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Optimal Borrowing Constraints,

Growth and Savings in an Open Economy

Amanda Michaud Jacek Rothert

Indiana University University of Texas at Austin

September 11, 2012

Abstract

We seek to understand how government intervention in mortgage markets affects exter-

nal 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 re-

stricted households access to mortgages. We add housing to a model of a small open economy

and show borrowing constraints for housing lower countrys 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 restric-

tions, 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

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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 im-

posed by the government.

3. They have higher households savings. Households savings in China, Korea, Hong-Kong, Sin-

gapore 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 res-

idential 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 ques-

tions: (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.

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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 quantitatively plausible, the natural question to ask is

whether policy constraining borrowing to finance residential housing purchases in a growing econ-

omy 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 bor-

rowing to finance land purchases or residential construction diverts resources from firms. A planner

can improve upon this outcome by limiting households 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 mech-

anisms 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.

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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

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current account deficits.

2.1 Household Savings is Important for National Savings

National Accounting Standards make it difficult to decompose national savings into three compo-

nents (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 1990s, 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 households 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.

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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 (SOEs). 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

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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

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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 2000s, the average loan-

to-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.

1This contrasts to LTVs in other emerging economies: 90 percent in Egypt and Mexico and 100 percent in

Thailand.2Comparison: Korea (27 percent), Hong Kong (China) (44 percent), or Singapore (61 percent).

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3 Model

A stand-in household has preferences over consumption of tradable good c, a non-tradable housing

good h and labor and maximizes the lifetime utility given by:

t=0

tU(ct, ht, t) (HH)

In each period t it faces the following constraints:

ct +ptxt + bt+1wtt + Rbt + t (3.1)

ht (1 )ht1 + xt (3.2)

ptxt wtt (3.3)

bt+1b (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

t of households 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 are

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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:

ct = atF(1,t)

xt = G(2,t),

where at is the productivity in the tradable sector, relative to the world frontier a = 1, and we

assume initially a0 < 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:

at+1 = (1,t) +

1 (1,t)

at

where (1,t) [0, 1] for all 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:

1,t + 2,t = t

Definition 3.1. Given initial housing stock h0, productivity a0, bond holdings b0 and the borrowing

constraint parameter , an equilibrium consists of sequences of allocations (ct, ht, xt, 1,t, 2,t, t, bt+1)

and prices (wt, pt) such that given the prices, (i) allocations solve the households and firms maxi-

mization 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

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that ht = xt in each period. Second, rather than trying to calculate the dynamics of net foreign

asset position bt, 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 () governing the

endogenous productivity catch-up. We assume the following:

(1; a) =

, if 1(a) < 1(a);

(1; a), if 1(a) 1(a);.

where 1(a) is the equilibrium allocation of labor in the tradable sector, in the economy de-

scribed above with constant productivity a and without the constraint (3.3); (1(a); a) = 1,

lim11

(a) (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 . Second, a

marginal increase in 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 planners problem:

V(a) = max

U(aF(1), G(2), 1 + 2) + V(a)

subject to:

a = + (1 )a

Let (1(a), 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 1(a).

Theorem 3.2. Suppose the utility function U(c,x,) is additively separable. Let 1, 2 be the

laissez-faire allocation and let

W(a, 1, 2) := U(aF(1), G(2), 1 + 2) + V((1; a) + (1 (1; a))a)

ThenW(a,1,2(a))

1

1=1(a)

> 0.

Proof. We have:

W

1

1=1(a)

= aF(1)U1 + U

3 + (1 a)

(1)V(a) = (1 a)(1)V

(a) > 0

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where the second equality follows from the fact that at the laissez-faire equilibrium we have aU1

11 + U3 = 0; the inequality follows from our assumptions on the learning-by-doing function

and from the fact that V is increasing in a (the last fact is an immediate consequence of U1 > 0and 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(1, 2; a) = U(aF(1), G(2), 1 + 2) + V((1; a) + (1 (1; a))a)

and notice that when evaluated at (1, 2) = (1(a),

2(a)) it equals the maximized value of the

households lifetime utility. We are interested in the sign of:

W

=(a)

where (a) :=G(

1)

G(2)(

1+

2) is the minimum value of such that the constraint (3.3) does not bind.

We have

W

=(a)

=W

1

1

+

W

2

2

=

W

1

1

where the second equality follows from the fact that W2

= 0 when evaluated at (1, 2). From

Theorem 3.2 we know W1

> 0. Hence, we only need to show that 1

< 0.

Theorem 3.3. Fix a and let = 1

1(a)1(a)+

2(a)

. Then1(a)

=

< 0.

Proof. In equilibrium the following constraint must hold:

U3 + aF(1)U1 +

G(2)U2 aF

(1)U1

= 0

Consider > 0, arbitrarily small. When = constraint (3.3) binds and [G(2)U2 aF(1)U1] >0. All we need to show is that now, 1 > 1. Suppose not, i.e. either

1 = 1 or 1 < 1. If

1 = 1

then for [G(2)U2 aF(1)U

1 ] > 0 we need 2 <

2. But this implies 1 + 2 <

1 +

2 and hence

U3 > U3 which implies U3 + aF

(1)U1 + [G(2)U2 aF

(1)U1] > 0. Next suppose 1 < 1.

Then F(1)U1 > F(1)U1 and, since the constraint is now binding, we need G

(2)U2 > G(2)U2 .

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This implies 2 < 2 and hence 1 + 2 <

1 +

2, which again yields U3 > U

3 which implies

U3 + aF(1)U1 + [G(2)U2 aF(1)U1] > 0. Hence, when = , we have 1 > 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 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 limx0 Ux = ).

3.3 Constraints and the current account

Next, we consider the impact of the borrowing constraints on changes in the countrys 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 countrys autarky interest rate in a laissez-faire equilibrium (i.e. with the constraint

(3.3) not binding). This is a natural assumption when = 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:

U1,tU1,t+1

= Rt

What is the marginal effect of lowering on the autarky interest rate? It is the same as the

effect onU1,tU1,t+1

.

Suppose the utility function is given by:

U(c,x,) = log c + u(x) v()

ThenU1,tU1,t+1

= ct+1ct

, which in autarky implies:

R =1

UcUc

=F(1)

F(1)+

(1 a)(1)

aF(1)(3.5)

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Theorem 3.4. Fix a. Suppose that = 0 and U(c,x,) = log c + u(x)v(). Suppose further that

(1(a))

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