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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 finds 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. Specifically, about half of the fitted 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-specific, region-specific or industry-specific. 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 benefits of risk-sharing are enormous. They can be manifested in theform of low consumption volatility (consumption smoothing) as households with accessto financial 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 first 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 as‘home 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, 326–341

doi:10.1111/j.1468-0335.2007.00606.x

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 first 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 China’s stage of economicdevelopment and the heterogeneity in the pace of its regional development.

The recent publication of two annual series by China’s 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 1980–2004 forwhich consistent data are available.

The major findings 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. Specifically, averaging acrossChinese provinces, about half of the fitted 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 significant 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 specifications 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 ¼ 1, 2, . . . , I.4 Household i owns a stochastic endowment of the consumptiongoods, Yt

i ¼ Yti(st) that depends on the realization of st. The expected lifetime utility

function of household i is expressed as

2008] CONSUMPTION RISK-SHARING IN CHINA 327


ð1Þ UðCiÞ ¼X1t¼0

Xst

btU½CitðstÞ�pðstÞ;

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:

ð2ÞX1t¼0

Xst

CitðstÞP0

t ðstÞ)X1t¼0

Xst

ðYits

tÞP0t ðstÞ:

The representative household’s problem is to choose a time-dependent consumptionpath Ci ¼ {Ct

i(st)} (tA(0, 1) to maximize expression (1) subject to budget constraint (2).The first-order condition for the household’s problem is

ð3Þ bUC½CitðstÞ�pðstÞ ¼ tiP0

t ðstÞ:

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

ð4Þ UC½CitðstÞ�

UC½CjtðstÞ�

¼ ti

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 i’s consumption Cti(st) is a constant

function of that of household j:

ð5Þ CitðstÞ ¼ U�1 UC½Cj

tðstÞ�ti

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

ð6Þ CaðstÞ ¼Xi

CitðstÞ)

Xi

YitðstÞ ¼YaðstÞ:

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

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

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

household’s 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 coefficient d. Equation (5) then implies that

ð7Þ CitðstÞ ¼ Cj

tðstÞti

tj

� ��1=d:

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

ð8Þ CitðstÞ ¼ miCa

t ðstÞ;

where mi ¼P

i ti

� �=ti

� �1=dis a constant.5

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

ð9Þ citðstÞ ¼ cat ðstÞ þ nit;

where the lower-case c terms represent the logarithm of C and nti represents the

measurement error.Thus, with a power utility function, the level of individual household i’s consumption

is 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, 1–l, of its income not pooled.

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

ð10Þ DcitðstÞ ¼ ð1� bÞX1k¼0

bk½Et � Et�1�yitþk;

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

ð11Þ DcitðstÞ ¼ lDcat ðstÞ þ ð1� lÞð1� bÞX1k¼0

bk½Et � Et�1�yitþk:

Equation (11) encompasses both complete risk-sharing captured by (9) and incompleterisk-sharing captured by (10). If provincial households completely share risk, then l ¼ 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 ¼ 0 and consumption changes willfollow a random walk. The advantage of this incomplete risk-sharing specification overcomplete risk-sharing is that the coefficient l can be taken as an indication of the degreeof regional risk-sharing.



II. EMPIRICAL SPECIFICATIONS, DATA AND RESULTS

Empirical specifications

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 specifications 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. Specifically,these are three specifications for regional income growth:

ð12Þ DyatDyit

� �¼ Ai

11 Ai12

Ai21 Ai

22

� �Dyat�1Dyit�1

� �þ vait

vit

� �;

ð13Þ Dyit ¼ riDyit�1 þ vit;

ð14Þ Dyit ¼ vit;

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

I estimated these three specifications in the first stage to obtain estimates of theunexpected changes in regional permanent income ðDy~pitÞ, so that in the second stage Iwas able to estimate the risk-sharing parameter as follows:

ð15Þ Dcit ¼ ai þ liDcat þ ð1� liÞDy~pit þ 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 specification proposed by Crucini (1999) is that it both nests the Mace (1991) fullconsumption risk-sharing specification 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 first-stage regression enter the second-stage regression.

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

330 ECONOMICA [MAY


Data

The data were drawn from the largest, most comprehensive household survey in Chinaconducted by the NBS, which covers both rural and urban households in all 31 provincesexcept Tibet. The NBS’s Rural Social and Economic Survey (RSES) team has about 8000full-time staff and some 10,000 temporary support staff working in the 31 provinces andtheir 857 counties. The RSES survey was started in 1954 and has run annually withinterruptions in just two periods, from 1958 to 1961 and 1966 to 1976 (NBS 2003, pp.325–27). The team that is responsible for the Urban Social and Economic Survey has asimilar number of staff working in the 31 provinces and their 226 cities. There are usually30,000–40,000 households in the urban sample and 60,000–70,000 households in the ruralsample. The NBS implements a two-tiered stratified sampling scheme to draw arepresentative random sample from the population. For the urban sample, eachhousehold remains in the survey for three consecutive years, and in each year one-third ofthe households rotate out of the sample and are replaced by newly drawn households.For the rural sample, each household remains in the survey for five consecutive years,and in each year one-fifth of the households rotate out of the sample and are replaced bynewly drawn households. All survey households are required to keep a record of theirincome and expenditure.

To study regional risk-sharing, data are needed on consumption and income percapita at the provincial level.6 The data were collected from the Rural Household Surveyyearbook and the Urban Household Survey yearbook (various years), as well as from theComprehensive Statistical Data and Materials on 50 Years of New China, also publishedby the NBS. The individual household survey data on consumption and income areaggregated based on the size of the population that survey respondents represent in thebroader provincial population. I was able to obtain data on consumption expenditure percapita and disposal income per capita for each province and for urban and ruralhouseholds in each province. ‘Disposal income’ refers to a household’s total incomeminus taxes and transfers. It includes both labour income and non-labour income such asinterest and rental income from asset-holding, but does not include non-cash benefits.‘Household consumption expenditure’ refers to a household’s spending on the followingcategories: food, clothing, household facilities, articles and services, medicine andmedical services, transportation and communication services, recreation, education andcultural services, residence, and miscellaneous goods and services. The sample covers theperiod 1980–2004 for 29 provinces (excluding Tibet and Chongqing from the original 31),for which consistent data for consumption expenditure and disposal income per capitaare available. As the survey data are all in nominal terms, I have deflated all data by therelevant consumer price index (CPI), collected from the Chinese Statistics Yearbook thatis published by the NBS (various years).

Descriptive statistics

Table 1 summarizes simple statistics for the average per capita income and consumptiongrowth rates for Chinese provincial households and for provincial urban and ruralhouseholds for the period 1980–2004, which makes it comparable with data for othercountry panels.7 The data for consumption and income are expressed in real per capitaterms and in log-differences.

As can be seen from Table 1, the average income growth and consumption growthare 6.13% and 5.50%, respectively, for provincial households. The average income and



consumption growth of provincial urban households are higher than those of ruralhouseholds. The average standard deviation of households’ disposable income andconsumption growth are 6.48% and 5.20%, respectively, for provincial households. Onedistinct feature of the urban and rural panels is that both income and consumptiongrowth are more volatile for rural residents than for urban households, with the volatilityof income growth of rural residents being twice as high as that of their urbancounterparts. This has important implications for welfare gains from risk-sharing (seeSection III). Compared with consumption volatility for Canadian provinces andJapanese prefectures, which are about 2% (Crucini and Hess 2000), Chinese provincialconsumption volatility of 5.2% is clearly much higher. The relatively high consumptionvolatility may be the first indication of less risk-sharing taking place in China.8

Regional consumption growth is pro-cyclical with respect to regional income in allprovinces, with an average correlation of 0.50 for provincial households and correlationsof 0.56 and 0.48 for urban and rural residents, respectively. Two provincesFBeijing andGuangdongFwere selected, and their consumption and income growth data are plottedin Figure 1, which by visual inspection suggests a higher correlation within a provinceover time.

TABLE 1

Summary Statistics of Household Income and Consumption Growth in China,

1980–2004

Mean

Standard

deviationCorrelation

of y and c

Correlation

with

aggregate

Cross-

section

correlation

y c y c y c y c

Province 6.13 5.50 6.48 5.20 0.50 0.69 0.65 0.46 0.41

Urban 6.20 5.44 5.84 5.64 0.56 0.77 0.68 0.58 0.45

Rural 5.39 4.79 11.1 7.22 0.48 0.65 0.62 0.42 0.37

Note: y and c refer to ‘income growth’ and ‘consumption growth’, respectively.

–.05

0

.05

.1

.15

.2

Con

sum

ptio

n an

d in

com

e gr

owth

: Bei

jing

1980 1985 1990 1995 2000 2005Year

Income Consumption

–.05

0

.05

.1

.15

Con

sum

ptio

n an

d in

com

e gr

owth

: Gua

ngdo

ng

1980 1985 1990 1995 2000 2005Year

Income Consumption

FIGURE 1. Provincial consumption and income growth: Beijing and Guangdong.

332 ECONOMICA [MAY


Complete risk-sharing suggests the co-movement of consumption but not income.Hence it is expected that the degree of regional co-movement of consumption would behigh relative to income co-movement if there is a high degree of regional risk-sharing.Two cross-sectional correlations were computed. The first is the cross-sectionalcorrelation of regional consumption or income growth. As shown in the final twocolumns of Table 1, consumption growth correlations across Chinese provinces, whichaverage 0.41, are lower than income growth correlations, which average 0.46. This resultis in sharp contrast to the findings of Crucini (1999) for intranational correlations,whereby cross-provincial consumption growth correlations tend to be higher than cross-provincial income growth correlations (0.56 v. 0.38 for Canadian provinces for the period1972–90). Yet the Chinese case seems congruent with the typical feature of internationalcorrelations, whereby international consumption growth correlations tend to be lowerthan international income growth correlations (0.14 v. 0.32 for OECD countries for theperiod 1970–87). This is another indication that less regional risk-sharing is taking placeacross Chinese provinces. Histograms of cross-regional consumption and income growthcorrelations for the provinces are presented in Figures 2 and 3. Using a separate data-setfrom the Chinese national accounts, Boyreau-Debray and Wei (2005) also reportrelatively lower consumption growth correlations than output across Chinese provinces(0.53 v. 0.65).

The second indicator of co-movement across regions is the co-movement of regionalincome and consumption with their aggregate counterparts, which are reported in thesixth and seventh columns of Table 1. Again, consumption growth correlations lowerthan income growth correlations can be observed across the regions (average 0.65 v.0.69).

Taken together, the foregoing simple descriptive statistics seem to suggest that thedegree of risk-sharing among Chinese regions is close to that across countries, ratherthan across regions within national boundaries.

Estimation results

I now turn to formal empirical investigation of the degree and pattern of regional risk-sharing across Chinese provinces. To facilitate comparison with other panels (in whatfollows, the results for US states, Canadian provinces, and G-7 countries are taken fromCrucini 1999), I begin by reporting estimates for the regional income-generating processfor Chinese provinces. Table 2 provides the results for two alternative incomespecifications, bivariate AR(1) and univariate AR(1), with the first row of each panel

FIGURE 2. Provincial consumption correlations (kernel estimates).



being the number of provinces for which a one-sided hypothesis test reveals a positive ornegative coefficient that is significant at the 10% level, and the second row being themultipliers that are derived from the income equation estimations (equation (12)). Thereported coefficients and R2 are averaged across all provinces.

Few coefficients are significant at the 10% level for both bivariate AR(1) andunivariate AR(1) specifications, although the rural panel displays more significantcoefficients than the urban panel. The R2 is very low for all regressions. Although the R2

for each provincial income regression is, on average, twice as large as that for theaggregate income specification and for the regional univariate income specification, theaverage R2 is only 0.08 for the regional bivariate income specification and 0.04 for theregional univariate income specification.

FIGURE 3. Provincial income correlations (kernel estimates).

The densities were constructed using a normal kernel with bandwidth 1.06sxn� 1/5 where sx is the cross-

sectional standard deviation of variable x (a pair-wise correlation of either consumption or income growth

between two regions). See Crucini (1999).

TABLE 2

Regression Results forVarious Specifications of the Income Process, 1980–2004

Statistic

Bivariate specificationUnivariate

specificationAggregate income Regional income

A11 A12 R2 A21 A22 R2 r̂j R2

Results for Chinese provincial households

Sign tests [0, 0] [3, 1] [1, 0] [1, 1] [1, 1]

Multipliers 1.01 1.11 0.04 1.12 1.11 0.08 0.01 0.04

Results for Chinese urban households

Sign tests [2, 0] [0, 3] [0, 0] [0, 0] [0, 0]

Multipliers 1.22 0.88 0.05 1.06 1.07 0.04 0.04 0.05

Results for Chinese rural households

Sign tests [0, 0] [3, 0] [3, 0] [4, 4] [4, 3]

Multipliers 0.95 1.13 0.05 –2.5 1.21 0.04 –0.07 0.09

Notes:The entries in the ‘Sign tests’ are the numbers of statistically significant positive ( þ ) or negative ( � )coefficients at the 10% level. ‘Multipliers’ are the weighting coefficients for innovation to income. The value of bused is 0.98. The parameter r̂jrefers to the coefficient on lagged income growth in the univariate specification.

334 ECONOMICA [MAY


On the basis of these results, it appears that neither bivariate AR(1) nor univariateAR(1) specifications of regional income-generating process provide a good construct forchanges in regional permanent income in China. Regional income growth for Chineseprovinces is approximately a random walk. According to Crucini (1999), regional incomegrowth for both US states and Canadian provinces are predictable from the past growthrates of regional and aggregate income growth, while G-7 results indicate that nationalincome growth is well approximated by a random walk. Consequently, the pattern ofregional income-generating process for Chinese provinces appears to be closer to that ofG-7 countries than to those of either US states or Canadian provinces.

Table 3A reports the average estimated risk-sharing parameters and standard errorsof estimates for the provinces and their urban and rural panels. The discussion here willfocus mainly on the random walk specification, for two reasons. First, the incomeregression that was performed above suggests that the regional income-generatingprocess for Chinese provinces may be better captured by a random walk than by abivariate AR(1) or a univariate AR(1). Second, the permanent income hypothesis seemsfar-fetched for the Chinese case, so that consumption may respond to income growththrough, for example, a credit-constraint channel. Thus, the random walk specificationmay well capture the local feature of regional risk-sharing in China. Nonetheless, we alsoreport results for the bivariate AR(1) and univariate AR(1) income specifications.

The estimated equations provide a good fit in accounting for variations in provincialconsumption growth, with an R2 of 0.54 (0.51 and 0.42 for urban and rural panels,respectively). As indicated in the third row of the provincial panel, the average estimatedrisk-sharing parameter for Chinese provinces is 0.71 (0.61 and 0.68 for urban and ruralpanels, respectively). This figure is lower than the risk-sharing parameters of

TABLE 3A

Risk-Sharing Parameter Estimates for Chinese Households, 1980–2004

Income process

Mean statistics

No. of provinces for which a 95% confidence

interval encompasses a risk sharing parameter

equal to:

l s.e. (l) R2 l ¼ 1 14l40 l ¼ 0 l ¼ 1or 0


Bivariate 0.91 (0.08) 0.51 19 10 0 0

Univariate 0.76 (0.13) 0.56 18 11 0 0

Random walk 0.71 (0.13) 0.54 9 19 0 1


Bivariate 0.84 (0.13) 0.45 22 7 0 0

Univariate 0.65 (0.15) 0.53 12 14 2 1

Random walk 0.61 (0.15) 0.51 9 19 0 1


Bivariate 0.88 (0.11) 0.39 23 6 0 0

Univariate 0.74 (0.15) 0.43 16 12 1 0

Random walk 0.68 (0.14) 0.42 13 14 2 0

Notes:The risk-sharing regressions are estimated using equation (15) by ordinary least squares. The regressors are theaverage consumption growth across Chinese provinces and the unexpected change in permanent income (thethree alternative regional income specifications) computed from the first-stage regressions that were reported inTable 2.



approximately 0.9 for US states and Canadian provinces, but higher than that of the G-7countries (ranging from 0.37 for random walk specification and 0.60 for bivariatespecification). This suggests that, on average, less risk-sharing is taking place acrossChinese provinces than across US states and Canadian provinces; but the extent ofregional risk-sharing across Chinese provinces is still somewhat higher than across thenational boundaries of industrial countries. Using a separate data-set from the Chinesenational accounts but a somewhat different consumption growth specification, Boyreau-Debray and Wei (2005) report a risk-sharing parameter of 0.84 for the period 1978–2000for Chinese provinces and a parameter of 0.63 for OECD countries.

Turning to the number of regions that engage in perfect risk-taking, completeconsumption insurance is not rejected for 9 of the 29 provinces. Here the value of nestingfull insurance and portfolio autarky proposed by Crucini (1999) is more apparent in theChinese case than in that of the United States and Canada. The fifth column of Table 3Areports the number of regions for which the 95% confidence interval for l falls between 0and 1. Nineteen out of 29 Chinese provinces do not perfectly share risks, which is ahigher proportion than in the United States (3 out of 48 states) and Canada (4 out of 10provinces); this too suggests that less risk-sharing is taking place in China. These 19Chinese provinces provide statistical evidence against either the complete or the no-risk-sharing hypothesis. The constraint that the coefficients on aggregate consumptiongrowth and regional income growth (three separate specifications) must sum to unity hasalso been tested, with very few results showing rejection of the restriction.9

How robust are the risk-sharing parameter estimates? Sampling method andmeasurement error are always two major concerns in survey data. First, there may beshifts in the data-generating process as people move in and out of the sample. Indeed, inthe sampling method that is used by the NBS in China for the urban (rural) sample, eachhousehold remains in the survey for three (five) consecutive years, and in each year one-third (one-fifth) of the households rotate out of the sample and are replaced by newlydrawn households. To check whether my results are robust against this sampling method,I divided the whole sample into two overlapping periods,10 1980–95 and 1990–2004, andran province-by-province regressions for each period based on equation (15). The resultsare presented in Table 3B. The average of the risk-sharing parameter estimates basedon the random walk specification is 0.60 (an R2 of 0.64) for the first periodand 0.76 (an R2 of 0.37) for the second period, which is not qualitatively differentfrom the estimate of 0.71 for the whole period, as in Table 3A. If these estimates ofregional risk-sharing parameters for the two sample periods are taken as an indication ofwhether or not provincial risk-sharing has improved over time, then there is no decline ofregional risk-sharing in China based on the data, as suggested in Boyreau-Debray andWei (2005).

The second concern is error in the measurement of the variables, consumption andincome. As my regressions use consumption as a dependent variable, measurement errorin consumption is part of the estimation residual and does not bias the estimatedcoefficients of the independent variables. The remaining concern is on measurement errorin income. To further avoid possible measurement error in income, averaging has beenperformed across provinces. Two provinces were chosen randomly and their averageconsumption and income were calculated so that the sample regions are reduced from 29provinces to 15. (One province remains as it is.) Again, the region-by-region regression isperformed based on equation (15) for random walk specification. The results show thatthe average risk-sharing parameter for these 15 regions is 0.79 with an R2 of 0.63, which

336 ECONOMICA [MAY


is also close to the result of 0.71 from the 29-province sample. Thus, my estimates of risk-sharing parameters are quite robust to different sampling periods and regions.

Finally, the extent of risk-sharing can also be examined in the context of variancedecomposition. The estimated equations can be used to decompose the variance of fittedconsumption growth into aggregate, regional and covariance components. If risk-sharingwere complete, then all of the variance would be accounted for by the commoncomponent. Table 4 presents results of such variance decomposition. For the case ofrandom-walk specification, about half (52%) of the variance in fitted provincialconsumption growth is accounted for by the common component, which is much lowerthan in the United States and Canada, where more than two-thirds (78%–92% and68%–72%, respectively) can be explained by the common component. Nonetheless, it isstill higher than what can be observed in the case of G-7 countries, where less than one-third of the variance in fitted national consumption growth is accounted for by thecommon component. For the urban and rural panels, about 40% of the variance of thefitted provincial urban and rural consumption growth is accounted for by the commoncomponent.

Taken together, these results are consistent with what the simple correlation patternsof consumption suggest about the extent of risk-sharing across Chinese provinces, and

TABLE 3B

Dynamic Risk Sharing for Chinese Households, 1980–2004

Random walk process

Mean statistics

No. of provinces for which a 95%

confidence interval encompasses a risk-

sharing parameter equal to:

l se(l) R2 l ¼ 1 14l40 l ¼ 0 l ¼ 1or 0

1980–1995 0.60 (0.18) 0.64 13 10 5 1

1990–2004 0.76 (0.17) 0.37 19 8 0 2

Notes: See Table 3.

TABLE 4

Variance Decomposition of Consumption Growth for Chinese Households

Income process Aggregate component Regional component Covariance component


Bivariate 0.74 0.10 0.16

Univariate 0.59 0.21 0.20

Random walk 0.52 0.28 0.20


Bivariate 0.61 0.20 0.19


Random walk 0.39 0.43 0.18


Bivariate 0.62 0.22 0.16


Random walk 0.42 0.41 0.17

Note: Consumption variability is measured as change in the log of real consumption.



which reaffirm Crucini’s (1999) major finding that the degree of risk-sharing is higheracross regions within countries, which extends to the case of China, than across industrialcountries, although it is less than perfect in all cases.

III. WELFARE IMPLICATIONS

As the foregoing empirical results suggest, after more than two decades of reform andopening up, the degree of risk-sharing among Chinese households remains low comparedwith their developed country counterparts. There is ample scope for further risk-sharingamong regional households in China. In this section I seek to explore the welfareimplications of improving risk-sharing.

In a pioneering paper, Lucas (1987) measured the cost of business cycles in terms ofthe fraction of a constant stream of consumption that a representative agent would bewilling to give up to avoid fluctuations in consumption over a business cycle. He showedthat the welfare cost of consumption variability is gðd2zÞ � ð1=2Þgd

2z , assuming a constant

relative risk aversion (CRRA) utility function, where d2z is the variance of consumptionaround a deterministic trend. He calculated that the welfare losses associated with thebusiness cycle are small, less than 0.1 percentage point of consumption.

However, van Wincoop (1994) demonstrated that, if consumption growth follows arandom walk, as the simple permanent income hypothesis would suggest, the welfaregain associated with a drop in consumption variability is �ð1=2Þgd2Dc=ðr� �mÞ, where�m ¼ m� ð0:5gd2DcÞ is the economy’s risk-adjusted growth rate and r ¼ ðb�1 � 1Þ þ ðg�mÞ isthe risk-free rate. In this paper I follow the welfare formula taken from van Wincoop(1994) and Crucini and Hess (2000) to calculate the welfare gains of a drop inconsumption variability, which is

� 1

2gd2Dc=ðr� �mÞ:

The incomplete risk-sharing specification of equation (15) provides a simple vehicle indecomposing the variation of regional consumption growth ðvarðD logðCi

tÞÞ into thefollowing components: a common component

ðl̂2i varðD logðCat ÞÞÞ;

a region-specific income shock

ðð1� l̂iÞ2varðD logðYitÞÞÞ;

the covariance between the two

ð2l̂ið1� l̂iÞcovðD logðCat Þ;D logðYi

tÞÞÞ

and an unexplained component that is the regression residual. The sum of the last threecomponents, referred to as regional-specific consumption growth net of common shocks,measures the part of consumption variation that cannot be accounted for by aggregateconsumption movements. The benefits of intranational consumption risk-sharing cantherefore be calculated by multiplying the welfare gains of a drop in consumptionvariability by the removal of region-specific consumption growth net of common shocks.

Table 5 presents the estimates of welfare gains from consumption risk-sharing inChina. To permit comparisons with the existing literature, the parameter values are takenfrom Crucini and Hess (2000) (i.e. g ¼ 4, and b ¼ 0.99), except that the economy’s

338 ECONOMICA [MAY


risk-adjusted growth rates are set at m ¼ 6%, which is reasonable for China. As can beseen from the fourth row of the table, the average Chinese provincial resident would havebeen willing to give up about 7.6% of his consumption to eliminate his regional-specificrisk in consumption. The average Chinese rural resident would have been prepared togive up an amount of consumption (17.2%) that is higher than what urban residentswould have been willing to give up (9.9%) to remove her regional-specific risks. Incontrast, according to Crucini and Hess (2000), given this set of parameters withm ¼ 1.7%, the estimated welfare gain of consumption risk-sharing is about 1% ofconsumption for the average Canadian and Japanese households, 1.5% for the meanOECD nation and 7% for the mean of US states (5.73% is attributed to error terms inUS states). Evidently, the low degree of regional risk-sharing in China, as estimated inthe previous section, gives rise to a higher welfare gain from regional risk-sharing inChina than in the United States, Canada and Japan.

Adhering strictly to the same set of parameters (i.e. g ¼ 4, m ¼ 1.7% and b ¼ 0.99)for China and for the other country panels, the lower risk-adjusted growth rates wouldgenerate an even higher magnitude of welfare gain for China at 23.7% of consumption.In sum, Chinese households would have been willing to pay dearly to ensure theirconsumption against idiosyncratic shocks.

Interestingly, a comparison between the urban and rural panels in Table 5 suggests thatthe welfare gain to Chinese rural residents is on average 17.2%,which is almost twice as highas thewelfare gain to urban residents (9.9%). Even thewelfare gain to rural residentswho arein the lowest quartile is close to that of urban residents who are in the highest quartile.

IV. CONCLUSION

It has now been well recognized that there are tremendous benefits in sharing risks acrossa large number of people. However, economists have found that there is a lack of risk-sharing across households within a nation, that there is very little risk-sharing across

TABLE 5

Welfare Gain from Consumption Risk-Sharing in China

Highest quartile Average Lowest quartile

Provinces

Region-specific 1.0 1.6 1.2

Covariance 1.5 0.9 0.4

Unexplained 6.5 5.1 3.1

Total 9.0 7.6 4.7

Urban residents




Total 11.9 9.9 6.9

Rural residents




Total 20.8 17.2 10.7

Notes: We set g ¼ 4, m ¼ 0.06, b ¼ 0.99, r ¼ 7.8%. See the main text for detailed explanations.



countries (the so-called ‘international consumption correlation puzzle’), and thatindividuals hold too little of their wealth in foreign assets relative to the predictions ofstandard portfolio theory (the so-called ‘home bias’ puzzle). As Shiller (1993) pointedout, the costs of the inability to manage risks are substantial for both developing anddeveloped countries.

In this paper, I use the theory of consumption risk-sharing to examine the case ofChina, a large developing country with a heterogeneous pace of regional economicdevelopment. The heterogeneity in the pace of regional economic developmenttheoretically implies potential gains to be derived from regional risk-sharing. However,my empirical assessment of the degree of risk-sharing in China tends to suggest that lessrisk-sharing is taking place across Chinese provinces than across US states and Canadianprovinces, although the extent of regional risk-sharing across Chinese provinces issomewhat higher than across the national boundaries of industrial countries. Myestimates reveal that Chinese households would be willing to pay dearly to insure theirconsumption against idiosyncratic shocks. This suggests that more attention should bepaid to the mechanisms that have prevented regions from sharing their risks withinChina. I leave that for future research.

ACKNOWLEDGMENTS

I wish to thank one referee for very detailed comments and suggestions which have improved thepaper significantly. All remaining errors are mine. Financial support from the Hong KongPolytechnic University (Grant no. G-U077) is gratefully acknowledged.

NOTES

1. From this perspective, local protectionism can be seen as the result of a lack of insurance againstproduction risk, which calls for a novel policy response.

2. Recognizing the tremendous benefits of risk-sharing, Shiller (1993, 2003) proposed an ambitious plan tocreate macro markets to share national risks.

3. An interesting paper by Boyreau-Debray and Wei (2005) also examined regional consumption risk-sharing in China, but it differs from this paper in several respects. First, I make use of household surveydata while they used national account data. They used resource limit as a measure of income, as inObstfeld (1994), while I use three alternative income specifications in the estimation of risk-sharing, as inCrucini (1999). Furthermore, the focus of their study was on China’s financial market integration, whilemy focus is on regional risk-sharing.

4. The assumption of a representative household in each province is strong, but is dictated by the type ofdata available (see Section II for a discussion of the data). It implies full risk-sharing within a provincebut not between provinces. This is a common assumption in the empirical literature on intranationalmacroeconomics (see e.g. Hess and van Wincoop 2000).

5. This can be illustrated as follows. Following expression (7), we have C2t ðstÞ ¼ C1

t ðstÞ t2=t1� ��1=d

: Itfollows that

Cat ðstÞ ¼ C1

t ðstÞ þ C1t ðstÞ

t2

t1

� ��1=dþ � � � þ C1

t ðstÞti

t1

� ��1=d¼ C1

t ðstÞP

i ti

t1

� ��1=d:

6. While the survey has been conducted for all provinces in the last fifty years, the individual householddata are available to researchers only for restricted years and with limited coverage (in most cases,limited to two provinces and only for some years).

7. For example, the sample period for US states is 1972–90, for Canadian provinces it is 1973–91, for G-7countries it is 1970–87 in Crucini (1999).

8. Although the volatility of consumption growth in US states is close to that of Chinese provinces,according to Crucini and Hess (2000), these authors note that the high consumption volatility in theUnited States is due to data measurement, whereby consumption is measured by retail sales as opposedto actual consumption.

9. The results are not reported here but are available from the author upon request.10. The whole sample is split into two overlapping periods purely for the consideration of the degree of

freedom.

340 ECONOMICA [MAY


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