David Fortunato and Matt W.Loftis each member of the cabinet,where greater values indi- than a point,we cycle through its 1.000 estimated val- cate a more right-leaning government.23 Following the ues,imputing each into our spending and deficit models above discussion on the common pool resource prob. in turn,estimating,and recording the results.We also lem in budgeting-as the diversity of spending priori- generate error estimates on our cabinet ideology mea- ties grows,the cabinet's temptation to spend to please sure following Lowe et al.(2011)and model these in its supporters increases-we include the number of the same fashion parties in the cabinet.We also include the effective The results of our first model,public spending,are number of legislative parties(Laakso and Taagepera summarized in Table 1.25 For our covariate of inter- 1979)to account for the possibility that diverse spend- est,expected duration,there is a statistically signifi- ing priorities outside the cabinet may coax budgets up- cant negative parameter estimate,indicating,as we pre- ward in a similar fashion. dicted,that decreasing expected duration will increase Our second set of controls are meant to account for a the cabinet's level of public spending.Further,each of state's ability or need to grow its spending obligations. our control variables,when reaching statistical signif- That is,does the state in question have the resources icance,are signed in the sensible direction and com- needed to increase spending responsibly,or,are there port with previous research on spending(e.g.,Bawn characteristics of the state that should systematically and Rosenbluth 2006:Martin and Vanberg 2013).giv- increase its spending obligations?These variables in- ing us confidence that our model is properly specified. clude:the overall level of economic productivity(mea- To better illustrate the predicted effect of expected sured as per capita GDP),a state's integration into the duration on public spending,Figure 2 plots the substan- 元 modern trade economy(called"trade openness"in the tive effect of a reduction in expected cabinet duration tables below;the export/import fraction of GDP),its from three years to one year,aggregated across all of unemployment rate,and the percentage of likely non- our 1,000 models.Each light density in Figure 2 plots productive population-those under 15 years of age the distribution of predicted changes in spending as a and those 65 and over (called the "dependency ratio"). percentage of GDP resulting from this reduction in the Finally,we include two variables meant to cap- expected durability of the cabinet from a single boot- ture domestic and supranational spending constraints. strap iteration.Thus,the shape of each light density il- The first is Martin and Vanberg's (2013)"budgetary lustrates the estimation uncertainty in one of our 1.000 constraint index,"a summary of formal rules that models and the light vertical lines mark the fifth per- "[c]onstrain the ability of parties to push for spending, centile of each distribution (our criterion for statistical and,"generate incentives for parties to oppose spend- significance).The thicker,darker lines give the global ing demands by their partners"(p.956).This variable density and fifth percentile over all bootstrap iterations. is bounded between 0 and 1 and is interacted with the Taken together,the figure shows that,not only is our number of parties in the cabinet.The second is a binary criterion for statistical significance met in virtually all variable indicating that the budget was submitted af- bootstrapped models,but also that there is very little ter the adoption of the Maastricht Treaty,which placed variation in this result across the 1,000 bootstrapped limits on the total debt a member state could carry,as models. well as the size of the deficit a state could generate in More substantively,on average,the decrease from any given year.Interested readers may see summary three years to one year of expected duration (about a S5.501g statistics for all variables in the appendix. 1.5 standard deviation change)increases public spend- With variables in hand,we now turn to estimation. ing by 0.26%of GDP.This is a very large spending in- We are analyzing panel data with substantial cross- crease.Using 2010 GDP and spending figures in US sectional variation,but also a great deal of autocor- dollars,we can get a better sense of how salient this relation within units.Following Bawn and Rosenbluth effect is:for Denmark(GDP $320 billion)the increase (2006)and Martin and Vanberg (2013)we estimate would be roughly $844 million,for the Netherlands an autoregressive distributed lag model (ADL),in- (GDP $836 billion)the increase would be over $2.2 cluding(one year)lags of both the dependent vari- billion,and for Germany in the same year(GDP $3.4 ables and independent variables as well as concurrent realizations of the economic variables and estimate panel-corrected standard errors.This is in keeping with that the VIF on expected duration is about 4.3,which is well under Philips's(2016)conclusion that modeling data dynam- the typical level of concern(10). We have summarized the 1,000 spending(and deficit)models in ics is vital in the analysis of public spending,as ignor- a familiar tabular format for the sake of clarity.We note,however, ing the autoregressive properties of spending patterns that these models should technically be assessed individually since 四 can lead to inflated estimates of cycling behavior.24 As parameter point estimates and standard errors from regressions us ing predictions from different bootstrap iterations of the cabinet sur- our focal explanatory variable is a distribution.rather vival model are not fully comparable-even though the substantive effects we generate from them are.We can make fully reliable com- parisons using so-called "pivotal statistics"(e.g.,z-scores)to draw 23 These positions are derived from the Comparative Manifestos conclusions about statistical significance of effect parameters across Project data following Fortunato,Martin,and Vanberg(2018)and the 1,000 spending or deficit models.Statistics are considered pivota nousreviewer correety points out that ADL models if their sampling distribution does not depend on unknown parame- ters,making them a good choice for comparing across models as we particularly those with lagged and contemporaneous values of co- do (Shao 2003).The results of this more appropriate comparison lead variates,can create multicollinearity and this is certainly the case with to exactly the same conclusions but make for a potentially confusing our model.However,the construction does not induce collinearity presentation,therefore we have included the appropriate graphic in for the variable of interest-a variance inflation factor test reveals Appendix Figure A.3. 946David Fortunato and Matt W. Loftis each member of the cabinet, where greater values indi￾cate a more right-leaning government.23 Following the above discussion on the common pool resource prob￾lem in budgeting—as the diversity of spending priori￾ties grows, the cabinet’s temptation to spend to please its supporters increases—we include the number of parties in the cabinet. We also include the effective number of legislative parties (Laakso and Taagepera 1979) to account for the possibility that diverse spend￾ing priorities outside the cabinet may coax budgets up￾ward in a similar fashion. Our second set of controls are meant to account for a state’s ability or need to grow its spending obligations. That is, does the state in question have the resources needed to increase spending responsibly, or, are there characteristics of the state that should systematically increase its spending obligations? These variables in￾clude: the overall level of economic productivity (mea￾sured as per capita GDP), a state’s integration into the modern trade economy (called “trade openness” in the tables below; the export/import fraction of GDP), its unemployment rate, and the percentage of likely non￾productive population—those under 15 years of age and those 65 and over (called the “dependency ratio”). Finally, we include two variables meant to cap￾ture domestic and supranational spending constraints. The first is Martin and Vanberg’s (2013) “budgetary constraint index,” a summary of formal rules that “[c]onstrain the ability of parties to push for spending,” and, “generate incentives for parties to oppose spend￾ing demands by their partners” (p. 956). This variable is bounded between 0 and 1 and is interacted with the number of parties in the cabinet. The second is a binary variable indicating that the budget was submitted af￾ter the adoption of the Maastricht Treaty, which placed limits on the total debt a member state could carry, as well as the size of the deficit a state could generate in any given year. Interested readers may see summary statistics for all variables in the appendix. With variables in hand, we now turn to estimation. We are analyzing panel data with substantial cross￾sectional variation, but also a great deal of autocor￾relation within units. Following Bawn and Rosenbluth (2006) and Martin and Vanberg (2013) we estimate an autoregressive distributed lag model (ADL), in￾cluding (one year) lags of both the dependent vari￾ables and independent variables as well as concurrent realizations of the economic variables and estimate panel-corrected standard errors. This is in keeping with Philips’s (2016) conclusion that modeling data dynam￾ics is vital in the analysis of public spending, as ignor￾ing the autoregressive properties of spending patterns can lead to inflated estimates of cycling behavior.24 As our focal explanatory variable is a distribution, rather 23 These positions are derived from the Comparative Manifestos Project data following Fortunato, Martin, and Vanberg (2018) and others. 24 An anonymous reviewer correctly points out that ADL models, particularly those with lagged and contemporaneous values of co￾variates, can create multicollinearity and this is certainly the case with our model. However, the construction does not induce collinearity for the variable of interest—a variance inflation factor test reveals than a point, we cycle through its 1,000 estimated val￾ues,imputing each into our spending and deficit models in turn, estimating, and recording the results. We also generate error estimates on our cabinet ideology mea￾sure following Lowe et al. (2011) and model these in the same fashion. The results of our first model, public spending, are summarized in Table 1. 25 For our covariate of inter￾est, expected duration, there is a statistically signifi￾cant negative parameter estimate,indicating, as we pre￾dicted, that decreasing expected duration will increase the cabinet’s level of public spending. Further, each of our control variables, when reaching statistical signif￾icance, are signed in the sensible direction and com￾port with previous research on spending (e.g., Bawn and Rosenbluth 2006; Martin and Vanberg 2013), giv￾ing us confidence that our model is properly specified. To better illustrate the predicted effect of expected duration on public spending,Figure 2 plots the substan￾tive effect of a reduction in expected cabinet duration from three years to one year, aggregated across all of our 1,000 models. Each light density in Figure 2 plots the distribution of predicted changes in spending as a percentage of GDP resulting from this reduction in the expected durability of the cabinet from a single boot￾strap iteration. Thus, the shape of each light density il￾lustrates the estimation uncertainty in one of our 1,000 models and the light vertical lines mark the fifth per￾centile of each distribution (our criterion for statistical significance). The thicker, darker lines give the global density and fifth percentile over all bootstrap iterations. Taken together, the figure shows that, not only is our criterion for statistical significance met in virtually all bootstrapped models, but also that there is very little variation in this result across the 1,000 bootstrapped models. More substantively, on average, the decrease from three years to one year of expected duration (about a 1.5 standard deviation change) increases public spend￾ing by 0.26% of GDP. This is a very large spending in￾crease. Using 2010 GDP and spending figures in US dollars, we can get a better sense of how salient this effect is: for Denmark (GDP $320 billion) the increase would be roughly $844 million, for the Netherlands (GDP $836 billion) the increase would be over $2.2 billion, and for Germany in the same year (GDP $3.4 that the VIF on expected duration is about 4.3, which is well under the typical level of concern (10). 25 We have summarized the 1,000 spending (and deficit) models in a familiar tabular format for the sake of clarity. We note, however, that these models should technically be assessed individually since parameter point estimates and standard errors from regressions us￾ing predictions from different bootstrap iterations of the cabinet sur￾vival model are not fully comparable—even though the substantive effects we generate from them are. We can make fully reliable com￾parisons using so-called “pivotal statistics” (e.g., z-scores) to draw conclusions about statistical significance of effect parameters across the 1,000 spending or deficit models. Statistics are considered pivotal if their sampling distribution does not depend on unknown parame￾ters, making them a good choice for comparing across models as we do (Shao 2003).The results of this more appropriate comparison lead to exactly the same conclusions but make for a potentially confusing presentation, therefore we have included the appropriate graphic in Appendix Figure A.3. 946 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000436