APPENDIX I Technical Appendix
The analytical framework on which the discussion in Sections I and II is based assumes a representative agent who maximizes the expected value of the discounted sum of current and future utilities subject to a series of dynamic budget constraints and a transversality condition that rules out Ponzi‐type schemes. Thus, the agent maximizes:
where β is the subjective discount factor, u(.) is the instantaneous utility function, and ctdenotes consumption. In addition to the transversality condition, consumers’ decisions must satisfy their dynamic budget constraints, which hold that in any period t
where bt denotes financial assets at time t, yt denotes real labor income, and r denotes the exogenous real interest rate. For the purpose of empirical implementation, a constant‐absolute‐risk‐aversion (CARA) form of the instantaneous utility function is adopted:
where α > 0 denotes the Arrow‐Pratt measure of (absolute) risk aversion.
Under the simplifying assumption that the interest rate is equal to the rate of time preference,39 the first order necessary condition is given by
This condition states that the marginal utility cost of giving up one unit of consumption at time r should be equated to the expected utility gain from consuming one more unit at t + 1. Alternatively, dividing the left‐hand side of equation (A4) by the right‐hand side, the condition states that the intertemporal marginal rate of substitution should equal the ratio of the prices of present and future consumption, which is unity here.
It is assumed that the variance referred to in equation (1) follows an AR(1) process with parameter ρ.40 To solve for the consumption function, a “guess and verify” method is used. Our guess for the consumption process is
where ξt is the innovation in life‐time labor income,
Λt‐1 is the stochastic slope of the consumption path between periods t – 1 and t, which depends on the variance of ξt-1 denoted
Substituting equation (A5) into equation (A4) yields:42
If the innovations to labor income have a normal distribution (with mean zero), then so will ξ. If, moreover, the innovations to the variance process follow a normal distribution, then the expectations in equation (A7) can be evaluated to yield
Once Λt has been obtained, a final form of the consumption function may be guessed as follows:
Thus, according to equation (A9), consumption in any period is equal to permanent income minus a term in the variance of labor income. To check the guess for the consumption function, it must be shown that equation (A9) satisfies equation (A5).43 Note from equation (A9):
But from the budget constraint equation (A2):
Substituting the process for Λt gives:
which is equation (A5), as was to be verified.
By definition, saving is equal to the change in financial assets. Using the budget constraint (A2) together with the solution for the consumption function given in equation (A9) gives a simple expression for saving as the present value of expected changes in labor income plus a term in the variance of the innovations to labor income:
where Δ is the (backward) difference operator,
APPENDIX II Data
The main sources of data were Institut National de la Statistique et des Etudes Economiques (INSEE) and Wharton Econometrics (WEFA). A deflator for all nominal variables was obtained by dividing INSEE’s measure of nominal household consumption by household consumption at 1980 prices. Other series obtained from INSEE were labor income, and household disposable income and saving, the latter being the difference between household disposable income and consumption. The saving ratio is household saving divided by household disposable income. Population data were obtained from several issues of l’Annuaire Statistique de la France, table B‐01–1. Three‐month bank deposit rates and stock prices were obtained from WEFA. Data on the stock of consumer credit were provided by the French authorities and prices of apartments in Paris were taken from Taffin (1993).
Allard, Patrick, “La moddlisation de la consummation des menages en France,” Revue d’economie polinque, Vol. 102 (September/October 1992), pp. 728–68.
Artus, Patrick, and others “Epargne des ménages, choix de portefeuille et fiscalite en France,” Revue economique, Vol. 42 (July 1991), pp. 663–700.
Bloch, Laurence, and F. Maurel, “Consommation‐revenue permanent: un regard d’econometre,” Economic et prevision, Vol. 99 (March 1991), pp. 113–44.
Caballero, Ricardo J., “Consumption Puzzles and Precautionary Savings,” Journal of Monetary Economics, Vol. 25 (January 1990), pp. 113–36.
Campbell, John Y., “Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis.” Econotnetrica, Vol. 55 (November 1987), pp. 1249–73.
Campbell, John Y., and Angus Deaton, “Why Is Consumption So Smooth?” Review of Economic Studies, Vol. 56 (July 1989), pp. 357–74.
Campbell, John Y., and N. Gregory Mankiw, “Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence,” NBER Macroeconomics Annual, ed. by Olivier Jean Blanchard and Stanley Fischer (Cambridge: MIT Press, 1989), pp. 185–216.
France, Finance Ministry, Direction de la Prevision, “Peut‐on expliquer revolution recente du taux d’epargne des menages?” (unpublished; Paris: Direction de la Prevision, 1993).
Hall, Robert E., “Stochastic Implications of the Life Cycle—Permanent income Hypothesis: Theory and Evidence,” Journal of Political Economy,Vol. 86 (December 1978), pp. 971–88.
Jappelli, Tullio, and Marco Pagano, “Saving, Growth, and Liquidity Constraints,” Quarterly Journal of Economics, Vol. 109 (February 1994), pp. 83–109.
Modigliani, Franco, “Life Cycle. Individual Thrift, and the Wealth of Nations,” American Economic Review, Vol. 76 (June 1986), pp. 297–313.
Sterdyniak, Henri, “Le choix des menages entre consommation et epargne en France de 1966 a 1986,” Observations et diagnostics économie, Vol. 21 (October 1987), pp. 191–210.
Taffin, C., “Crise immobiliere: une lecon a retenir,” Revue d’Economie Finallciêre (special issue on La crise financiere de l’immobilier, 1993), pp. 151–64.
Zerah, Dov, Le systeme financier frangais: dix ans de mutations, Notes et Etudes Documentaires, No. 4980–81 (Paris: La documentation Francaise, 1993).
Jonathan D. Ostry, a Senior Economist in the Research Department, holds a doctorate from the University of Chicago, as well as degrees from the London School of Economics and Political Science, Oxford University, and Queen’s University. Joaquim Levy is an Economist in the European I Department. He holds a Ph.D. from the University of Chicago and a Master’s degree from the Fundacão Getúilio Vargas, Rio de Janeiro. The authors thank Tamim Bayoumi, Eduardo Borensztein, Rex Ghosh, Paul Masson. Carmen Reinhart, and Peter Wickham for helpful discussions and comments on a previous draft, and Nii Kote Nikoi for assistance with the data.
Such a view might be rationalized by a model in which, prior to deregulation, consumption growth matched income growth because consumers were liquidity constrained, but following deregulation, the share of liquidity‐constrained consumers fell, increasing the sensitivity of consumption and saving to changes in the interest rate (see, for example, Campbell and Mankiw (1989)).
As mentioned previously, a housing price index for Paris exists, but its reliability as a proxy for house prices in France remains in doubt.
Uncertainty about whether the generosity of public pensions would be reduced may also have contributed to a precautionary demand for saving.
Statistically, the effect is insignificant.
Below, we refer to the precautionary saving model as the “augmented” Campbell model—augmented to include the effects of precautionary saving.
Neither model, however, is nested in the other.
Innovations to the variance process that die out quickly (low value of ρ) will have little effect on precautionary saving, while shocks to the variance that are permanent (as in the random walk case of ρ = 1) will have larger effects on saving.
One consequence of this would be that the extent of uncertainty (captured by
The Schwartz‐Bayes Information Criterion (SBIC) was used to determine the order of the VAR.
As pointed out by Caballero (1990), any divergence between the interest rate and the subjective rate of time preference will introduce a trend into the saving function. This deterministic trend in saving is removed prior to estimation of the VAR. Although the model identifies the trend in saving with consumption‐tilting dynamics related to divergences between the interest and time preference rates, more generally it could capture other deterministic factors as well.
Γ also depends on the interest rate, r. In all calculations, an annual real interest rate of 4 percent was assumed. The results are insensitive to annual interest rates in the range 2–6 percent.
As described in Appendix II, the saving data used in this paper are calculated as household disposable income minus household consumption. Labor income, however, is only available on a gross basis. See Bloch and Maurel (1991) for previous estimation of Campbell’s model using similar data.
The time series on pdν is obtained according to the formula given in equation (4) above. The results for the Γ vector are presented in Table 1, panel b.
Saving began to turn down in the second quarter of 1993. This turning point is also captured by the model, and suggests that part of the reason for reduced household saving is an improvement in the outlook for future income, and thus a reduction in the extent to which households are saving for a rainy day.
It should he noted that an increase in pdνimplies that households have reduced their forecast of the expected future growth of labor income, which causes them to increase their saving. Conversely, in the last few quarters of the sample, an improved outlook for the future course of labor income may have contributed to a reduction in household saving.
An alternative way of obtaining
The constructed regressor,
The interpretation would be that the role of our proxy for time‐varying uncertainty in generating a precautionary demand for saving is small, possibly reflecting low persistence of variance shocks. In contrast, the role of the saving for a rainy day term—captured by pdν—is highly significant.
The excessive variability of saving (excessive, that is, in light of actual shocks to pdν may reflect an omitted variable. It is possible, for example, that, in addition to the stochastic process for labor income, saving behavior in France may have been influenced by a number of different factors, including institutional changes relating to the deregulation of the financial sector, which cannot easily he accommodated within the formal permanent income model developed in this section. This issue is investigated below in Section IV.
To the extent that time‐varying uncertainty has played only a limited role in saving behavior in France, the relevant model would be Campbell’s unaugmented version, as reported in Table 1. It may be noted that the x2 test for the strong implications of the model (essentially the restrictions on the Γ vector reported in Table 1, panel b) is equal to 8.23, which does not reject the model at the 1 percent level.
All changes are relative to the average value of the variables during the entire sample excluding the last four years.
Changes in public debt management—particularly the practice (adopted after 1985) of auctioning public debt—also affected household saving behavior by contributing to the market determination of interest rates. The growth of mutual funds in France dates from the early 1980s and was initially due to interest rate ceilings imposed in 1981. Such growth was strengthened over the past decade by a series of fiscal incentives (Zerah (1993)). As regards liberalization of banking, the Banking Law of 1984 removed most of the distinctions between commercial and merchant banks and was followed by the abandonment of direct credit controls (encadrement) in 1986. This liberalization had a particularly strong effect on consumer credit (credit de tresorerie), the stock of which doubled between 1986 and 1989. For details of the financial deregulation process in France, see Pilverdier‐Latreyte (1988). Vincent (1993), and Zerah (1993).
The specification is a simplified version of the one applied w United Kingdom data by Bayoumi (1993).
The dependent variable in the model of Section II was the level of saving, rather than the saving ratio. This reflected mainly analytical tractability since, in the model of Section II, saving (rather than the saving ratio) could be shown to be a function of the expected present value of future declines in labor income. The solution for the saving ratio in the permanent income model as a function of the expected present value of future declines in the log of labor income is only an approximation (see Campbell and Deaton (1989)).
Asset prices are included here as a proxy for household wealth.
The value of the proxy for deregulation peaks in 1990:4. It is assumed to be equal to its maximum value (unity) in the remaining two years of the estimation. This assumption has no significant effect on any of the results reported below. Finally, an alternative proxy for financial deregulation would be the ratio of consumer credit to total bank credit. Using this alternative proxy produced results that arc virtually identical to those reported below.
The adequacy of the instrument set is discussed below.
Although the estimation was conducted using quarterly data, the magnitude of the coefficients on income growth, inflation, and the real interest rate reflects the fact that these variables were expressed at annual rates.
The insignificance of the demographic variable was not altered by introduc‐ ing as separate regressors its two components.
See, for example, Bloch and Maurel (1991), who report results for the effects of interest rate changes on saving in a model that abstracts from the effects of financial deregulation.
Bayoumi (1993) also finds that financial deregulation in the United Kingdom raised the interest sensitivity of saving. His results suggest an interest semi‐ elasticity of saving above 4.0 in the period after deregulation.
Recall that once the effect of financial deregulation on the interest sensitivity of saving is allowed for, the estimated effect of an increase in the real interest rate on saving is positive.
As can be seen, the sum of these changes exceeds (by about I percentage point) the actual decline in saving observed over the period. Obviously, this reflects the fact that the fit of the regression is not perfect, so that the predicted decline in saving was larger than the actual decline.
That is, the income effect outweighs the substitution effect.
This assumption is not restrictive since, as indicated in the text, the effect of any difference between the rate of interest and the rate of time preference is taken into account in the estimation. Specifically, as explained in Caballero (1990), if the interest rate differs from the rate of time preference, there will be a deterministic trend in the saving function. Such a trend is taken into account in the empirical work by removing a deterministic (linear) trend from the saving data prior to estimation of the VAR.
The variance at time r is assumed to be in the time‐t information set of the representative household.
It is straightforward to verify that the innovation to the A process. wt, is proportional to the innovation to the variance process. Also, it is clear that if the varianceprocess is an AR(1) with parameter p. then the A process will also be an AR(1) with parameter p; see Caballero (1990).
We assume that and w are independent stochastic processes.
Recall that equation (A5) itself satisfies the Euler condition (A4), given equation (A7).