This letter deals with a very simple question: if we have grouped data with a binary-dependent variable and want to include fixed effects in the specification, can we meaningfully compare results using a linear model to those estimated with a logit? The reason to doubt such a comparison is that the linear specification appears to keep all observations, whereas the logit drops the groups where the dependent variable is either all zeros or all ones. This letter demonstrates that a linear specification averages the estimates for all the homogeneous outcome groups (which, by definition, all have slope coefficients of zero) with the slope coefficients for the groups with a mix of zeros and ones. The correct comparison of the linear to logit form is to only look at groups with some variation in the dependent variable. Researchers using the linear specification are urged to report results for all groups and for the subset of groups where the dependent variable varies. The interpretation of the difference between these two results depends upon assumptions which cannot be empirically assessed.

The articles in this special issue all use multilevel methods to study comparative political behavior. This is obviously a good thing, for both methodology and comparative politics. Clearly comparative politics means comparing things and not just studying nations other than the United States. This is equally true of micropolitical studies. These articles all do a very nice job of showing how one can do comparative micropolitics (and tie together micro and macro variables).

The issue of how qualitative and quantitative information can be used together is critical. Brady, Collier, and Seawright (BCS) have argued that “causal process observations” can be adjoined to “data set observations.” This implies that qualitative methods can be used to add information to quantitative data sets. In a symposium in Political Analysis, I argued that such qualitative information cannot be adjoined in any meaningful way to quantitative data sets. In that symposium, the original authors offered several defenses, but, in the end, BCS can be seen as recommending good, but hopefully standard, research design practices that are normally thought of as central in the quantitative arena. It is good that BCS remind us that no amount of fancy statistics can save a bad research design.

This article compares a variety of models of presidential approval in terms of their dynamic properties and their theoretical underpinnings. Exponential distributed lags, partial adjustment, error correction, and transfer function models are considered. The major difference between the models lies in interpretation rather than statistical properties. The error correction model seems most satisfactory. Approval models based on individual level theories are examined, and found to give no additional purchase.

Carter and Signorino (2010) (hereinafter “CS”) add another arrow, a simple cubic polynomial in time, to the quiver of the binary time series—cross-section data analyst; it is always good to have more arrows in one's quiver. Since comments are meant to be brief, I will discuss here only two important issues where I disagree: are cubic duration polynomials the best way to model duration dependence and whether we can substantively interpret duration dependence.

In a previous article we showed that ordinary least squares with panel corrected standard errors is superior to the Parks generalized least squares approach to the estimation of time-series-cross-section models. In this article we compare our proposed method with another leading technique, Kmenta's “cross-sectionally heteroskedastic and timewise autocorrelated” model. This estimator uses generalized least squares to correct for both panel heteroskedasticity and temporally correlated errors. We argue that it is best to model dynamics via a lagged dependent variable rather than via serially correlated errors. The lagged dependent variable approach makes it easier for researchers to examine dynamics and allows for natural generalizations in a manner that the serially correlated errors approach does not. We also show that the generalized least squares correction for panel heteroskedasticity is, in general, no improvement over ordinary least squares and is, in the presence of parameter heterogeneity, inferior to it. In the conclusion we present a unified method for analyzing time-series-cross-section data.

It is hardly surprising that I applaud the fine work of both Durr and Ostrom and Smith. I am on record in favor of the utility of the error correction model (e.g., Beck 1985) and it is impossible to obtain a visa to visit the economics department at UCSD without swearing an oath of loyalty to the methodology of cointegration. The two works here are notable for their methodological sophistication, their exposition of a relatively unknown and highly technical area, and, most important, their substantive contributions. Both articles show that political attitudes (approval and policy mood) adjust, in the long run, to changes in objective and subjective economic circumstance. Both articles are good examples of the synergy of methods and theory, since it is the methodology of cointegration that leads to this type of theorizing, and this type of theorizing can most easily be tested in the context of cointegration or error correction.

The Kalman filter is useful to estimate dynamic models via maximum likelihood. To do this the model must be set up in state space form. This article shows how various models of interest can be set up in that form. Models considered are Auto Regressive-Moving Average (ARMA) models with measurement error and dynamic factor models.

The filter is used to estimate models of presidential approval. A test of rational expectations in approval shows the hypothesis not to hold. The filter is also used to deal with missing approval data and to study whether interpolation of missing data is an adequate technique. Finally, a dynamic factor analysis of government entrepreneurial activity is performed.

Appendices go through the mathematical details of the filter and show how to implement it in the computer language GAUSS.

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.

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).

What follows is a longish controversy (two critiques, a reply and two rejoinders) over the quality of the estimates and associated SEs provided by Plümper and Troeger's (2007) “fixed-effect vector decomposition” (FEVD) procedure; Plümper and Troeger (PT) will refer to that article and not any persons. My role is to lay out some issues that separate the authors rather than to adjudicate between them. As with many controversies, a bit of heat is generated along with some light. Readers care a bit less than the authors about what was said when, but they do care a lot about what appropriate method to use when a panel data model has both unit-specific intercepts and variables that are invariant over a unit. Thus, I also take it upon myself to discuss some things that I gleaned from this controversy; this discussion has a bit less heat than what follows, but of course readers should judge the evidence for themselves.

When I first read King, Keohane, and Verba (1994) (KKV), I was excited by the general theme of what seemed to me the obvious, but usually unspoken, idea that all political scientists, both quantitative and qualitative, are scientists and governed by the same scientific standards. KKV, as Henry Brady (Brady and Collier 2004, chap. 3) cleverly notes, clearly were preaching to the qualitative researcher, and the subject of the sermon was that qualitative researchers should adopt many of the ideas standard in quantitative research. Thus, to abuse both the metaphor and KKV, one might compare KKV to the view of the Inquisition that we are all God's children. But, having sat through many talks based on case studies, it is clear to me that getting everyone to think about the nature of the scientific enterprise we are all engaged in can only be a good thing.

Much as we would like to believe that the high citation count for this article is due to the brilliance and clarity of our argument, it is more likely that the count is due to our being in the right place (that is, the right part of the discipline) at the right time. In the 1960s and 1970s, serious quantitative analysis was used primarily in the study of American politics. But since the 1980s it has spread to the study of both comparative politics and international relations. In comparative politics we see in the 20 most cited Review articles Hibbs's (1977) and Cameron's (1978) quantitative analyses of the political economy of advanced industrial societies; in international relations we see Maoz and Russett's (1993) analysis of the democratic peace; and these studies have been followed by myriad others. Our article contributed to the methodology for analyzing what has become the principal type of data used in the study of comparative politics; a related article (Beck, Katz, and Tucker 1998), which has also had a good citation history, dealt with analyzing this type of data with a binary dependent variable, data heavily used in conflict studies similar to that of Maoz and Russett's. Thus the citations to our methodological discussions reflect the huge amount of work now being done in the quantitative analysis of both comparative politics and international relations.

In this article, we show that de Marchi, Gelpi, and Grynaviski's substantive analyses are fully consistent with our prior theoretical conjecture about international conflict. We note that they also agree with our main methodological point that out-of-sample forecasting performance should be a primary standard used to evaluate international conflict studies. However, we demonstrate that all other methodological conclusions drawn by de Marchi, Gelpi, and Gryanaviski are false. For example, by using the same evaluative criterion for both models, it is easy to see that their claim that properly specified logit models outperform neural network models is incorrect. Finally, we show that flexible neural network models are able to identify important empirical relationships between democracy and conflict that the logit model excludes a priori; this should not be surprising since the logit model is merely a limiting special case of the neural network model.

Donald P. Green, Soo Yeon Kim, and David H. Yoon argue that many findings in quantitative international relations that use the dyad-year design are flawed. In particular, they argue that the effect of democracy on both trade and conflict has been vastly overstated, that researchers have ignored unobserved heterogeneity between the various dyads, and that heterogeneity can be best modeled by “fixed effects,” that is, a model that includes a separate dummy for each dyad.

We argue that the use of fixed effects is almost always a bad idea for dyad-year data with a binary dependent variable like conflict. This is because conflict is a rare event, and the inclusion of fixed effects requires us to not analyze dyads that never conflict. Thus while the 90 percent of dyads that never conflict are more likely to be democratic, the use of fixed effects gives democracy no credit for the lack of conflict in these dyads. Green, Kim, and Yoon's fixed-effects logit can tell us little, if anything, about the pacific effects of democracy.

Their analysis of the impact of democracy on trade is also flawed. The inclusion of fixed effects almost always masks the impact of slowly changing independent variables; the democracy score is such a variable. Thus it is no surprise that the inclusion of dyadic dummy variables in their model completely masks the relationship between democracy and trade. We show that their preferred fixed-effects specification does not outperform a model with no effects (when that model is correctly specified in other ways). Thus there is no need to include the masking fixed effects, and so Green, Kim, and Yoon's findings do not overturn previous work that found that democracy enhanced trade.

We agree with Green, Kim, and Yoon that modeling heterogeneity in time-series cross-section data is important. We mention a number of alternatives to their fixed-effects approach, none of which would have the pernicious consequences of using dyadic dummies in their two reanalyses.

We address a well-known but infrequently discussed problem in the quantitative study of international conflict: Despite immense data collections, prestigious journals, and sophisticated analyses, empirical findings in the literature on international conflict are often unsatisfying. Many statistical results change from article to article and specification to specification. Accurate forecasts are nonexistent. In this article we offer a conjecture about one source of this problem: The causes of conflict, theorized to be important but often found to be small or ephemeral, are indeed tiny for the vast majority of dyads, but they are large, stable, and replicable wherever the ex ante probability of conflict is large. This simple idea has an unexpectedly rich array of observable implications, all consistent with the literature. We directly test our conjecture by formulating a statistical model that includes its critical features. Our approach, a version of a “neural network” model, uncovers some interesting structural features of international conflict and, as one evaluative measure, forecasts substantially better than any previous effort. Moreover, this improvement comes at little cost, and it is easy to evaluate whether the model is a statistical improvement over the simpler models commonly used.

We examine some issues in the estimation of time-series cross-section models, calling into question the conclusions of many published studies, particularly in the field of comparative political economy. We show that the generalized least squares approach of Parks produces standard errors that lead to extreme overconfidence, often underestimating variability by 50% or more. We also provide an alternative estimator of the standard errors that is correct when the error structures show complications found in this type of model. Monte Carlo analysis shows that these “panel-corrected standard errors” perform well. The utility of our approach is demonstrated via a reanalysis of one “social democratic corporatist” model.