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I would like to thank Annamaria Lusardi, Ronald MacDonald, Eswar Prasad, Bart Turtelboom, Mark Salmon and participants at seminars at the University of Toronto and European University Institute for useful comments on an earlier draft.
For example Mace (1991), Cochrane (1991), and Townsend (1994). Townsend also provides a survey of evidence from other work. Obstfeld (1994) uses a similar approach to look at consumption across countries.
The “excess” sensitivity of consumption to income was originally highlighted by Flavin (1981). Subsequent work estimating the size and importance of such “liquidity constraints” includes Campbell and Mankiw (1989 and 1990) and Japelli and Pagano (1991) on the macroeconomic side, and Hall and Mishkin (1982), Hayashi (1985), Zeldes (1989), and Hubbard, Skinner and Zeldes (1994) on the microeconomic side. Other authors using microeconomic data, however, have failed to find evidence of liquidity constraints, including Altonji and Siow (1987), Runkle (1991), and Maringer and Shaw (1993). This microeconomic evidence is surveyed in Browning and Lusardi (1995). One reason for this variety in results from microeconomic studies may be different approaches to the problems of the underlying microeconomic data, as discussed in Lusardi (1995).
This assumption is relaxed later.
An alternative derivation of this result considers the path for consumption which would be chosen by a benign social planner. For any given trajectory for total consumption, the Pareto optimal solution for each individual or province involves identical comovements in consumption. This reflects the more general proposition that the solution with full contingent markets should correspond to one chosen by a social planner.
To ensure the model is identified, the dummy variable for the first time period is excluded in the estimation.
Dummy variables for each period have been included in most empirical microeconomic studies of consumption in order to eliminate the impact of aggregate changes in activity. However, the focus of this work has remained on the size of the coefficient on income or other personal characteristics, not on the relative contribution of alternative hypotheses. In principle, however, the same methodology could be applied. Indeed, by measuring the information content of the risk sharing model, the approach adopted here might help to determine the importance of noise in the data.
Other workers with microeconomic data have used data over several years. Cochrane’s paper is used to illustrate a potential derivation of the estimating equation.
They also include direct estimates of the ex ante real interest rate in some regressions.
Results using nondurable consumption without including services are very similar.
Alberta, British Columbia, Manitoba, New Brunswick, Newfoundland, Nova Scotia, Ontario, Price Edward Island, Quebec, and Saskatchewan. Full data were not available for the Yukon or Northwest Territories.
On the other hand, the data may suffer from aggregation bias. As discussed earlier, it would certainly be interesting to also run this specification on data for individual consumers.
The U.S. data come from the state-by-state personal income accounts. U.S. data on consumption by state do not exist, except for retail sales every several years. The U.S. data cover the period 1974−87.
If the objective was simply to test the risk sharing model then there is no need to instrument the change in income, as all movements in permanent income are represented by the time dummies. However, the risk sharing model is a refinement of the more general permanent income model, which makes no assumptions about the correlation of movements in permanent income across provinces. Results without instrumental variables are also reported below.
Maringer and Shaw (1993) criticize earlier (microeconomic) studies of consumption by noting that, although expectational errors should be uncorrelated over time, they need not be uncorrelated across individuals or provinces within a single time period. As different instruments are being used across provinces, this issue does not arise in the current analysis.
Coefficients on individual provinces show little obvious relationship between the estimated values and per capita income, raw material production, or economic size. Ontario, the largest and one of the richest provinces per capita has a middling coefficient on income. Quebec, the second largest province, and tiny Prince Edward Island have small values. Alberta, a major oil-producing and relative prosperous province, has a large coefficient, while Saskatchewan, another western province, does not.
The model was also run using changes in the levels of real nondurable consumption per capita and real disposable income per capita instead of the logarithms of these variables. The results from these regressions were very similar to those using change in logarithms, and are not reported.
As might be expected, the significance of the time dummies increases.
The coefficient restrictions implied by the assumptions of equal discount rates and equal rates of intertemporal substitution across provinces were accepted in all three regressions.
The statistic 1/2 ln[(1+r)/(1-r)], where r is the correlation coefficient, is distributed approximately normally, with mean 1/2 ln[(1+ϱ)/(1-ϱ)] and variance (T-3) (Kendall and Stuart, 1967, pp. 262-263). For ϱ=0, this implies a 5 percent confidence interval of + or -0.48.
As discussed earlier, this restriction is narrowly rejected by formal tests.
A further argument for using least squares is that income should not be instrumented in the pure risk sharing model, as the change in permanent income should be fully accounted for by the time dummies, and hence there will be no simultaneity bias.
When the instrumented values for the income terms were substituted for the actual income terms in the least squares regression, the fit of the equation fell, suggesting that the lack of explanatory power of the actual income terms does not reflect errors in measurement.
Earlier work on these issues includes Mankiw, Rottenberg, and Summers (1985) and Eichenbaum, Hansen, and Singleton (1988) on labor supply, Bernanke (1985) on durable goods, and Aschauer (1985) on government purchases. Empirical microeconomic work has generally ignored these nonseparabilities (Browning and Lusardi, 1995).
Lewis (1994) argues that nonseparabilities between traded and nontraded goods can explain most of the correlation between consumption and income across countries. Our data do not distinguish between traded and nontraded goods, hence we are only able to consider nonseparabilities between durable and nondurable goods.
Comprehensive data on hours worked are not available for all provinces. Hourly wages are only available from 1983, which would have severely restricted the sample.
Strictly speaking, this specification will only occur if the underlying utility function has a Cobb-Douglas form. For other utility functions there should also be interaction terms between the various types of consumption and leisure. The chosen specification, however, is the one usually used in the literature.
The unemployment coefficients are constrained to be the same in the risk sharing specification, as the utility functions are assumed to be the same across provinces.
When the coefficients on income are constrained to be equal across provinces the coefficient is 0.16, very similar to that found in the simpler model discussed earlier.