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Consumption Risk-Sharing in China

By XINPENG XU

Hong Kong Polytechnic University

Final version received 18 October 2006.

This paper empirically examines the degree of regional consumption risk-sharing in China. It nds that less

risk-sharing is taking place across Chinese provinces than across US states and Canadian provinces,

although its extent across the latter is somewhat higher than across the national boundaries of industrial

countries. Specically, about half of the tted annual variation in provincial consumption growth is

common to all Chinese provinces, compared with more than two-thirds (less than one-third) in the case of

US states and Canadian provinces (G-7 countries). My estimates reveal that Chinese households would be

willing to pay dearly to insure their consumption against idiosyncratic shocks.

INTRODUCTION

Households in all countries are buffeted by various shocks to their income. These shockscan be household-specic, region-specic or industry-specic. They can also be commonnational or international shocks. The costs of inadequate risk management aresubstantial for all countries (Shiller 1993). Fortunately, insuring against such risks ispossible because regional economies do not always move in synchronization. Mostimportantly, the benets of risk-sharing are enormous. They can be manifested in theform of low consumption volatility (consumption smoothing) as households with accessto nancial markets, for example, can diversify their risks and possibly raise their levelsof income, consumption and savings (Townsend 1995). More risk-sharing is alsoconsistent with higher specialization in production and potentially higher output(Kalemli-ozcan et al. 2001).1 The sharing of risk across a large number of people is alsoan incentive for productive work (Shiller 2003).2

An assessment of the degree of risk-sharing that is involved constitutes the rst steptowards its effective management. Thus, the extent of risk-sharing among individualsacross regions and countries has been an intense focus of recent research. Financialeconomists have long observed that individuals hold too little of their wealth in foreignassets relative to the predictions of standard portfolio theory in a phenomenon known ashome bias (see e.g. Levy and Sarnet 1970). Related to this is the consumptioncorrelation puzzle in macroeconomics, whereby, in theory, individual consumptiongrowth rates should be more correlated across countries than income growth rates, assuggested by complete market general equilibrium models. However, the evidence hassuggested otherwise (see e.g. Backus et al. 1992; Obstfeld 1994; Canova and Ravn 1996;Lewis 1996). Risk-sharing studies at the level of individuals include those of Mace (1991)and Cochrane (1991) for the United States, and Townsend (1994) and Morduch (2002)for India. Alternatively, by looking into risk-sharing across economic regions within anation, researchers seek to identify whether the lack of consumption risk-sharing thatBackus et al. (1992) pointed out is due to international factors and exchange rateuncertainty or is merely a matter of geography and independent of national boundaries.This approach has been taken up by Bayoumi and McDonald (1995), Asdrubali et al.(1996), Crucini (1999) and van Wincoop (1995), among others. (See the excellent surveyby Hess and van Wincoop 2000.) These studies have generally found that intranational

Economica (2008) 75, 326341

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r The London School of Economics and Political Science 2007

risk-sharing is higher than international risk-sharing, but that the risk-sharing withincountries is far from complete.

Empirical studies on regional risk-sharing abound, yet little is known about it outsideNorth America and Europe. This paper adds to the literature by examining the case ofChina, a large developing country that has attracted worldwide attention for its rapidgrowth in the last two decades while the issue of huge potential welfare gains fromregional risk-sharing has been left largely unexplored. To the best of my knowledge, thisis the rst attempt to use household survey data to examine risk-sharing among Chinesehouseholds from an intranational perspective.3 Focusing on a large developing countrysuch as China is important, because knowledge about the sources and distribution ofeconomic shocks, and about the scope for and the extent of risk-sharing acrosshouseholds, is badly needed by policy-makers. It is also important for the study ofconsumption risk-sharing and incomplete markets, given Chinas stage of economicdevelopment and the heterogeneity in the pace of its regional development.

The recent publication of two annual series by Chinas National Bureau of Statistics(NBS) has made available a data-set that is by far the largest and most representativesurvey of Chinese households, both urban and rural. I collected data on per capitaconsumption expenditure and per capita disposable income for each province and forurban and rural residents in each province. My sample covers the period 19802004 forwhich consistent data are available.

The major ndings are as follows. Results from simple statistics suggest that thepatterns of consumption growth correlations relative to income growth correlationsacross Chinese provinces tend to be congruent with those across G-7 countries, ratherthan across regions within national boundaries as in the United States and Canada.However, formal investigation provides a more elaborate picture, showing that Chineseprovinces are engaged in incomplete risk-sharing, and that less risk-sharing is takingplace across Chinese provinces than across US states and Canadian provinces, but thatthe extent of regional risk-sharing across Chinese provinces is still somewhat higher thanacross the national boundaries of industrial countries. Specically, averaging acrossChinese provinces, about half of the tted annual variation in provincial consumptiongrowth is common to all provinces, compared with more than two-thirds (less than one-third) in the case of US states and Canadian provinces (G-7 countries). The low degree ofrisk-sharing among Chinese provinces indicates that there is signicant potential forwelfare gains from further risk-sharing. My estimates suggest that Chinese householdswould have been willing to pay dearlyFabout 7% of their total consumptionFfor areasonable set of parameters to insure their consumption against idiosyncratic shocks.

The remainder of this paper is organized as follows. The next section presents thetheory of consumption risk-sharing in the setting of a decentralized economy. Section IIdescribes the specications of the empirical model, the data and the estimation results; acheck of the robustness of the results is also provided. The estimation results on thewelfare gains from risk-sharing are provided in Section III, and Section IV concludes.

I. THEORY OF CONSUMPTION RISK-SHARING

There is one representative household in each province, with a total of I households(provinces), i 1, 2, . . . , I.4 Household i owns a stochastic endowment of the consumptiongoods, Yt

i Yti(st) that depends on the realization of st. The expected lifetime utilityfunction of household i is expressed as

2008] CONSUMPTION RISK-SHARING IN CHINA 327

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1 UCi X1t0

Xst

btUCitstpst;

where Cti(st) is the consumption for household i at time t in state st, bA(0, 1) is the

discount factor that is assumed to be the same across households, and p(st) is theprobability the state st will occur.

Suppose that there is a complete set of securities and that households can trade state-contingent claims to one unit of consumption at price Pt

0(st) if event st has been realized,where the superscript 0 refers to the date at which trades occur while the subscript t refersto the delivery date. The feasibility constraint for the household is as follows:

2X1t0

Xst

CitstP0t st)X1t0

Xst

YitstP0t st:

The representative households problem is to choose a time-dependent consumptionpath Ci {Cti(st)} (tA(0, 1) to maximize expression (1) subject to budget constraint (2).The rst-order condition for the households problem is

3 bUCCitstpst tiP0t st:

Taking the ratio of rst-order conditions (3) for household i with respect to itscounterpart household j gives

4 UCCitst

UCCjtst t

i

tj

for all pairs (i, j) at all dates t and in all states st. Thus, with a set of contingentconsumption claims to hedge against individual income uncertainty, the ratio of themarginal utilities of consumption of any two agents is constant across all states anddates.

Note that equation (4) implies that household is consumption Cti(st) is a constant

function of that of household j:

5 Citst U1 UCCjtstti

tj

:

Given the economy-wide constraint that aggregate consumption Ca(st) must be lessthan the aggregate endowment Ya(st) at each date and in each state, we have

6 Cast Xi

Citst)Xi

Yitst Yast:

Together with equation (5), we have that household is consumption Cti(st) is only a

function of Ca(st), the aggregate consumption, for all i. Individual household is incomeYti(st) does not enter the determination of individual household is consumption

allocation Cti(st), given aggregate consumption. Note that the shadow value of the

households income ti depends on the market price of the goods, which in turn isdetermined by the aggregate consumption and aggregate income.

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Suppose we consider a special case of a time-separable, constant relative risk-averse(CRRA) utility function with a risk aversion coefcient d. Equation (5) then implies that

7 Citst Cjtstti

tj

1=d:

Equation (7) and the economy-wide constraint (6) together imply that

8 Citst miCat st;where mi Pi ti =ti 1=dis a constant.5

Taking the logarithm and rst-differencing equation (8), we have

9 citst cat st nit;where the lower-case c terms represent the logarithm of C and nt

i represents themeasurement error.

Thus, with a power utility function, the level of individual household is consumptionis perfectly correlated with the level of aggregate consumption or aggregate income, butnot with individual income (Mace 1991). With a set of contingent consumption claims tohedge against individual income uncertainty, there is extensive cross-state and cross-timeperfect consumption insurance. This is the essence of the theory of consumption risk-sharing.

However, the assumption of complete risk-sharing has not been congruent with thesituation in the real world. Evidence of less than risk-sharing is actually the rule ratherthan the exception. Hence a model of complete risk-sharing may seem limited inempirical tests. To capture the empirical regularity of incomplete risk-sharing, we followCrucini (1999) by assuming that the representative household in each region pools only afraction, l, of its income, with the remaining fraction, 1l, of its income not pooled.

Suppose that representative households are able to engage their income that is notpooled (i.e. 1l) in intertemporal consumption-smoothing through borrowing andlending a risk-free bond; we can easily show (Deaton 1992, p. 83) that

10 Dcitst 1 bX1k0

bkEt Et1yitk;

which has the familiar interpretation that consumption follows a random walk since theinnovations to income are not predictable (Hall 1978).

Taking (9) and (10) together, we have

11 Dcitst lDcat st 1 l1 bX1k0

bkEt Et1yitk:

Equation (11) encompasses both complete risk-sharing captured by (9) and incompleterisk-sharing captured by (10). If provincial households completely share risk, then l 1,and their consumption changes move one-for-one with the aggregation consumptionchanges, as the second term on the right-hand side of (11) disappears. On the other hand,if provincial households do not share risk at all, then l 0 and consumption changes willfollow a random walk. The advantage of this incomplete risk-sharing specication overcomplete risk-sharing is that the coefcient l can be taken as an indication of the degreeof regional risk-sharing.

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II. EMPIRICAL SPECIFICATIONS, DATA AND RESULTS

Empirical specications

The key element in estimating the degree of risk-sharing is the issue of forecastingregional income to determine regional income innovation as captured by the second termon the right-hand side of equation (11). To facilitate comparison with the results thatCrucini (1999) obtained for the cases of regional risk-sharing in the United States,Canada, and OECD countries, I followed Crucini by experimenting with threealternative specications of regional income-generating process: (i) a bivariate vectorautoregression model (VAR(1)) with aggregate and regional income variables, (ii) aunivariate autoregression model (AR(1)), and (iii) a random walk model. Specically,these are three specications for regional income growth:

12 Dyat

Dyit

A

i11 A

i12

Ai21 Ai22

Dyat1Dyit1

v

ait

vit

;

13 Dyit riDyit1 vit;

14 Dyit vit;

where Dyat and Dyit refer to aggregate income growth and regional income growth,

respectively.I estimated these three specications in the rst stage to obtain estimates of the

unexpected changes in regional permanent income Dy~pit, so that in the second stage Iwas able to estimate the risk-sharing parameter as follows:

15 Dcit ai liDcat 1 liDy~pit eit;

where the error term eit is interpreted as a measurement error in consumption growth oran individual preference shock that is uncorrelated with the innovation to permanentincome. Equation (15) is the empirical correspondent of (11). One distinct advantage ofthis specication proposed by Crucini (1999) is that it both nests the Mace (1991) fullconsumption risk-sharing specication and portfolio autarky, and allows one to estimatethe degree of risk-sharing in a setting of incomplete consumption risk-sharing. Equation(15) is estimated for each province to avoid the problem of regressing provincialconsumption growth on its cross-sectional mean. All equations are estimated by ordinaryleast squares, which has the correct standard error because only the unanticipatedregressors from the rst-stage regression enter the second-stage regression.

The hypothesis tests are summarized as follows. If there is full consumption risk-sharing, then the coefcient on the aggregate consumption growth should be signicantand take the value of 1, while the coefcient on individual income growth should not besignicantly different from 0. If risk-sharing is incomplete, then the coefcient onindividual income growth should be statistically signicantly different from 0. Thecoefcient on aggregate consumption growth l can be used to gauge the extent ofincomplete risk-sharing. In the case of autarky, the coefcient on aggregate consumptiongrowth should be 0, while the coefcient on individual income growth should besignicant and take the value of 1.

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