Andrew Chesher

Identification in Nonseparable Models

Weak nonparametric restrictions are developed, sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable. These derivatives can exhibit stochastic variation. In a microeconometric context this allows the impact of a policy intervention, as measured by the value of a structural derivative, to vary across people who are identical as measured by covariates. When the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified. The identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought. The conditions do not include the commonly required independence of latent variables and covariates. They include local versions of the classical rank and order conditions and local quantile insensitivity conditions. Values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions.

RESIDUAL ANALYSIS IN THE GROUPED AND CENSORED NORMAL LINEAR-MODEL

Graphical and numerical analysis of residual can be informative about model misspecification even when data are censored or grouped. This paper provides simple procedures for calculating diagnostic statistics to detect model misspecification when grouped or censored data are analysed using a normal linear model. Graphs can reveal the nature of the correlations that these statistics pick up but when grouping or censoring is severe they can be difficult to interpret. We discuss the processing of graphs so that they are more easily interpreted and provide examples based on artificial data and on grouped data relating to unemployment durations.

The information matrix test: Simplified calculation via a score test interpretation

Abstract In Chesher (1982) I show that the Information Matrix test introduced by White (1982) is a score test for parameter constancy. In this letter I show that this result leads to a simple computational procedure for calculating the Information Matrix test. The procedure involves computing, for a sample of n observations, n times the R2 from the least squares regression of a column of ones on a matrix whose elements are functions of 1st and 2nd derivatives of the log density function.

Taste Variation in Discrete Choice Models

This paper develops an extension of the classical multinomial logit model which approximates a class of models obtained when there is uncontrolled taste variation across agents and choices in addition to the stochastic noise inherent in the logit model. Unlike semiparametric and parametric alternatives, the extended logit model is easy to estimate even when there are many potential choices. Unlike parametric alternatives, it does not require the specification of a distribution of varying tastes. The extended logit model can give a quick indication of the impact of taste variation on estimates and it generates estimates of the covariances of the taste shifters. It can be used as an exploratory device en route to the construction of a model incorporating a particular form of random taste variation and it can be used to determine whether such effort is required at all. When the amount of taste variation is not excessive the approximate model can be adequate itself. The model nests the conventional logit model which leads to a misspecification diagnostic. A method for estimating the model using conventional logit model software is proposed, asymptotic properties of estimators are derived and an application is presented.

The Estimation of Models of Labour Market Behaviour

In this paper we view the labour market experience of individuals as a process of movement between the states of employment and unemployment. We note that there are three main ways of sampling members of the labour force namely sampling the members of a specific state, sampling the people entering or leaving a state and sampling the population regardless of state. The joint distribution of observable and unobservable characteristics of individuals depends on the mode of sampling adopted. We examine this dependence and its implications for the interpretation of estimates of models of labour market behaviour.

Welfare Measurement and Measurement Error

The approximate effects of measurement error on a variety of measures of inequality and poverty are derived. They are shown to depend on the measurement error variance and functionals of the error contaminated income distribution, but not on the form of the measurement error distribution, and to be accurate within a rich class of error free income distributions and measurement error distributions. The functionals of the error contaminated income distribution that approximate the measurement error induced distortions can be estimated. So it is possible to investigate the sensitivity of welfare measures to alternative amounts of measurement error and, when an estimate of the measurement error variance is available, to calculate corrected welfare measures. The methods are illustrated in an application using Indonesian household expenditure data.

Specification testing when score test statistics are identically zero

We investigate the problem of previous specification testing when the score vector evaluated at the restricted MLE is identically zero. Several econometric examples are provided. A general test procedure which generalizes the geometric principle of the score test is proposed. The Wald and the likelihood ratio tests are also analyzed. Even under such irregularities, the usual asymptotic distribution of the likelihood ratio statistics is still valid. However, the Wald-type statistics need to be modified. The generalized score, the likelihood ratio and the modified Wald tests are shown to be asymptotically equivalent. The asymptotic efficiency of the tests is derived.

Likelihood ratio specification tests

Moment based tests for mispecification of parametric models (e.g., of mean equals variance in a Poisson model) are studied. The moment restrictions under test are embedded in an extension of the model so that the moment test is a score test of the hypothesis that a vector of added parameters is zero. Second-order asymptotic properties of the likelihood ratio version of this test are studied. Unlike the conventional test, the likelihood ratio version is Bartlett correctable. The correction depends on the curvature at the origin of the function used to incorporate the moment restriction in the extended model.

The finite-sample distributions of heteroskedasticity robust Wald statistics

The Imhof procedure is used to calculate the exact finite-sample distributions of alternative heteroskedasticity robust Wald-type tests of scalar linear hypothesis in the normal linear model. The tests are distinguished by the variance estimator that they use. These include the White-Eicker and jackknife estimators. The calculations demonstrate the importance of regression design in determining the quality of conventional first-order asymptotic approximations to the null distributions of the tests.

Non-normal variation and regression to the mean

Non-normal variation across repeated measurements leads to nonlinear and heteroskedastic regression to the mean unlike the simple linear and homoskedastic regression to the mean found in normal models. This paper investigates the nature of the regression to the mean phenomenon in non-normal settings using (a) small variance approximations and (b) exact results obtained using normal mixtures to approximate non-normal distributions.