We conducted a Feldstein-Horioka test for the degree of China's inter-provincial capital mobility each year from 1978 to 2007 using the spatial error model (SEM), a model of spatial econometrics considering spatial dependence, and a data set reflecting revision of historical national and provincial accounts after China's first economic census in 2004. We found that the likelihood ratio test rejected the null of no spatial error correlation, or the appropriateness of the standard OLS model (OLSM), for 17 out of 30 years and that the Akaike information criterion selected the SEM over the OLSM for 20 years. Our estimations demonstrate that the mobility was high until the late 80's, fell to a bottom in the mid-90's, recovered, peaked in the early 2000's, and has weakened recently, even though it has been argued that mobility has been low since 1978 reform, leaving the impression that it has consistently been low.fiscal and financial reform; Feldstein-Horioka paradox; spatial econometrics

Chen, Kuang-hui

Hashiguchi, Yoshihiro

English

Research Papers in Economics

Has China’s Interregional Capital Mobility
Been Low?
A Spatial Econometric Estimation of the
Feldstein-Horioka Equation
Yoshihiro HASHIGUCHIy CHEN Kuang-huiz
August 2010
Abstract
WeconductedaFeldstein-HoriokatestforthedegreeofChina’sinter-provincial
capital mobility each year from 1978 to 2007 using the spatial error model (SEM),
a model of spatial econometrics considering spatial dependence, and a data set re-
ﬂecting revision of historical national and provincial accounts after China’s ﬁrst
economic census in 2004. We found that the likelihood ratio test rejected the null
of no spatial error correlation, or the appropriateness of the standard OLS model
(OLSM), for 17 out of 30 years and that the Akaike information criterion selected
the SEM over the OLSM for 20 years. Our estimations demonstrate that the mobil-
ity was high until the late 80’s, fell to a bottom in the mid-90’s, recovered, peaked
in the early 2000’s, and has weakened recently, even though it has been argued
that mobility has been low since 1978 reform, leaving the impression that it has
consistently been low.
Keywords: ﬁscal and ﬁnancial reform, Feldstein-Horioka paradox, spatial econo-
metrics
JEL: C21, O16, P21
1 Introduction
A distinctive phenomenon has emerged in post-1978 reform China. Oi [15] has called
it “local state corporatism,” and Jin, Qian, and Weingast [8] have called it “federalism,
Chinese style.” The “ﬁscal contracting system” introduced in 1980 provided strong
This work was supported by Japan Society for the Promotion of Science Grant-in-Aid for Scientiﬁc
Research 20252007.
yGraduate School of Economics, Kobe University, Nada, Kobe 657-8501, Japan. Email: yhashiguchi@
port.kobe-u.ac.jp.
zGraduate School of International Cooperation Studies, Kobe University, Nada, Kobe 657-8501, Japan.
Email: chen@person.kobe-u.ac.jp.
1ﬁscal incentives for local governments to boost their economies. While such decen-
tralization achieved some success in economic development, arguments have been put
forward that it decreased the central government’s redistribution function and worsened
regional inequality [9, 10] and that local governments tended to interfere in the capi-
tal market and cause its fragmentation [4, 16]. Often regarded as evidence supporting
these claims, previous estimates using the Feldstein-Horioka equation [5] have shown
that post-1978 China’s capital mobility among regions was low. The mobility seems
to have been regarded as consistently low despite a sequence of ﬁscal and ﬁnancial re-
forms, such as implementation of the “tax assignment system,” enforcement of the Law
of the People’s Bank of China and of the Commercial Bank Law, in the mid-1990’s and
large “western development plan” investments in this decade [3, 4, 12, 18].
Our argument is threefold. First, most previous studies presumed that mobility
was stable for a considerable period. Their estimates may have been ﬂawed by this
constant parameter presumption, and, in fact, Hashiguchi and Hamori’s year-by-year
estimationshowedthatmobilitybegantoincreaseinthemid-1990’s[6]. Second, China
conducted its ﬁrst economic census in 1994 and has substantially revised its historical
national account estimates [14, 19]. Previous estimates may also change if revised
data are used. Third, although several versions of the Feldstein-Horioka equation have
been estimated for various countries and regions using various methods [2], spatial
dependenceincross-regionalandpaneldatahasnotbeenconsidered, possiblyaﬀecting
properties of estimators [1].
Using revised cross-provincial data and a method of spatial econometrics, we made
a year-by-year estimation from 1978 to 2007 and showed that capital mobility has not
been consistently low. We describe our model in the next section, report estimation
results in Section 3, and conclude in Section 4.
2 Model
The basic Feldstein-Horioka equation is of the form:
Ii
Yi
     
S i
Yi
  ui; (1)
whereYi iscountry regioni’sGDP, Ii isgrossinvestment, S i issaving, andui isanerror.
Now well-known as the Feldstein-Horioka paradox, Feldstein and Horioka [5] found
, the saving-retention coeﬃcient, was signiﬁcantly larger than zero and was rather
close to one in 21 OECD countries, indicating a tendency that incremental savings
were invested domestically even though capital mobility was thought to be large among
developed countries.
We estimate Equation (1) by taking account of spatial dependence in the error term.
Using matrix notation and rewriting Equation (1) as
y   X   u; (2)
we assume that the error u follows the spatial autoregressive process:
u   Wu   "; (3)
2where W is a row-standardized spatial weight matrix such that the ith element of the
vector Wu is the mean error of region i’s neighbors,  is a coeﬃcient of autocorrela-
tion, and " is a vector of iid errors.1
The above model is called the spatial error model (SEM), which is reduced to the
ordinary least square model (OLSM) if    0. It can be estimated by the maximum
likelihood method. Assuming the error " to be normally distributed with a zero mean
vector and a covariance matrix of 2I, we have from Equations (2) and (3) a log-
likelihood function of
logL(;;2)    
N
2
log2  
N
2
log2  
1
2
logj
j
 
1
22(y   X)0

 1(y   X);
(4)
where

  
[
(I   W)0(I   W)
] 1 ;
I is an identity matrix, and N is sample size. The usual ﬁrst-order condition yields the
maximum likelihood estimators of  and 2 given :
ˆ    (X0

 1X) 1X0

 1y;
ˆ 2
  
1
N
(y   X ˆ )0

 1(y   X ˆ );
(5)
substitutionofwhichintoEquation(4)yieldsthefollowingconcentratedlog-likelihood
function:
logL()    
N
2
[
log(2)   1
]
 
N
2
log
(
u
0u
N
)
  logjI   Wj; (6)
where
u  
[
I   X(X
0X) 1X
0]
y;
X   (I   W)X;
y   (I   W)y:
The maximum likelihood estimate of  is the value that maximizes Equation (6), and
its substitution into Equation (5) gives the estimates of  and 2.
For estimation we use a weight matrix W of the queen contiguity type, which treats
two regions as neighbors if they share a border or a point, and the data on gross regional
expenditure, on ﬁnal consumption, and on ﬁxed capital formation of 29 province-level
regions, excluding Hainan and Chongqing.2 The OLS model is also estimated for
comparison. R version 2.10.1 [17] is used for calculation.
1The u can be considered to be a random individual eﬀect [11, Ch. 2].
2Hainan and Chongqing are excluded because of lack of data. Data are obtained from the National
Bureau of Statistics [13] with the following modiﬁcations: Inner Mongolian 2005 expenditure is from the
Inner Mongolia Autonomous Region Bureau of Statistics [7]; Zhejiang ﬁxed capital formations until 2004
are judged to be misprinted under the entry net export [13, p. 433].
33 Estimation Results
Parameter estimates of the SEM and OLSM per year from 1978 to 2007 are given in
Tables 2 and 3.
Table 1: Model Selection Statistics
AIC
LR
SEM OLSM
1978 4.086 -40.9 -38.8
1979 2.765 -32.3 -31.5
1980 5.325 -63.1 -59.8
1981 4.954 -75.9 -72.9
1982 4.380 -63.5 -61.1
1983 7.120 -72.1 -67.0
1984 4.439 -75.8 -73.4
1985 4.686 -60.8 -58.1
1986 2.639 -65.4 -64.7
1987 1.734 -60.5 -60.8
1988 5.914 -76.8 -72.9
1989 5.786 -78.6 -74.8
1990 2.824 -73.4 -72.6
1991 2.137 -69.7 -69.6
1992 0.958 -60.7 -61.7
1993 0.011 -60.6 -62.6
1994 0.046 -51.8 -53.7
1995 0.035 -57.1 -59.1
1996 1.473 -60.1 -60.6
1997 3.783 -64.9 -63.1
1998 3.746 -64.0 -62.2
1999 1.960 -65.5 -65.5
2000 3.277 -61.4 -60.1
2001 4.966 -57.3 -54.3
2002 5.994 -55.5 -51.5
2003 3.343 -43.4 -42.0
2004 1.863 -52.6 -52.7
2005 1.162 -51.1 -51.9
2006 1.748 -54.4 -54.6
2007 2.525 -50.2 -49.7
Note: , , and  next to LR values
denote that the null of    0 is rejected
at the 10%ɼ5%, and 1% signiﬁcance
level, respectively.  in the columns of
AIC are given to smaller values.
Table 1 compares the two models. The likelihood ratio (LR) test rejects the null
of the spatial autoregressive parameter    0, or the appropriateness of the OLSM, at
4the 10% signiﬁcance level for 17 out of 30 years and at the 5% level for 10 years. The
Akaike information criterion (AIC) selects the SEM for 20 years. The LR and AIC are
consistent. The AIC selects the SEM whenever the LR rejects    0.
Figure 1 shows the SEM and OLSM conﬁdence intervals (solid lines) and point
estimates (dashed line) of the saving-retention coeﬃcient . The two estimates are
similar, providing support to Hashiguchi and Hamori [6]. The coeﬃcient, according to
them, waslowuntil thelate 1980’s, roseto thepeak in themid-90’s, declinedthereafter,
and bottomed in the early 2000’s. Estimates for the early 2000’s are signiﬁcantly less
than zero, indicating a tendency that investments were large in regions where savings
were small, a tendency which now seems to have disappeared.
1980 1985 1990 1995 2000 2005
−1.0
−0.5
0.0
0.5
1.0 SEM
1980 1985 1990 1995 2000 2005
−1.0
−0.5
0.0
0.5
1.0 OLSM
Figure 1: Conﬁdence Intervals and Point Estimates of the Retention Coeﬃcient
4 Conclusion
It has been argued that following 1978 reform China’s decentralization decreased the
redistribution function of the central government, tended to cause local governments’
interference in the capital market, and, as a result, depressed interregional capital mo-
bility, which has seemingly been regarded as consistently low. According to our esti-
mate of the saving-retention rate, however, mobility was high until the late 1980’s, fell
to a bottom in the mid-90’s, recovered, peaked in the early 2000’s, and has weakened
recently. It appears that mobility, depressed by “excessive decentralization,” was raised
by ﬁscal and ﬁnancial reforms in the mid-90’s and “western development plan” invest-
ments in the 2000’s, although we have no evidence that whether problems identiﬁed
have been solved. Indeed, mobility is estimated to have weakened recently.
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7Table 2: SEM Estimates
ˆ  ˆ  ˆ 
1978 0.338 (0.065) -0.210 (0.153) 0.461 (0.190)
1979 0.347 (0.070) -0.241 (0.172) 0.382 (0.205)
1980 0.275 (0.044) -0.089 (0.099) 0.551 (0.171)
1981 0.219 (0.034) 0.004 (0.080) 0.528 (0.176)
1982 0.272 (0.041) -0.045 (0.099) 0.477 (0.187)
1983 0.287 (0.041) -0.067 (0.092) 0.585 (0.163)
1984 0.304 (0.038) -0.062 (0.090) 0.500 (0.182)
1985 0.357 (0.056) -0.096 (0.133) 0.509 (0.181)
1986 0.341 (0.048) -0.054 (0.123) 0.413 (0.200)
1987 0.327 (0.056) -0.011 (0.145) 0.329 (0.214)
1988 0.226 (0.055) 0.229 (0.132) 0.566 (0.168)
1989 0.161 (0.058) 0.291 (0.145) 0.563 (0.168)
1990 0.183 (0.056) 0.233 (0.144) 0.422 (0.198)
1991 0.212 (0.054) 0.205 (0.137) 0.361 (0.209)
1992 0.180 (0.066) 0.355 (0.158) 0.268 (0.223)
1993 0.217 (0.069) 0.348 (0.160) 0.031 (0.249)
1994 0.169 (0.074) 0.463 (0.172) -0.064 (0.255)
1995 0.182 (0.070) 0.404 (0.163) 0.058 (0.247)
1996 0.288 (0.072) 0.167 (0.168) 0.350 (0.211)
1997 0.348 (0.071) 0.030 (0.158) 0.495 (0.184)
1998 0.400 (0.074) -0.041 (0.164) 0.478 (0.187)
1999 0.430 (0.070) -0.123 (0.161) 0.350 (0.211)
2000 0.515 (0.075) -0.307 (0.171) 0.472 (0.188)
2001 0.640 (0.083) -0.575 (0.187) 0.547 (0.172)
2002 0.713 (0.090) -0.709 (0.201) 0.583 (0.164)
2003 0.704 (0.113) -0.602 (0.250) 0.447 (0.193)
2004 0.597 (0.100) -0.320 (0.213) 0.327 (0.214)
2005 0.593 (0.094) -0.262 (0.197) 0.239 (0.227)
2006 0.581 (0.094) -0.198 (0.193) 0.268 (0.223)
2007 0.506 (0.111) -0.009 (0.225) 0.302 (0.218)
Note: Standard errors in parentheses. , , and  denote signiﬁcance
at the 10%ɼ5%, and 1% signiﬁcance level, respectively.
8Table 3: OLSM Estimates
ˆ  ˆ 
1978 0.362 (0.059) -0.272 (0.154)
1979 0.367 (0.065) -0.298 (0.171)
1980 0.293 (0.036) -0.150 (0.101)
1981 0.243 (0.028) -0.079 (0.081)
1982 0.278 (0.034) -0.083 (0.099)
1983 0.282 (0.033) -0.072 (0.093)
1984 0.302 (0.032) -0.072 (0.088)
1985 0.336 (0.047) -0.072 (0.127)
1986 0.328 (0.042) -0.047 (0.118)
1987 0.316 (0.051) -0.007 (0.138)
1988 0.219 (0.050) 0.208 (0.133)
1989 0.170 (0.050) 0.228 (0.135)
1990 0.169 (0.049) 0.243 (0.134)
1991 0.201 (0.050) 0.213 (0.132)
1992 0.182 (0.061) 0.339 (0.150)
1993 0.218 (0.070) 0.345 (0.163)
1994 0.170 (0.079) 0.464 (0.183)
1995 0.177 (0.071) 0.414 (0.165)
1996 0.247 (0.065) 0.243 (0.155)
1997 0.286 (0.065) 0.143 (0.151)
1998 0.351 (0.067) 0.040 (0.152)
1999 0.405 (0.063) -0.080 (0.145)
2000 0.446 (0.065) -0.168 (0.151)
2001 0.545 (0.073) -0.379 (0.171)
2002 0.615 (0.081) -0.505 (0.190)
2003 0.644 (0.104) -0.472 (0.234)
2004 0.562 (0.092) -0.246 (0.197)
2005 0.583 (0.090) -0.240 (0.189)
2006 0.577 (0.090) -0.189 (0.185)
2007 0.511 (0.108) -0.021 (0.219)
Note: Standard errors in parentheses. , , and
 denote signiﬁcance at the 10%ɼ5%, and 1%
signiﬁcance level, respectively.
9

Has China's Interregional Capital Mobility Been Low? A Spatial Econometric Estimation of the Feldstein-Horioka Equation

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