We examine the effects of male and female labor supply on household demands and present a simple and robust test for the separability of commodity demands from labor supply. Using data on individual households from six years of the UK FES we estimate a demand system for seven goods which includes hours and participation dummies as conditioning variables. Allowance is made for the possible endogeneity of these conditioning labor supply variables. We find that separability is rejected. Furthermore, we present evidence that ignoring the effects of labor supply leads to bias in the parameter estimates.
The invariance properties of some well known asymptotic tests are studied. Three types of invariance are considered: invariance to the representation of the null hypothesis, invariance to one-to-one transformations of the parameter space (reparameterizations), and invariance to one-to-one transformations of the model variables such as changes in measurement units. Tests that are not invariant include the Wald test and generalized versions of it, a widely used variant of the Lagrange multiplier test, Neyman's C(a) test, and a generalized version of the latter. For all these tests, we show that simply changing measurement units can lead to vastly different answers even when equivalent null hypotheses are tested. This problem is illustrated by considering regression models with Box-Cox transformations on the variables. We observe, in particular, that various consistent estimators of the information matrix lead to test procedures with different invariance properties. General sufficient conditions are then established, under which the generalized C(a) test becomes invariant to reformulations of the null hypothesis and/or to one-to-one transformations of the parameter space as well as to transformations of the variables. In many practical cases where Wald-type tests lack invariance, we find that special formulations of the generalized C(a) test are invariant and hardly more costly to compute than Wald tests. This computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test. We conclude that noninvariant asymptotic tests should be avoided or used with great care. Further, in many situations, the suggested implementation of the generalized C(a) test often yields an attractive substitute to the Wald test (which is not invariant) and to other invariant tests (which are more costly to perform).
This paper analyzes asset prices in a representative agent exchange economy with habit-forming preferences. For a general class of utility indices and endowment processes, the authors characterize the optimal demand for consumption and derive explicit solutions for the interest rate and asset risk premia. They show that consumption smoothness may obtain even when the interest rate is stochastic. The consumption capital asset pricing model may not hold when the endowment process has stochastic coefficients; asset risk premia are larger under mild assumptions. The interest rate depends on the growth in the standard of living. Malliavin calculus is employed in the analysis. Copyright 1991 by The Econometric Society.
This paper develops a discrete state space solution method for a class of nonlinear rational expectations models. The method works by using numerical quadrature rules to approximate the integral operators that arise in stochastic intertemporal models. It is particularly useful for approximating asset pricing models and has potential applications in other problems as well. An empirical application uses the method to study the relationship between the risk premium and the conditional variability of the equity returns under ARCH endowment processes. Copyright 1991 by The Econometric Society.
It is shown that an increasing policy function that is the solution of a C(superscript "2") dynamic programming problem is always C(superscript "1"). This implies that the value function is C(superscript "2"). Examples are given to show that the policy function might not be twice differentiable and therefore the value might not be three times differentiable, even if the program is C(superscript "3"). Copyright 1991 by The Econometric Society.
Consider an economy with one public enterprise that is subject to a budgetary constraint and charges prices according to the first-order necessary conditions suggested by M. Boiteux (1956) or F. P. Ramsey (1927). The authors state conditions sufficient to ensure that the resulting allocation is second best. The proof builds on arguments used to demonstrate the Pareto efficiency of marginal cost pricing under appropriate assumptions. Copyright 1991 by The Econometric Society.
It is shown that a Pareto optimal and continuous single-valued choice function defined on the compact convex subsets of the positive orthant of the n-dimensional Euclidean space maximizes a real-valued function if and only if it satisfies the independence of irrelevant alternatives condition if n=2, and the strong axiom of revealed preference otherwise. The results can be applied to consumer demand theory to deal with nonlinear budget sets, and to bargaining game theory to generalize the Nash bargaining solution.
The information matrix (IM) test is shown to have a finite sample distribution which is poorly approximated by its asymptotic χ 2 distribution in models and sample sizes commonly encountered in applied econometric research. The quality of the χ 2 approximation depends upon the method chosen to compute the test. Failure to exploit restrictions on the covariance matrix of the test can lead to a test with appalling finite sample properties. Order O(n -1 ) approximations to the exact distribution of an efficient form of the IM test are reported. These are developed from asymptotic expansions of the Edgeworth and Cornish-Fisher types. They are compared with Monte Carlo estimates of the finite sample distribution of the test and are found to be superior to the usual χ 2 approximations in sample sizes of the magnitude found in applied micro-econometric work. The methods developed in the paper are applied to normal and exponential models and to normal regression models. Results are provided for the full IM test and for heteroskedasticity and nonnormality diagnostic tests which are special cases of the IM test. In general the quality of alternative approximations is sensitive to covariate design. However commonly used nonnormality tests are found to have distributions which, to order O(n -1 ), are invariant under changes in covariate design. This leads to simple design and parameter invariant size corrections for nonnormality tests.
A dynamic programming model of job exit behavior and retirement is constructed and estimated using the method of simulated moments. The model and estimation method allow for both unobserved individual effects and unobserved job-specific "match" effects. The model is estimated using two different assumptions about individual discount factors. First, a static model, with the discount factor equal to zero, is estimated. Then a dynamic model, with the discount factor equal to .95 is estimated. In both models, it is found that bad health, age, and lack of education increase the probability of retirement. The dynamic model performs better than the static model and has different implications for retirement behavior. The job-specific effects are an important source of unobserved heterogeneity. Copyright 1991 by The Econometric Society.