Thomas Pluemper

The Estimation of Time-Invariant Variables in Panel Analyses with Unit Fixed Effects

This paper analyzes the estimation of time-invariant variables in panel data models with unit-effects. We compare three procedures that have frequently been employed in comparative politics, namely pooled-OLS, random effects and the Hausman-Taylor model, to a vector decomposition procedure that allows estimating time-invariant variables in an augmented fixed effects approach. The procedure we suggest consists of three stages: the first stage runs a fixed-effects model without time-invariant variables, the second stage decomposes the uniteffects vector into a part explained by the time-invariant variables and an error term, and the third stage re-estimates the first stage by pooled-OLS including the time invariant variables plus the error term of stage 2. We use Monte Carlo simulations to demonstrate that this method works better than its alternatives in estimating typical models in comparative politics. Specifically, the unit fixed effects vector decomposition technique performs better than both pooled OLS and random effects in the estimation of time-invariant variables correlated with the unit effects and better than Hausman-Taylor in estimating the time-invariant variables correlated with the unit effects. Finally, we re-analyze recent work by Huber and Stephens (2001) as well as by Beramendi and Cusack (2004). These analyses seek to cope with the problem of time-invariant variables in panel data.

The Politics of EU Eastern Enlargement: Evidence from a Heckman Selection Model

This paper perceives the politics of EU eastern enlargement to be a twofold process, in which governments of transition countries decide whether or not to apply for membership and in turn EU members decide whether or not to accept these applicants. Specifically, we argue that the level of democracy and the extent of market reforms together determine the first decision, while the second decision is largely determined by the EU observing the reform process in applicant countries imposed by the acquis communautaire conditionality. The natural procedure to test this theory is a Heckman selection model. We use a Heckman specification with panel probit estimators in both stages. The data supports our argument that uncontested reforms signal the policy support of relevant political parties to the EU and increase the likelihood of joining the Union. We also test for specification errors and check the robustness of our findings.

Efficient Estimation of Rarely Changing Variables in Fixed Effects Models

The estimation of slowly and rarely changing variables in panel data with unobserved unit effects suffers from inefficiency of the fixed effects estimator. Point estimates lack reliability when the within variance (the variation across time) remains small. The estimates efficiency can be enhanced if the between variance (the variation across space) increases. However, this comes at the cost of increasing potential omitted variable bias. We describe a three-stage estimator (called xtfevd) that allows to maintain the between variance of cross-sectionally dominant variables while estimating the variables with sufficient within variation by fixed effects. Monte Carlo simulations show that this procedure performs better than the fixed effects model in cases where the between variance exceeds the within variance by at least factor 2.5. Thus, xtfevd outperforms the standard fixed effects model if the within variance is small and the between variance significantly larger.

Model Uncertainty and Robustness Tests: Towards a New Logic of Statistical Inference

We augment the increasingly common practice of typically ad hoc robustness tests into a research methodology that allows reliable inferences when researchers do not know the true data-generating process. We identify three principal sources of model uncertainty. First, theories simplify and aim at isolating causal mechanisms under ceteris paribus conditions. Theories thus cannot sufficiently specify the data-generating process. Second, empirical researchers are uncertain about what constitutes the population – the set of cases for which a theory claims validity – from which to draw a representative sample as required for econometric estimation. Finally, model uncertainty also results from the fact that many concepts used in social science theories cannot be observed and therefore can only be measured by proxy variables, which deviate in unknown, but potentially systematic ways from the theoretical concepts. These three causes of model uncertainty result in at least 16 specific aspects of uncertainty about model specification that can be subjected to various robustness tests. Defining robustness as stability of causal inferences, we argue against the misplaced focus on single point estimates from any specific test. Instead, we suggest scholars employ model averaging techniques to assess robustness in terms of the entire set of empirical evidence from the baseline and all robustness test models. This method avoids the type-II error bias of current practice and encourages researchers to undertake a larger set of robustness tests instead of carefully hand-selecting only those tests that do not deviate from their baseline model results. We illustrate our proposal using an example of an existing study by the authors on the political determinants of famine mortality, which contained only two robustness tests and thus begs the question whether the causal inferences are fragile. Subjecting our baseline model to a battery of additional tests, we conclude that our causal inferences are in fact robust: democracies respond more elastically than autocracies to the simultaneous presence of international food aid and a large share of the population being affected, which results in lower famine mortality.

Number of Parties, Endogenous Partisan Preferences and Electoral Turnout Rates: A Stochastic Equilibrium Analysis

This paper analyzes the impact of the number of parties on turnover rates within an endogenous partisan preference framework. Our results show that the turnover increases in the number of parties under various levels of individual propensity to abstain. We find strong interactions effects between both motives for abstention, alienation and indifference, and the abstention propensity. The results are based on an agent-based computer simulation of multi-party electoral competition in a two-dimensional policy space.

Case Selection and Causal Inference in Qualitative Research

Traditionally, social scientists perceived causality as regularity. As a consequence, qualitative comparative case study research was regarded as unsuitable for drawing causal inferences since a few cases cannot establish regularity. The dominant perception of causality has changed, however. Nowadays, social scientists define and identify causality through the counterfactual effect of a treatment. This brings causal inference in qualitative comparative research back on the agenda since comparative case studies can identify counterfactual treatment effects. We argue that the validity of causal inferences from the comparative study of cases depends on the employed case-selection algorithm. We employ Monte Carlo techniques to demonstrate that different case-selection rules strongly differ in their ex ante reliability for making valid causal inferences and identify the most and the least reliable case selection rule.

Tax Competition Under Budget Rigidities and Fairness Norms

This paper analyzes fiscal competition under budget rigidities and tax equity (fairness norms). We outline a numerically solvable political economic model that treats the outcome of tax competition as one argument in the governments utility function, the others being public expenditure and tax equity. In accordance with theoretical research, we demonstrate that tax competition tends to reduce taxes on mobile capital while increasing the tax rates on relatively immobile labor. However, taxes on mobile capital do not vanish in equilibrium. Instead, the government being least restricted by budget constraints and equity norms reduces tax rates slightly below the lowest tax rates of those countries, in which governments are more constrained. Analyzing data from 21 OECD countries between 1965 and 2000 we find empirical support for the hypotheses derived from our theoretical model.

Fixed Effects Vector Decomposition: Reply

This article reinforces our 2007 Political Analysis publication in demonstrating that the fixed effects vector decomposition (FEVD) procedure outperforms any other estimator in estimating models which suffer from the simultaneous presence of time-varying variables correlated with unobserved unit effects and time-invariant variables. We compare the finite sample properties of FEVD not only to the Hausman-Taylor (HT) estimator but also to the pre-test estimator and the shrinkage estimator suggested by Breusch et al. (BWNK) in this symposium. Moreover, we correct Greene’s and BWNK’s discussion of FEVD’s asymptotic and finite sample properties.