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This article provides an overview of the panel vector autoregressive models (VAR) used in macroeconomics and finance to study the dynamic relationships between heterogeneous assets, households, firms, sectors, and countries. We discuss what their distinctive features are, what they are used for, and how they can be derived from economic theory. We also describe how they are estimated and how shock identification is performed. We compare panel VAR models to other approaches used in the literature to estimate dynamic models involving heterogeneous units. Finally, we show how structural time variation can be dealt with.

This paper provides a selective survey of the panel macroeconometric techniques that focus on controlling the impact of “unobserved heterogeneity” across individuals and over time to obtain valid inference for “structures” that are common across individuals and over time. We consider issues of (i) estimating vector autoregressive models; (ii) testing of unit root or cointegration; (iii) statistical inference for dynamic simultaneous equations models; (iv) policy evaluation; and (v) aggregation and prediction.

It is shown in the literature that the Arellano–Bond type generalized method of moments (GMM) of dynamic panel models is asymptotically biased (e.g., Hsiao & Zhang, 2015; Hsiao & Zhou, 2017). To correct the asymptotical bias of Arellano–Bond GMM, the authors suggest to use the jackknife instrumental variables estimation (JIVE) and also show that the JIVE of Arellano–Bond GMM is indeed asymptotically unbiased. Monte Carlo studies are conducted to compare the performance of the JIVE as well as Arellano–Bond GMM for linear dynamic panels. The authors demonstrate that the reliability of statistical inference depends critically on whether an estimator is asymptotically unbiased or not.

We analyse the dynamics of social assistance benefit (SA) receipt among working-age adults in Britain between 1991 and 2005. The decline in the annual SA receipt rate was driven by a decline in the SA entry rate rather than by the SA exit rate (which also declined). We examine the determinants of these trends using a multivariate dynamic random effects probit model of SA receipt probabilities applied to British Household Panel Survey data. We show how the model may be used to derive year-by-year predictions of aggregate SA entry, exit and receipt rates. The analysis highlights the importance of the decline in the unemployment rate over the period and other changes in the socio-economic environment including two reforms to the income maintenance system in the 1990s and also illustrates the effects of self-selection (‘creaming’) on observed and unobserved characteristics.

Advances in Econometrics is a series of research volumes first published in 1982 by JAI Press. The authors present an update to the history of the Advances in Econometrics series. The initial history, published in 2012 for the 30th Anniversary Volume, describes key events in the history of the series and provides information about key authors and contributors to Advances in Econometrics. The authors update the original history and discuss significant changes that have occurred since 2012. These changes include the addition of five new Senior Co-Editors, seven new AIE Fellows, an expansion of the AIE conferences throughout the United States and abroad, and the increase in the number of citations for the series from 7,473 in 2012 to over 25,000 by 2022.

The authors use a reduced form state-dependent labor participation decision model to illustrate that parameter stability is achieved only if a model properly takes account the observed sample heterogeneity and unobserved sample heterogeneity provided (external) conditions of a model stay constant. Our analysis of the dynamic response path to a health shock using Australian HILDA panel data from 2002 to 2009 shows that experiencing an event by itself can only have a temporary effects. The long-run equilibrium condition is independent of initial conditions or shocks that do not last. In other words, if experiencing an event does not lead to changes in the response parameters such as the real business cycle (Kydland & Prescott, 1977, 1982) or dynamic stochastic general equilibrium model (DSGE, e.g., Sbordone et al., 2010) assumed, policy change may only change the short-run response path. There is no long-term impact for a policy change. On the other hand, if a policy change leads to changes in the decision rules (e.g., the recent US–China trade friction) as the Lucas critique (1976) implies, then there is no other way to evaluate the impact of a policy except to explicitly model how agents respond to the policy change.

The authors consider the quasi maximum likelihood (MLE) estimation of dynamic panel models with interactive effects based on the Ahn et al. (2001, 2013) quasi-differencing methods to remove the interactive effects. The authors show that the quasi-difference MLE (QDMLE) over time is inconsistent when N→∞ whether T is fixed or goes to infinity. On the other hand, the QDMLE is consistent and asymptotically unbiased if the difference is taken over individuals when T is large whether N is fixed or large. Monte Carlo studies are conducted to compare the performance of the QDMLE using different quasi-difference methods.

This chapter conducts a Monte Carlo investigation into small sample properties of some of the dynamic panel data estimators that have been applied to estimate the growth-convergence equation using Summers-Heston data set. The results show that the OLS estimation of this equation is likely to yield seriously upward biased estimates. However, indiscriminate use of panel estimators is also risky, because some of them display large bias and mean square error. Yet, there are panel estimators that have much smaller bias and mean square error. Through a judicious choice of panel estimators it is therefore possible to obtain better estimates of the parameters of the growth-convergence equation. The growth researchers may make use of this potential.