Optimal Borrowing Constraints, Growth and Savings in an Open Economy

Optimal Borrowing Constraints, Growth and Savings in an Open Economy Amanda Michaud Indiana University Jacek Rothert University of Texas at Austin September 4, 2012 Abstract We seek to understand how government intervention in mortgage markets affects external imbalances and domestic welfare. We document two facts about fast growing emerging economies: (1) Household savings are an important determinant of net aggregate savings. (2) Emerging lenders differ from emerging borrowers in that government policy substantially restricted households access to mortgages. We add housing to a model of a small open economy and show borrowing constraints for housing lower country s autarky interest rate. Next we show a learning-by-doing externality in the tradeable goods sector, under fairly mild conditions, can rationalize this policy as welfare improving. We also derive conditions under which borrowing constraint for housing will simultaneously generate productivity catch-up (vis-a-vis rest of the world) and current account surplus. A calibrated version of our model shows borrowing restrictions, similar to those observed in China, increase the average current account surplus by 7% of GDP over the competitive allocation. The welfare increase is equivalent to an annual increase of consumption by 5.6% in each year. These numbers fall short of the optimal allocation of 11% of GDP for current account and 6.6% of equivalent consumption increase. 1 Introduction In recent decades some rapidly growing economies have held large and persistent current account surpluses. The most notable example is China (see e.g. Buera and Shin (2009), Gourinchas and Jeanne (2007), Mendoza et al. (2009), Song et al. (2011)). Between 1980 and 2005 Chinese per capita income grew from 5% to 10% of that in the United Stateswhile Chinese net foreign 1

asset (NFA) position improved from 5% to 15% of its GDP. There is a number of theories that try to understand this behavior. We add to this debate by providing new evidence that many other emerging economies over the same time period have instead held current account deficits. Among countries with growth episodes, only six economies have been net savers: Botswana, China, Korea, Hong-Kong, Singapore and Taiwan. Motivated by this finding, we seek to understand the determinants of external imbalances by asking: how are these economies different? We provide evidence that households savings and housing demand are key determinants of the current account balance in emerging economies. Economies holding a positive net foreign asset position are unique in the following ways: 1. They had a sharper rise in residential housing demand, either through rapid urbanization (China, Korea) or rapid immigration with limited land supply (Hong Kong, Singapore). 2. They have tighter constraints on mortgages, housing development, and land ownership imposed by the government. 3. They have higher households savings. Households savings in China, Korea, Hong-Kong, Singapore and Taiwan average 25% of GDP, compared to an average of 15% in other developing countries that have also experienced rapid growth rates of per capita income. We propose a theory in which differences in external imbalances arise from differences in residential housing demand and government restrictions on mortgage lending. If households cannot borrow to buy a home, they must hold large savings to self-finance a home purchase. This is different from Buera and Shin (2009) or Song et al. (2011) in that we focus on households rather than firms. It is also different from Mendoza et al. (2009) or Carroll and Jeanne (2009) in that we consider government imposed restrictions, rather than exogenous credit constraints from credit market imperfections or underdeveloped banking sectors. We then ask the following two questions: (1) Can restrictions on mortgage lending generate levels of household savings and current account surplus consistent with the data? (2) Can such restrictions be justified, i.e. can they improve welfare? Our preliminary results suggest the answer to both questions is positive. 2

The mechanism through which constraints on mortgage borrowing can raise household savings is straightforward. What is not obvious is whether this theory can simultaneously generate levels of household savings and current account surplus consistent with the data. We show net capital outflows require two effects to be large. First, consumer demand for housing loans must remove a large quantity of capital investment and labor from the tradeable sector. Second, if the government imposes limits on housing loans, household demand for savings is large enough to lower domestic rates below the world interest rate and produce a current account surplus. We then show housing has unique characteristics from other assets that make these effects large: (1) housing requires a large lump-sum payment; and (2) this effect is large if home ownership is sufficiently complementary with leisure and consumption. Since we find this mechanism to be quantiatively plausible, the natural question to ask is whether policy constraining borrowing to finance residential housing purchases in a growing economy is welfare improving. This possibility has been explored in the endogenous growth literature. Deaton and Laroque (1999) and Jappelli and Pagano (1994) provide theories where household borrowing to finance land purchases or residential construction diverts resources from firms. A planner can improve upon this outcome by limiting household s borrowing, which induces households to save and subsequently invest in firms. This results in what is sometimes referred to as a virtuous cycle of endogenous growth: rapid capital accumulation and even higher growth. These theories are appealing reasons why governments may choose to limit consumer borrowing for housing finance as we find strong evidence for. These theories are at odds with the current account surpluses we document. If the goal of the government is to channel household savings and resources that would have gone to residential development to firms for capital accumulation, why are these resources instead being transferred abroad? To produce savings that flow out of a small open economy, we consider additional mechanisms to amplify welfare loss from diverting resources from the tradeable sector and rationalize observed restrictions on borrowing. The first is learning by doing. The more labor invested in the tradeable sector, the quicker productivity in the tradeable sector approaches the world frontier. 3

The second is technology transfer through foreign direct investment. Capital flows from foreign investors raise productivity in the tradeable sector, but domestic investment does not. This gives the policy maker incentive to limit mortgage borrowing because it prevents crowding out of lending to firms in the tradeable sector. Additionally, the return on domestic investment has lower return than investment from abroad and could lead to a current account surplus, despite large inflows of foreign direct investment (FDI). Our work is related to recent literature that provides evidence that housing demand shocks are a good candidate driver of current account dynamics (Gete (2009), Adam et al. (2011)). Gete (2009) shows cross-country differences in employment in the construction sector can explain differences in current accounts. The environment we consider links housing and the tradeable sector in the same way as the model of Gete. The mechanism is that demand for housing, a non-traded good, takes resources away from the tradeable sector. Our work takes this structural link as given and seeks to understand whether government policy to both limit household borrowing and maintain a current account surplus can be rationalized as optimal. We will also specifically consider the importance of long-run growth dynamics while Gete is concerned with the short term fluctuations. 2 Savings, Housing, and the Current Account in China Since 1980 Chinese per capita income relative to the income in the United States increased by over 100 percent. At the same time, China has been running persistent current account surpluses and accumulating foreign assets. This saving behavior is very different than the one observed in the majority of developing countries. It is also at odds with a workhorse small open economy model, which would predict that (i) households in faster growing countries would borrow to smooth consumption and that (ii) investment would flow into the country with high productivity growth. This behavior has been the major motivation behind recent studies by Buera and Shin (2009) or Gourinchas and Jeanne (2007). In this section we establish three key differences between China and other economies with 4

current account deficits. 2.1 Household Savings is Important for National Savings National Accounting Standards make it difficult to decompose national savings into three components (i) Household (ii) Corporate and (iii) Public. However, there is strong evidence that household savings rates exceed corporate savings in most countries (Loayza (1998)). Over the period 1965-1990, household savings rates were consistently two basis points higher than corporate savings rates as a percentage of private disposable income. Furthermore, the level of household savings typically accounts for more than half of national savings. We briefly summarize the evidence that household savings are important for aggregate savings in China. Statistics for China are complicated by a lack of reliable reporting standards. Kraay (2000) uses national household surveys to estimate the portion of aggregate savings that is public, corporate, household and residual. Throughout the high growth period of the 1990 s, household savings were far more important than public and corporate savings combined. In a study covering more recent years, Bayoumi et al. (2010) compare the savings of 1557 Chinese listed firms with those of 29330 listed firms from 51 countries over the time period 2002 to 2007. They find that Chinese firms do not have higher level of savings rates than the global norm. Further evidence comes from Yang et al. (2011) who consider the years 1992-2007. They find household savings consistently accounts for a larger share of gross national savings than corporate savings and had a larger increase over the time period, rising from 16.7 to 22.2 percent of GDP. Government savings is less important for understanding the level, but contributes to the rise in savings increasing from 2.6 to 10.8 percent of GDP over the same time period. It must be noted that the small change in aggregate household savings masks an increase in household s marginal propensity to save in the face of declining labor share. In sum, we leave the rise in corporate savings rates, widespread across countries, a separate trend to be explored and focus our theory on the historically significant contribution of household savings rates to national savings. 5

2.2 Chinese Demand for Residential Housing Grew Rapidly In most countries, residential housing investment typically accounts for to 3%-8% of GDP and 15%- 30% of gross fixed capital formation. In developing countries, housing can account for one-quarter and one-half of the capital stock, more than 80 percent of household wealth and more than half of national wealth. These statistics motivate us to consider the role of housing in understanding differences in households savings across countries. The rapid growth in Chinese housing demand is a product of two forces: rapid urbanization and privatization of housing supply. From 1980 to 2000, the proportion of population living in urban areas grew from 20 to 36 percent. The largest agglomerates grew by over 130%. In just five years, from 2000 to 2005, this proportion grew to 43 percent implying a growth rate of almost 10% per year. Provision of housing in China has a unique history. From 1949-1987 urban housing was provided by the government often through the employer, State Owned Enterprises (SOE s). Throughout this time rural housing remained mostly private. From 1988 to 1998 the government provided households with the option to purchase housing by establishing ownership rights over structures (but not land) for the first time. Subsidies were used to encourage purchasing, but because of the low quality 6

of the housing and willingness of employers to continue to provide housing as part of employment contracts only a small proportion of properties were bought. In 1994, the government announced substantial rent increases to rise over the next years to more aggressively encourage ownership. In 1998, the 23rd Decree was announced by the national government mandating full privatization of residential housing. This required housing to be purchased in private markets, although local governments maintain ownership of urban lands and span of control over development. 2.3 Policy Restrictions on Housing Loans and Construction in Emerging Lenders An important component of residential construction finance are Provident Funds. Provident funds are mandatory savings accounts that require minimum contributions from employees matched to some ratio by employers. Provident funds in China differ from US Social Security because they have higher minimum contributions and permit withdrawal of accrued savings for down payment on a house. These funds were established during the 1990s and early 2000s by provincial governments requiring a contribution by both employers and employees to provident funds at rates varying from 5 to 20% of the employees wages. In 1994, the Housing Accumulation Fund or Provident Funds were established at the national level with optional participation. The provident fund in China 7

has simultaneously raised savings while limiting housing development: as of 2005 the fund had accumulated RM 626 billion, but only 8% of the contributors had been provided housing loans. Loans are restricted by imposing controls on mortgage terms. In the early 2000 s, the average loanto-value ratio was around 60 percent, with lower values for speculative markets such as Shanghai. 1 Non-mortgage construction loans are regulated by mandating banks require 35 percent equity from developers. Additionally, the length of mortgages cannot extend 20 years or 65 minus the borrowers age. There is also some degree of government monopolization of mortgage lending. All other banks are required to offer higher interest rates than the national banks. Lastly, government ownership of urban land in many Chinese cities further allows restriction of residential construction. The cumulative effect of these policies lead total outstanding mortgages to remain below 10 per cent of GDP until 2005. 2 Over two-thirds of these loans originate in state-owned banks. 1 This contrasts to LTVs in other emerging economies: 90 percent in Egypt and Mexico and 100 percent in Thailand. 2 Comparison: Korea (27 percent), Hong Kong (China) (44 percent), or Singapore (61 percent). 8

3 Model A stand-in household has preferences over consumption of tradable good c, a non-tradable housing good h and labor l and maximizes the lifetime utility given by: β t U(c t, h t, l t ) t=0 In each period t it faces the following constraints: (HH) c t + p t x t + b t+1 w t l t + R b t + π t (3.1) h t (1 δ)h t 1 + x t (3.2) p t x t θw t l t (3.3) b t+1 b (3.4) The first constraint is the budget constraint, the second is the law of motion of the housing stock, the third one is the constraint that expenditures on new construction goods cannot exceed fraction θ t of household s current income. In the constraints above w denotes wage, p denotes relative price of new construction goods, R is the world (fixed) interest rate, b are bond holdings and π are 9

firms profits that are rebated in a lump-sum fashion to households that own the firms. Both goods are produced by competitive firms. Labor is the only factor of production. The production function are as follows: c t = a t F (l 1,t ) x t = G(l 2,t ), where a t is the productivity in the tradable sector, relative to the world frontier a = 1, and we assume initially a 0 < a. As long as the country is below the frontier there is scope for productivity catch-up. The catch-up arises endogenously through learning-by-doing in the tradable sector: a t+1 = φ(l [ 1,t ) + 1 φ(l ] 1,t ) a t where φ(l 1,t ) [0, 1] for all l 1,t. This specification implies the country will never exceed the world frontier. Total labor employed in the two sectors must equal the total labor supplied by the stand-in household, implying the following market clearing condition: l 1,t + l 2,t = l t Definition 3.1. Given initial housing stock h 0, productivity a 0, bond holdings b 0 and the borrowing constraint parameter θ, an equilibrium consists of sequences of allocations (c t, h t, x t, l 1,t, l 2,t, l t, b t+1 ) and prices (w t, p t ) such that given the prices, (i) allocations solve the household s and firms maximization problems and (ii) markets clear. We are interested in the effect that the constraints on construction expenditures has on (i) growth, (ii) welfare and (iii) current account. 3.1 Sub-optimality of the laissez-faire allocation The economy we outlined above is quite general and in order to characterize it analytically we will impose some more structure on it. First we will consider a case when housing fully depreciates, so 10

that h t = x t in each period. Second, rather than trying to calculate the dynamics of net foreign asset position b t, we will consider a closed economy and analyze the behavior of the equilibrium interest rate R. Finally, we need to make some assumptions on the function φ( ) governing the endogenous productivity catch-up. We assume the following: φ, if l 1 (a) < l φ(l 1 1 ; a) = (a); φ(l 1 ; a), if l 1 (a) l 1 (a);. where l 1 (a) is the equilibrium allocation of labor in the tradable sector, in the economy described above with constant productivity a and without the constraint (3.3); φ(l 1 (a); a) = φ 1, lim l1 l 1 (a) φ (l 1 ; a) > 0. These assumptions have the following implications. First, in a laissez-faire equilibrium, the productivity catches-up to the world frontier at the constant rate φ. Second, a marginal increase in l 1 will have positive impact on productivity in the second period. With the above assumptions, it is straightforward to show the competitive allocation solves the following planner s problem: V (a) = max { U(aF (l 1 ), G(l 2 ), l 1 + l 2 ) + βv (a ) } subject to: a = φ + (1 φ)a Let (l 1 (a), l 2 (a)) be the policy function for the above problem. We can show that the optimal allocation of labor in the tradable sector is higher than l 1 (a). Theorem 3.2. Suppose the utility function U(c, x, l) is additively separable. Let l 1, l 2 laissez-faire allocation and let be the W (a, l 1, l 2 ) := U(aF (l 1 ), G(l 2 ), l 1 + l 2 ) + βv (φ(l 1 ; a) + (1 φ(l 1 ; a))a) Then W (a,l 1,l 2 (a)) l1 l 1 > 0. =l 1 (a) Proof. We have: W l 1 = af (l 1)U1 + U3 + (1 a)φ (l 1 )V (a ) = (1 a)φ (l 1 )V (a ) > 0 l1 =l 1 (a) 11

where the second equality follows from the fact that at the laissez-faire equilibrium we have αau1 l 1 α 1 + U3 = 0; the inequality follows from our assumptions on the learning-by-doing function φ and from the fact that V is increasing in a (the last fact is an immediate consequence of U 1 > 0 and the corollary to the contraction mapping (see Stokey et al. (1989), chapter 3.)). 3.2 Welfare improving constraints Next we will show that marginal tightening of the borrowing constraint (3.3) will improve welfare. Consider the following function: W (l 1, l 2 ; a) = U(aF (l 1 ), G(l 2 ), l 1 + l 2 ) + βv (φ(l 1 ; a) + (1 φ(l 1 ; a))a) and notice that when evaluated at (l 1, l 2 ) = (l 1 (a), l 2 (a)) it equals the maximized value of the household s lifetime utility. We are interested in the sign of: where θ (a) := We have W θ θ=θ (a) G(l 1 ) G (l 2 ) (l 1 +l 2 ) is the minimum value of θ such that the constraint (3.3) does not bind. W θ θ=θ (a) = W l 1 l 1 θ + W l 2 l 2 θ = W l 1 l 1 θ where the second equality follows from the fact that W l 2 Theorem 3.2 we know W l 1 > 0. Hence, we only need to show that l 1 θ < 0. Theorem 3.3. Fix a and let θ = 1 l 1 (a) α l 1 (a)+l (a). Then l 1 (a) 2 θ θ=θ < 0. Proof. In equilibrium the following constraint must hold: U 3 + af (l 1 )U 1 + θ [ G (l 2 )U 2 af (l 1 )U 1 ] = 0 = 0 when evaluated at (l 1, l 2 ). From Consider ɛ > 0, arbitrarily small. When θ = θ ɛ constraint (3.3) binds and θ [G (l 2 )U 2 af (l 1 )U 1 ] > 0. All we need to show is that now, l 1 > l 1. Suppose not, i.e. either l1 = l 1 or l 1 < l 1. If l1 = l 1 then for [G (l 2 )U 2 af (l 1 )U 1 ] > 0 we need l 2 < l 2. But this implies l 1 + l 2 < l 1 + l 2 and hence U 3 > U3 which implies U 3 + af (l 1 )U 1 + θ [G (l 2 )U 2 af (l 1 )U 1 ] > 0. Next suppose l 1 < l 1. Then F (l 1 )U 1 > F (l 1 )U 1 and, since the constraint is now binding, we need G (l 2 )U 2 > G (l 2 )U 2. 12

This implies l 2 < l 2 and hence l 1 + l 2 < l 1 + l 2, which again yields U 3 > U3 which implies U 3 + af (l 1 )U 1 + θ [G (l 2 )U 2 af (l 1 )U 1 ] > 0. Hence, when θ = θ ɛ, we have l 1 > l 1. The above theorem proves tightening of the constraint (3.3) increases the employment in the tradable sector. With the scope for learning by doing externality, such tightening of the constraint will increase welfare. Note that we only talk about tightening of the constraint relative to the situation when it is not binding. By no means do we claim the tighter the constraint, the higher the welfare. In fact, when θ is close to 0, welfare will certainly be lower, as it will reduce the output of the non-tradable good close to 0 (recall that lim x 0 U x = ). 3.3 Constraints and the current account Next, we consider the impact of the borrowing constraints on changes in the country s net foreign asset position. In general, whether the small economy will run current account surplus or deficit, will depend on the world interest rate R. In what follows we assume the world interest rate R is the same as the country s autarky interest rate in a laissez-faire equilibrium (i.e. with the constraint (3.3) not binding). This is a natural assumption when φ = 0 which is what we will assume now (i.e. in a laissez-faire equilibrium the economy will stay at the same productivity level relative to the world frontier). The inter-temporal Euler equation for the problem of the household is: U 1,t U 1,t+1 = βr t What is the marginal effect of lowering θ on the autarky interest rate? It is the same as the effect on U 1,t U 1,t+1. Suppose the utility function is given by: U(c, x, l) = log c + u(x) v(l) Then U 1,t U 1,t+1 = c t+1 c t, which in autarky implies: R = 1 β U c U c = F (l 1 ) F (l 1 ) + (1 a)φ(l 1) af (l 1 ) (3.5) 13

Theorem 3.4. Fix a. Suppose that φ = 0 and U(c, x, l) = log c + u(x) v(l). Suppose further that φ (l 1 (a)) < a 1 a F (l R 1 ). Then θ θ=θ < 0. Proof. First note, that when U(c, x, l) = log c + u(x) v(l), then the allocation of labor is independent of a. Differentiating (3.5) and evaluating the derivative at l 1 = l 1 = l 1 yields: R θ = φ (l 1 )(1 a)af (l 1 ) a 2 F (l 1 )F (l 1 ) a 2 F (l 1 ) 2 which implies R θ < 0 if φ (l 1 )(1 a) < af (l 1 ). This finishes the proof. The above theorem states that as long as the learning by doing effect is not too strong (albeit positive) then tightening of the constraint (3.3) will lower the country s autarky interest rate. Then, a small open economy that faces the fixed interest rate R will run current account surplus, despite having higher growth than the rest of the world. Note that this result will likely to be strengthened with additional assumption (and arguably more realistic) of complementarity between tradable and non-tradable good in the utility function. 4 Quantitative Analysis We will now present preliminary results of the quantitative effects of mortgage constraints from a calibrated version of the economy similar to the one described in previous section. 4.1 Functional forms and parameter values Preferences The period utility function for the household is assumed to take the following form: { [ ] ω c c η 1 η + (1 ω c )v(h, l) η 1 η } 1 σ η 1 η U(c, h, l) = 1 σ ] where v(h, l) = [ω h h γ 1 γ + (1 ω h )(1 l) γ 1 γ γ 1 γ. There is a constant elasticity of substitution between consumption of housing services and leisure, and we assume the two goods are gross complements, i.e. γ < 1. There is also a constant elasticity of substitution between consumption of tradable good c and the housing-leisure composite. Again, the two are assumed to be gross complements, with the elasticity of substitution being η < 1. 14

Household s constraints The constraints household faces in the utility maximization problem are almost identical to (3.1) - (3.4), with one exception. We allow for a stronger constraint construction expenditure. In particular, we assume households expenditures on construction cannot exceed fraction θ of the household s net wealth plus its current income: p t x t θ (w t l t + R b t ) (4.1) This specification better captures the actual regulatory policies observed in the mortgage market in China. Of course it generates stronger motive for saving. We will discuss how important is that extra requirement for generating current account surplus. We will also show, it generates greater welfare gains than the specification without the extra requirement on net wealth. Technology Production functions take the following form: α c t = a t F (l 1,t ) = a t l 1,t x t = G(l 2,t ) = l α 2,t, The productivity parameter a t evolves according to the following law of motion, featuring learningby-doing in the tradable sector: a t+1 = min{a, (1 + φ max{0, l 1,t n})a t } where a is the world frontier. Government policy The tightness of the constraint (3.3), θ, is the only policy tool available to the government. Manipulating the value of θ, the government can affect the allocation of labor in the tradable sector, and thus affect the growth rate of the economy. 4.1.1 Parameter values At this point we use ad-hoc numbers of some parameters, but we calibrate the value of the one major interest to us, which is θ: the tightness of the constraint (4.1). The number was chosen so that residential investment is on average 10% of GDP. 15

Table 1: Parameter values Preference parameters Discount factor β 0.96 Consumption share ω c 0.5 Elast of subst - housing and leisure γ 0.5 Elast of subst - consumption and v(h, l) η 0.5 Inter-temporal elast of subst 1/σ 0.5 Technology Housing depreciation δ 0.1 Curvature in manufacturing α 0.40 Curvature in construction α 0.40 Threshold employment for LBD n 0.98 l 1 LBD paramter φ 0.05 World frontier / initial TFP a /a 0 1.25 Policy Constraint tightness θ 0.1 4.2 Effects of the constraint - simulation results We first explore some results from comparative statics w.r.t. to the constraint parameter θ. Figure 1 plots the lifetime utility of the stand-in household against the measure of constraint tightness - θ. As we have shown in the simplified model in the previous section, tightening the constraint improves welfare. However, the effect of the constraint on welfare is non-monotone. There is an optimal level of borrowing constraint, and if the restriction is too tight, welfare is lower. The intuition is pretty straightforward - there is a trade-off between faster growth and lower consumption of housing services and leisure. Figure 2 emphasizes the main effect the constraint has on the economy, which is speeding up the technological progress through the reallocation of labor into the tradable sector. The left panel plots the allocation of labor in the tradable sector along the equilibrium path. The blue line corresponds 16

Welfare 0.0808 0.75 Constraint Tightness (θ) Figure 1: Welfare vs. constraint tightness to the allocation in the economy with optimal constraints. The dashed black line corresponds to the allocation in the laissez-faire equilibrium. The allocation of labor in manufacturing in the first few years is substantially larger in the economy with credit constraints. This has direct impact on higher productivity growth via learning-by-doing, as seen in the right panel which plots the evolution of productivity. The catch-up in the economy with constraints is almost immediate - it takes 6 years for the economy to completely catch-up with the world frontier. 0.68 Labor in manufacturing 1.3 Productivity 0.67 0.66 0.65 Lasseiz faire Optimal constraints 1.25 1.2 0.64 1.15 0.63 0.62 0.61 0.6 0 20 40 60 80 100 1.1 1.05 Lasseiz faire Optimal constraints 1 0 20 40 60 80 100 Figure 2: Employment in manufacturing and productivity catch-up The model also predicts the economy with constraints will run current account surplus during the years of catching-up. This is depicted in Figure 3. Trade balance is positive for the first 10 years. This is the manifestation of Theorem 3.4 from the previous section. The increase in current 17

output of tradeables is large enough to generate current account surplus, despite generating a substantial growth at the same time. Moreover, the very nature of the credit constraints in fact induces households to save (construction expenditures are limited not only by current income, but also by wealth). 0.1 NX / GDP 0.08 0.06 0.04 0.02 0 0.02 Lasseiz faire Optimal constraints 0.04 0 20 40 60 80 100 Figure 3: Dynamics of the trade balance 4.3 Quantitative results We perform the following exercise. The economy starts at period t = 1 in its initial steady state, corresponding to the constant productivity level a 0. Government sets the policy parameter θ = 0.1 in period t = 1, 2,..., 20. That constraint is then relaxed forever. We then compute the equilibrium path for the economy with that constraint in place and compare it to the allocations arising if that constrain was set at the optimal level and to the allocations in a laissez-faire equilibrium. The results are presented in Table 2. Implementing the policy similar to the one observed empirically generates average current account of about 5% of GDP during the first 10 years. If the policy is set at its optimal level the implies average CA surplus of 9% of GDP. Comparing to the laissez-faire allocation this is a 7% and 11% increase, respectively. The benchmark policy generate welfare gain, equivalent to an annual increase of consumption by 5.6%. An optimal policy would generate gain equivalent to a 6.6% increase in annual consumption. The major source of the welfare gain from the time needed to reach 18

Table 2: Simulation results Laissez-faire Policy set at θ = 0.1 Optimal policy (θ = 0.08) Average CA / GDP -0.02 0.05 0.09 Welfare change 0 5.6 % 6.6 % # of years to reach frontier 55 11 6 NOTES: Average CA/GDP calculated over the first 10 years. Welfare change measures the equivalent annual increase in consumption of manufacturing in a laissez-faire allocation to achieve the same level of utility. All parameter values the same as in Table 1. the world frontier. In the laissez-faire allocation it takes 55 years before the economy catches-up completely. With borrowing constraints that time reduces to 11 years when the constraint is set to a number corresponding to Chinese data. The optimal level of the constraint in the model would imply even faster catch-up of 6 years. 5 Summary and Conclusions In this paper we explored the role that credit constraints in housing markets play in determining long-run international capital flows. First, we documented governments in rapidly growing economies in East Asia restricted access to credit to finance residential housing purchases. We have shown such policies may generate persistent current account surpluses, consistent with the empirical observations. Finally, we have argued such policies result in reallocation of resources towards manufacturing sector and may be welfare improving if the manufacturing sector is the engine of technological progress. The small open economy perspective sheds some new light on the endogenous growth literature of learning by doing. The long-run behavior of the current account may be informative about the way in which learning by doing occurs. The fact that fast growing countries in East Asia have been accumulating foreign assets may suggest learning by doing comes from labor rather than capital being allocated in the manufacturing sector 19

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