1. No category

Financial Development and Aggregate Saving Rates:
A Hump-Shaped Relationship
Pengfei Wang, Lifang Xu, and Zhiwei Xu
Hong Kong University of Science and Technology
First version: October 17, 2011
This version: June 06, 2012
Abstract
This study has documented a hump-shaped empirical relationship between …nancial development
and the national saving rate across 12 East Asian and 31 OECD economies. An incomplete-market
model featuring both heterogeneous households and heterogeneous …rms is provided to explain this
hump-shaped relationship. The key insight of the model is that …nancial development tends to reduce
the precautionary-saving incentives of households but increase …rms’ability to borrow and invest. As
a result, the aggregate saving rate may rise initially with …nancial development because of greater
investment by …rms, but then declines with further …nancial development because of substantially
reduced precautionary savings by households. The model also predicts that the market interest rate
lies substantially below the rate of return to capital in emerging economies, but the gap diminishes
with …nancial development, as observed in the data.
Keywords: High Saving Rate Puzzle, Financial Development, Hetergenous Firms, Hetergenous
Households, Borrowing Constraints
JEL Classi…cation: E21, E22, E44
We thank Yi Wen for numerous conversations that have led to some of the ideas in this paper and for his detailed suggestions that have improved the quality of the paper. We also thank Charles Horioka for useful comments. Correspondence:
Pengfei Wang, Economics Department, Hong Kong University of Science and Technology Phone: 852-2358-7612. Email:
[email protected].
1
1
Introduction
How does …nancial development a¤ect saving rates? Understanding the link between …nancial development and saving rates is important for several reasons. First, the saving rate is a crucial determinant of
a country’s long-run per capita income. The neoclassical exogenous growth model (Solow, 1956) suggests
that the higher the rate of saving, the richer the country in per capita income. The endogenous growth
theory pioneered by Romer (1986) and Lucas (1988) predicts that the saving rate determines long-run
growth: a higher saving rate leads to a higher economic growth rate. Understanding the link between
…nancial development and the saving rate is thus important for understanding how …nancial development
a¤ects economic growth, which is a useful step towards understanding the cross-country dispersion in
measured per capita income levels.
Understanding the link between …nancial development and the saving rate is also important for policy.
Aiyagari (1994) has shown that the optimal tax on capital income should be positive instead of zero in
a …nancially underdeveloped economy, which contradicts the well-known recommendation of zero capital
income taxation in the long run (Chamley, 1986). Krugger (2010) has further shown quantitatively that
a positive capital income tax rate has sizeable welfare gains in a carefully calibrated general equilibrium
model. However, such policy recommendations rely on the prerequisite that …nancial underdevelopment
will lead to oversaving. If …nancial underdevelopment causes undersaving, such policies may lead to
welfare losses.
Finally, understanding the link between …nancial development and the saving rate is important for
its own sake. The high saving rates in developing Asian countries have drawn signi…cant attention
from both academics and policy makers. The high saving rates in emerging Asia are claimed to cause
worldwide low real interest rates, to exacerbate asset price bubbles in the developed countries, and even
to have triggered the recent …nancial crisis1 . One popular explanation provided by the global imbalance
literature (e.g., Caballero, Farhi, and Gourinchas, 2008; Mendoza, Quadrini and Rios-Rull, 2009; Song,
Kjetil, and Fabrizio, 2011; Wen, 2011) attributes the high saving rates to …nancial underdevelopment in
those countries. However, Wei and Zhang (2011) recently criticize such explanations using the fact that
there has been …nancial development in those countries but at the same time the saving rate continued
to increase. This continuously rising saving rate along with …nancial development lead Wei and Zhang
(2011) to conclude that other factors such as a growing sex-ratio imbalance are the more important causes
1
On June, 3, 2008, in a speach at an international monetary conference, US Federal Reseve chairman Ben Bernanke said,
"In the …nancial sphere, the three longer-term developments I have identi…ed are linked by the fact that a substantial increase
in the net supply of saving in emerging market economies contributed to both the U.S. housing boom and the broader credit
boom. The sources of this increase in net saving included rapid growth in high-saving East Asian countries and, outside of
China, reduced investment rates in that region; large buildups in foreign exchange reserves in a number of emerging markets;
and the enormous increases in the revenues received by exporters of oil and other commodities. The pressure of these net
savings ‡ows led to lower long-term real interest rates around the world, stimulated asset prices (including house prices),
and pushed current accounts toward de…cit in the industrial countries–notably the United States–that received these ‡ows."
2
of the high saving rate in China (and some of other Asian emerging economies). Again, this criticism
by Wei and Zhang is valid only if the relationship between …nancial development and the saving rate
is monotonic. If the relationship is nonlinear, …nancial market development may induce high saving
countries to save even more.
The purpose of this study is hence twofold: First, to examine the relationship between …nancial
development and saving rates empirically; and second, to explain the empirical relationship theoretically
in a general equilibrium model. Our empirical analysis demonstrates a hump-shaped relationship between
…nancial development and the saving rate. Using a panel of 31 OECD countries and 12 East Asian
countries with annual time series observations from 1960 to 2008, …nancial development is shown to
increase with the aggregate saving rate initially, but further …nancial development reduces saving, after
controlling for demographic factors, income level, economic growth, in‡ation, and the interest rate, etc.2
A number of scholars have noted a statistical relationship between …nancial development and the
saving rate. For example, King and Levine (1993) …nd that higher levels of …nancial development are
associated with faster capital accumulation. Loayza, Schmidt-Hebbel and Serven (2000) and Horioka and
Yin (2010) …nd a negative correlation. Park and Shin (2009) …nd the impact of …nancial development
to be insigni…cant. Finally, Horioka and Hagiwara (2010) use data from 12 economies in developing
Asian countries during 1996-2007 to demonstrate that the relationship between …nancial development
and saving rate is nonlinear and hump-shaped. The empirical results of this study reconcile some of
those con‡icting …ndings and con…rms the hump-shaped relationship in a larger cross-country sample.
Con…rming the nonlinear relationship with a broader sample beyond East Asian countries is important,
since one may argue that East Asian countries in the sample of Horioka and Hagiwara (2011) might be
special, as they have historically had high saving rates. The existence of a uniform nonlinear relationship
between …nancial development and the saving rate in a broader sample also calls for a uni…ed theory to
explain the relationship. That is the main goal of this study.
The hump-shaped relationship between …nancial development and the aggregate saving rate cannot
easily be reconciled with the existing models of precautionary saving. The precautionary saving models
developed by Leland (1968), Kimball (1990), Weil (1993), Aiyagari (1994), and many others typically
predict a negative monotonic relationship between …nancial development and the saving rate. In these
models households mainly rely on savings to self-insure against idiosyncratic risks due to incomplete
…nancial markets. Greater …nancial development can hence reduce households’ reliance on saving for
self-insurance and thus reduce the saving rate. Such a negative relationship has been used to explain the
high saving rates in some …nancially underdeveloped countries. For example, Wen (2009, 2011) apply
the precautionary savings story to explain the puzzle of high Chinese saving. He shows that with large
uninsured risks and severe borrowing constraints, rapid income growth can increase (instead of decrease)
2
The ratio of domestic private credits to GDP is used as a measure of …nancial development following King and Levine
(1993). Other …nancial indicators are also tested as measures of …nancial development, and the hump-shaped relationship
are robust to these di¤erent indicators.
3
the household saving rate, thus explaining the puzzle that China’s household saving rate is one of the
highest in the world despite a 10% per year average income growth rate over recent decades.3
The global imbalance literature also relies on a negative monotonic relationship between …nancial
development and precautionary saving to explain capital out‡ows from emerging countries to developed
ones. However, such a monotonic relationship is contradicted by the data. Take China as an example.
The private credits to GDP ratio in China has increased from 50.9% in 1977 to 103.7% in 2008, but
China’s national saving rate has climbed to 51.8% from 28.9% during the same period. A similar pattern
can be found in South Korea. In the 1960s, the Koreans saved less than 10 percent (8.6%) of their gross
national product, with the average private credits to GDP ratio equal to 20.6%. The average national
saving rate in the 1990s had risen to 36.3% while at the same time the average private credits to GDP
ratio has increased to 67.5%. The Korean saving rates do decline to 30% in 2008 as the average private
credits to GDP ratio increased further to 108.8%.
On the other hand, the existing models of …rm-level …nancial constraints typically imply a positive
relationship between …nancial development and a …rm’s saving rate, in contrast to the previous literature
on household savings. In his seminal work, Myers (1977) …rst points out that debt can prevent a …rm
from making an investment project with positive net present value, a problem commonly referred to
as the debt overhang or underinvestment problem. Most macroeconomic workhorse models of …nancial
contracts feature such underinvestment problems. Examples include the credit rationing model of Stiglitz
and Weiss (1981), the costly state veri…cation models of Townsend (1979), Gale (1985), and Bernanke
and Gertelr (1989), the limited contract enforcement model of Kiyotaki and Moore (1997), and the moral
hazard model of Holmstrom and Tirole (1998). Since investment equals saving at equilibrium, these
models imply undersaving due to …nancial frictions. Financial development and saving can therefore
exhibit a positive monotonic relationship. But, such a pattern is not fully consistent with the empirical
evidence marshalled in this study.
We combine the insights generated by the aforementioned two literatures to explain our empirical
…ndings. In particular, we propose that the observed hump-shaped relationship between …nancial development and the saving rate can be explained by imposing …nancial frictions on both the household
and the …rm side. Generally speaking, this assumption should complicate a dynamic general equilibrium
model substantially, since to compute the general equilibrium in such a model one must keep tract of the
distribution of household wealth and the distribution of …rms’ capital stocks simultaneously, and both
distributions have typically in…nite dimensionality. In addition, the two distributions interact endoge3
We do not argue that no model of precautionary saving can explain the hump-shaped relationship between …nancial
development and the aggregate saving rate. A hump-shaped relationship is possible if …nancial development can stimulate
economic growth. Wen (2009, 2011) points out that economic growth can increase saving dramatically in a general equilibrium
model. Financial development may increase saving initially due to a rising rate of income growth but decrease if eventually
by reduction of the self-insurance motivation. The interaction of these two opposite forces may be able to generate a
nonlinear relationship between …nancial development and the aggregate saving rate. But, con…rming these conjectures with
an endogenous growth model is an interesting topic left for future research.
4
nously at general equilibrium. For example, the distribution of capital depends on the pricing kernel,
which equals the marginal investor’s discounting factor, which depends on the wealth distribution of the
households. Yet the households’wealth distribution is a¤ected by the …rms’distribution of capital as it
a¤ects the returns on the households’portfolios. Solving such a model can be daunting.
To overcome such technical di¢ culties, we borrow the household model of Wen (2009, 2011) assuming
a quasilinear preference function. This allows us to characterize the household saving behavior in closed
form even though households face uninsurable idiosyncratic liquidity shocks and borrowing constraints.
For any given interest rate, households are found to save excessively compared to an economy without
uninsurable risks, as Wen (2009, 2011) has shown. A higher level of …nancial development will thus lead
to less incentive to save, everything else equal.
Our major innovation lies on the …rm side. We add to heterogenous …rms to Wen’s heterogenoushousehold model. In the enriched model, the …rms discover investment opportunities randomly, which
captures the idea that investment at …rm and plant level is lumpy. Hence, only a fraction of …rms invest in
each period. This creates a need to transfer funds among the …rms. However, friction arises when moving
funds between …rms, which is due limited enforcement problems. In other words, the …rms are …nancially
constrained. Assuming constant returns to scales allows us to characterize the …rms’investment decision
rules analytically and permit exact aggregation, so only the mean of the distribution of capital matters for
aggregate equilibrium.
4
We show that borrowing constraints on the …rms create a gap between the return
on capital and the e¤ective real interest rate for saving. A relaxation in the borrowing constraints on
…rms will narrow this gap and increase the real interest rate. Hence a high level of …nancial development
will also generate an incentive for …rms to increase their saving (or investment) rates. The overall e¤ect
on aggregate saving rate will then depend on which side of the economy (the household side or the …rm
side) dominates.
Our model is able to generate a hump-shaped relationship between …nancial development and the
aggregate saving rate as with reasonable parameter values. To understand the intuition, imagine an
extreme case in which …rms have to borrow to invest but they cannot borrow at all. In such an extreme
case, the total investment demand would be zero. Since at equilibrium total saving must equal to total
investment, the aggregate saving rate will always be zero regardless of the saving incentives on the
4
Our modelling of …nancial frictions at the …rm level is motivated by a vast empirical literature that studies the interaction
between …nancial constraints and corporate investment. Numerous studies have found that …nancial constraints on corporate
investment are pervasive even in the developed economies. (See Hubbard (1998) for a recent survey on the earlier literature
using the Q-theory of investment, and Inessa (2003) for recent international evidence from structural investment models). At
the same time, an equally vast theoretical literature pioneered by Bernanke and Gertler (1989), Kiyotaki and Moore (1997),
Bernanke, Gertler and Gilchrist (1999), Albuquerque and Hopenhayn (2004) and Cooley, Marimon, and Quadrini (2004)
has developed full dynamic general equilibrium models of investment with …nancial constraints to examine the aggregate
implications of …nancial frictions for business cycles ‡uctuations. Our heterogenous-…rm model with limited enforcement
frictions and random investment opportunities is also closely related to the recent general-equilibrium-heterogeneous-…rm
models of Wang and Wen (2010, 2011) in which the assumption of constant returns to scale allows them to characterize the
…rms’investment decision rules in closed forms and permit exact aggregation. Wang and Wen (2010, 2011) do not consider
heterologous households. Miao and Wang (2010) exploit the property of constant returns to scale to analytically model
credit risk in a DSGE model. Miao and Wang (2011) study asset bubbles in a …nancially underdeveloped economy with
heterogenous …rms.
5
household side. Although households have strong precautionary saving motives under large idiosyncratic
risks, the e¤ective rate of return (the interest rate) on household saving is too low to induce them to
save. As the borrowing constraints in such an economy gradually relax (for both …rms and households),
the aggregate saving rate will initially go up as …rms start to invest heavily. Beyond a critical level,
however, the downward trend in household saving starts to dominate. Thus, further relaxation in …nancial
constraints will reduce the aggregate saving rate.
The rest of the paper is organized as follows. Section 2 presents the empirical evidence of a humpshaped relationship between …nancial development and the aggregate saving rate. Section 3 presents
our model in which both households and …rms may face …nancial constrains. Section 4 de…nes and
characterizes the general equilibrium. Section 5 examines the impact of …nancial development on the
aggregate saving rate for di¤erent scenarios in the model. Finally, section 6 concludes.
2
Empirical Evidence
Anecdotal evidence usually suggests that the e¤ect of …nancial development on saving is negative. Indeed,
many previous empirical studies, including those by Loayza, Schmidt-Hebbel and Serven (2000), Horioka
and Yin (2010) and those surveyed by Schmidt-Hebbel and Serven (2002), con…rm such a negative
relationship. However, those studies typically use the aggregate credits to the private sector as a measure
of …nancial development, yet presume that the relationship between …nancial development and saving is
linear, which may not be the case in reality.
Beck et al. (2012) …nd that leading to …rms and lending to households have fairly di¤erent e¤ects on
the outcomes of real sectors. For saving rate, on one hand, …nancially constrained household may save due
to precautionary motives, hence expanding credits to the households can lead to a decreasing household
saving rate5 ; on the other hand, …nancially constrained …rms cannot invest to their optimal level due
to the limit of fund, thus, expanding credits to the …rms can lead to an increasing …rm investment and
hence an increasing …rm saving rate. As a result, the e¤ects of increasing aggregate private credits on
the aggregate saving rate are ambiguous, depending on which sector is favored and gets the expanding
credits. Thus, at least in theory, a non-monotonic relationship is possible. Actually, when Horioka and
Terada-Hagiwara (2010) relax the assumption of linearity, they …nd that the relationship between the
saving rate and …nancial development (aggregate private credits) is concave for a sample of 12 East Asian
countries.
In this study, we collect time series data ranging from 1960 to 2008 on saving rates and its potential
explanatory variables for the same 12 East Asian countries6 and extra 31 OECD economies, and use
5
In Appendix D, we use a sample of 26 OECD economies to show that household saving rate does decrease when the
household credits expand or when the size of household …nance increases.
6
India and Pakistan are also included in the sample, in order to be comparable to the results of Horioka and TeradaHagiwara (2010). But it is not crucial for the results presented in this paper.
6
various subsamples and estimators to re-examine the possibility of nonlinearity in the relationship.
2.1
Data
Our sample draws from the World Development Indicators and the Penn World Table. The data set
consists of annual time series observations from 1960 to 2008 for 41 countries, which locate in East Asia
or belong to OECD7 . A detailed description of the data is presented in Appendix B.
Following Loayza et al. (2000), we set a threshold of
50% annual in‡ation rate to exclude the
episodes of high in‡ation in the sample. To accommodate the joint endogeneity problem of explanatory
variables, we will implement dynamic panel regression with GMM-IV estimators described below. Thus,
we choose to work with the original data instead of phase-averaged data to retain relevant information.
As a result, we have a maximum of 976 observations for 41 countries.
The data show that both saving rates and levels of …nancial development display signi…cant variations
across di¤erent countries and time. Saving rate ranges from less than 5% in Indonesia in the early 1960s
to more than 50% in China today, private credits to GDP ratio also ranges from less than 10% in the
early years of those developing countries to larger than 2 in currently developed economies.
Figure 1 displays the scatterplots of gross saving rate against private credits to GDP ratio for the 12
East Asian countries, stacked with the quadratic …t and LOWESS …t. It is evident from the graph that
the relationship between saving rate and …nancial development (private credits to GDP ratio) displays a
humped shape, with …nancial development initially increasing and then decreasing the saving rate. This
pattern is consistent with what Horioka and Terada-Hagiwara (2010) found in their sample of these same
12 East Asian economies.
While East Asia might be a bit special due to its eye-catching high saving rates, our panel regression
using a broader sample that also includes 31 OECD economies and using various speci…cations and
estimators, further con…rms the hump-shaped relationship.
2.2
Empirical speci…cation
Consider the following reduced-form regression equation:
sit =
1 sit 1
0
2 Xit
+
+
i
+ uit ;
(1)
where s is the gross domestic saving rate, X is a vector of explanatory variables re‡ecting …nancial
development, age structure, rates of return, uncertainty, …scal policy, income level and growth, which
have been shown to a¤ect the saving rate in the literature,
denotes the unobserved country …xed
e¤ects, and uit is the error term.
7
Japan and South Korea belong to both groups, thus the total number of countries studied is 41, instead of 43. The size
of the sample is determined by availability of observations.
7
.5
.4
Gross saving rate
.2
.3
.1
0
Scatterplots
LOWESS f it
0
.5
1
1.5
Priv ate credits to GDP ratio
Quadratic f it
2
2.5
Figure 1: Scatterplot of gross saving rate and private credits/GDP ratio, East Asia
Various theories have emphasized on di¤erent factors in explaining the saving behavior. Life-cycle
models imply that demographic factors play a non-trivial role in determining the saving rate, so each
economy’s aged dependency ratio, youth dependency ratio and life expectancy are included in the regression. Precautionary saving theory emphasizes that people will save against future uncertainties, thus
in‡ation rate is employed to capture macroeconomic uncertainty and public expenditure on health and
education is used to re‡ect people’s concern about uncertainty on future health and education expenditures. The permanent income hypothesis suggests that income and its growth determine economic agents’
consumption and savings, so per-capita real GDP and its square, and the growth rate of per-capita real
GDP are all included in the regressions. The square of income level in the model is included in an attempt
to capture the potential nonlinear relationship between income and the saving rate. Both Park and Shin
(2009) and Horioka and Terada-Hagiwara (2010) …nd that the relationship is convex in their samples of
Asian countries. Several other common variables such as real interest rate and current account balance
are also included.
However, the main purpose of this regression is to investigate the presumable nonlinear e¤ects of
…nancial development on the saving rate, after properly controlling those relevant factors mentioned
above. There are various possible measures of …nancial development8 , some of which rely on the size of
the whole …nancial sector, while the others focus on the role of …nancial intermediation. To be consistent
8
See the survey by Cook (2003). Thorsten Beck also writes about "two concepts of …nancial development" recently,
one is the "…nancial intermediation view", the other is the "…nancial center view". For details, please refer to his article:
http://www.voxeu.com/index.php?q=node/7185
8
with the argument in this paper and with the most popular measure used in the literature, this paper
uses the private credits to GDP ratio as a measure of …nancial development9 . In order to capture the
possible nonlinearity, we employ both of the level and its square as explanatory variables10 .
2.3
Econometric Methodology
We employ this …xed-e¤ects dynamic panel speci…cation to account for unobserved country-speci…c e¤ects
and to deal with the possible inertia in the annual time series. In our static panel regressions, Wooldridge
test for …rst-order serial correlation of the errors always rejects the null hypothesis of zero autocorrelation,
which implies that the time series display serious inertia. That’s why we include the lagged saving rate
in the regression.
However, …xed-e¤ects dynamic panel speci…cation brings about several problems in estimation. To
eliminate the unobserved country-speci…c e¤ects, we need to work with the mean-di¤erence or …rstdi¤erenced model derived from equation (1). Unfortunately, neither the within estimator nor the IV
estimation using lags is feasible in the mean-di¤erence model, because any lag sit is correlated with
ui and hence (uit
ui ), which is the error term in mean-di¤erence model11 . OLS estimator is also
inconsistent in the …rst-di¤erenced model, because
sit
1
is correlated with
uit , which is the error
term now. Thus, we need to resort to some other methods. Arellano and Bond (1991) describe a GMMIV estimator (Arellano-Bond di¤erence estimator henceforth) and the test for serial correlation of the
errors that apply to the …rst-di¤erenced model in detail. The estimator assumes that the errors uit are
serially uncorrelated and E(sis uit ) = 0 for s
t
2. By this assumption, fsit
j gj=2;3;::: can
be used as
instruments for sit in the …rst-di¤erenced model and GMM estimation using lags as instruments delivers
consistent and e¢ cient results.
The Arellano-Bond di¤erence estimator can also control for endogeneity of the other explanatory
variables, which is particular relevant in our study here. We already know that introducing lagged
dependent variable causes endogeneity problem. It is also highly possible that credits, income and its
growth are jointly determined with the saving rate, so they might be correlated with the errors as
well. Thus, IV estimator is necessary. However, since the model is potentially over-identi…ed, GMM-IV
estimator is more e¢ cient than two-stage least squares (2SLS).
9
This measure refers to the "…nancial intermediation" view of …nancial development in Thorsten Beck’s article. To be
sure, a larger …nancial sector does not necessarily imply a higher level of …nancial development. Thorsten Beck provides an
example of Nigeria in the 1980s, where expanding of …nancial sectors was accompanied by "…nancial dis-intermediation".
Another example is China, large-scale state-owned bank sector provide limited credits to private-owned …rms. On the
contrary, aggregate credits to private sectors directly measure the activities of …nancial intermediation. Hence, we consider
it as a more appropriate measure of …nancial development in the context of this paper.
10
While quadratic …t is enough to capture nonlinearity, it is also interesting to see what happens under semiparametric
regression, in which …nancial development enters non-parametrically and other explanatory variables enter parametrically.
In Appendix E, we apply the Baltagi&Li (2002) estimator for partially linear …xed-e¤ects panel data models to our full
sample, and …nd that the relationship is indeed hump-shaped.
11
To be speci…c, within estimator is no longer consistent, because sit 1 is correlated with uit 1 and hence with ui . As a
result, the regressor (sit 1 si ) in the mean-di¤erence model is correlated with the error term (uit ui ). Similarly, any lag
sit is correlated with ui and hence with (uit ui ), thus IV estimation using lags is not feasible either.
9
Following Loayza et al. (2000), in the following regressions, we assume that those endogenous explanatory variables are correlated with past and current errors but not with future errors. That is,
E(Xit uis ) 6= 0 for s
t, but E(Xit uis ) = 0 for s > t. In other words, they are "weakly exogenous".
As argued by Loayza et al. (2000), this is a fair restriction, because the past realizations of explanatory
variables are less likely to be in‡uenced by future innovations to saving rates. By this assumption, weakly
exogenous variables in Xit can be instrumented using their own lags fXit
j gj=2;3;:::
in the …rst-di¤erenced
model.
However, the Arellano-Bond di¤erence estimator do have some problems, because lags could be weak
instruments in the …rst-di¤erenced model if the corresponding level variables display serious inertia over
time. Thus, the system estimator that incorporates both of the level equation and its …rst di¤erence
is proposed by Arellano and Bover (1995) and Blundell and Bond (1998). They add another moment
condition beyond those in the di¤erence estimator, namely, E( sit
instrumented using its own …rst di¤erence
sit
1
1 uit )
= 0. As a result, sit can be
in the level equation (1). Similar moment conditions
can be imposed on those endogenous explanatory variables, so that they can be instrumented using their
…rst lag di¤erences in the level equation. This system estimator is shown to be be more precise and to
have better …nite sample properties.
Thus, we …nally choose the system GMM-IV estimator. In the following regressions, we treat two
dependency ratios, life expectancy and public expenditures as strictly exogenous variables, and assume
that the others are all weakly exogenous.
We present the main results in the next subsection. In deriving these results, we instrument the
endogenous variables using their own …rst two lags in the …rst-di¤erenced equation and using …rst lag
di¤erence in the level equation12 . We also employ the …nancial development index prepared by Abiad et
al. (2008) as an external instrument in the level equation, because Roodman (2009a) …nds that lags of
several popular …nancial development measures, including private credits used in this paper, all perform
badly in the system GMM estimation, when he replicates the exercises done by Levine et al. (2000).
It is worth mentioning that using lags as instruments typically generates numerous instrument count.
Roodman (2009a) shows that "too many instruments" can over…t the endogenous variables and weaken
the Hansen test of joint validity of instruments, making the results unreliable. Thus, as a robustness
check, we also consider reducing the instrument count in our regression exercises by "collapsing" the
instrument matrix, as suggested by Roodman (2009a).
12
The main results are robust if we use 3 lags as intruments in the …rst-di¤erenced equation, while the results are mixed if
only one lag is used. To be speci…c, when only one lag is used, in all cases the coe¢ cients still imply a concave relationship,
but they are only signi…cant in the East Asia subsample, no matter the IV matrix is collapsed or not. In the full sample,
they are signi…cant only when the IV matrix is not collapsed. Nevertheless, Hansen tests for joint validity of instruments
in Table 2-4 indicate that using 2 lags as instruments are valid, even when we take care of the problem of "too many
instruments" using the method suggested by Roodman (2009a). Thus, we interpret those results as supportive for a humpshaped relationship between …nancial development and saving rate. Our semiparametric regression in Appendix E further
con…rms that.
10
2.4
Empirical Results
The coe¢ cients of most interest in model (1) are those on the …nancial development and its square. Table
1 summarizes the regression coe¢ cients on these two variables for our full sample of 41 countries, using
three di¤erent estimators13 . Table 2
4 in Appendix C report the full results. We brie‡y discuss these
results in this section.
All of these regressions show that the relationship between aggregate private credits and the saving
rate is hump shaped. When credit volume is low, the saving rate increases with credit expansion; when
credit volume increases further, the relationship is reversed. They con…rm what has been observed in
Figure 1 with our naked eyes, and are consistent with the results presented by Horioka and TeradaHagiwara (2010), who only considered the sample of East Asian countries. Indeed, the last two columns
of Table 2 in Appendix C actually replicate Horioka and Terada-Hagiwara’s results.
Table 1: Summary of the coe¢ cients on private credits and its quadratic term, full sample
Estimator
Collapsed IV
Private credits
Private credits sq.
Country e¤ects
Observations (Number of cn)
(1)
GMM-System
No
(2)
GMM-System
Yes
(4)
Within
–
(5)
RE
–
0.0210***
(0.00676)
-0.00706**
(0.00310)
Yes
809 (37)
0.0321**
(0.0144)
-0.0127***
(0.00491)
Yes
809 (37)
0.0925***
(0.0287)
-0.0296***
(0.0100)
Yes
976 (41)
0.105***
(0.0308)
-0.0321***
(0.0101)
No
976 (41)
Note: *** p<0.01, ** p<0.05; robust standard errors in parentheses. The regression
coe¢ cients on age dependencies, income growth, income level, real interest rate, in‡ation
rate, public expenditure and current account surplus are in listed in tables 2 to table 4 in
Appendix C.
The regression results are broadly consistent with the these of Loayza et al. (2000) and Horioka and
Terada-Hagiwara (2010) regarding other explanatory variables. For example, Two age dependencies show
signi…cant negative e¤ects on the saving rate, as senior citizens tend to consume their previous saving
and kids usually consume without their own income. The per-capita GDP growth has a highly signi…cant
positive e¤ect in almost all of the cases. Real interest and in‡ation rates have ambiguous e¤ects; Higher
public expenditure typically has a negative e¤ect, which may re‡ect households’precautionary saving to
some extent. The current account surplus has a positive and signi…cant e¤ect.
13
In unreported tables, we also try the Arellano-Bond di¤erence estimator, and the main results are robust.
11
In short, our results are essentially the same with those of Loayza et al. (2000), expect for the e¤ect
of …nancial development. Loayza et al. (2000) presume that the e¤ect is linear and …nd a negative e¤ect.
However, when we explicitly take nonlinearity into account, we …nd that the relationship is hump-shaped.
The hump-shaped relationship is consistent with what Horioka and Terada-Hagiwara (2010) have recently
found in a sample of 12 East Asian countries. In fact such a hump-shaped relationship is not a surprise
if both households and …rms face credit constraints, as our model will show.
3
The Model
We consider an in…nite-horizon economy. There is no aggregate uncertainty. The economy has two
types of agents, consumers and …rms with equal mass normalized to unity. We use i 2 [0; 1] to index
households and j 2 [0; 1] to index …rms. Firms accumulate capital and combine labor and capital to
produce consumption goods. Households supply labor to the …rms and own their stock. Both households
and …rms are subject to uninsurable idiosyncratic risks and …nancial constraints to be speci…ed below.
3.1
Households
The household side is similar to that modelled by Wen (2009, 2011). Household i derives utility from
consumption cit and leisure nit . The instantaneous utility function is uit =
it log cit
an idiosyncratic preference shocks with the distribution function F ( ) = Pr [
i
The mean of
i
is normalized to one, E
i
nit , where
] and support [0;
it
is
max ].
= 1. Each time period is divided into two sub-periods. The
idiosyncratic shocks are realized in the second sub-period. Each household i chooses labor supply nit
in the …rst sub-period without observing
it ,
and chooses consumption cit and savings in bonds (sit+1 )
and stocks (ait+1 ) in the second sub-period after observing
it .
With such an information and market
structure, labor income cannot be used to fully diversify the idiosyncratic risk and savings become a
bu¤er stock to smooth consumption. Taking as given the real interest rate Rf t and real wage Wt , the
household i solves
max
fc;s0 a0 g
where
(
max Ei
fng
"
1
X
t
(
it log cit
t=0
#)
nit )
;
(2)
2 (0; 1) is the discount factor. The household i faces a period-by-period budget constraint,
cit +
sit+1
+ ait+1 Qt
Rf t
sit + Wt nit + (Qt + Dt ) ait ;
(3a)
where ait+1 is the share of a portfolio of stocks purchased by household i. Assume each household is
subject to a limited borrowing capacity:
sit+1
+ ait+1 Qt
Rf t
12
Bt ;
(4)
where Bt is an exogenous borrowing limit. Denote the Lagrangian multipliers for (3a) and (4) as
it ;
it
and
respectively. The …rst-order condition for labor is
Wt Ei [
it ]
= ;
(5)
where Ei is an expectation operator over idiosyncratic risk
serving
i,
the household will take the distribution of
i.
Since labor is determined before ob-
into account. The …rst-order conditions for
i
fcit ; sit+1 ; ait+1 g are given, respectively, by
it
cit
it
it
3.2
it
it
=
it ;
(6)
= Rf t Ei [
= Ei
it+1
it+1 ] ;
(7)
Dt+1 + Qt+1
:
Qt
(8)
Firms
Each …rm j combines labor (Nj ) and capital (Kj ) to produce output employing Cobb-Douglas technology,
1
Yjt = Kjt Njt
;
2 (0; 1) :
Following Kiyotaki and Moore (1997, 2008), we assume that …rms encounter investment opportunities
randomly14 . In each period, …rm j encounters an investment opportunity with probability
probability 1
: With
; the …rm has no investment opportunity. Assume the random investment opportunities
are independent across …rms and over time. Denote as Ijt the investment level of …rm j in period t if it
can invest, the capital accumulation rule then follows
Kjt+1 =
(1
) Kjt + Ijt
with probability
(1
) Kjt
with probability 1
:
(9)
With heterogenous households, the …rm’s dynamic programing problem becomes slightly more complicated. The …rst step is to …nd the right discounting factor. We like Hansen and Richard (1987),
Ingersoll (1988), and Cochrane (1991) assume that a sequence of prices Pt exist such that a …rm’s value
is determined by
Jjt =
1
X
Pt+
=0
Pt
Djt+ ;
where fDjt+ g1=0 is the dividend ‡ow generated by …rm j. De…ne
(10)
t
= Pt = t , where
< 1, and we can
rewrite the …rm’s value as
14
Miao and Wang (2011) use a similiar assumption to study asset bubbles in a …nancially underdeveloped economy with
heterogenous …rms but a representative household.
13
Jjt =
1
X
t
t+
Djt+ ;
(11)
t
=0
which can be rewritten recursively as
Jjt = Djt +
t+1
Jjt+1 :
(12)
t
Here
is a discount factor, but notice that because of heterogeneity on the household side,
does not
necessarily equal households’discount factor : With the the …rm value given by (12), each …rm’s problem
is then to maximize its value Jjt by choosing its optimal labor use and investment.
The optimal labor choice is static. It is straightforward to show that the …rm’s operating pro…ts are
linear function of its capital stock,
1
Rt Kjt = max Kjt Njt
Wt Njt ;
Njt
(13)
1
where Wt is the real wage and Rt =
1
Wt
. The optimal labor demand is hence
Njt =
1
1
Wt
Kjt :
(14)
Denote the …rm value in period t as Jt (Kjt ), and it now can be de…ned recursively using the proper
discounting factor
t+1
t
as
Jt (Kjt ) = max Rt Kjt
Ijt
Ijt +
t+1
[ Jt+1 ((1
) Kjt + Ijt ) + (1
) Jt+1 ((1
) Kjt )] :
(15)
t
Assume that …rm j can use both internal funds, Rt Kjt , and outside funds from borrowing, Ljt , to …nance
investment, its maximum investment is thus subject to the constraint
Ijt
Ljt + Rt Kjt :
(16)
For simplicity, assume that the external funds are raised through intra-period loans: …rms borrow from
…nancial intermediaries at the beginning of period t and pay back with zero interest rate at the end
of period t through raising additional equity. (Dividends maybe negative at the …rm level.) One key
assumption of this model is that loans are subject to collateral constraints, as in the model of Kiyotaki
and Moore (1997). Firm j pledges a fraction
t as collateral. The parameter
2 (0; 1] of its …xed assets Ktj at the beginning of period
may represent the tightness of the collateral constraint or the extent
14
of …nancial market imperfections. At the end of period t, the market value of the collateral is equal to
t+1
t
Jt+1 ( Kjt ), which is the discounted expected market value of …rm j if it owns capital stock Kjt
at the beginning of period t + 1 and faces the same investment and collateral constraints in the future.
The amount of loans Ljt cannot exceed this collateral value, otherwise, the …rm would choose to default
on its debt and lose the collateral value. This leads to the following collateral constraint:
t+1
Ljt
Jt+1 ( Kjt ) :
(17)
t
To sum up, each …rm j solves problem (15) subject to constraints (16) and (17).
3.3
Financial intermediation
The …nancial intermediation is quite simple. The …nancial intermediate holds a portfolio consisting of
stock in all of the …rms and collects aggregate dividends from all of the …rms,
Dt =
Z
(Rt Kjt
Ijt ) dj:
(18)
[Qt+1 + Dt+1 ]:
(19)
The price of the portfolio Qt ; is thus
Qt =
t+1
t
The presence of …nancial intermediation is just to simplify the notation of the households’maximization
problem. One can also assume that households directly hold a market portfolio that consists of stock in
all …rms, and the equilibrium results will be the same.
3.4
General Equilibrium
R1
R1
R1
R1
R1
R1
Let Kt = 0 Ktj dj; It =
0 Ijt dj; Nt = 0 Njt dj; Yt = 0 Yjt dj; nt = 0 nit di; St = 0 sit di; and
R1
Ct = 0 cit di be the aggregate capital stock, investment, labor demand, output, labor supply, household
saving and consumption, respectively. General equilibrium is then de…ned as sequences of aggregate
variables, (Kt ; It ; Nt ; Yt ; Dt ; nt ; St ; Ct ) ; individual …rms’choices, (Kjt ; Ijt ; Njt ; Ljt ; Yjt ) ; individual households’choices, (nit ; sit+1 ; cit ) and prices (Qt ; Wt ; Rt ; Rf t ) ; such that each …rm and each household solve
their optimization problems, and all markets clear:
N t = nt ;
(20)
St+1 = 0;
(21)
15
Z
ait di = 1;
(22)
Ct + It = Yt ;
(23)
Kt+1 = (1
4
) Kt + It :
(24)
Characterization of the Equilibrium
Let us …rst derive the optimal decision rules on a single …rm and a single household, then aggregate their
individual choices and characterize the competitive equilibrium by a nonlinear equation system.
4.1
A Single Firm’s Decision Problem
We conjecture that the value of a …rm has the following functional form:
Vt (Ktj ) = vt Ktj ;
(25)
where vt is a to-be-determined variable that only depends on the aggregate states. De…ne qt = Et
t+1
t
vt+1 ,
which will proved to be the traditional Tobin’s q. With the conjectured value function, the …rm’s investment problem becomes
vt Kjt = max Rt Kjt
Ijt + qt [(1
Ijt
) Kjt + Ijt ] ;
(26)
with the liquidity constraint
Ijt
Ljt + Rt Kjt ;
(27)
qt Kjt :
(28)
and the collateral constraint
Ljt
The following Proposition characterizes the optimal decisions for …rm j.
Proposition 1 If qt is greater than 1, the …rm always chooses to invest the maximum amount whenever
it has an investment opportunity. In particular, the optimal investment decision is
Ijt = qt Kjt + Rt Kjt :
(29)
In addition,
vt = Rt + (1
)qt + (qt
1)(qt + Rt );
(30)
where qt evolves according to
qt =
t+1
[Rt+1 + (1
)qt+1 + (qt+1
t
16
1)(qt+1 + Rt+1 )]:
(31)
Proof: See the Appendix A.1.
Here, vt is the average market value of one unit of capital and qt is the ex-dividend value of one unit of
installed capital, which is the marginal bene…t of new investment. Since the cost of investment is one, the
additional gain from investing is positive if qt
1 > 0. In this case the …rm will want to borrow as much
as possible to invest, so its borrowing constraint binds. The value vt consists of three parts on the right
hand side of equation(30). First, one unit of capital can generate Rt units of operating pro…t in period
t. Second, one unit of capital can carry 1
unit of capital to the next period with value (1
) qt after
depreciation and paying dividends. Finally, the capital can also be used as collateral. With probability
the …rm will have an investment opportunity and one unit of capital is able to obtain qt units of loans,
which can expand the expected net bene…t from investing by (qt
1)(qt + Rt ):
Equation (31) comes from the de…nition of qt : In fact, after multiplying both sides by Kt+1 ; equation
(31) is equivalent to the asset pricing formula (19). To see this, aggregating (29) gives total investment
of
It =
(qt + Rt ) Kt :
(32)
The aggregate capital follows as
Kt+1 = It + (1
)Kt :
It is easy to see that the aggregate dividend is given by Dt = Rt Kt
(33)
It . Multiply both sides of (31) by
Kt+1 ; and we have
qt Kt+1 =
t+1
[Rt+1 Kt+1 + (1
)qt+1 Kt+1 + (qt+1
1) (qt+1 + Rt+1 )Kt+1 ]
t
=
t+1
[Rt+1 Kt+1
It+1 + (1
)qt+1 Kt+1 + qt+1 It+1 ];
[Rt+1 Kt+1
It+1 + qt+1 Kt+2 ];
t
=
t+1
(34)
t
where the second line comes from aggregate investment equation (32) and the third line comes from the
law of motion of aggregate capital (33). Comparing it with (19) yields
qt Kt+1 = Qt :
4.2
(35)
A Single Household’s Decision Problem
For household i, the …rst-order conditions are list by (5) to (8). Following Wen (2009, 2011) by denoting
Hit = (Qt + Dt ) ait +Wt nt (i)+sit as the total income of household i in period t, the following proposition
shows that the income distribution is degenerate Hit = Ht and there exists an unique cuto¤
the borrowing constraint (4) will bind if and only if
17
it
t.
t
such that
Proposition 2 Given Wt and Rf t , Ht and
t
= Rf t (Ht + Bt ) Et
and
Wt
Given
t
are jointly determined by the following two equations:
t
Z
;
Wt+1
(36)
max( ; t )
f ( )d = :
Ht + Bt
(37)
and Ht , the optimal consumption of household level can be summarized as
cit = min
it
; 1 (Ht + Bt ) ;
(38)
t
and Lagrangian multipliers
and
it
it
are given by
it
it
=
max( it ; t )
;
Ht + Bt
(39)
max( it
t ; 0)
:
Ht + Bt
(40)
=
Finally the risk free rate and the asset price are determined, respectively, by
1
= Rf t
Ht + B t
Ht+1 + Bt+1
Z
max( ;
t+1 )f
( )d ;
(41)
Qt+1 + Dt+1
Ht+1 + Bt+1
Z
max( ;
t+1 )f
( )d :
(42)
t
and
t
Ht + Bt
Qt =
Proof. See Appendix A.2.
Similar to Wen (2009, 2011),15 with quasilinear preferences, the household can achieve a target wealth
Ht in period t to bu¤er the idiosyncratic preference shocks through adjusting his labor supply. The
quasilinear utility function implies that the marginal disutility of acquiring additional labor income is
a constant (equal to
Wt )
for all households. Since the preference shock is i.i.d, the expected marginal
utility from consumption depends only on the total wealth in period t (not on the history of idiosyncratic
shocks). The household supplies his labor to a point where the marginal disutility equals the expected
gains in the marginal utility, which implies a common target wealth for all households.
15
Also see Wen (2010).
18
In the absence of aggregate uncertainty, equations (41) and (42) then imply
Qt =
Qt+1 + Dt+1
:
Rf t
(43)
Namely, the risk free rate is the proper discounting factor for the …rms. With the decision rules of the
…rms and the households in hand, we are ready to characterize the aggregate equilibrium by a set of
nonlinear equations below.
4.3
Aggregation
Equation (14) implies that the capital-labor ratio is the same for all …rms, so Kjt =Njt = Kt =Nt . It follows
that the aggregate production is given by
Yt = Kt Nt1
;
(44)
and the two factor prices Rt , and wt are given by
Rt =
Yt
Kt
Wt = (1
)
(45)
and
Yt
:
Nt
(46)
Since the wealth distribution is degenerate (Hit = Ht ), aggregating Hit yields
Z
Hit di = Ht = (Qt + Dt )
Z
ait di + Wt Nt +
Z
sit di
= Qt + Dt + Wt Nt
= qt Kt+1 + Yt
The second line comes from the fact that
R
It :
(47)
ait di = 1 and
fact that Qt = qt Kt+1 by equation (35), Dt = Rt Kt
R
sit di = 0; the third lines come from the
It and Rt Kt + Wt Nt = Yt by equations (45) and
(46). Aggregating equation (38) yields the aggregate consumption with heterogenous households and
borrowing constraints as
Ct = (Ht + Bt )
Z
min(
; 1)f ( )d ;
(48)
t
which resembles a Keynesian consumption function, with the propensity to consumption equal to
R
min( ; 1)f ( )d <
t
1. The reason why the propensity to consume is less than one is that idiosyncratic preference shocks and
19
borrowing constraints give the households a precautionary motive to accumulate wealth. Equation (31)
and aggregate (43) imply
qt =
1
[Rt+1 + (1
Rf t
)qt+1 + (qt+1
1)(qt+1 + Rt+1 )]
(49)
in the absence of aggregate uncertainty.
The equilibrium can now be characterized in the model by the following proposition.
Proposition 3 The equilibrium path of the model is characterized by dynamic movements of 8 aggregate
variables {Ct ; It ; Yt ; Nt ; Kt+1 ; Rf t ; qt ; "t }, which can be solved by the system of 8 nonlinear equations:
( t+1 )
( t)
= Rf t
(
Ct
Ct+1
( t ) ( t+1 )
(1
Ct+1
)
t+1 )
(50)
Yt
=
Nt
(51)
Yt = Kt Nt1
Kt+1 = (1
(52)
)Kt + It
(53)
Ct + It = Yt
It =
qt =
Yt+1
1
[
+ (1
Rf t Kt+1
Yt
Kt
Kt
qt +
)qt+1 + (qt+1
Ct = (qt Kt+1 + Yt
where
( t) =
R
min( ;
t )f (
)d ,
(
t+1 )
=
R
(54)
(55)
1)(qt+1 +
Yt+1
)]
Kt+1
(56)
It + Bt ) G( t );
max( ; 1)f ( )d > 1, and G( t ) =
t
(57)
R
min( ; 1)f ( )d .
t
Equation (50) follows from equation (48). Equation (51) is derived from (37) by replacing Ht + Bt by
the aggregate consumption and replacing the real wage by equation (46). Equation (52) is identical to
equation (44). Equation (53) describes how aggregate capital evolves, and equation (54) is the aggregate
resource constraint. Equations (50) to (54) are similar to those of a standard RBC model. Equation
(55) is the aggregate investment equation. The …nancial frictions introduce two new variables, qt and
t,
which are determined by equations (56) and (57). Equation (56) is obtained by substituting out Rt+1
using equation (45) on the right hand side of equation (49). Finally combining equation (47) and equation
(48) yields equation (57).
20
5
The Saving Rate and Financial Development
In this section, we discuss the relationship between the aggregate saving rate and …nancial development in
the steady state. The saving rate is measured by the investment to output ratio, s =
and the steady state ratio b
I
Y
. The parameter
B=qK measure the …nancial development on the …rm side and household
side, respectively. To better understand the hump-shaped relationship between …nancial development and
the saving rate, we consider four di¤erent scenarios: (i) the case without any …nancial constraints (the
…rst-best allocation), (ii) the case with …nancial constraints only on …rms, (iii) the case with …nancial
constraints only on households, and (iv) the case with both …rms and households subject to …nancial
constraints.
5.1
The First-Best Allocation
Consider …rst an economy without any …nancial frictions. The two borrowing constraints (4) and (17)
then nerve bind. In such a case, equations (5), (6), and (7) imply that
it
cit
=
jt
cjt
;
(58)
for any i and j. The aggregate consumption can be obtained by integrating cjt over j, which gives
Ct =
Z
1
cjt dj =
it Ct .
cit
it
0
or cit =
1
Z
1
jt dj
=
1
cit ;
(59)
it
0
Each individual’s consumption is proportional to the idiosyncratic shock he faces. Equation
(7) then becomes
1
Ct
1
= Rf t Ct+1
and equation (5) can be rewritten as
these two equations are equivalent to equations (50) and (51) if
t
1
Ct Wt
and
t+1
other hand, if the borrowing constraint (28) does not bind, then qt = 1.
imply that Rf t =
Yt+1
Kt+1
+ (1
= . It is easy to see that
are equal to
max .
On the
Equation (56) would then
)qt+1 . Appendix A.3 shows that such an allocation is also the …rst-best
allocation for a central planner. And at the steady state,
Rf =
1
=
Y
+1
K
:
(60)
The steady-state saving rate can then be determined as
s =
I
K
=
=
Y
Y
1
which is identical to that of a standard RBC model.
21
(1
)
;
(61)
The …nancial constraints on households and …rms create two wedges between the discount factor
; the interest rate Rf , and the marginal product of capital. First, notice that equation (50) gives a
steady-state interest rate of
1
1
< ;
( )
Rf =
since
(62)
( ) > 1 as long as the borrowing of some households is constrained. As we will show in section
5.3, this tends to increase the saving rate above the …rst-best saving rate due to precautionary saving
(as Aiyagari (1994) has shown). If q > 1 at the steady state, then …nancial constraints on the …rm side
create a gap between the interest rate and the marginal product of capital. At the steady state, with
q > 1 equation (56) implies
Rf
=
Y 1 + (q
K
q
6=
Y
+1
K
1)
+1
+ (q
1)
(63)
:
We will show that …nancial constraints on the …rm side alone will reduce the saving rate below the …rstbest level in section 5.2. The intuition is suggested by equation (63): …nancial constraints on …rms may
reduce the interest rate for given marginal product of capital, so households have less incentive to save.
5.2
Financial Constraints only on Firms
Assume that only …rms but not households are subject to …nancial constraints. As a result, Rf =
1
at the steady state as discussed in section 5.1. We will show that the aggregate saving rate in this case
increases with the level of …nancial development measured by : Given that Rf =
1
at the steady state,
equation (56) becomes
q= [
Y
+ (1
K
)q + (q
1)(q +
Y
)]:
K
(64)
The following proposition shows that the saving rate is an increasing function of …nancial development
level
if it is below some critical value
.
Proposition 4 There exists a critical value
q=
(
=
1
1
1
+ 1, such that
if
> 1 if
1
+1
>
;
(65)
and the steady state saving rate is given by
I
s=
=
Y
(
1= 1+
1= 1+
1= 1+
22
if
if
>
(66)
Proof. See Appendix A.4.
Recall that a …rm’s borrowing constraint (28) will be binding with q > 1. It is then clear that the
saving rate is increasing in
according to equation (66). Borrowing constraints on …rms will prevent
them from undertaking investments that yield positive net present value, a problem commonly referred
as the underinvestment problem as discussed in the introduction. To see that, …rst calculate the gross
marginal production of capital
MPK =
Y
+1
K
1
= (1
)
+1
+ 1;
(67)
which is the social gross return on one unit of capital. One unit of investment can yield output of
the next period, and after depreciation the consumption value of this unit is 1
MPK >
if
1
= Rf ;
Y
K
in
. Notice that
(68)
.
This di¤erence between capital’s social return and the interest rate prevents households from investing
in capital to its socially optimal level despite that capital yields high social return. At steady state, the
households need to pay q to purchase one unit of capital (indirectly through buying stock). While the
social cost of building one unit of capital is one. In other words, the households pay a premium to acquire
capital, which weakens their incentive to save. An increase in
leads to a decrease in q, which increases
the households’incentive to save.
5.3
Financial Constraints only on Households
When only households are subject to the …nancial constraints, the Tobin’s q, qt , equals to 1, and equation
(56) becomes
Rf = M P K =
Y
+1
K
at steady state. Solving for the saving rate as a function of the interest rate
s=
I
=
Y
Rf
1+
:
(69)
The saving rate has a negative slope with respect to the user’s cost of capital (the interest rate). Since
…rms are the demanders for savings, equation (69) can be considered the demand function for loanable
funds. Equations (50) and (57) then lead to another relationship between saving and the real interest
23
rate from the suppliers of loanable funds. Equation (50) implies that
Z
max(
; 1)f ( )d =
which de…nes an implicit function for the cuto¤
abuse of notation, de…ne such function as
=
1 1
;
Rf
(70)
as a function of the interest rate Rf . With a slight
(Rf ). It is easy to see that
@
@Rf
> 0: A higher interest
rate induces households to save more and hence reduces the probability of being liquidity constrained.
Equation (57) implies that at the steady state the saving rate is
s=
1
1=G(
where
=
) 1 (1
+ b) +
;
(71)
(Rf ) is increasing in Rf , and G( ) de…ned in proposition 3 is the marginal propensity
to consume. The saving rate increases with the interest rate. Since the households are the suppliers of
loanable funds, equation (71) describes the supply curve for funds with respect to the interest rate. The
demand curve (69) and supply curve (71) are plotted in …gure 2. The steady state value of the interest
rate Rf and the saving rate s can be found at the intersection of these two curves. An increase in b, which
relaxes the households’borrowing constraint and reduces the incentive for households to save, shifts the
supply curve inward and moves the equilibrium from point A to point B. So the steady state saving
declines and the interest rate increases. The following proposition summarizes the result.
Figure 2: The e¤ect of relaxing in the households’borrowing constraint on the saving rate
Proposition 5 If only households are subject to …nancial constraint, the saving rate at steady state will
decrease with increasing …nancial development:
24
5.4
Financial Constraints on both Households and Firms
When both households and …rms are subject to …nancial constraint, the aggregate equilibrium is characterized by the system of equations from (50) to (57). In order to study the impact of …nancial constraints
on the saving rate at steady state, we must …rst derive the relationships between saving/investment rate
and the interest rate from the perspective of both households and …rms. As in the previous section, the
demand and supply curves can again be used to study the impact of these two borrowing constraints
on saving. Derive …rst the demand curve for saving using equation (53), (55), and (56). This gives the
relationship between saving rate and the interest rate from the demand side:
s=
1
I
=
Y
1
1
+ = (Rf
1)
;
(72)
which decreases with interest rate Rf . An increase in Rf , representing a higher user’s cost of capital,
depresses demand for investment (saving). The supply curve can be derived in similar steps as in section
5.3. First, equation (70) still holds, so
=
(Rf ) and
@
@Rf
> 0 for the reasons discussed in section 5.3.
The next step is to use equation (57) to solve for the saving rate as a function of the interest rate from
the supply side. After re-arranging terms, as an intermediate step,
Y
G( )
=
q (1 + b) + ;
K
1 G( )
where
=
(73)
(Rf ), and G( ) is de…ned in proposition 3. q can then be derived as a function of the
interest rate from equation (56)
1
q = q(Rf ) =
+ Rf
1
;
(74)
which decreases with the interest rate. The intuition is simple: from the households’point of view, the
value of one unit of capital, q; is the sum of the present value of all future dividend ‡ows. An increase in
the interest rate reduces the present value and hence reduces q. Finally replace K by I= at steady state
and q by (74), to obtain the supply of saving s as
(s)
Recall that
1
=
G( )=
q(Rf ) (1 + b) + 1:
1 G( )
is increasing with Rf and G( ) is decreasing with
, so G( ) decreases with Rf .
(75)
G( )=
1 G( )
thus decrease with Rf . By equation (74), q is also decreasing with Rf . So the right hand side as a whole
is decreasing with Rf . We can therefore conclude that the total saving rate, the inverse of the right hand
side, is an increasing function of the interest rate.
25
Figure 3: The e¤ect of relax in household’s borrowing constraint on the saving rate
Figure 3 shows the e¤ect of the households’borrowing constraints on saving rate. The relationship
between interest rate and saving rate implied by equation Equation (72) is graphed by the downward
sloping curve labeled D. The real interest rate, Rf , is shown on the vertical axis. Saving rate, s, is
measured on the horizontal axis. Equation (75) is graphed by the upward sloping curve labeled S. The
equilibrium interest rate and saving rate are at the intersection of the demand and supply curves. The
initial steady state equilibrium is at point E. According to equation (75), an increase in b reduces the
saving rate for any given interest rate Rf . As the borrowing constraint relaxes, there is less need to
save to self-insure against the idiosyncratic preference shocks. In other words, an increase in b shifts the
supply curve to the left from S to S 0 . The new steady-state equilibrium is at point E 0 . Interest rate Rf
increases, but the saving rate, s, decreases.
26
Figure 4: The e¤ect of …rm’s borrowing constraints on saving rate
The e¤ect of changing the …rms’ borrowing constraint is illustrated in Figure 4. First, by equation
(72), an increase in
increases …rm investment at any given interest rate. It is easy to understand since
…rms’investments are constrained by their borrowing capacities. In other words, an increase in
the demand curve to the right from D to
equation (74), an increase in
D0 .
But an increase in
shifts
also changes the supply curve. By
reduces Tobin’s q, the households’cost of obtaining one unit of capital,
so it increases the households’incentive to save. As is more evident from equation (75), an increase in
increases the saving rate from the supply side. In other words, an increase in
also shifts the supply curve
to the right from S to S 0 . The new steady state equilibrium is at point E 0 . The saving rate increases for
sure, but the e¤ect on the interest rate is not clear. Proposition 6 summarizes these results.
Proposition 6 The equilibrium saving rate can be expressed as a function of b and , namely, s = s( ; b)
with
@s
@
> 0 and
@s
@b
< 0 if borrowing constraints on both households and …rms bind.
The above proposition also suggests that if …nancial development increases b and
simultaneously,
the overall e¤ect on the saving rate will be ambiguous. As increase in the households’borrowing reduces
the saving rate but an increase in the …rms’borrowing increases it. A numerical example in section 5.5
will now illustrate how it is possible for this model to explain the observed hump-shaped relationship
between …nancial development and the saving rate.
27
5.5
Explaining the Hump-Shaped Relationship: A Numerical Example
For the purpose of a numerical example16 , set the parameters in a way such that the model economy is
best interpreted as an emerging economy with a high average saving rate. Set capital share in production
at 0:42, depreciation rate
at 0:012 and the discount factor
at 0:999. These generate a high saving
rate and low interest rate in the steady state, broadly consistent with the data on emerging Asian. Set
the probability that each …rm receives an investment opportunity
at 0:1 and assume the idiosyncratic
preference shock (i) follows Pareto distribution with shape parameter
= 1:15. These two assumptions
make …rms’ and households’ demand for borrowing large, so they can potentially face severe …nancial
constraints if the …nancial market is imperfect. We assume b and
are driven by a common force f that
indicates the …nancial development level :
b = f;
= a1 f + a2
(76)
(77)
where parameters fa1 ; a2 g are non-negative. Set a1 = 0:15 and a2 = 0:005 to induce a hump-shaped
relationship in data.
Figure 5: Financial development and the saving rate
Figure 5 plots the steady-state saving rate for di¤erent values of f 17 . The dashed line shows the …rstbest saving rate. It is evident from Figure 5 that …nancial underdevelopment can induce either oversaving
16
A quantitative exercise would be more desirable if it were possible. A careful calibration exercise, however, requires
micro data on the dispersion of household consumption and incomes to measure the idiosyncratic risks and the consumer
credit to GDP ratio to measure to what extent households are …nancially constrained. Due to data unavailability, we leave
this as a future research topic.
17
Notice that f has one-to-one mapping with the credit to GDP ratio.
28
or undersaving. Figure 5 shows a clear hump-shaped relationship between …nancial development and the
aggregate saving rate. The saving rate is about 25% when both households and …rms can barely borrow.
The saving rate starts to increase as the borrowing constraints relax. The peak in the saving rate is close
to 51%. Interestingly, with a higher level of …nancial development, the saving rate can double. This
model thus puzzles of China’s saving rate discussed by Wen (2011). While the saving rate in China was
less than 30% in late 70s, but has climbed to 51.8% in 2008 along with improvements in …nancial markets
as many studies suggest.18
Figure 6: Financial development and saving rates for alternative cases
Figure 6 shows that a hump-shaped relationship is not possible if only …rms or only households are
subject to credit constraints. As expected, the left panel of …gure 6 shows that saving rates increases
monotonically with the level of …nancial development if only …rms are constrained. While the left panel
shows that saving rate monotonically decreases with …nancial development. Neither prediction is validated
by the data, nor are they consistent with the recent pattern in emerging Asia. Although the left panel of
the …gure is consistent with the fact that saving rates increases with …nancial development in emerging
Asian, it suggests that saving rates in emerging Asia will be systemically lower than in economies with
similar cultures but better …nancial development, which is counterfactual. It is well known that China
has had a much higher saving rate than that in South Korea, Japan or Taiwan in recent years. The right
panel shows that …nancial underdevelopment can indeed generate very high saving rates. But with only
18
Financial markets in China has developed in many ways. Ma and Wang (2010) document that bank loans to Chinese
households have expanded substantially, reaching 15% of the total outstanding bank loans lately from less than 1% in the
late 1990s.
29
households being …nancial constrained, such predictions are prone to the criticism by Wei and Zhang
(2011) using time series evidence.
6
Conclusion
This study has documented a hump-shaped relationship between …nancial development and the national saving rate. It has shown that …nancial development increases saving if only …rms are …nancially
constrained, but reduces saving if only households are borrowing constrained. When both …rms and
households are …nancially constrained, our theoretical model can predict the observed hump-shaped relationship between …nancial development and the aggregate saving rate. This model also shows that
…nancial frictions can cause either undersaving or oversaving depending on the stage of …nancial development. A natural policy recommendation would be that the optimal taxation on capital income may
either be negative (in the case of undersaving) or positive (in the case of oversaving). Given its enormous
welfare consequences, a complete more characterization of the optimal capital income taxation should
be a very important research topic for future. With both …rms and households …nancially constrained,
the model also generates another interesting prediction: the coexistence of high returns on capital and
low real interest rates, which is consistent with the evidence from emerging economies.19 An interesting
implication of this is that if these economies were open to countries with more advanced …nancial markets,
…nancial capital would ‡ow out from the developing countries to the developed countries, while physical
capital will ‡ow (in terms of FDI) from the developed countries to the developing ones to enjoy high
capital returns (see evidence by Ju and Wei (2011)). Explaining such two-way ‡ows in an open economy
model will be another worthwhile research topic for future.
19
See Wen (2009) for an alternative model to explain this fact. Wen (2009) assumes an imperfectly competitive (stateowned) banking sector generating a spread between the deposit rate and the loan rate. Here we obtain the same e¤ect by
allowing …nancial constraints on the …rm side.
30
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34
Appendix
A
A.1
Proofs
Proof of Proposition 1
Suppose qt > 1, …rm j then always chooses to invest as much as possible when investment opportunities
arise, which is
Ijt = qt Kjt + Rt Kjt :
(A.1)
Substituting this decision rule to equation (26) and comparing terms, gives equation (30). Using the
de…nition qt =
t+1
t
vt , easily yields
qt =
t+1
[Rt+1 + (1
)qt+1 + (qt+1
1)(qt+1 + Rt+1 )];
(A.2)
t
which is equation (31). Q.E.D.
A.2
Proof of Proposition 2
Prove …rst that the total wealth Hit = (Qt + Dt ) ait + Wt nt (i) + sit is degenerate. In the second subperiod, the households’ consumption, saving, and stock holdings, can be written as a function of their
wealth Hit , liquidity shock
it ,
and the aggregate variables,
it
it
=
cit
=
it
ct (Hit ;
(A.3)
it )
Equation (7) can then be written as
it
ct (Hit ;
it )
=
Rf t Ei [
=
Rf t
where the second line has used equation (5). De…ne
it
Hit + Bt
Since cit
Hit + Bt , then
it
ct (Hit ;
it
it )
Hit +Bt
for
it ,
+
+
it ;
Wt+1
(A.4)
it
such that
= Rf t
it .
it
it+1 ]
Wt+1
:
By (A.4) and (A.5),
(A.5)
it
> 0. Or the borrowing
constraint (4) binds, and the household’s consumption cit = Hit + Bt . On the other hand,
it
ct (Hit ;
it )
=
35
it
Hit + Bt
;
it
= 0, so
(A.6)
or cit = (Hit + Bt )
it
it
: Since cit
Hit + Bt , then
it .
it
Finally, using the consumption rule derived
above, we can rewrite equation (5) as
Wt
"Z
it
<
it
f ( )d +
Hit + Bt
Equations (A.5) and (A.7) jointly determine
Z
>
it
Hit + Bt
#
f ( )d
= 1:
and Hit . It is evident that Hit and
it
on aggregate variables in the economy. Hence Hit = Ht , and
it
=
t.
(A.7)
it
only depend
Dropping the subscripts from
equation (A.5) yields equation (36). Writing equation (A.7) more compactly and dropping the subscripts
gives equation (37). Equations from (38) to (42) are straightforward to obtain. Q.E.D.
A.3
The First Best Allocation
The social planner’s problem is to maximize the total welfare:
max
cit ;nit ;It
(
max
nit
Z
Ei
i
"
1
X
t
#
it log cit
)
nit di
t=0
(A.8)
with the following resource constraint
Z
cit di + It
Z
Kt
1
nit di
;
(A.9)
and the aggregate capital evolves according to
Kt+1 = (1
)Kt + It :
(A.10)
The social planner decides individual i0 s labor supply nit before observing individual i0 s idiosyncratic
shock
it
as in the decentralized economy. Since the labor decision is made before the realization of
idiosyncratic shock, for each household i, nit is the same. Denote the optimal aggregate labor as Nt . It
satis…es
= (1
)
t
Yt
:
Nt
(A.11)
For the consumption cit ;
it
cit
for all i. De…ne the aggregate consumption
i; we have
R
=
t;
(A.12)
cit di = Ct ; and integrate the last equation with respect to
1
=
Ct
36
t:
(A.13)
Here we assume E (
it )
= 1: The …rst order condition with respect to capital is then
Yt+1
+1
Kt+1
Ct
Ct+1
1=
:
(A.14)
At steady state, the saving rate can be calculated as
I
K
=
=
Y
Y
1
A.4
(1
:
)
(A.15)
Proof of Proposition 4
Suppose
>
: We aim to show that at the equilibrium, the steady state q equals 1; and the liquidity
constraint on investment (27) is never binding. Equation (64) implies the saving rate is
I
K
=
=
Y
Y
1=
In addition, it is easy to show that if
In contrast, if
<
>
;
I
K
<
:
1+
( + R), i.e. the liquidity constraint is not binding.
; q > 1 and aggregating the the …rms’optimal investment decisions we obtain
It =
[qt + Rt ] Kt
Kt+1 = It + (1
(A.16)
)Kt
(A.17)
These last three equations together with (64) imply that at the steady state
R=
Y
=
K
1
+1
1
+ :
(A.18)
;
(A.19)
We can immediately get the saving rate
I
=
Y
1
1
+
+1
1
+1
and
q =
=
1
(
R)
(1
)
+1
This establishes the proof. Q.E.D.
37
:
(A.20)
B
Sample description
B.1
Variables used in the gross saving regression
Variable
Gross domestic saving rate
Domestic credit to private sector
Aged dependency ratio
Youth dependency ratio
Consumer price in‡ation
GDP de‡ator in‡ation
Real interest rate
Per-capita GDP
Per-capita GDP growth
Public expenditure
Current account balance
Life expectancy
B.2
Data source
WDI
WDI
WDI
WDI
WDI
WDI
WDI
WDI
WDI
PWT 7.0
WDI
WDI
Note
% of GDP
% of GDP
Population aged 65 and above/total population
Population aged 0-14/total population
Annual rate
Annual rate
Annual rate
In constant 2000 US dollar
Annual rate
% of GDP
% of GDP, positive if surplus
Life expectancy at birth, in years
Variables used in the household saving regression
Variable
Household saving rate
Household liabilities
Aged dependency ratio
Youth dependency ratio
Consumer price in‡ation
GDP de‡ator in‡ation
Real interest rate
Per-capita household disposable income growth
Per-capita household disposable income
Social expenditures
Life expectancy
Data source
OECD
OECD
WDI
WDI
WDI
WDI
WDI
OECD
OECD
OECD
WDI
Note
% of household disposable income
Loans
Population aged 65 and above/total population
Population aged 0-14/total population
Annual rate
Annual rate
Annual rate
Annual rate
% of GDP
Life expectancy at birth, in years
Note: WDI stands for World Development Indicators from World Bank; PWT stands for
PENN World table from University of Pennsylvania; OECD stands for OECD database from
the OECD website.
38
B.3
Economies in the sample
Country
Australia
Belgium
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland *
Ireland *
Israel *
Italy
Japan *
Korea
Luxembourg
Mexico *
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden
Switzerland
United Kingdom
United States
China
Hong Kong, China
India
Indonesia
Malaysia
Pakistan
Philippines
Singapore
Thailand
Vietnam
World Bank Code
AUS
BEL
CAN
CZE
DNK
EST
FIN
FRA
DEU
GRC
HUN
ISL
IRL
ISR
ITA
JPN
KOR
LUX
MEX
NLD
NZL
NOR
POL
PRT
SVK
SVN
ESP
SWE
CHE
GBR
USA
CHN
HKG
IND
IDN
MYS
PAK
PHL
SGP
THA
VNM
Region or Group
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD, East Asia
OECD, East Asia
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
OECD
East Asia
East Asia
East Asia
East Asia
East Asia
East Asia
East Asia
East Asia
East Asia
East Asia
Note: OECD countries with asterisk are not included in the household saving regression,
due to unavailability of data.
39
C
Gross saving rate regression
Table 2: Gross domestic saving regression: alternative estimators, East Asia subsample
Estimator
Regression
Number of IV
Collapsed IV
Lagged saving rate
Private credits
Private credits sq.
In‡ation rate
Real interest rate
Per-capita GDP growth
Per-capita GDP (log)
Per-capita GDP (log) sq.
Current account surplus
Public expenditures
Aged dependency ratio
Youth dependency ratio
Life expectancy
Wald test (p-val)
Hansen-Sargan test (p-val)
Wooldridge test (p-val)
Arellano-Bond test (p-val):
_1st-order
_2nd-order
_3rd-order
Observations (No. of cn)
(1)
GMM-System
Levels-Di¤s
312
No
(2)
GMM-System
Levels-Di¤s
32
Yes
(3)
Within
Deviation
–
–
(4)
RE
Levels
–
–
0.851***
(0.0411)
0.0327**
(0.0160)
-0.00808*
(0.00446)
-0.0445
(0.0301)
-0.0431
(0.0415)
0.241***
(0.0267)
0.00835
(0.0143)
-0.000617
(0.000900)
0.121***
(0.0146)
-0.0340
(0.0726)
-0.106
(0.0759)
0.0172
(0.0390)
-0.00293
(0.0338)
0.0000
0.936
–
0.805***
(0.0948)
0.109**
(0.0531)
-0.0271*
(0.0160)
-0.210**
(0.102)
-0.213*
(0.127)
0.209
(0.129)
-0.0205
(0.0645)
0.000999
(0.00402)
0.0275
(0.0676)
-0.173
(0.183)
-0.281
(0.233)
0.169
(0.111)
0.0193
(0.0491)
0.0000
1.000
–
–
–
0.140***
(0.0206)
-0.0318***
(0.00817)
0.0696*
(0.0420)
0.0257
(0.0544)
0.272***
(0.0546)
0.0986***
(0.0328)
-0.000233
(0.00235)
0.227***
(0.0360)
0.214
(0.313)
-1.490***
(0.158)
-0.0317
(0.101)
-0.296***
(0.0599)
0.0000
–
0.0002
0.261***
(0.0263)
-0.0816***
(0.0115)
0.134**
(0.0555)
0.0306
(0.0682)
0.673***
(0.0765)
0.183***
(0.0333)
-0.0109***
(0.00207)
0.497***
(0.0464)
-0.577***
(0.118)
-0.470***
(0.157)
-0.172**
(0.0724)
-0.225***
(0.0606)
0.0000
–
0.0002
0.025
0.831
0.248
265 (12)
0.009
0.615
0.320
265 (12)
–
–
–
313 (12)
–
–
–
313 (12)
Notes: Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1; others see
notes in Table 3-4.
40
Table 3: Gross domestic saving regression: alternative estimators, OECD subsample
Estimator
Regression
Number of IV
Collapsed IV
Lagged saving rate
Private credits
Private credits sq.
In‡ation rate
Real interest rate
Per-capita GDP growth
Per-capita GDP (log)
Per-capita GDP (log) sq.
Current account surplus
Public expenditures
Aged dependency ratio
Youth dependency ratio
Life expectancy
Wald test (p-val)
Hansen-Sargan test (p-val)
Wooldridge test (p-val)
Arellano-Bond test (p-val):
_1st-order
_2nd-order
_3rd-order
Observations (No. of cn)
(1)
GMM-System
Levels-Di¤s
701
No
(2)
GMM-System
Levels-Di¤s
32
Yes
(3)
Within
Deviation
–
–
(4)
RE
Levels
–
–
0.794***
(0.0114)
0.0106**
(0.00469)
-0.00670***
(0.00208)
0.0231***
(0.00881)
-0.0817***
(0.0106)
0.348***
(0.0166)
-0.00769
(0.0195)
0.000521
(0.00102)
0.184***
(0.0140)
0.0143
(0.0158)
-0.101***
(0.0159)
-0.0395***
(0.00852)
0.0223
(0.0213)
0.0000
1.0000
–
0.830***
(0.0485)
0.0241
(0.0188)
-0.0132**
(0.00530)
0.00758
(0.0440)
-0.0853
(0.0568)
0.279***
(0.0763)
-0.0779
(0.0874)
0.00413
(0.00460)
0.142***
(0.0413)
0.0160
(0.0375)
-0.0945***
(0.0318)
-0.0155
(0.0259)
0.0966
(0.0964)
0.0000
0.492
–
–
–
0.0552**
(0.0225)
-0.0168**
(0.00802)
0.0304
(0.0456)
-0.136***
(0.0485)
0.200***
(0.0610)
0.329*
(0.188)
-0.0136
(0.0102)
0.285***
(0.0594)
-1.101***
(0.263)
-0.612***
(0.195)
-0.278**
(0.124)
-0.767***
(0.274)
0.0000
–
0.0000
0.0513**
(0.0230)
-0.0165*
(0.00848)
0.0239
(0.0465)
-0.169***
(0.0516)
0.235***
(0.0578)
0.259
(0.176)
-0.0107
(0.00996)
0.285***
(0.0570)
-0.811***
(0.203)
-0.583***
(0.190)
-0.316***
(0.0996)
-0.673***
(0.181)
0.0000
–
0.0000
0.0040
0.2748
0.1087
603 (27)
0.001
0.316
0.114
603 (27)
–
–
–
731 (31)
–
–
–
731 (31)
Notes: i) Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1; ii) Two
lags are used as intruments in the …rst-di¤erenced equation, …rst lag di¤erence is used as
instruments in the level equation; iii) Financial development is also intrumented using the
41
…nancial development index prepared by Abiad et al. (2008).
Table 4: Gross domestic saving regression: alternative estimators, full sample
Estimator
Regression
Number of IV
Collapsed IV
Lagged saving rate
Private credits
Private credits sq.
In‡ation rate
Real interest rate
Per-capita GDP growth
Per-capita GDP (log)
Per-capita GDP (log) sq.
Current account surplus
Public expenditures
Aged dependency ratio
Youth dependency ratio
Life expectancy
Wald test (p-val)
Hansen-Sargan test (p-val)
Wooldridge test (p-val)
Arellano-Bond test (p-val):
_1st-order
_2nd-order
_3rd-order
Observations (Number of cn)
(1)
GMM-System
Levels-Di¤s
806
No
(2)
GMM-System
Levels-Di¤s
32
Yes
(4)
Within
Deviation
–
–
(5)
RE
Levels
–
–
0.783***
(0.0136)
0.0210***
(0.00676)
-0.00706**
(0.00310)
-0.00451
(0.0107)
-0.0814***
(0.0137)
0.313***
(0.0184)
0.00906
(0.00953)
-0.000566
(0.000571)
0.169***
(0.0153)
0.0349*
(0.0186)
-0.0937***
(0.0191)
-0.0256**
(0.0114)
0.00596
(0.00902)
0.0000
0.381
–
0.846***
(0.0514)
0.0321**
(0.0144)
-0.0127***
(0.00491)
0.00472
(0.0613)
-0.0662
(0.0844)
0.288***
(0.101)
-0.0146
(0.0561)
0.000835
(0.00338)
0.0999*
(0.0573)
0.0459
(0.0325)
-0.0744
(0.0453)
-0.00880
(0.0219)
0.0212
(0.0537)
0.0000
0.549
–
–
–
0.0925***
(0.0287)
-0.0296***
(0.0100)
0.0332
(0.0424)
-0.0644
(0.0510)
0.245***
(0.0495)
0.174**
(0.0780)
-0.00582
(0.00480)
0.226***
(0.0421)
-0.824***
(0.271)
-0.969***
(0.246)
-0.110
(0.131)
-0.265
(0.254)
0.0000
–
0.0000
0.105***
(0.0308)
-0.0321***
(0.0101)
0.0403
(0.0431)
-0.0866
(0.0553)
0.291***
(0.0484)
0.180***
(0.0658)
-0.00779*
(0.00404)
0.259***
(0.0403)
-0.645***
(0.198)
-0.861***
(0.203)
-0.212**
(0.0944)
-0.251
(0.232)
0.0000
–
0.0000
0.0033
0.4178
0.3291
809 (37)
0.002
0.452
0.397
809 (37)
–
–
–
976 (41)
–
–
–
976 (41)
Notes: i) Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1; ii)
Two lags are used as intruments in the …rst-di¤erenced equation, …rst lag di¤erence is used
42
as instruments in the level equation; ii) Financial development is also intrumented using the
…nancial development index prepared by Abiad et al. (2008).
D
Household saving rate regression
In this section, we investigate how the household saving rate changes with household credits for the
sample of OECD countries. We focus on OECD countries, simply because of data accessibility. For East
Asian countries, there does not exist any single data source for us to retrieve all of the data needed in
this regression.
We collect the time series data of household saving rate and its potential explanatory variables for
OECD economies from the OECD databases, whenever the data are available20 . As a result, we have a
sample of 26 countries, with the time series ranging from 1995 to 2008, because the earliest observations
on household …nance start from 1995.
Consider the following reduced-form regression equation:
shit =
h
1 sit 1
+
0
h
2 Xit
+
h
i
+ uhit ;
(D.1)
where sh denotes the household net saving rate, X h is a vector of explanatory variables re‡ecting volume
of household credits, size of household …nance, household disposable income and its growth, age structure,
social expenditures, rates of return and uncertainty, which we believe are important to household saving
behavior,
h
denotes the country-speci…c e¤ects, and …nally uh is the error term.
For the same reasons explained in the main text about gross saving rate regression, we choose to work
with such a dynamic speci…cation. We use the the household liabilities to household disposable income
ratio to measure the size of credits going to households.
Table 5 summarizes the regression results, using three di¤erent estimators: the Arellano-Bond system
estimator for the dynamic speci…cation in equation (D.1), the within estimator, and the RE estimator
for static speci…cation without lagged dependent variable.
It is evident from the table that household saving rate is decreasing in the volume of household credits.
These results imply that households tend to save less when the level of household …nance development is
high, which may justify our modeling of the household side in this paper.
20
We focus on OECD countries, simply because of data accessibility. For East Asian countries, there does not exist any
single data source for us to retrieve all of the data needed in this regression.
43
Table 5: OECD household saving regression: with household credits, alternative estimators
Estimator
Regression
Number of IV
Collapsed IV
Lagged household saving rate
Household credits
Per-capita household disp. inc. (log)
Per-capita household disp. inc. (log) sq.
Per-capita household disp. inc. growth
In‡ation rate
Real interest rate
Social expenditures
Aged dependency ratio
Youth dependency ratio
Life expectancy
Wald test (p-val)
Hansen-Sargan test (p-val)
Wooldridge test (p-val)
Arellano-Bond test (p-val):
_1st-order
_2nd-order
_3rd-order
Observations (Number of countries)
(1)
GMM-System
Levels-Di¤s
19
Yes
(2)
GMM-System
Levels-Di¤s
26
Yes
(3)
Within
Deviation
–
–
(4)
RE
Levels
–
–
0.724***
(0.109)
-0.0262**
(0.0107)
-0.422**
(0.215)
0.0224**
(0.0101)
-0.184
(0.284)
0.171
(0.128)
0.272***
(0.0844)
-0.107
(0.158)
0.0234
(0.131)
-0.119
(0.134)
0.469*
(0.264)
0.0000
0.567
–
0.791***
(0.0598)
-0.0255*
(0.0138)
-0.496**
(0.231)
0.0265**
(0.0109)
0.0711
(0.123)
0.233***
(0.0795)
0.328***
(0.0630)
-0.0633
(0.141)
-0.0349
(0.112)
-0.0889
(0.131)
0.541*
(0.280)
0.0000
0.560
–
–
–
-0.0747***
(0.0183)
-0.532
(0.694)
0.0353
(0.0374)
0.283***
(0.0653)
0.259**
(0.119)
0.289**
(0.124)
1.366
(0.875)
-0.296
(0.320)
0.425*
(0.214)
-0.246
(0.491)
0.0000
–
0.0000
-0.0705***
(0.0160)
-0.709
(0.534)
0.0422
(0.0300)
0.269***
(0.0597)
0.332***
(0.0979)
0.393***
(0.128)
0.618*
(0.369)
-0.296
(0.250)
0.271
(0.195)
-0.0690
(0.449)
0.0000
–
0.0000
0.035
0.255
0.516
170 (24)
0.023
0.313
0.394
170 (24)
–
–
–
229 (26)
–
–
–
229 (26)
Notes: i) Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1; ii)
Results (1) in column 2 uses only one lag as instrument, Results (2) in column 3 uses only
two lags as instrument in the di¤erenced equation; iii) The coe¢ cient on household credits in
column 3 has p-value=0.064.
44
E
Semiparametric estimation
In this section, we apply the Baltagi-Li (2002) estimator for partially linear panel data models to our full
sample. We choose this estimator among many others, simply because there exists a handy user-written
Stata command xtsemipar to implement it.
We consider the following semiparametric speci…cation:
sit =
0
~ it + g(zit ) + ~ i + u
X
~it ;
(E.1)
~ it contains those explanatory variables of saving rate explained in Section 2.2, except the measure
where X
of …nancial development (private credits), zit donotes the aggregate private credits to GDP ratio, ~ i is
the unobserved country …xed e¤ects, and …nally u
~it is the error term.
Thus, …nancial development enters non-parametrically while the other explanatory variables enter
parametrically in this partially linear speci…cation. To eliminate the …xed e¤ects, we choose to work with
the …rst-di¤erenced model:
sit =
where
K
0
~ it + [g(zit )
X
g(zit
1 )]
+
u
~it ;
(E.2)
denotes the …rst di¤erence. Baltigi and Li (2002) propose using series pK (z) of dimension
1 to approximate g(z), where pK (z) denotes the …rst K elements of series fpj (z)gj=1;2;3;::: . The
series of functions have the property that as K grows there exists a linear combination of pK (z) that can
approximate any g(z) belonging to an additive class of functions arbitrarily well in mean square error.
As a result, g(zit )
g(zit
1)
can be approximated using pK (zit )
sit =
Baltagi and Li (2002) show that
0
~ it +
X
and
pK (zit )
pK (zit
pK (zit
1)
1)
u
~it :
+
and equation (E.2) becomes:
can be consistently estimated. Once
(E.3)
and
are known, we
can get the residuals and hence by equation (E.1), we have
residuals = sit
0
~ it
X
~ i = g(zit ) + u
~it :
(E.4)
Thus, g(zit ) can be …tted by some standard univariate non-parametric regression of above residuals
on zit . Table 6 reports the coe¢ cients on the other explanatory variables. It is evident that these results
are consistent with what we get in Section 2, using parametric regression. Figure E.1 displays the …t
of saving rate on private credits, using quartic B-spline smoothing. The graph looks similar if we set
the power equal to 3, 5 or 6. It con…rms that the relationship between gross saving rate and …nancial
development is hump-shaped.
45
Table 6: Gross saving rate regression: Baltagi&Li estimator, full sample
In‡ation rate
-0.0245
(0.0381)
-0.0978***
(0.0351)
0.100***
(0.0297)
0.182
(0.109)
-0.00201
(0.00606)
0.305***
(0.0349)
-1.110***
(0.307)
-0.761***
(0.231)
0.125
(0.121)
-0.292*
(0.149)
920
0.379
Real interest rate
Per-capita GDP growth
Per-capita GDP (log)
Per-capita GDP (log) sq.
Current account surplus
Public expenditures
Aged dependency ratio
Youth dependency ratio
Life expectancy
Observations
R-squared
0
-.05
-.1
Gross saving rate
.05
.1
Note: Robust standard errors in parentheses***, p<0.01, ** p<0.05, * p<0.1
Scatterplots
0
.5
1
1.5
B-spline smooth
2
2.5
Private credits to GDP ratio
Figure E.1: Nonparametric …t of gross saving rate on private credits, full sample
46