This paper proposes a standardized version of Swamy’s test of slope homogeneity for panel data models where the cross section dimension (N) could be large relative to the time series dimension (T). The proposed test, denoted by ˜ ∆, exploits the cross section dispersion of individual slopes weighted by their relative precision. In the case of models with strictly exogenous regressors, but with non-normally distributed errors, the test is shown to have a standard normal distribution as (N, T) j → ∞ such that √ N/T 2 → 0. When the errors are normally distributed, a mean-variance bias adjusted version of the test is shown to be normally distributed irrespective of the relative expansion rates of N and T. The test is also applied to stationary dynamic models, and shown to be valid asymptotically so long as N/T → κ, as (N, T) j → ∞, where 0 ≤ κ < ∞. Using Monte Carlo experiments, it is shown that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. Similar results are also obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and so long as T ≥ N.

We study the identification of panel models with linear individual-specific coefficients, when T is fixed. We show identification of the variance of the effects under conditional uncorrelatedness. Identification requires restricted dependence of errors, reflecting a trade-off between heterogeneity and error dynamics. We show identification of the density of individual effects when errors follow an ARMA process under conditional independence. We discuss GMM estimation of moments of effects and errors, and introduce a simple density estimator of a slope effect in a special case. As an application we estimate the effect that a mother smokes during pregnancy on child’s birth weight.

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledged and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treat-ment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks of forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of “real time econometrics”. This paper attempts to provide an overview of some of these developments.

Where Y t (ω) is the observable random variable, the t ∈ {0, 1, 2,..., T} and ω ∈ {1, 2,..., N} indexes designate the time and the population of individuals respectively. We suppose that: (i) {εt (ω)} is an independent sequence of univariate random variables with mean zero and variance σ2 ω. (ii) Ai (ω), 1 ≤ i ≤ p are independent random variables with E {A1 (ω),..., Ap (ω)} = (α1,..., αp) ′. (iii) Ai (ω), 1 ≤ i ≤ p are mutually independent of εt (ω) and Yt (ω) for each t. (iv) {A(ω), ω = 1,..., N} is an independent sequence of p × p matrices with