Using the result that under the null hypothesis of no misspecification an asymptotically efficient estimator must have zero asymptotic covariance with its difference from a consistent but asymptotically inefficient estimator, specification tests are devised for a number of model specifications in econometrics. Local power is calculated for small departures from the null hypothesis. An instrumental variable test as well as tests for a time series cross section model and the simultaneous equation model are presented. An empirical model provides evidence that unobserved individual factors are present which are not orthogonal to the included right-hand-side variable in a common econometric specification of an individual wage equation.

/pdf/specification-tests-in-econometrics-9sg4xr62ii.pdf

Specification Tests in Econometrics

On the Pooling of Time Series and Cross Section Data

A panel data approach is advocated and implemented for studying growth convergence. The familiar equation for testing convergence is reformulated as a dynamic panel data model, and different panel data estimators are used to estimate it. The main usefulness of the panel approach lies in its ability to allow for differences in the aggregate production function across economies. This leads to results that are significantly different from those obtained from single cross-country regressions. In the process of identifying the individual "country effect," we can also see the point where neoclassical growth empirics meets development economics.

https://www.jstor.org/stable/pdf/2946651.pdf

Growth Empirics: A Panel Data Approach

Formulation and estimation of dynamic models using panel data

Observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit. Different assumptions about the initial conditions are (a) initial state fixed, (b) initial state random, (c) the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed, and (d) the unobserved individual effect independent of the unobserved dynamic process with initial value random. Asymptotic properties of the maximum likelihood and “covariance” estimators are obtained when T → ∞ and when N → ∞. The relationship between the pseudo and conditional maximum likelihood estimators is clarified. A simple consistent estimator that is independent of the initial conditions and the way in which T or N → ∞ is also suggested.

/pdf/estimation-of-dynamic-models-with-error-components-3n6ytxq3x2.pdf

Estimation of Dynamic Models with Error Components

The paper argues that variance components models are very useful in pooling cross section and time series data because they enable us to extract some information about the regression parameters from the between group and between time-period variation-a source that is often completely eliminated in the commonly used dummy variable techniques. The paper studies the applicability and usefulness of the maximum likelihood method and analysis of covariance techniques in the analysis of this type of model, particularly when one of the covariates used is a lagged dependent variable.

/pdf/the-use-of-variance-components-models-in-pooling-cross-1ewwoy3pjn.pdf

G. S. Maddala

Papers

The use of variance components models in pooling cross section and time series data