The aim of this paper is testing the three first-order conditions of an intertemporal optimization model for a representative individual who chooses simultaneously for her level of consumption and leisure, assuming a separable utility function. We estimate these conditions jointly in a system of equations, using a Spanish pseudo-panel data set built by combining the Family Expenditure Survey and the Labor Survey over the period 1987–1997. Our results are in line with previous empirical evidence as regards the elasticity of intertemporal substitution for consumption, as our estimate for this elasticity is between 0.4 and 0.5. Further, we also obtain the first estimate for Spain of the intertemporal elasticity of leisure. This value is above 0.3, and is comparable to other estimates found for other economies.
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As Chetty et al. (2011, p 471) point out, “micro estimates of intertemporal substitution (Frisch) elasticities are an order of magnitude smaller than the values needed to explain business cycles fluctuations in aggregate hours by preferences”.
Hall (1988), using aggregate data, was unable to get a statistically significant estimate for this parameter. Further studies, also using aggregate data, obtain similar results as regards the intertemporal elasticity of consumption. Contrarily to these works, those using microeconomic data estimate a positive and statistically significant parameter, although generally below one, what indicates the appropriability of microdata in this respect (Attanasio & Weber, 1993).
However, it is important to note that during the period of analysis, both the budgetary difficulties of the Spanish government made it very difficult to modify some of these taxes (either the VAT or the social security contribution) to incentivize employment.
There are two further approaches to this concept: the Hicksian and the Marshallian elasticities. However, these depend on assuming that either the utility or wealth remain constant when wage is changing, respectively.
Recently, a new survey has been launched in Spain (the Families Financial Survey, Encuesta Financiera de las Familias, EFF), which combines statistical information on both labor and consumption variables. However, these data are available every 3 years and the sample overrepresents wealthy households.
Additionally, the main Spanish Labor Force Survey (Encuesta de Población Activa, EPA), does not provide information on wages or income, what complicates the empirical analysis of labor supply decisions.
Cutanda (2019) uses aggregate regional data and does not obtain a statistically significant estimate for the elasticity of intertemporal substitution of leisure.
See the influential survey by Keane (2011) on the empirical labor supply research.
Our estimates for the elasticity of intertemporal substitution for consumption are larger than their estimates, what might be related to the fact that we use more homogeneous cohorts, and we have a more appropriate definition of expenditure to analyze the intertemporal elasticity of consumption.
Our estimate for the Frisch elasticity is within the range of MaCurdy (1981) estimates (0.1–0.45) and Altonji (1986) estimates (0.08–0.54), which vary depending on the specification or the set of instruments used. Keane (2011) surveys 12 influential studies and reports an average estimate of 0.83 with a median estimate of 0.17, although these numbers are upward biased due to, at least, a clear outlier. More importantly, Chetty et al. (2013) conclude, from an exhaustive meta-analysis of fifteen empirical studies, that the mean extensive margin for the intertemporal elasticity of leisure is around 0.25.
In the period we analyze, the Spanish unemployment and temporary average rates reached 17.19% and 30.17%, respectively. There is a broad consensus about the dual behavior of the Spanish job market, what is usually explained by the high rate of temporary workers, which reached values above 30% before the last crisis (see Dolado et al., 2002). It is expected that temporal workers restrict their intertemporal substitution of leisure, what might explain, at least partially, the lower estimated we obtain.
We generically name Rt as the interest rate.
More recently, Bredemeir et al. (2019) apply a modified version of this utility function to the joint analysis of intertemporal consumption and leisure.
In particular, k2s = k1c, and k1s = k1c/k1l.
It is important to underline that much of the empirical analyses of aggregate consumption, based on the expression (10), also assume separability, and, as emphasized by Mankiw et al. (1985), this weakness is aggravated by the fact that the aggregate analyses ignore the information provided by the expression (9). In this respect, Carrasco et al. (2004) find evidence of no intertemporal separabilities in Spanish intertemporal consumption behaviour.
This would imply discarding households where the head is unemployed, what would have implications for the empirical sample used. There might be other individuals suffering (potentially) from liquidity constraints, such as young individuals with low income. To avoid this problem, we also discard individuals younger than 23 years in 1987. On the effect of borrowing constraints in the elasticity of intertemporal substitution of leisure, see Domeij and Flodén (2006) and Bredemeier et al. (2019).
Mankiw et al. (1985) jointly estimate the three equations with aggregate data, rejecting systematically the test of over identifying restrictions. Cutanda (2019) also tests the three equations system with regional Spanish data without obtaining a statistically significant value for the intertemporal elasticity of substitution for leisure.
Therefore, Frisch demands depend on observable within period variables and the marginal utility of wealth as the only variable outside the current period.
These elasticities have been widely analyzed in studies researching the effect of changes in taxes on labor supply, both in a static (Eklöf and Sacklén 2000; Bloomquist et al. 2001) or in a dynamic context (Aaronson & French, 2009; Blundell & Walker, 1986; Ziliak and Kniesner 2005). See Browning et al. (1985) for the analytical relationship between them.
We have estimated the model using the gmm Stata command. This does not provide the first stage estimation results and the under identification and weak identification tests. The main reason to use it, instead of the xtivreg2 command, is that we estimate the complete system of intertemporal equations. Nevertheless, to check that our results are not affected by a weakness instruments problem, we have verified that the fixed-effects estimates obtained by using the xtivreg2 command are quite similar to the reported results, and are not affected by this problem.
Although it is possible to identify individual’s income across appropriate sample selection, the problem we have to face is the loss of observations. The most obvious selection would be the sample of households composed only by one labor income earner.
Lugilde et al. (2018) also discuss the lack of Spanish data for the jointly analysis of consumption and labor supply of the household.
It is important to notice that our period includes the 1992 recession that occurred between two long expansionary phases for the Spanish economy.
We have applied all the usual filters in this kind of studies. In this sense, we have discarded households with no data in expenses, income, hours of work or any other sensible variables, both in the ECPF or EPA. Also, following the usual practice, in the ECPF we have withdrawn all households with income in the first and last percentile of the distribution.
It is important to recall that the period considered in our analysis is characterized by a very low rate of women participation in the Spanish labor market, for different historical reasons. This, combined with the fact that we use pseudo-panel data techniques that require a relatively high sample size (to reduce the impact of measurement error problems in the cohorts), makes the analysis of Spanish female labor supply unfeasible for these years.
Also, and for similar reasons, Lugilde et al. (2018) restrict their sample to households where the reference person is an employee, although they do not impose any requirement on the labor status of the partner. However, we are aware of the relevance of the household perspective for labor decisions (Duguet and Simonnet 2007; Apps and Rees 2010; and more recently, Blundell et al. 2016 and 2018).
The average size of the sample of households whose head is a labor income woman in the period is 74. We have also tried other samples. For example, we have selected married couples where both members are working, in an attempt to analyze household’s labor supply, however this is not viable due to the downfall in the average cohort size (the average number of individuals in the ECPF cohorts drops between 40 and 50%). In a second attempt, we also checked the possibility of including self-employed males in our sample. But we abandoned this option, as the gain associated with the increase in the average size of the cohorts did not compensate the problems we had to face due to the lack of sample homogeneity.
This selection issue is quite standard in this literature. For example, the sample used in MaCurdy (1983) has 121 individuals, and in Blundell and Walker (1986) it amounts to 1378 individuals. These sample numbers could suggest to tackle some sort of the sample selection correction. However, Keane (2011, p 977) points out that it is common in this literature “to ignore selection on the grounds that the large majority on adult non-retired do participate in the labor market”, differently to what happens in the female labor supply literature.
We would like to note that our results do not change when we estimate the model demeaning the data to eliminate the fixed effects. These results are available upon request.
In Table 2, the Hansen tests reported refer to the whole system, not to a single equation.
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This paper received the Best Paper Award I in the 33 Eurasian Business and Economics Society (EBES) conference held in Madrid 2020. We are very grateful to the committee. We also thank two anonymous referees and the Editor for their helpful comments and suggestions.
This research has received financial support from the Spanish Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional through projects ECO2017- 86793-R and ECO2017-84632-R (AEI/FEDER, UE); and from Generalitat Valenciana (PROMETEU/2019/095 and PROMETEU/2020/83).
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See Table 4 .
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Cutanda, A., Sanchis-Llopis, J.A. Joint estimation of intertemporal labor and consumption decisions: evidence from Spanish households headed by working men. Eurasian Econ Rev (2021). https://doi.org/10.1007/s40822-021-00176-3
- Euler equation
- Instrumental variables
- Intertemporal substitution
- Panel data