What To Do (and Not to Do) with Time-Series Cross-Section Data

Abstract

Table 1 provides an incomplete list of relevant articles whose conclusions are based on the use of this problematic technique. All of these articles use an application of the generalized least squares (GLS) method first described by Parks (1967), a method designed to deal with some common problems that occur in TSCS data. We show that the Parks method produces dramatically inaccurate standard errors when used for the type of data commonly analyzed by students of comparative politics. We then offer a new method that is both easier to implement and produces accurate standard errors.Time-series cross-section data are characterized by having repeated observations on fixed units, such as states or nations. The number of units analyzed would typically range from about 10 to 100, with each unit observed over a relatively long time period (often 20 to 50 years). Both the temporal and spatial properties of TSCS data make the use of ordinary least squares (OLS) problematic. In particular, models for TSCS data often allow for temporally and spatially correlated errors, as well as for heteroscedasticity. Parks proposed a method for dealing with these problems based on GLS.1 The use of this method can lead to dramatic underestimates of parameter variability in common research situations.Why the severe problems with the Parks method? Is it not just an application of well-known GLS? While GLS has optimal properties for TSCS data, it assumes that we have knowledge about the error process that, in practice, we never have. Thus analysts use not GLS, but feasible generalized least squares (FGLS). It is "feasible" because it uses an estimate of the error process, avoiding the GLS assumption that the error process is known. The FGLS formula for standard errors, however, assumes that the error process is known, not estimated. In many applications this is not a problem because the error process has few enough parameters that they can be well estimated. Such is not the case for TSCS models, where the error process has a large number of parameters. This oversight causes estimates of the standard errors of the estimated coefficients to understate their true variability. We provide a measure of how much the Parks standard errors understate true sampling variability, that is, how much the Parks method falsely inflates confidence in the findings of TSCS studies. Unfortunately, it is not possible to provide analytic formulae for the degree of overconfidence introduced by the Parks method. Instead, we provide evidence from Monte Carlo experiments using simulated data to assess the performance of the various estimators. This evidence clearly shows the overconfidence induced by the Parks method. The Parks estimator may understate variability by between 50% and 300% in practical research situations. It is this extreme overconfidence that leads us either to overturn or to cast doubt on the findings of many analyses based on the Parks method.Having demonstrated the problems of the Parks method, we instead advocate a simpler method for estimating ...

Generational Basis of Turnout Decline in Established Democracies

“…This approach considers the time serial dependencies as giving rise to non-random errors and tries to remove those errors. Even after removing the time-serial Mark N. Franklin et al Generational Basis of Turnout Decline dependencies, however, the set of cases that constitute each panel are probably more like each other than they are like cases from other panels, giving rise additionally to the need for 'panel corrected' standard errors (Beck and Katz, 1995).…”

Foreign aid and the governance of international financial organizations: the Brazilian-bloc case in the IMF and the World Bank

“…T r a n s p o r t a n d s t o r a g e G e n e r a l b u d g e t s u p p o r t (BECK and KATZ, 1995). Due to the "membro" variable displaying little variation in the period analyzed, being practically the same countries in the Brazilian coalition between 2003 and 2010, and due to the fact that the models estimated in the cross-sectional dataset displayed better measures of fit, only the latter models were chosen for this article, with the others presented in the appendices, available on BPSR website at bpsr.org.br/files/archives/Dataset_Apolinario.…”

Power, Markets, and Top Income Shares

“…(2) cross-sectionally heteroskedastic, and (3) cross-sectionally correlated as well as (4) conceal unit and period effects and (5) reflect some causal heterogeneity across space, time, or both." We follow Beck and Katz's (1995) recommended procedure, using panel-corrected standard errors, corrections for first-order auto-regressiveness, and imposition of a common rho for all crosssections. Since there is some trend in our data, we do not include a lagged dependent variable as recommended by Beck and Katz (1996) because in this situation the lagged dependent variable inappropriately suppresses the power of other independent variables, as Achen (2000) has shown.…”