In this article, we introduce dynamac, a suite of commands designed to assist users in modeling and visualizing the effects of autoregressive distributed lag models and in testing for cointegration. We discuss the bounds cointegration test proposed by Pesaran, Shin, and Smith (2001, Journal of Applied Econometrics 16: 289–326), which we have adapted into a command. Because the resulting models can be dynamically complex, we follow the advice of Philips (2018, American Journal of Political Science 62: 230–244) by introducing a flexible command designed to dynamically simulate and plot a variety of types of autoregressive distributed lag models, including error-correction models.

R ecent work in the time-series literature has stressed the importance of testing for unit roots as well as the existence of long-run relationshipsor cointegration-between variables. 1 Since the presence or absence of each of these characteristics ultimately determines the appropriate model, failure to perform such pretesting makes spurious inferences more likely. Even with existing tools designed to identify unit roots and test for cointegration, short series, the weak power of statistical tests, and the dangers of overfitting make pretesting time-series data particularly problematic. Although recent articles have helped to identify these issues (Grant and Lebo 2016;Keele, Linn, and Webb 2016), users have been left without a straightforward solution about how to deal with such problems. 2 I propose using the autoregressive distributed lag model and associated bounds testing procedure (ARDLbounds) developed by Pesaran, Shin, and Smith (2001) as a comprehensive approach to model specification and Andrew Q. Philips is assistant professor, Department of Political Science, University of Colorado at Boulder, UCB 333, Boulder, CO 80309-0333 (andrew.philips@colorado.edu).I would like to thank Lorena Barberia, Allyson Benton, Harold Clarke, Peter Enns, Nathan Favero, Eric Guntermann, Mark Pickup, Joe Ura, B. Dan Wood, and participants of the Texas A&M methodology brownbag lunches. Special thanks go to Soren Jordan, Paul Kellstedt, and Guy D. Whitten. Despite this helpful advice, any errors and omissions remain my own.1 Covariance stationary series exhibit constant mean, variance, and covariance. A linear combination of two or more first-order nonstationary series that yields a stationary series is said to be cointegrating.2 Grant and Lebo (2016) provide two solutions, including the one discussed herein. However, their discussion is brief. cointegration testing. Depending on the results of the cointegration test, this strategy absolves users from having to distinguish between stationary (henceforth I(0)) and first-order nonstationary (I(1)) regressors. This is an advantage since unit root testing is difficult in short series and introduces "a further degree of uncertainty into the analysis" (Pesaran, Shin, and Smith 2001, 289). The ARDL-bounds procedure involves the following:1. Ensuring the dependent variable is I(1). 2. Ensuring the independent variables are not explosive or higher orders of integration than I(1). 3. Estimating the ARDL model in error correction form, and ensuring there is no autocorrelation. 4. Performing the bounds test for cointegration.

One potential consequence of increasing women's numeric representation is that women elected officials will behave differently than their men counterparts and improve women's substantive representation. This study examines whether electing women to local offices changes how local government expenditures are allocated in ways that benefit women. Using compositional expenditure data from over 5,400 Brazilian municipalities over eight years, we find significant differences in the ways men and women mayors allocate government expenditures. Our findings indicate that women mayors spend more on traditionally feminine issues, and less on traditionally masculine issues, relative to men mayors. In regards to specific policy areas, we find that women spend more on women's issues, including education, healthcare, and social assistance, and less on masculine issues, including transportation and urban development, relative to men mayors. We further find that women's legislative representation significantly influences the allocation of expenditures as a larger percentage of women councilors increases spending on traditionally feminine issues, as well as education, healthcare, and social assistance, relative to other policy issues. These findings indicate that women local elected officials improve women's substantive representation by allocating a larger percentage of expenditures to issues that have historically and continue to concern women in Brazil.Word Count: Approx. 9570 (manuscript), 199 (abstract)

The substance of politics involves competition that evolves over time. While our theories about competition emphasize trade-offs across multiple categories, most empirical models tend to oversimplify them by considering trade-offs between one category and everything else. We propose a research strategy for testing theories about trade-off relationships that shape dynamic compositional variables. This approach improves current methods used to analyze compositional dependent variables by addressing two limitations. First, although scholars have considered compositional dependent variables, they have done so in contexts that were not dynamic. Second, current approaches toward graphical presentations become unwieldy when the compositional dependent variable has more than three categories. We demonstrate the utility of our strategy to expand current theories of party support and political budgeting. In both cases, we can extend trade-offs across pairs of alternatives (e.g., prime minister versus all other parties or spending on defense versus everything else) to competition across multiple alternatives. for their helpful critiques and comments. Despite this wealth of helpful advice, the authors take full responsibility for any errors that remain. The data and programming files needed to replicate the analyses presented in this article are available in the AJPS Data Archive on Dataverse at https://thedata.harvard.edu/dvn/(doi:10.7910/DVN/29316). relationships over time, most have limited their analyses of this type of variable over time to models of the size of a single piece of the pie.In this article, we propose a research strategy for testing theories about trade-off relationships that shape compositional variables over time. This approach improves on current methods used by political scientists to analyze compositional dependent variables by addressing two limitations in the extant literature. First, although political scientists have considered compositional dependent variables, they have done so either in contexts that are not dynamic or in contexts in which they ignore the dynamic nature of their data. Second, current approaches to graphical presentations become unwieldy when the

Despite a vast number of articles, the political budget cycle literature contains many conflicting theories and empirical results. I conduct the first ever meta-analysis of this literature in order to establish whether a link between elections and government budgets exists. Using data on 1198 estimates across 88 studies published between 2000 and 2015, I find evidence of a statistically significant-yet substantively small-increase in government expenditures and public debt around elections, and reductions in revenues and fiscal balance. Using meta-regression analysis combined with Bayesian model averaging, I find support for some of the context-conditional theories in the literature. Although the findings of political budget cycles are robust to publication bias as well as some of the methodological-and study-specific choices authors are forced to make, they also shed light on how certain decisions may affect a study's findings. This has implications for current and future research on political budget cycles.

Decades of research has debated whether women first need to reach a “critical mass” in the legislature before they can effectively influence legislative outcomes. This study contributes to the debate using supervised tree-based machine learning to study the relationship between increasing variation in women's legislative representation and the allocation of government expenditures in three policy areas: education, healthcare, and defense. We find that women's representation predicts spending in all three areas. We also find evidence of critical mass effects as the relationships between women's representation and government spending are nonlinear. However, beyond critical mass, our research points to a potential critical mass interval or critical limit point in women's representation. We offer guidance on how these results can inform future research using standard parametric models.

While autoregressive distributed lag models allow for extremely flexible dynamics, interpreting the substantive significance of complex lag structures remains difficult. In this paper we discuss dynamac (dynamic autoregressive and cointegrating models), an R package designed to assist users in estimating, dynamically simulating, and plotting the results of a variety of autoregressive distributed lag models. It also contains a number of post-estimation diagnostics, including a test for cointegration for when researchers are estimating the error-correction variant of the autoregressive distributed lag model.

Across a broad range of fields in political science, there are many theoretically interesting dependent variables that can be characterized as compositions. We build on recent work that has developed strategies for modeling variation in such variables over time by extending them to models of time series cross-sectional data. We discuss how researchers can incorporate the influence of contextual variables and spatial relationships into such models. To demonstrate the utility of our proposed strategies, we present a methodological illustration using an analysis of budgetary expenditures in the US states.