In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of the preference parameters. When utility is isoelastic and a sample covering a long time period is available, consistent estimates are obtained from the log-linearized Euler equation when the innovations to the conditional variance of consumption growth are uncorrelated with the instruments typically used in estimation. We perform a Montecarlo experiment, consisting in solving and simulating a simple life cycle model under uncertainty, and show that in most situations, the estimates obtained from the log-linearized equation are not systematically biased. This is true even when we introduce heteroscedasticity in the process generating income. The only exception is when discount rates are very high (47% per year). This problem arises because consumers are nearly always close to the maximum borrowing limit: the estimation bias is unrelated to the linearization. Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the discount factor is very high, is remarkably flat. This implies that claims that demographic variables in log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted.

There is a renewed interest in the size of labour supply elasticities and the discrepancy between micro and macro estimates. Recent contributions have stressed the distinction between changes in labour supply at the extensive and the intensive margin. In this paper, we stress the importance of individual heterogeneity and aggregation problems. At the intensive margins, simple specifications that seem to fit the data give rise to non linear expressions that do not aggregate in a simple fashion. At the extensive margin, aggregate changes in participation are likely to depend on the cross sectional distribution of state variables when a shock hits and, therefore, are likely to be history dependent. We tackle these aggregation issues directly by specifying a life cycle model to explain female labour supply in the US and estimate its various components. We estimate the parameters of different component of the model. Our results indicate that (i) at the intensive margin, Marshallian and Hicksian elasticities are very heterogeneous and, on average, relatively large; (ii) Frisch elasticities are, as implied by the theory, even larger; (iii) aggregate labour supply elasticities seem to vary over the business cycle, being larger during recessions.

We characterize the joint evolution of cross-sectional inequality in earnings, other sources of income and consumption across generations in the U.S. To account for cross-sectional dispersion, we estimate a model of intergenerational persistence and separately identify the influences of parental factors and of idiosyncratic life-cycle components. We find evidence of family persistence in earnings, consumption and saving behaviours, and marital sorting patterns. However, the quantitative contribution of idiosyncratic heterogeneity to cross-sectional inequality is significantly larger than parental effects. Our estimates imply that intergenerational persistence is not high enough to induce further large increases in inequality over time and across generations.