Intertemporal preference parameters for some European monetary union countries

Abstract

In the European Monetary Union, the estimation and analysis of preference parameters in its members is of special interest because possible differences could help us to understand why a common monetary policy could have different effects on the different economies involved. In this article, we have focused our attention on the elasticity of intertemporal substitution, one of the key preference parameters in intertemporal macroeconomic models. Several studies have shown a possible underestimation of such elasticity for different countries. It is common practice to estimate the parameter using only nondurable goods and services consumption data, without referring to the flow of services generated by durable consumption. This is only admissible if the intratemporal utility can be separated among the different consumption components. Our first objective is, therefore, to test the assumption of intratemporal separability for a selection of European countries (Germany, Spain and France), and then to analyse the effect of durable consumption on the estimated values of the intertemporal elasticity of substitution of these countries, our ultimate goal. Knowledge of such elasticity will enable us to characterise how saving in these economies reacts to variations in the real interest rate.

Acknowledgements

The authors thank the Fundación Banco Herrero for the research grant received to finance the project which this article is based on. They likewise acknowledge the work of Prof. Rafael Myro as the project director. An extended version of this work is available as: Fundación FUNCAS Working Papers n° 207, July 2005 (www.funcas.es).

Notes

¹ Using the terminology typical of asset pricing literature, we could say that, to a certain extent and according to the specification of the preferences employed, the results reflect both the risk premium puzzle, Mehra and Prescott (1985), and the interest rate puzzle, Weil (1989). A detailed analysis of the empirical puzzles of the CCAPM model, and of some of the solutions proposed, can be found, among others, in Campbell (2003).

² We are referring to the consideration of phenomena such as durability or the formation of consumption habits, as in the case, among others, of Dunn and Singleton (1986) or Campbell and Cochrane (2000), or to the rupture with the expected utility approach in the work of Epstein and Zin (1991).

³ Focusing on the Spanish case, López Salido (1993) analyses the intratemporal separability of preferences using microeconomic data from the Encuesta Continua de Presupuestos Familiares for the period 1985 to 1989. On the other hand, Márquez de la Cruz (2005) uses macroeconomic data for the period 1954 to 2002. Here, however, we consider a different sample period, more adjusted to the availability of data for the other two countries studied, in order to be able to compare the results. We also consider the case of nonhomothetic current preferences and the assets used here in the estimation of intertemporal elasticity of substitution are also different.

⁴ Note that if ε = 1, expression (2) converges to the Cobb--Douglas function, whereas if ε = 0 the current utility would converge to Leontief 's utility function. For a detailed analysis, see Pakos (2004).

⁵ We can therefore test the assumption of intratemporal separability by testing the null hypothesis ε = σ.

⁶ Specifically, Ogaki and Reinhart consider an endowment economy in which their logarithm is stationary. On the other hand, Ogaki and Reinhart (1998a) and Okubo (2002) show that, although the stationarity of UMa _1,τ+1/UMa _{1, t} is not necessarily derived from the model's assumptions, it is a valid assumption, at least from an empirical perspective.

⁷ For a detailed study of this technique, see, among others, Ogaki (1993) and Ogaki et al . (2003).

⁸ The difference between the two concepts is based on the fact that the cointegration vector which eliminates the stochastic trends among the variables can also eliminate deterministic trends or not. In the first case, we refer to deterministic cointegration, whereas if the deterministic trends are not eliminated by the cointegration vector, this is a case of stochastic cointegration. For details of the deterministic and stochastic cointegration concepts, see, among others, Ogaki (1993).

⁹ Other methods also lead to estimators with all the desirable properties. This is the case for the methods of Phillips and Hansen (1990) and Stock and Watson (1993).

¹⁰ This method (the properties of which make it particularly useful in a multivariate context) also allows for stationarity tests on the series involved in the analysis, so it is possible to complete the study of their order of integration provided by unit root tests.

¹¹ See Hendry and Juselius (2001).

¹² In this respect, we have followed Esteve and Tamarit (1994).

¹³  is the real interest rate of country j, j = Germany, Spain, France and is the real gross rate of return of financial asset i, i = DAX30, IGTBM, CAC40 (abbreviations of the stock indices used to calculate the nominal rates of return for Germany, Spain and France, respectively).

¹⁴ To determine the cointegration rank, the information provided by the trace test in Table 2 has been completed, in all cases, with an analysis of the roots of the characteristic polynomial and with the t statistics of the adjustment coefficients α.

¹⁵ According to the stationarity tests applied, (c_t  − d_t ) cannot be rejected as stationary, in line with the results of the ADF and PP unit root tests, when we consider a constant in the data-generating process. In all the estimated cointegration relations, we have performed the relevant exclusion, stationarity and weak parameter exogeneity tests by means of LR tests distributed like a χ², the degrees of freedom of which depend on the constraints established. We have also tested the VAR residuals to verify that they present neither autocorrelation nor heterocedasticity and that they verify the hypothesis of normality (although, if this hypothesis is not confirmed, Gonzalo (1994) showed that the results of the estimation would continue to be robust). According to the information criteria of Akaike and Schwarz, the number of lags used in the VAR is 1 in the estimations for Spain and Germany and 2 for France.

¹⁶ The results of the ADF and PP unit root tests for variables c_t and d_t show that we cannot reject them as nonstationary. The results are available upon request to the authors.

¹⁷ The unit root tests do not reject the stationarity of variables c_t and d_t for some of their specifications. The results of these tests are available upon request from the authors and they are confirmed to a certain extent by the results obtained for this specification of preferences with the Johansen method.

¹⁸ With r = 2, both price and durable consumption react significantly to deviations in the long-term relationship.

¹⁹ Moreover, in this case, it cannot be rejected that c_t and d_t are stationary variables.

²⁰ With this level of significance, the stationary test applied enables us to reject that relative consumption is stationary.

²¹ For an explanation, see Ogaki (1993) and Ogaki et al . (2003).

²² See Section III.

²³ In the case of France, since the real interest rate is not stationary, the variable on levels has been replaced by its gross growth rate.

²⁴ We are referring to the Hansen and Singleton model (1982, 1983).

²⁵ The results are somewhat less puzzling when we consider utility function specifications which are not intertemporally separable.

²⁶ For example, Ogaki and Reinhart plug a value of β equal to 0.99 and 0.995 for quarterly data; in other words, the annual subjective discount factor takes on values of 0.9605 and 0.9801.

²⁷ We are unaware of microeconometric estimations of this parameter for the other two countries considered.

²⁸ The link method is described in Márquez de la Cruz (2004).

²⁹ We are referring to the Order of the Ministry of Economy and Public Finance of 15 December 1998, Annex IV. In these tables, we have taken the number of years after which the value of the vehicle in question is less than 15% of its initial value. The parameters have been estimated considering larger and smaller periods of time, without the results varying significantly. All the results are available upon request from the authors. Since we are unaware of the existence of similar tables for Germany and France, we have applied the procedure used for Spain to these two countries.

³⁰ Depreciation rates have been taken from the aforementioned tables.