 δ)k i t + I i t, where δ is the rate at which capital depreciates, and I i t is the investment in capital at time t in country i. Productivity and population grow over time at rates gz,t i and gi L,t, respectively, such that: Z i t+1 = (1 + g i Z,t )Zi t and L i t+1 = (1 + g i L,t )Li t. Firms in the consumption and capital goods sector maximize their profits. Factors markets are competitive, so that wt i and r k,i t at time t in country i. are, respectively, the marginal product of labor and capital Production: Housing We assume that there is a fixed supply of housing each period, H i t, such that: H i t = N i t, where N i t is the stock of land at time t in country i. We also assume that the stock of land grows over time at the same rate as the population, gl,t i, so that: N i t+1 = (1 + g i L,t)N i t. 2.2 Households There are 3 stages in the life cycle of each individual: j {y, m, o}. Like capital, housing must be purchased one period before use. We do not model housing tenure considerations. We assume that young households start with no housing stock and must therefore rent a house in order to get housing services; middle-aged and old individuals instead own a house. Let c i j,t denote non-housing consumption of individuals at age j, in country i in period t; fy,t i is rental spending of the young at time t; and h i j,t is house purchase by individual of age j {m, o} that provides housing services in period t + 1. The lifetime utility of an individual in country i at time t is: Ut i = u(c i y,t, fy,t) i + βu(c i m,t+1, h i m,t+1) + β 2 u(c i o,t+2, h i o,t+2) 8

9 where β is the rate at which individuals discount the future. We assume that the utility function has the following functional form: ( (c ) i γ ( ) ) j,t x i 1 γ 1 σ j,t u(c, x) =, 1 σ where x denotes housing services from renting or owning a house, the parameter γ is the share of non-housing consumption in total expenditure, and σ is the coefficient of relative risk aversion. Individuals may hold two types of assets in this model: housing or deposits at financial institutions. Let a i j,t denote deposits at financial institutions (claims to capital and rental housing stock) by individual j in country i at time t. We assume there is a minimum downpayment requirement an individual must pay to buy a house; this requirement is denoted by (1 θ i ). The remaining balance on the house is financed by borrowing from financial institutions. Hence θ i denotes the maximum loan-to-value ratio and it captures the degree of financial development. More financially developed countries are characterized by higher θ i s. Young households born in country i in period t solve: max U i t = u(c i y,t, f i y,t) + βu(c i m,t+1, h i m,t+1) + β 2 u(c i o,t+2, h i o,t+2) s.t.: c i y,t + r f,i t fy,t i + qth i i m,t+1 + a i y,t+1 = wtε, i c i m,t+1 + q i t+1h i o,t+2 + a i m,t+2 = w i t+1 + q i t+1h i m,t+1 + a i y,t+1(1 + r i t+1), c i o,t+2 = q i t+2h i o,t+2 + a i m,t+2(1 + r t+2 ) i, a i y,t+1 θ i q i th i m,t+1, a i m,t+2 θq i t+1h i o,t+2. where r f,i t is the rental price at time t in country i; qt i is the housing price at time t in country i; and rt i is the rate of return on deposits at time t in country i. When individuals are young they receive a fraction ε of the competitive wage, where ε stands for the productivity of young relative to middle-age workers. Young individuals decide consumption of non-durable goods c i y,t, housing services from renting f i y,t, housing purchases h i m,t+1 to deliver housing services when middle-aged and saving. We define net worth as the sum of deposits (a) plus the market value of the owned house (qh) that is carried to the next period. When individuals are young it is optimal for them to borrow up to the limit a i y,t+1 = θ i q i th i m,t+1. 9

10 Middle-aged individuals receive the competitive wage and the return from the net worth they decided to carry over when young. For the generation born at time t this includes the repayment of the loan a i y,t+1(1+rt+1) i and the housing value qt+1h i i m,t+1. Then, they decide nonhousing consumption c i m,t+1 and net worth for the next period, a i m,t+2 and h i o,t+2. Middle-age individuals get housing services from the amount of housing they purchased when young. Old individuals get housing services from the amount of housing purchased when middleaged and get the return on net worth they carry from the previous period. They consume all their resources. 2.3 Financial Intermediaries Financial intermediaries ( mutual funds ) receive deposits from and make loans to households and decide how to allocate the resources between capital (K i t) and rental housing stock (H f,i t ). Formally, financial intermediaries solve the following problem: max (1 + rt+1)k k,i t+1 i + (r f,i t+1 + qt+1)h i f,i t+1 Kt+1 i,hf,i t+1 s.t. K i t+1 + q i th f,i t+1 = A i t+1, where A i t+1 = L i y,ta i y,t+1 + L i m,ta i m,t+1. A i t+1 is the total amount of deposits net of loans held at financial institutions of country i at the end of period t. Defining the portfolio shares invested in capital and rental housing as θ k,i t+1 = Ki t+1 A i t+1 θ f,i t+1 = qi t Hf,i t+1 A i t+1, we can restate this problem as: and max θ k,i t+1,θf,i t+1 (1 + r k,i t+1)θ k,i t+1 + R f,i t+1θ f,i t+1 s.t. θ k,i t+1 + θ f,i t+1 = 1, where R f,i t+1 = rf,i t+1 +qi t+1. For this problem to have an interior solution, we must have (1+r q t+1) k,i = t i Rt+1. f,i We also define the rate of return on household savings as 1+rt i (1+rt+1)θ k,i t+1+r k,i t+1θ f,i t+1. f,i 10

11 2.4 Government The government owns the new housing stock and sells it on the market at price q t. government uses this revenue to finance wasteful spending, G t : The G t = q t (N t+1 N t ). 2.5 Autarky vs. Integrated Equilibrium In the autarkic equilibrium, the clearing market condition in the asset market is given by: L i y,ta i y,t+1 + L i m,ta i m,t+1 = K i t+1 + q i th f,i t+1. In words, the amount of net deposits held by individuals at financial institutions in each country equals the capital stock plus the market value of the housing stock rented in each country. However, in the integrated equilibrium, asset market clears in the global economy: ( ( ) L i y,t a i y,t+1 + L i m,tam,t+1) i = Kt+1 i + qth i i,f t+1. i Clearing conditions in other markets are the same in both equilibria given that labor is not mobile across countries and housing is a non-tradable good. Thus, market clearing conditions are: i (a) Housing market: (b) Rental market: (c) Labor market: (d) Goods market: L i y,th i m,t+1 + L i m,th i o,t+1 + H f,i t+1 = N i t+1. L i y,tf i y,t = H f,i t. εl i y,t + L i m,t = L i t. Y i t = C i t + I i t + G i t + T B i t, where T B i t is the trade balance at time t in country i. Note that, i (T Bi t) = 0 in the integrated equilibrium; and T B i t = 0, i, in the autarkic equilibrium. 11

12 3 Computational Experiments We are interested in the joint behavior of the current account and housing prices in the global economy and how this behavior is affected by differences in growth and financial development among countries under financial integration. To this end, we run two experiments. In the first experiment we focus on the United States and China; initially the two countries are in financial autarky and we analyze the dynamics of house prices and the current account when the countries open up to trade. In the second experiment, we focus on the United States and Japan, which we assume to be already financially integrated, and we analyze the effects of an unanticipated recession in Japan. 3.1 The United States and China The first experiment focuses on the period from 1990 to the global financial crisis of During this period, China, a country with low financial development and high growth rate, became one of the main trade partners of the United States U.S. trade weight for China increased from 0.05 to 0.2, making China the xth U.S. trading partner in 2007, as shown in Figure 3. In this first experiment we study the implications for the current account and housing prices of financial integration and the role played by asymmetries in growth and in the level of financial development. In this experiment we label the United States as country H and China as country L; we assume that the two economies are initially in autarky and they unexpectedly open to trade. We identify China as an economy with lower financial development (θ L < θ H ) and faster productivity growth (gz L > gh Z ) relative to the United States. As in Coeurdacier et al. (2015), we further assume that, before openness, the Chinese economy is scarce in capital and therefore in a transition to its autarkic steady state. 3.2 The United States and Japan The second experiment focuses on the Japanese recession that started in At this time, Japan and the United States were already financially integrated and Japan was one of the main trade partners of the U.S. economy. The Japanese economy, like U.S. one, is characterized by a high level of financial development. In this experiment we study the implications for the current account and housing prices of a deep recession in Japan. More specifically, we assume that the two economies (H for the United States, and L for Japan) are already open to trade when the L-economy suffers an unexpected and temporary 12

13 recession (gz,2 L < gl Z,1 ). We keep the same assumptions for the U.S. economy as in the previous experiment and model Japan (L) as equally developed (θ L = θ H ) as the United States in financial terms. 4 Calibration Since our three-period version of the model is used to illustrate qualitatively the importance of differences in growth rates (gz,t i ) and the degree of financial development (θi ), we keep all other parameters equal across countries. In our model, we need to calibrate the parameters associated with preferences (β, γ, σ), the downpayment requirement (θ i ) for each country i, and parameters associated with technology (α), as well as the population growth rate (g L ), the depreciation rate (δ), and the relative productivity of young workers (ε). We also need series for productivity growth rates (gz,t i ) in each country i and for each t. We choose standard values for parameters common to all countries. The discount factor is set to be β = 0.97 on an annual basis; the intertemporal elasticity of substitution is σ = 2; the depreciation rate of the capital stock is δ = 0.1 per year; the share of non-housing consumption in the utility function is γ = 0.65; the capital share is set at α = 0.28; and the relative productivity of young workers is ε = The United States and China We assume that, before openness, the Chinese economy is in transition to its autarkic steady state. We need to make an assumption on the initial level of capital stock of the Chinese economy (K 1, L namely on the level of capital in 1970, which corresponds to the period of autarky between China and the United States). We need to specify the path of the productivity growth rate in China, {gz,t L }T t= 1, where T is the period in which both economies reach the integrated steady-state equilibrium; we assume that U.S. productivity growth, gz H, remains constant over time. From Penn World Tables we compute the productivity growth rates and the relative output of China. The latter is equal to 20% in 1970, 32% in 1990, and 85% in The productivity growth we set for China is 4.5; for U.S., the productivity growth is 1.5. We assume that θ H = 0.8 which is equivalent to a loan-to-value ratio of 80% in the US economy. For China we follow Coeurdacier et al. (2015) and assume θ L =

14 4.2 The United States and Japan In this experiment, we keep the same calibration for the U.S. economy. Since we assume that both economies are already trading before the recession, we calibrate them to have a balanced current account before the recession in Japan. This is consistent with the evidence shown in Figure. We assume that both economies have an equal level of financial developed, such that θ H = θ L, as shown in Figure 4. We use the Penn World Tables and calibrate the relative output of Japan to be 40% in 1990 (and therefore in 1970), and 30% in We assume that long-run productivity growth is the same in the United States and Japan and equal to xx. 5 Results 5.1 The United States and China The results of this experiment are plotted in Figure 6. Each period of time in the model is equivalent to 20 years. Period t = 1 in the graphs correspond to the autarkic equilibrium of each economy. The period of time between t = 1 and t = 0 corresponds to the period between 1970 and 1990, and the period between t = 0 and t = 1 corresponds to the period from 1990 to At period t = 0 the two countries become unexpectedly integrated; country L has faster technological growth than H (gz L > gh Z ) for periods t = 1, 0, 1; starting in period t = 2, which corresponds to 2030, country L s productivity growth rate becomes the same as in country H. Before integration takes place, at t = 1, China has a higher rate of return because it is a capital scarce economy. After integration (t = 1), the interest rate converges in both economies. It starts to decrease since the amount of capital increases over time because of the increase in the weight of country L in the global economy. As pointed out in Coeurdacier et al. (2015), there are three factors that determine the interest rate evolution: the growth effect in China that would increase the marginal product of capital thus increasing interest rates; the convergence effect in China since it is a capital scarce economy, thus decreasing interest rates because of the increasing amount of capital in the economy; and the integration effect that determines the interest rate as a function of the size of each country in the global economy. Between period t = 0 and t = 1, the saving rate in the more advanced economy decreases, driven by the increase in borrowing of the young. At the same time the investment rate 14

15 Figure 6: The US and China. Integration. Qualitative implications. 15

16 increases implying a current account deficit in the US. Also, housing prices in the US grow at a higher rate than in the balance growth path. Thus, the model predicts higher housing prices growth rate together with current account deficit in the US economy, as data show. This is a result of the integration with a less financial developed economy. The saving rate of the more constrained economy between period t = 0 and t = 1 increases, driven by an increase in deposits by the middle-aged. In this period of time, China runs a current account surplus together with a positive housing prices growth rate. This matches the behavior of the current account and house prices in China in the data. Thus, after both economies become integrated, independently of running a current account deficit or surplus, housing prices increase in both economies. Figure 7: The US and China. Integration (only Growth differentials). Qualitative implications. In our model, before openness, there are three asymmetries that make the Chinese economy different from the US economy: higher growth rate, less financial development, and capital scarcity. Thus, we are interested in understanding the driving forces behind our qualitatively results. To this end, we run some counterfactual experiments and isolate asymmetries between 16

17 countries. The first counterfactual experiment consists in analyzing the predictions of the model after openness when there are differentials just in the growth rates, while both economies are equally financially developed and have the same amount of capital when they become integrated. The results of this first experiment are plotted in Figure 7. The qualitative results of this experiment show that the main predictions are maintained. After openness, between period t = 0 and t = 1, the results are qualitatively in line with those of the base case model, but with quantitative differences. Figure 8: The US and China. Integration (only Financial Development differentials). Qualitative implications. The second experiment consists in analyzing the predictions of the model when both countries become integrated with different levels of financial development but they start with the same amount of capital and they always grow at the same rate. The results of this experiment are plotted in Figure 8. Between period t = 0 and t = 1, the predictions of the model are the opposite of those of the base case model. In the last counterfactual experiment one of the economies is capital scarce but both economies have the same level of financial development and they grow at the same rate. 17

18 Figure 9: The US and China. Integration (only Capital Scarcity differentials). Qualitative implications. 18

19 The results of this experiment are plotted in Figure 9. In this case, the qualitative results between period t = 0 and t = 1 are in line with the base case model but with a much smaller quantitative impact of openness on all variables. Add a conclusion: growth rates differences are the main driving mechanism. Financial development differences reinforce the impact of this growth rate differentials, based on results reported in Appendix. 5.2 The US and Japan In this experiment, we assume that both economies are already open before the recession in country L happens. Each period of time in the model is, as before, equivalent to 20 years. Period t = 1 in the graphs correspond to the equilibrium where both economies are integrated, with zero current account deficit in both economies at that time. The period of time between t = 0 and t = 1 corresponds to the period between 1990 and At period t = 0 the L economy, previously growing at the same growth rate as the H economy, experiences an unexpected temporary recession and, at this time, country L starts growing at a slower growth rate (gz L < gh Z ) for two more periods, until period t = 2. In this period country L growth rate becomes again the same as in country H. Figure 10 shows the results of this experiment. Before the recession takes place, t = 1, the US and Japan have the same rate of return because they are already integrated. After the recession (t = 1), the interest rate decreases since the amount of capital increases over the time the recession lasts in the Japanese economy. The factor that determines the interest rate evolution is the growth effect in Japan that would decrease the marginal product of capital thus decreasing interest rates. Between period t = 0 and t = 1, the saving rate in the US remains constant. At the same time the investment rate increases, thus implying a current account deficit in the US. Also, housing prices in the US grow at a higher rate than in the balanced growth path. Thus, the model predicts that as a result of a temporary recession in the Japanese economy, there is a higher growth rate of housing prices together with a current account deficit in the US economy, as the data shows. The saving rate of Japan between period t = 0 and t = 1 increases, driven by an increase in deposits by the middle-aged. In this period of time, Japan runs a current account surplus together with a negative housing prices growth rate, as the data shows. Thus, after an unexpected and temporary recession in the Japanese economy, housing prices increase in the economy running a current account deficit and decrease in the one running a current account 19

20 Figure 10: The US and Japan. Recession in Japan. Qualitatively implications. 20

21 surplus. 6 Conclusion In this paper we develop a two country model with housing to study the joint behavior of housing prices and the current account in the global economy when countries are financially integrated and they are asymmetric. Asymmetries among countries arise from differences in growth rates and the level of financial development. We focus on the period from the 1990 to 2007 when China and Japan were the main trade partners of the US economy. Then, we carry out two experiments. In the first one, the US vs. China, we assume that both economies are in autarky and then they open to trade. China is a fast growing, capital scarce, and less financial developed economy. We compute the transition from autarky to a financially integrated steady state. In the second experiment, the US vs. Japan, we assume that both economies are already financially integrated and the Japanese economy experiences a sudden recession. Then, we compute the transition of the model after an unexpected and temporary recession in the Japanese economy. In the US vs. China experiment, we find that the model is able to replicate what we observed in the data. When both economies become financially integrated, housing prices increase in the two countries, the US economy runs a current account deficit and the Chinese economy runs a current account surplus. At the same time, the international interest rate goes down in the global economy. We also analyze the importance of each of the components of this experiment separately and find that growth rate differentials are the main driving force behind the results and that financial development differentials by themselves can not explain the qualitative findings of the base case model. However, when combined whit growth differentials, they help to quantitatively fit the data. In the US vs. Japan case, the model is also able to replicate the pattern we observe in the data. When the recession in the Japanese economy happens, housing prices in the US increase at the same time that the economy runs a current account deficit. On the other hand, housing prices in Japan decrease and the economy runs a current account surplus. Also in this case, the international interest rate goes down along the transition. 21

22 References Abiad, Abdul, Enrica Detragiache, and Thierry Tressel, A new database of financial reforms number , International Monetary Fund, Adam, Klaus, Pei Kuang, and Albert Marcet, House price booms and the current account, in NBER Macroeconomics Annual 2011, Volume 26, University of Chicago Press, 2011, pp André, Christophe, A bird s eye view of OECD housing markets, Bernanke, Ben, Caballero, R.J., E. Farhi, and P.O. Gourinchas, An Equilibrium Model of Global Imbalances and Low Interest Rates, American Economic Review, 2008, 98, Coeurdacier, Nicolas, Stéphane Guibaud, and Keyu Jin, Credit constraints and growth in a global economy, The American Economic Review, 2015, 105 (9), Ferrero, Andrea, House price booms, current account deficits, and low interest rates, Journal of Money, Credit and Banking, 2015, 47 (S1), Franjo, Luis, International interest rates and housing markets, Technical Report, Centre for Fiscal Policy Gete, Pedro, Housing demands, savings gluts and current account dynamics, Iacoviello, Matteo, House prices, borrowing constraints, and monetary policy in the business cycle, The American economic review, 2005, 95 (3), Kiyotaki, Nobuhiro, Alexander Michaelides, and Kalin Nikolov, Winners and losers in housing markets, Journal of Money, Credit and Banking, 2011, 43 (2-3), Lane, Philip R and Gian Maria Milesi-Ferretti, A global perspective on external positions, in G7 current account imbalances: sustainability and adjustment, University of Chicago Press, 2007, pp Mendoza, E., V. Quadrini, and V. Ríos-Rull, Financial Integration, Financial Development, and Global Imbalances, The Journal of Political Economy, 2009, 117 (3), Obstfeld, Maurice and Kenneth Rogoff, Global imbalances and the financial crisis: products of common causes,

23 Punzi, Maria Teresa, Housing market and current account imbalances in the international economy, Review of International Economics, 2013, 21 (4),

24 Appendix A: Normalization De-trending Let ˆx t = xt Z t denote the detrended variable for any x t (for example, ŵ t = wt Z t ). Also, let β t 1 = β(1 + g Z,t ) γ(1 σ), and β t 2 = β 2 ((1 + g Z,t )(1 + g Z,t+1 )) γ(1 σ). Reformulation of the household problem We can re-write household optimization problem as: max (ĉγ y,tf 1 γ y,t 1 σ ) 1 σ + β 1 t (ĉγ ) m,t+1h 1 γ 1 σ m,t+1 1 σ + β 2 t s.t. ĉ y,t + ˆr f t f y,t + ˆq t h m,t+1 + â y,t+1 (1 + g Z,t ) = ŵ t ε, (ĉγ ) o,t+2h 1 γ 1 σ o,t+2 1 σ ĉ m,t+1 + ˆq t+1 h o,t+2 + â m,t+2 (1 + g Z,t+1 ) = ŵ t+1 + ˆq t+1 h m,t+1 + â y,t+1 (1 + r t+1 ), ĉ o,t+2 = ˆq t+2 h o,t+2 + â m,t+2 (1 + r t+2 ), â y,t+1 θˆq th m,t g Z,t, â m,t+2 θˆq t+1h o,t g Z,t+1. We need the t subscripts only for the transition periods, and we can drop them when looking at the BGP solution (where all the relevant variables will remain constant). The no-arbitrage condition for the financial intermediaries becomes: 1 + r k t+1 = (ˆrf t+1 + ˆq t+1 )(1 + g Z,t ) ˆq t. First-order and market-clearing conditions Let k t = Kt Z tl t. Assuming (which we need to check) that borrowing limit is binding for the young, but not binding for the middle-aged, equilibrium is described by the following system of optimality and market-clearing conditions: 24

25 [ĉ y,t ] : γ ( fy,t [f y,t ] : (1 γ) [ĉ m,t+1 ] : β1 t γ [ĉ o,t+2 ] : β2 t γ ) 1 γ (ĉγ ĉ y,t ( ĉy,t f y,t ( hm,t+1 ĉ m,t+1 ( ho,t+2 ĉ o,t+2 y,tf 1 γ y,t ) γ (ĉγ ) σ = λy,t, y,tf 1 γ y,t ) σ = λy,tˆr f t, ) 1 γ (ĉγ m,t+1h 1 γ ) 1 γ (ĉγ o,t+2ho,t+2) 1 γ σ = β2 t λ o,t+2, m,t+1) σ = β1 t λ m,t+1, [â y,t+1 ] : β1 t λ m,t+1 (1 + r t+1 ) + µ y,t = λ y,t (1 + g Z,t ), [â m,t+2 ] : β2 t λ o,t+2 (1 + r t+2 ) = β t 1 λ m,t+1 (1 + g Z,t+1 ), ( ) γ ĉm,t+1 (ĉγ [h m,t+1 ] : β1 t (1 γ) [h o,t+2 ] : β2 t (1 γ) h m,t+1 ( ĉo,t+2 h o,t+2 m,t+1h 1 γ m,t+1 ) σ + β1 t λ m,t+1ˆq t+1 + µ y,t θˆq t 1 + g Z,t = λ y,tˆq t, ) γ (ĉγ o,t+2h 1 γ o,t+2) σ + β2 t λ o,t+2ˆq t+2 = β 1 t λ m,t+1ˆq t+1, [BC y,t ] : ĉ y,t + ˆr f t f y,t + ˆq t h m,t+1 + â y,t+1 (1 + g Z,t ) = ŵ t ε, [BC m,t+1 ] : ĉ m,t+1 + ˆq t+1 h o,t+2 + â m,t+2 (1 + g Z,t+1 ) = ŵ t+1 + ˆq t+1 h m,t+1 + â y,t+1 (1 + r t+1 ), [BC o,t+2 ] : ĉ o,t+2 = ˆq t+2 h o,t+2 + â m,t+2 (1 + r t+2 ) [BL y,t ] : â y,t+1 = θˆq th m,t g Z,t, [MC K,t ] : ϕ y â y,t+1 + ϕ m â m,t+1 = (1 + g L ) [MC H,t ] : ( ) ˆq t k t+1 + ϕ y f y,t+1, 1 + g Z,t ϕ y h m,t+1 + ϕ m h o,t+1 + ϕ y (1 + g L )f y,t+1 = (1 + g L ) n, [F OC L,t ] : ŵ t = (1 α)k α t, [F OC K,t ] : r k t = αk α 1 t δ, [NoArb t ] : (1 + r k t+1) = (ˆrf t+1 + ˆq t+1 )(1 + g Z,t ) ˆq t. This gives us 17 equations in 17 unknowns: ĉ y,t, ĉ m,t+1, ĉ o,t+2, f y,t, h m,t+1, h o,t+2, â y,t, â m,t+1, λ y,t, λ m,t+1, λ o,t+2, ŵ t, ˆr f t, r k t, ˆq t, µ y,t, k t+1. Integrated (open trade) equilibrium Market-clearing condition for capital (savings) changes to: 25

26 L H y,ta H y,t+1 + L H m,ta H m,t+1 + L L y,ta L y,t+1 + L L m,ta L m,t+1 = K H t+1 + K L t+1 + q H t H H,f t+1 + q L t H L,f t+1. With growth Let Γ H t = ZH t (εl H y,t +LH m,t) F i=h Zi t(εl i y,t +Li m,t) effective labor in period t. re-written as: be the share of effective labor in country H to the total world Then the above market-clearing condition for savings can be Γ H t ( ϕ H y â H y,t+1(1 + g H Z,t) + ϕ H mâ H m,t+1(1 + g H Z,t) ) + (1 Γ H t ) ( ϕ L y â L y,t+1(1 + g L Z,t) + ϕ L mâ L m,t+1(1 + g L Z,t) ) ) ) = Γ H t (1 + g L ) (ˆkt+1 (1 + gz,t) H + ˆq t H ϕ H y ft+1 H + (1 Γ H t )(1 + g L ) (ˆkt+1 (1 + gz,t) L + ˆq t L ϕ L y ft+1 L since ˆk H t+1 = ˆk L t+1 with open capital market, in which we must have r kh t+1 = r kl t+1. Appendix B: Definitions The net foreign asset position at the end of period t is defined as: or in terms of GDP: NF A t+1 = L y,t a y,t+1 + L m,t a m,t+1 K t+1 q t H f t+1, NF A t+1 = L y,ta y,t+1 + L m,ta m,t+1 K t+1 q t H f t+1 Y t+1 Z t+1 L t+1 kt+1 α Z t+1 L t+1 kt+1 α Z t+1 L t+1 kt+1 α Z t+1 L t+1 kt+1 α 1 = ((1 + g (1 + g L )(1 + g Z,t )kt+1 α Z,t )ϕ y â y,t+1 + (1 + g Z,t )ϕ m â m,t+1 = ((1 + g L )(1 + g Z,t )k t+1 + (1 + g L )ˆq t ϕ y f y,t+1 )) The current account position in period t is defined as: or in terms of GDP: CA t = NF A t+1 NF A t, CA t = NF A t+1 NF A t = NF A t+1y t+1 NF A t = Y t Y t Y t Y t+1 Y t Y t 26

27 = (1 + g Z,t )(1 + g L ) Investment in period t is given by: ( kt+1 ) α NF A t+1 k t Y t+1 NF A t Y t I t K t+1 (1 δ)k t, or in terms of GDP: I t Y t = Y t+1 Y t K t+1 Y t+1 (1 δ) K t = (1 + g Z,t )(1 + g L ) Consumption in period t is given by: = Z t+1l t+1 kt+1 α Y t Z t L t kt α ( kt+1 k t k 1 α t+1 (1 δ)k 1 α t = ) α kt+1 1 α (1 δ)kt 1 α or in terms of GDP: C t = L y,t c y,t + L m,t c m,t + L o,t c o,t, C t Y t = L y,t L t = 1 k α t c y,t 1 Z t kt α + L m,t L t c m,t Z t 1 k α t ( ϕ y ĉ y,t + ϕ m ĉ m,t + Aggregate savings in period t is given by: + L o,t L t ϕ m (1 + g L )ĉo,t c o,t 1 Z t k α t ) = S t = Y t + r t NF A t C t, or in terms of GDP: S t NF A t = 1 + r t C t Y t Y t Y t Relative output of the more constrained economy in period t is given by: Y L t Y H t = ZL t L L t (k L t ) α Z H t L H t (k H t ) α = Z L t LL t F i=h Zi t Li t Zt HLH t F i=h Zi t Li t (k L t ) α (k H t ) α = 1 ΓH t Γ H t The level of saving of the young in period t is given by: or in terms of GDP: S y,t = L y,t ( w t ε c y,t r f t f y,t ), 27 (k L t ) α (k H t ) α

28 S y,t Y t = L y,t L t k α t (ŵ t ε ˆr ft f y,t ĉ y,t ) = ϕ y k α t The level of saving of the middle-age in period t is given by: ( ŵ t ε 1 ) γ ĉy,t or in terms of GDP: S m,t = L m,t (w t + r t a y,t c m,t ), S m,t = L m,t (ŵ Y t L t kt α t + r t â y,t ĉ m,t ) = ϕ m (ŵ kt α t + r t â y,t ĉ m,t ) The level of saving of the old in period t is given by: or in terms of GDP: S o,t = L o,t (r t a m,t c o,t ), S o,t Y t (r t â m,t ĉ o,t ) = (r (1 + g L )kt α t â m,t ĉ o,t ) Aggregate savings in period t by aggregating individuals savings is given by: = L o,t L t k α t ϕ m S t = S y,t +S m,t +S o,t = L y,t w t ε+l m,t w t +L m,t r t a y,t +L o,t r t a m,t (L y,t c y,t + L m,t c m,t + L o,t c o,t ) L y,t r f t f y,t = or in terms of GDP: = w t (L y,t ε + L m,t ) + r t (L m,t a y,t + L o,t a m,t ) C t r f t L y,t f y,t = = w t L t + r t (L y,t 1 a y,t + L m,t 1 a m,t ) C }{{} t r f t L y,t f }{{ y,t = } S t Y t = =NF A t+k t+q t 1 H f t = w t L t + r t K t }{{} =Y t δk t +r t NF A t + =H f t ( ) r t q t 1 r f t L y,tf y,t C t = }{{} =q t q t 1 = Y t δk t + r t NF A t + (q t q t 1 ) L y,t f y,t C t, NF A t 1 + r t C t Y t Y }{{ t} =Aggregate Savings in terms of GDP NF A t = 1 + r t C t δ Y t Y }{{ t Z } t L t kt α =Aggregate Savings in terms of GDP 28 δ K t Y t + (q t q t 1 ) Y t L y,t f y,t = K t + (q t q t 1 ) L Z t L t kt α y,t f y,t =

29 NF A t = 1 + r t C t Y t Y }{{ t} =Aggregate Savings in terms of GDP NF A t = 1 + r t C t Y t Y }{{ t} =Aggregate Savings in terms of GDP δk 1 α δk 1 α t + t + (q t q t 1 ) ( ˆq t Z t L y,t L t f y,t k α t = ) ˆq t 1 f y,t ϕ y (1 + g Z,t 1 ) kt α = 29