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Consumption risk-sharing in ItalyAntonello E. ScorcuPublished online: 04 Oct 2010.

To cite this article: Antonello E. Scorcu (1998) Consumption risk-sharing in Italy, Applied Economics, 30:3, 407-414,DOI: 10.1080/000368498325921

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1 Obviously, the two hypotheses are distinct and each of them can hold or fail independently of the other.

Applied Economics, 1998, 30, 407 ± 414

Consumption risk-sharing in Italy

ANTONELLO E. SCORCU

Department of Economics, University of Bologna, Strada Maggiore 45, 40126 Bologna, Italy

This paper analyses the issue of consumption risk-sharing in the 20 Italian regionsduring the period 1983 ± 94. The tests proposed allow for regional speci® c departuresfrom the hypothesis of complete risk-sharing and for the existence of non-separabili-ties among groups of commodities. Empirical evidence suggests the rejection of thehypothesis of complete consumption risk-sharing.

I . INTRODUCTION

Complete consumption risk-sharing is assumed to hold inseveral models based on the representative agent hypo-thesis. In such a framework, the structures of the preferencesof the individual consumers are assumed to be similar, thechanges in individual consumption are a� ected only byuninsurable aggregate shocks in income and wealth and aretherefore orthogonal to any additional consumer-speci ® cshock.

The independence of households’ consumption from idio-syncratic shocks is usually regarded as the cross-sectioncounterpart of the permanent income hypothesis: in the ® rstcase there is consumption smoothing across agents, while inthe latter case agents smooth consumption over time in thepresence of transitory shocks.1

Several formal and informal institutions permit consump-tion insurance at various (household, regional and national)levels. If markets are complete, consumers can reach thePareto optimal allocation; moreover, under not particularlyrestrictive assumptions, similar allocations can be reachedalso with incomplete markets. Other mechanisms can con-tribute to this outcome: unemployment bene® ts and othertypes of insurance schemes, welfare and several publictransfer programmes and gifts and loans from relatives andfriends are often available to consumers whose incomeand/or wealth is a� ected by negative idiosyncratic shocks.

However, the empirical evidence about these risk-sharingmechanisms, like that about permanent income, is far frombeing clear and in many instances complete consumptioninsurance is merely considered a useful benchmark againstwhich various departures are evaluated.

A number of papers analyse the issue at the country level,from an international risk-sharing perspective. The results

in Canova and Ravn (1996) support the hypothesis whentransitory shocks are considered, but evidence is less favour-able when more persistent shocks are introduced. Lewis(1996) points out that consumption risk-sharing emergesonly for a selected group of countries, characterized by analmost perfect capital mobility.

Even in the absence of full international consumptionrisk-sharing, consumption insurance might hold at a lessaggregate level, because it `may hold more closely amonggroups that are geographically close’ (Cochrane, 1991,p. 974): the degree of social and economic cohesion withincountries (at the household or regional level) is probablyhigher than among countries.

In fact, other papers analyse the issue at the householdlevel, evaluating the e� ects of the changes in several house-holds’ idiosyncratic characteristics (like job loss, illness, in-come or wage shocks) on consumption behaviour. Mace(1991) and Cochrane (1991) consider di� erent assumptionsabout the separability of the utility function with respect tonon-tradables , durables or more narrowly de® ned groups ofcommodities, and ® nd empirical support for some quali® edversions of the hypothesis. On the other hand, Attanasioand Davis (1996) and Hayashi et al. (1996) ® nd more un-favourable empirical evidence.

The mixed evidence about the degree of consumptionrisk-sharing which arises from previous empirical workmight also be explained, in part at least, by inadequateempirical testing.

The present paper attacks this latter point by developinga set of tests that encompasses the ones proposed so far inthe literature. We consider the case in which the changes inconsumption of the various consumers also di� er with per-fect risk-sharing, because of the di� erences in wealth and thestructure of the preferences.

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2 Time separability is usually assumed in these analyses. For a formal derivation of Equation (1) cf., among others, Cochrane (1991).3 A CRRA speci® cation is widely used in empirical analyses.4 For the sake of simplicity, only one additional regressor rather than a vector is considered.

In order to identify these individual speci® c e� ects, theintroduction of the time dimension in the risk-sharing test isneeded. The re® nements required by the existence of non-separabilities in the utility function of the consumers arealso considered.

We test the hypothesis of consumption insurance for 20Italian regions over the period 1983 ± 94. This case is parti-cularly interesting. The social and economic conditions ofthe Italian regions di� er markedly: for example, the GDPper capita of Calabria, the lowest in the ranking, is only45% of the GDP of Lombardia, the highest in the ranking.At the same time, in the recent past, regional policies havebeen considered important and (partially) e� ective.

Evidence turns out quite unambiguous: only partial con-sumption risk-sharing emerges when the tests take intoaccount regional and time speci® c di� erences and the non-separabilities in the utility function, since regional consump-tion growth depends upon regional GDP growth.

The consequence of the incomplete regional consumptionrisk-sharing is to cast some doubts on the usefulness of thecountry representative consumer approximation. More-over, macroeconomic analyses that rely on the countryrepresentative consumer or that concern internationalconsumption risk-sharing or capital mobility should beconsidered with great caution.

II . CONSUMPTION RISK-SHARING TESTS .

Let us consider the case of a single consumption good.Consumption risk-sharing tests are typically based on the® rst-order conditions which describe the optimal pro-gramme of the (regional) representative consumer i for anygiven periods t and t - 1. In this case the marginal utilitygrowth is the same for each consumer, but might changeover time because of the uninsurable aggregate shocks:2

g iu 9it+ 1 (cit+ 1 )/u 9it(cit) = l t/ l t ± 1 (1)

where cit denotes the level of real per capita consumption ofregion i (i = 1, ¼ , N) at time t (t = 1, ¼ , T ), ui t(cit) denotesthe period t instantaneous utility function of the representa-tive consumer of region i, l t denotes the Lagrangeanmultiplier that the central planner attaches to time t con-sumption, in common for all regions, and g i denotes thediscount factor for region i. If the same speci® cation of theutility function holds for all regions,3 if regional preferencesand discount factors do not change systematically acrossindividuals and over time and if heterogeneity is only due todi� erent regional preference shift parameters, a linear ap-proximation of the ® rst order conditions (Equation (1))under the assumption of complete consumption risk-

sharing is given by the following (panel) regression

gcti = a + zti (2)

where gc denotes the rate of growth of real consumptionand zti the error term, which also includes the measurementerrors in the dependent variable. With a large number ofconsumers, a simple cross-section analysis can be performedwith a limited loss of information. Therefore, the modelcollapses to gci = a + ui, with the error term which collectsthe idiosyncratic di� erences among individuals. In the caseunder scrutiny (but also in international comparisons) onlya limited number of observations is available in each periodand the degree of consumption insurance might depend oncyclic ¯ uctuations ± a panel analysis appears certainly moreappropriate.

Even if in the general case of systematic di� erences inregional consumers’ behaviour the speci® cation (2) turnsout to be inaccurate, we retain it for a moment, in order topresent the standard consumption risk-sharing tests.

If consumption growth is smoothed over individuals, anobvious test of consumption risk sharing is to augment (2)with an exogenous variable4 xti, regress gcti againsta + b xti + zti, and test for b = 0. Natural candidates forxti are all household, regional or country idiosyncraticshocks (depending upon the aggregation level used in theanalysis) that a priori are more likely to in¯ uence consump-tion growth. Given the nature of the error term’ in Equa-tion (2), the lack of correlation between xti and zti is a resultdi� cult to obtain in panel or cross-section regressions (espe-cially in the case of income shocks) and, consequently,genuine departures from consumption risk-sharing are hardto detect: a signi® cant estimate of b in the augmentedregression cannot be regarded as unambiguous evidenceagainst consumption risk-sharing. On the other hand, be-cause of this likely bias, the cases in which consumptionrisk-sharing cannot be rejected provide more reliable in-sights.

This problem has often been attacked with the use of theIV estimation but the paper will o� er a more structural’treatment.

In Equation (2) each zti depends upon the speci® c func-tional form of the utility function of the representativeconsumer of region i and upon time and idiosyncraticchanges in the parameters of this utility function: meanconsumption growth rates systematically di� er among re-gions when the utility functions of the representative con-sumers di� er in their parameters, rates of time preference orfunctional forms.

The greater the heterogeneity between the utility func-tions, the less accurate is the linear approximation (2) andthe less clear the design of the empirical exercises. In short,

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5 On the other hand, also complete aggregation, advocated, among others, by Canova and Ravn (1996), could be an equally restrictiveassumption. As suggested by Obstfeld (1989), `[I]mplicit (or explicit) ¼ is the arbitrary assumption that the excluded portion ofconsumption [durables] enters the utility function in a separable manner ¼ the separability assumption is implausible ¼ some degree ofmisspeci® cation seems likely no matter what consumption measure is chosen’ (Obstfeld, 1989, p. 143).6 Aggregation within these three categories of consumption is obviously assumed.7 Data are provided by ISTAT, the Italian Central Statistical O� ce. The ® rst three observations are used as instruments in the estimation.

even with full consumption insurance, there might emergesystematic regional e� ects, unrelated to the exogenousx-variable, making speci® cation (2) unnecessarily restrictive.

The ® rst point of departure of this paper from the stan-dard framework is therefore to model the error term’ zti.The panel approach enables us to identify di� erent constantregional e� ects. Time e� ects are also considered, since ag-gregate shocks change over time. zti is hence sorted out intothree elements:

zti = a1 i dregi + a2 tdtt + uti (3)

The ® rst two series concern systematic e� ects (regional andtime controls, respectively); the third element, the true’ errorterm, takes into account only preferences shocks andmeasurement errors. The regional dummies, dregi, captureall time-invariant households’ speci® c characteristics thatare crucial in modelling consumption risk-sharing. The timedummies, dtt, capture the e� ects of the aggregate uninsur-able shocks ± an unexpected change in the national orinternational output or in the interest rates, etc. ± possiblydi� erent in each period. These two series of dummies im-prove the modelling of the individual consumption growthrates and should reduce the spurious correlation betweenthe exogenous variable and the error’ term. Therefore, sig-ni® cant estimates of the coe� cient b can be more con® dent-ly explained by the failure of the risk sharing hypothesis.

Also in our case, in order to test for the hypothesis of fullconsumption risk-sharing, the test regressions are aug-mented with idiosyncratic variables (the rate of change ofreal income) that could characterize the behaviour of therepresentative agent. This additional variable should beirrelevant with complete insurance, a case in which regionscan always insure against their e� ects. The most general(linear) alternative of incomplete risk-sharing is given bygcit = a1 idregi + a2 tdtt + b itxit + uit and, under the hypoth-esis of complete risk-sharing, b it = 0 " t, " i. Obviously, thisregression cannot be estimated because of the lack of de-grees of freedom; some restrictions on the case of incompleterisk-sharing must be introduced.

A drastic but widely used simpli® cation is

gcti = a1 i dregi + a2 tdtt + b xti + uti (4)

Under the hypothesis of complete insurance, the coe� cientb is equal to zero. Regression (4) will be used as the bench-mark speci® cation. However, the restrictions b it = b , " t, " iare not warranted a priori under the alternative hypothesisof incomplete risk-sharing: the same regional income shockmight lead to di� erent changes in regional consumption.

These restrictions might reduce the empirical adequacy ofthe test and might lead to a fall in its power.

Less stringent speci® cations can be easily introduced.Departures from complete consumption risk-sharing mightbe regional speci® c and therefore, in our test, the e� ects ofthe exogenous variables are distinguished by region anda di� erent b i is estimated for each region. This necessarilyalso implies the introduction of the time dimension into theregression and, since aggregate shocks are expected tochange signi® cantly over time, also time speci® c e� ects aremodelled. The regression is therefore:

gci t = a1 idregi + a2 tdtt + b 1 ixit + b 2 txit + uit (5)

and, for full risk-sharing, b 1 i = 0.Previous speci® cations are referred to a single good utility

function. However, in most cases, di� erent goods and ser-vices are considered: tradables and non-tradables , durablesand non-durables and (sometimes) leisure are the typicalarguments of the instantaneous utility function. The empiri-cal tests often consider non-durables only, assuming com-plete separability with respect to all other categories ofconsumption.

The recognition that complete separability is a strongassumption has led some authors to a further augmentationof the regressions, with the introduction of a number ofconditioning regressors.5 For example, Lewis (1996) teststhe hypothesis of complete risk sharing in tradables throughthe regression gc1ti = a2 tdtt + b 1 gc2ti + b 2 gc3ti + b 3 xti

+ uti with gc1 the rate of growth of tradables, gc2 the rate ofgrowth of non-tradables and gc3 the rate of growth ofleisure.6 In our case we estimate the system of J equations

gcj it = a1 i dregi + a2 tdtt + b 1 idregixit + b 2 tdttxit

+ g 1 gc1 it + ¼ + g j ± 1 gcj ± 1 it + g j+ 1 gcj+ 1 it

+ ¼ + uj it (6)

where j, j = 1, ¼ , J denotes the di� erent groups of com-modities in which total consumption is divided. In thefollowing, leisure is completely separable with respect to theother types of consumption, and therefore does not enter inthe regression.

III . THE DATA AND THE APPROACH

Annual data on per capita households’ total real consump-tion expenditure are available for the 20 Italian regions overthe interval 1980 ± 94.7 Over the period under scrutiny these

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8 Obviously, international risk-sharing might fail even with full regional consumption insurance within a country.9 The data set does not permit the distinction between of tradables and non-tradables. This distinction, far from being trivial, seemshowever to be less crucial than in the case of international comparisons.1 0 In the estimation, the linear dependency among dummies is avoided through suitable normalizations. The tests are not a� ected by thesechoices.1 1 The instruments used in the estimation of all the regressions considered in the paper are the lagged levels of the various categories ofconsumption and of the GDP, sorted out by year and region only. Lags two and three are used, in order to take into account the likelyautocorrelation in the error term.1 2 Also the results for the time controls are shown in Table 1. The relevance of these country-wide e� ects can be immediately appreciatedfrom the result of the statistics x 2 (12).

regions are characterized by quite diversi ® ed but relativelystable population structures. The Life Cycle hypothesis inthis case suggests the existence of consumption patterns thatdi� er systematically across regions; we take into accountthese regional e� ects with the set of dummies a1 i.

Obviously, a di� erent meaning must be attached to con-sumption risk-sharing tests when data refer to householdsor to representative consumers. Tests at the internationallevel use a representative national agent and implicitly relyon the assumption of complete risk-sharing within eachcountry. An analogous assumption is postulated here: com-plete consumption risk-sharing is assumed to hold withineach region and a regional representative consumer is intro-duced. Risk-sharing is therefore tested against idiosyncraticregional shocks; however, aggregate shocks (internationaland national as well) are considered uninsurable.8

Perfect capital mobility within the country is also as-sumed. Hence, a signi® cant extra regressor in Equations (5)and (6) can be due either to the misspeci® cation in thestructure of the preferences of the representative consumeror (and this is our preferred interpretation) to incompleteconsumption risk-sharing.

Two series of dummies over time and regions (whichaccount for the aggregate time-speci ® c shocks and the ® xedregional e� ects, respectively) are introduced in the regres-sions. Were the preferences of the representative regionalconsumer identical, no di� erence should arise in the re-gional dummies a1 i. Were the aggregate shocks always thesame, all regional representative consumers should react inthe same way and no systematic di� erences should arise inthe time dummy coe� cients a2 t. These dummies interactalso with the additional regressor xti, the regional per capitaGDP, whose e� ects are therefore distinct through time-speci® c and regional-speci ® c controls. In this paper di� erenthypotheses about the structure of the utility function of therepresentative regional consumers are considered. First,consumption expenditures are aggregated into a single con-sumption good. The disaggregation into nine groups ofcommodities is then introduced, as is the more usual distinc-tion between durables and non-durables.9 We expect thatthis approach could enhance the reliability of consumptionrisk-sharing tests.

IV. EMPIRICAL ANALYSIS

Single consumption good

We are interested in testing the hypothesis of regional risk-sharing with respect to regional idiosyncratic e� ects. At ® rstwe control for the exogenous regional speci® c e� ects on theaverage consumption growth by means of the regional dum-mies dregi (i = 1, ¼ , 20). The time-speci® c e� ects of theshocks on the growth rate in national income (or of anyother national or international e� ect), that are common toall 20 regions, are also considered in the regressions throughthe time dummies1 0 dtt (t = 1983, ¼ , 1994).

We consider as a benchmark the case in which only oneadditional series is added, the growth in regional GDP,gyreg. In column 1 of Table 1 the results of the estimation ofthe regression

gcit = S ta1 tdtt + S ia2 idregi + b gyregit + uit (8)

are shown. The test for full consumption risk-sharing issimply b = 0. Since OLS estimates could lead to inconsist-ent estimates, because of the possible correlation betweenconsumption news and GDP growth, the IV estimator isused.1 1

In the second column of Table 1, we estimate a regressionin which the idiosyncratic regional time-independent e� ectson the GDP growth and the auxiliary controls for thecommon time e� ects of the regional GDP are introduced

gcit = S ia1 idregi + S ta2 tdtt + S i b 1 i dregi gyregit

+ S t b 2 t dtt gyregit + uit (9)

The relevant test for the hypothesis of full risk-sharing isa x 2 (20) for b 1 i = 0, " i.1 2

The test in column 1 refers to the case of the average’regional e� ect on GDP shocks on consumption growth andthe empirical ® ndings show the existence of positive correla-tion between GDP and consumption growth rates ± a cleardeparture from the hypothesis of complete insurance. Theprevious sections suggest that this ® nding might be a� ectedby misspeci® cation problems because, if the dynamics ofregional GDP growth rates are led by common uninsurablenationwide e� ects, spurious correlation is likely to emerge.

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Table 1. Consumption risk-sharing test, total consumption, 20 regions, 1983± 94, IV estimation.

No e� ects Time controls and regional e� ects(b gyregit ) ( S b tdttgyregit + S b idregigyregit)

No. of observations 240 240Degrees of freedom 208 178GDP coe� cient 0.11 Ð

Tests b = 0 (col. 1) or b i = 0 (col. 2) x 2 (1) 5.65 x 2 (12) 197.96 v 2 (20) 73.21(0.02) (0.00) (0.00)

Note: dtt t = 1983, ¼ , 1994 are time dummies; dregi i = 1, ¼ , 20 are regional dummies; P-values of the v 2 (.) inparentheses.

Table 2. Consumption risk-sharing tests for durables and non-durables, 20 regions, 1983 ± 94, non-separable utilityfunction, 3SLS estimation

No e� ects Time controls and regional e� ects(b gyregit ) (S b tdttgyregit + S b idregigyregit)

No. of observations 240 240Degrees of freedom 207 177Non-durables coe� cient - 0.35 - 0.58

(0.00) (0.00)

Tests for durables x 2 (1) 1.78 x 2 (12) 26.91 x 2 (20) 17.11b = 0 (col. 1), b i = 0, " i and/or b t = 0, " t (col. 2) (0.18) (0.01) (0.65)Durables coe� cient - 0.24 - 0.35

(0.00) (0.00)Tests for non-durables x 2 (1) 15.43 v 2 (12) 29.49 x 2 (20) 35.66b = 0 (col. 1), b i = 0, " i and/or b t = 0, " t (col. 2) (0.00) (0.00) (0.02)

Note: dtt t = 1983, ¼ , 1994 are time dummies; dregi i = 1, ¼ , 20 are regional dummies; P-values of the v 2 (.) inparentheses.

1 3 The regressions for the separability case are shown in the Appendix, Table A1.1 4 All the systems in Tables 2 and 3 are estimated with 3SLS. Analogous results can be obtained, however, from limited informationmethods of estimation. The results, available on request, are not reported for the sake of brevity.

However, when aggregate time controls are introduced incolumn 2 (and the relevance of the previous problem isconsequently reduced) regional speci® c GDP e� ects remainsigni® cant; therefore the failure of the complete consump-tion risk-sharing turns out to be quite robust.

Durables and non-durables

Sometimes the use of total consumption expenditure hasbeen criticized because of the inclusion of durables thatinduce autocorrelation in gcit. This, in turn, could bias thecoe� cients b i in our regressions if gcit ± 1 is a valid predictorof gyit, as in the saving for the rainy day’ permanent incomemodel of consumption. The literature often approaches thisissue by focusing the analysis on non-durables and servicesonly.

In Table 2 we introduce the distinction between durableand non-durable consumption expenditures. Two cases canbe considered, depending on the separability between thesetwo categories of consumption. For each case, the two

previous speci® cations of the tests are considered (no con-trols and time and regional controls).

For example, with non-separability in the arguments ofthe utility function we estimate the following regression fornon-durable consumption

gndcit = S ia1 idregi + S ta2 tdtt + a3 gdcit

+ S i b 1 i dregi gyregi t + S t b 2 t dtt gyregi t

+ uit (10)

with gndc and gdc that denote the rates of growth innon-durable and durable consumption, respectively. Ananalogous expression holds for durables.

The estimated coe� cients a3 are always signi® cant.Therefore, even if the separability case (in which these coe� -cients are constrained to zero) is also considered, we shallfocus our attention on the non-separability case.1 3 How-ever, the conclusions that can be drawn from both empiricalanalyses are similar.

Table 2 shows the estimated coe� cients of the two-equa-tion system.1 4 As for the case of the regression for durables

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Table 3. Consumption risk-sharing tests for nine categories of consumption, 20 Italian regions, 1983± 94, non-separability, 3SLS estimation.

A. No controls: gcj it = S ta1 tdtt + S a2 idregi + S ja3 jgcj it + b gyregit + uj it

Household Transpor- Medical RecreationHousing furnishing tation Food Tobacco Clothing care Education Other

GDP coe� . - 0.03 0.02 0.13 - 0.01 - 0.02 - 0.03 0.03 - 0.11 0.29test b = 0 0.14 0.08 1.15 0.13 0.03 0.18 0.02 2.10 9.02x 2 (1) (0.71) (0.78) (0.28) (0.71) (0.87) (0.67) (0.90) (0.15) (0.00)

B. Time controls and regional e� ects: gcj it = S a1 idregi + S ta2 tdtt + S ja3 jgcj it + S i b 1 idregigyregit + S t b 2 tdttgyregit + uj it

Household Transpor- Medical RecreationHousing furnishing tation Food Tobacco Clothing care Education Other

test b t = 0 " t 20.65 31.34 36.38 25.31 21.01 29.54 35.00 26.50 26.23x 2 (12) (0.06) (0.00) (0.00) (0.01) (0.05) (0.00) (0.00) (0.01) (0.01)test b i = 0 " i 29.73 46.28 34.00 32.47 24.26 33.52 52.21 27.69 35.28x 2 (20) (0.06) (0.00) (0.03) (0.04) (0.23) (0.03) (0.00) (0.12) (0.02)

Note: dtt t = 1983, ¼ , 1994 are time dummies; dregi i = 1, ¼ , 20 are regional dummies; P-values of the v 2 (.) in parentheses; # obs = 240;# dgs. freedom = 200 for the no-control case; # dgs. freedom = 170 for the time controls and regional e� ects case.

1 5 The case of separability among these categories of consumption is shown in the Appendix, Table A2.

(rows 5± 6), the majority of controls do not reject completerisk sharing. This result might be unsurprising for column1 (no controls), because of the likely misspeci® cation of thetest, whereas the ® ndings of column 2 are somewhatunexpected.

The results are reversed for the non-durables and servicesregressions (rows 9 ± 10): both speci® cations in columns1 and 2 reject the hypothesis of risk sharing. This latterresult is in line with other tests of the hypothesis of con-sumption risk-sharing on non-durables and services ina univariate framework.

However, because of the possible weaknesses in the treat-ment of durables, we rely mostly on non-durables ratherthan on the other case and regard the overall outcome asweak evidence against risk sharing.

Nine categories of consumption

So far, total consumption expenditure or rather large cate-gories of consumption have been considered; all previousconclusions depend on the adequacy of the assumptionsabout separability and aggregation in the utility function.A di� erent perspective can be gained when consumptionis disaggregated into quite narrowly de® ned groups ofcommodities. Nine categories are considered: housing,household furnishing, transportation (previously groupedtogether as durables), foods and beverages, tobacco, cloth-ing, medical care, education and recreation and other

consumption expenditures ± typically personal services (pre-viously grouped as non-durables and services).

Table 3 shows the results for the nine-equation system inwhich the dependent variables are the households’ percapita consumption growth rates of each group. Again, thepreferred speci® cation is the non-separable one, but also forthe other case similar conclusions can be reached.1 5 Thetable is divided in two, depending upon the type of controlintroduced.

In part A, the no-controls regressions are considered. Theresults are striking: the hypothesis of consumption risk-sharing is rejected only in the ninth, residual category ofconsumption. The test x 2 (9) for the joint signi® cance of theGDP coe� cients is 12.37 (P-value 0.21) and this is obviouslyin line with the ® ndings for each equation of the system.Therefore, consumption risk-sharing seems to emerge whendisaggregated consumption data are used. While these re-sults are at variance with the previous tests in the paper,they are roughly in line with Cochrane (1991), Mace (1991)and Lewis (1996).

However, if speci® c regional GDP e� ects on consumptiongrowth rates are allowed and time controls are also intro-duced in each equation of the system, the picture changescompletely. In part B of Table 3, risk-sharing is not rejectedat the signi® cance level of 5% only in three cases out of nine± tobacco, education and housing (marginally). Moreover,the overall picture that emerges from the nine equationsystem is rather clear: the test for the joint signi® cance of the

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APPENDIX

Table A1. Consumption risk-sharing tests for durables and non-durables, 20 regions, 1983± 94, separable utility function,3SLS estimation

No e� ects Time controls and regional e� ects(b gyregit) (S b tdttgyregit + S b idregigyregit)

No. of observation 240 240Degrees of freedom 208 178Durables tests x 2 (1) 0.08 x 2 (12) 17.80 x 2 (20) 18.21b = 0 (col.2), b i = 0, " i and/or b t = 0, " t (col. 3) (0.78) (0.07) (0.57)

Non-durables tests x 2 (1) 14.95 x 2 (12) 22.78 x 2 (20) 41.57b = 0 (col.2), b i = 0, " i and/or b t = 0, " t (col. 3) (0.00) (0.03) (0.00)

180 control coe� cients is x 2 (180) = 218.13, with P-value0.03. The hypothesis of consumption risk-sharing amongthe 20 Italian regions over the period 1983 ± 94 can be neatlyrejected.

At a more general level, the results in part B of Table3 suggest the likely misspeci® cation of the standard tests ofconsumption risk-sharing which the literature has de-veloped so far, whose results are shown in part A.

V. CONCLUSIONS

Correlations between the per-capita consumption growthrates of di� erent regions or countries turn out to be quitelow, a result that suggests a low level of consumptionrisk-sharing (see, among others, Obstfeld, 1994; vanWincoop, 1995).

More formal tests (Montiel, 1993; Mace, 1991; Cochrane,1991; Canova and Ravn, 1996; Lewis, 1996) sometimes re-verse this conclusion and support the view of a quite signi® -cant degree of risk-sharing at various aggregation levels.

This paper has developed a re® nement of the standardconsumption risk-sharing test developed so far in the litera-ture. The empirical evidence suggests that these standardtests might fail to detect important departures from com-plete risk-sharing, because they impose quite restrictivespeci® cations on the situation of incomplete consumptioninsurance. This speci® cation uses a panel data approachand allows for time and regional speci® c e� ects of the GDPon consumption. These tests should therefore be quiterobust to possible misspeci® cations in the utility functionsof the individual consumers.

We apply these tests to aggregate consumption, to dur-able and non-durable consumption expenditure and to ninecategories of consumption for the 20 Italian regions over theperiod 1983 ± 94. The empirical evidence strongly supportsthe hypothesis of less than complete risk-sharing in regionalper-capita consumption.

ACKNOWLEDGEMENT

I would like to thank an anonymous referee for the usefulcomments on a previous version of the paper. Responsibilityfor errors rests solely with the author.

REFERENCES

Altug, S. and Miller, R. (1990) Household choices in equilibrium,Econometrica , 58, 543 ± 70.

Attanasio O. and Davis, S. J. (1996) Relative wage movements andthe distribution of consumption, Journal of Political Economy,104, 1227 ± 62.

Bayoumi, T.A. and McDonald, R. (1994) On the optimality ofconsumption across Canadian provinces, CEPR DiscussionPaper.

Campbell, J. Y. (1987) Does saving anticipate declining laborincome? An alternative test of the permanent income hypoth-esis, Econometrica , 55, 1249 ± 73.

Canova, F. and Ravn, M. O. (1996) International consumption risksharing, International Economic Review, 37, 573 ± 601.

Cochrane, J. H. (1991) A simple test of consumption insurance,Journal of Political Economy, 99, 957 ± 76.

Hayashi, F., Altonji, J. and Kotliko� , L. (1996) Risk-sharing be-tween and within families, Econometrica , 64, 261 ± 94.

Lewis, K.K. (1996) What can explain the apparent lack of interna-tional consumption risk-sharing?, Journal of Political Econ-omy, 104, 267 ± 97.

Mace, B. (1991) Full insurance in presence of aggregate uncertain-ty, Journal of Political Economy, 99, 928 ± 56.

Montiel, P. (1993) Capital mobility in developing countries: somemeasurement issues and empirical estimates, World Bank Eco-nomic Review, 8, 327 ± 42.

Obstfeld, M. (1989) How integrated are world capital markets?Some new tests, in Debt, Stabilization and Development, G.Calvo et al., (Ed.) Basil Blackwell, Oxford.

Obstfeld, M. (1994) Are industrial-country consumption risk glo-bally diversi® ed?, in Capital Mobility; the Impact on Consump-tion, Investment and Growth, L. Leidermann and A. Razin,(Eds) Cambridge University Press, Cambridge.

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Table A2. Consumption risk-sharing tests for nine categories of consumption, 20 Italian regions, 1983± 94, separability, 3SLS estimation.

A. No controls: gcj it = S ta1 tdtt + S a2 idregi + b gyregit + uj it

Household Transpor- Medical RecreationHousing furnishing tation Food Tobacco Clothing care Education Other

GDP coe� . 0.03 0.08 - 0.01 0.07 0.02 0.03 0.34 - 0.08 0.45Test b = 0 0.18 1.62 0.00 4.77 3.09 0.27 2.53 1.26 22.21

x 2 (1) (0.67) (0.20) (0.96) (0.03) (0.08) (0.60) (0.11) (0.26) (0.00)

B. T ime controls and regional e� ects: gcj it = S a1 idregi + S ta2 tdtt + S i b 1 idregigyregit + S t b 2 tdttgyregit + uj it

Household Transpor- Medical RecreationHousing furnishing tation Food Tobacco Clothing care Education Other

test b t = 0 " t 17.66 28.01 21.67 18.87 10.09 24.44 23.69 28.20 25.32x 2 (12) (0.13) (0.01) (0.04) (0.09) (0.61) (0.02) (0.02) (0.01) (0.01)

test b i = 0 " i 32.11 27.14 25.52 43.48 16.90 41.67 41.05 18.57 32.11x 2 (20) (0.034) (0.13) (0.18) (0.00) (0.66) (0.00) (0.00) (0.55) (0.04)

Note: dtt t = 1983, ¼ , 1994 are time dummies; dregi i = 1, ¼ , 20 are regional dummies; P-values of the v 2 (.) in parentheses; # obs = 240;# dgs. freedom = 208 for the no-control case; # dgs. freedom = 178 for the time control and regional e� ects case.

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