This special issue of Political Analysis hopefully marks a watershed in how we as a discipline think about modeling time-series—cross-section (TSCS) data. By that I mean moving beyond thinking of TSCS data as only presenting a series of technical estimation problems that are seen as violations of the Gauss-Markov assumptions, problems that can be treated by better estimation methods. The articles in this special issue point to ways of moving forward in thinking of TSCS data as providing opportunities to model intrinsic and important features of the data (while also paying attention to the various statistical issues).

In 1995, Beck and Katz (B&K) instructed the profession on “What to do (and not to do) with time-series, cross-section data,” and almost instantly their prescriptions became the new orthodoxy for practitioners. Our assessment of the intellectual aftermath of this paper, however, does not inspire confidence in the conclusions reached during the past decade. The 195 papers we reviewed show a widespread failure to diagnose and treat common problems of time-series, cross-section (TSCS) data analysis. To show the importance of the consequences of the B&K assumptions, we replicate eight papers in prominent journals and find that simple alternative specifications often lead to drastically different conclusions. Finally, we summarize many of the statistical issues relative to TSCS data and show that there is a lot more to do with TSCS data than many researchers have apparently assumed.

This paper suggests a three-stage procedure for the estimation of time-invariant and rarely changing variables in panel data models with unit effects. The first stage of the proposed estimator runs a fixed-effects model to obtain the unit effects, the second stage breaks down the unit effects into a part explained by the time-invariant and/or rarely changing variables and an error term, and the third stage reestimates the first stage by pooled OLS (with or without autocorrelation correction and with or without panel-corrected SEs) including the time-invariant variables plus the error term of stage 2, which then accounts for the unexplained part of the unit effects. We use Monte Carlo simulations to compare the finite sample properties of our estimator to the finite sample properties of competing estimators. In doing so, we demonstrate that our proposed technique provides the most reliable estimates under a wide variety of specifications common to real world data.

In this paper, we demonstrate the econometric consequences of different specification and estimation choices in the analysis of spatially interdependent data and show how to calculate and present spatial effect estimates substantively. We consider four common estimators—nonspatial OLS, spatial OLS, spatial 2SLS, and spatial ML. We examine analytically the respective omitted-variable and simultaneity biases of nonspatial OLS and spatial OLS in the simplest case and then evaluate the performance of all four estimators in bias, efficiency, and SE accuracy terms under more realistic conditions using Monte Carlo experiments. We provide empirical illustration, showing how to calculate and present spatial effect estimates effectively, using data on European governments' active labor market expenditures. Our main conclusions are that spatial OLS, despite its simultaneity, performs acceptably under low-to-moderate interdependence strength and reasonable sample dimensions. Spatial 2SLS or spatial ML may be advised for other conditions, but, unless interdependence is truly absent or minuscule, any of the spatial estimators unambiguously, and often dramatically, dominates on all three criteria the nonspatial OLS commonly used currently in empirical work in political science.

The analysis of time-series cross-sectional (TSCS) data has become increasingly popular in political science. Meanwhile, political scientists are also becoming more interested in the use of multilevel models (MLM). However, little work exists to understand the benefits of multilevel modeling when applied to TSCS data. We employ Monte Carlo simulations to benchmark the performance of a Bayesian multilevel model for TSCS data. We find that the MLM performs as well or better than other common estimators for such data. Most importantly, the MLM is more general and offers researchers additional advantages.

This article considers random coefficient models (RCMs) for time-series—cross-section data. These models allow for unit to unit variation in the model parameters. The heart of the article compares the finite sample properties of the fully pooled estimator, the unit by unit (unpooled) estimator, and the (maximum likelihood) RCM estimator. The maximum likelihood estimator RCM performs well, even where the data were generated so that the RCM would be problematic. In an appendix, we show that the most common feasible generalized least squares estimator of the RCM models is always inferior to the maximum likelihood estimator, and in smaller samples dramatically so.