Transformative Policy Change Matt W. Loftis and Peter B. Mortensen mattwloftis@ps.au.dk peter@ps.au.dk∗ Aarhus University April 14, 2015 Abstract Theories of policy change vary in their concepts and explanations. Nevertheless, they all depict a process in which decision makers’ weighting and evaluation of what matters to policy decisions changes over time. That is, relationships between inputs to the policy process and eventual outcomes are not static. Despite the theoretical consensus on dynamic relationships, this expectation has not been systematically empirically tested. This paper sets out to do so by using state space models to estimate time-varying relationships between inputs to the policy process and outcomes. We apply this econometric technique to data spanning several decades across a variety of contexts. The results indicate that many relationships are, indeed, time-varying and suggest a variety of implications for future empirical research. Most researchers studying public policy and public spending decisions with time series analysis assume that the explanatory factors - whether political, economic, or institutional have a time-invariant influence. Yet, this assumption about constant effects through time has little grounding in substantive theories of public policy. Whereas the empirical approach has been dominated by a search for stable estimates, important theories of policy change, developed over the past decades, imply time-varying effects. The Advocacy Coalition Framework proposed by Sabatier (1987, 1988) and later developed in collaboration with Jenkins-Smith (Sabatier & Jenkins-Smith 1993) is one. A second is the theory of social learning and policy paradigms introduced by Hall (1989, 1993), and a third theory is the Punctuated Equilibrium Theory developed by Baumgartner & Jones (1993). ∗ Working paper, please do not cite without permission. 1 The three theoretical approaches differ in their conceptualization, description and explanation of policy change, but they all depict a policy-making process in which the decisionmakers’ weighting and evaluation of what is important to policy decisions is likely to change over time. Such change may be slow or fast, gradual or punctuated, and it may reflect changes in core beliefs, policy paradigms or policy images. Nevertheless, a common implication of the different theoretical approaches to policy change is that the importance of explanatory factors varies over time. This means that scholars of policy change need to redirect focus from estimating stable relationships between X and Y to a higher order level of theorizing and modeling why and when the relationship between X and Y may change. Inspired by (Lieberman 2002, 700) we denote the latter type of change transformative change. The aim of this paper is to integrate the empirical study of public spending with the dominant theories of temporal instability in policy and spending decisions. First, we review traditional time series studies of public policy change. Second, we introduce the concept of transformative change and show how it relates to the dominant theoretical accounts of the policy-making process. Third, we discuss what the concept of transformative change implies for time series studies of changes in public policy. Fourth, inspired by recent developments in public opinion studies, we motivate our choice of method to study transformative change empirically. Fifth, using U.S. public spending time series compiled by the Policy Agendas Project we demonstrate how this approach can be implemented and what it can teach us about spending change. An important aim of the paper is to argue for a new research agenda that links the empirical approach to policy change closer to the theoretical emphasis on transformative change, and it concludes by highlighting some of the next questions that such a research agenda may focus on. 2 Time-series studies of public policy change For decades public spending has been a widely used measure of public policy. The validity of this policy indicator can be discussed, but to illustrate the non-dynamic character of most time-series studies of public policy it suffices to review a wide range of time-series studies using public spending as the dependent variable. Thus, we focus on research using spending time series as the dependent variables, but claim that the general point about a mismatch between the empirical approach and dominant theories of policy change is of broader relevance to time series studies including those using other indicators of public policy besides spending. Davis, Dempster & Wildavsky (1966) were some of the first scholars to utilize spending time series data. Based on Wildavsky’s (1964) qualitative studies of incremental decisionmaking in the U.S. Congress, they derived the implication that: “Since the budgetary process appears to be stable over periods of time, it is reasonable to estimate the relationships in budgeting on the basis of time series data” (Davis, Dempster & Wildavsky 1966, 531). More particularly, they argued that year-to-year changes in budget appropriations could be accounted for by a set of simple, linear equations. Of special interest to the argument of this paper is, however, the conclusion they draw based on the simple regression analyses (ibid., 542): “... the budget process is only temporally stable for short periods... scholarly efforts would be better directed toward knowledge of why, where, and when changes in the process occur.” In 1974 the authors followed up on this conclusion and approached the temporal instabilities as an omitted variable problem (Davis, Dempster & Wildavsky 1974). Adding eighteen exogenous variables to the simple time series models they hoped to be able to account for the temporal instabilities. However, the impression is that the extended models do not explain away the shifts in coefficients identified in the 1966-article. Surprisingly, given the focus of the two seminal articles by Davis, Dempster, and Wildavsky, the identification of epochs and shifts in the estimated parameters had very little impact on the field of time series analyses 3 of public spending. The part about stability and order had a much more lasting influence. The time series approach to public spending has not been confined to studies of incrementalism. In particular, we have seen many studies trying to model time series of U.S. defense spending, partly reflecting a genuine interest in this policy field during the Cold War, partly reflecting availability of rather reliable and long data time series within this policy field. A broad range of drivers of U. S. defense and military spending have been examined in these time series studies including election cycles (Nincic & Cusack 1979, Cusack & Ward 1981, Zuk & Woodbury 1986, Kamlet & Mowery 1987), measures of unemployment (Griffin, Wallace & Devine 1982, Cusack 1992, Su, Kamlet & Mowery 1993, Majeski 1992, Kiewiet & McCubbins 1991), arms races (Ostrom 1977, Correa & Kim 1992, Ostrom 1978, Ostrom & Marra 1986), inertia (Ostrom 1977, Majeski 1983, Correa & Kim 1992), and public opinion (Hartley & Russett 1992, Wlezien 1996, Higgs & Kilduff 1993). As good time series data has become available within other policy domains, we have seen an expansion of time series studies of non-defense spending changes (see e.g. Jones & Baumgartner 2005, Soroka & Wlezien 2010). The U.S. defense spending studies disagree with respect to many model assumptions, but common to all of them is the assumption about invariant relationships over time. Apparently, this assumption is so uncontested that it is not given any serious consideration. Nevertheless, the focus on ordered and stable relationships is difficult to justify based on the shift points already identified in the first time series regressions produced by Davis, Dempster & Wildavsky. Furthermore, as argued in the next section, the time invariance assumption is not consistent with dominant theories of policy change. In other words, there are good reasons to expect that the relevance and weight of the various determinants of public spending vary over time. 4 Dynamic Models of Transformative Policy Change In the late 1980s and early 1990s, three important theories about policy change were developed. One is the theory about Advocacy Coalition Frameworks proposed by Sabatier (1987, 1988) and later developed in cooperation with Jenkins-Smith (Sabatier & JenkinsSmith 1993). A second is the theory of social learning and policy paradigms introduced by Hall (1989, 1993) and the third theory is the Punctuated Equilibrium Theory developed by Baumgartner & Jones (1993). The three theoretical approaches differ in their conceptualization, description and explanation of policy change (for comparative reviews, see Cairney & Heikkila 2014). Nevertheless, all three theoretical approaches share an important implication about politics, namely that the logic of public policy making may change over time. According to the Advocacy Coalition Framework, every coalition of policy makers contains secondary aspects, policy core beliefs, and so called deep core beliefs. Secondary aspects comprise a large set of narrower beliefs of the policy makers concerning, for instance, their evaluation of relevant problems and performances within a policy subsystem as well as their preferences regarding regulations or budgetary allocations (Sabatier 1998, 104). Policy core beliefs refer to a coalition’s basic normative commitments and causal perceptions across an entire policy domain, and deep core beliefs include basic ontological and normative beliefs operating across almost all policy domains (Sabatier 1998, 103). When it comes to the core beliefs, these are assumed to be very stable, but they are not time-invariant. Even if changes mainly involve secondary aspects, this may, for instance, have implications for the relative importance of various causal factors within a given policy domain (Sabatier 1998, 104). In Hall’s approach to policy change, a distinction is made between first-order, secondorder, and third-order changes (Hall 1989, Hall 1993). First-order changes regard changes in the instrument settings, whereas second-order change is when the instruments as well as their settings are altered even though the overall goals of policy remain the same (Hall 1993, 278-9). Third-order change occurs when all three components of policy change simultaneously: the instrument setting, the instruments themselves, and the hierarchy of goals behind 5 policy. Hall’s prime example of a third-order change is the paradigmatic change in British macroeconomic policy in the 1970s and 1980s from a Keynesian mode of policy making to one based on monetarist economic theory. Just as changes in deep core beliefs are assumed to be very rare according to the ACF, paradigmatic third-order changes are very rare according to Hall’s theory. It is important to note, however, that even second-order changes or, in the parlance of ACF, changes in policy core beliefs will most likely be reflected in time-varying relationships in time-series models of public policy. A second-order change, for instance, reflects an alternation of the hierarchy of goals behind policy (Hall 1993, 282), and a change in the policy core beliefs of policy makers may involve a change of their causal perceptions of a policy domain (Sabatier 1993, 103). Put differently, if the decision makers’ causal understanding of the relationship between problems and solutions changes within policy domains such as defense, welfare, transportation, or environmental policies, then the relationship between X and Y probably changes as well. The latter implication also follows from the depiction of the policy-making process provided by the Punctuated Equilibrium Theory (PET). According to the original formulation of the theory, the policy-making process is dominated by policy monopolies based on a dual foundation of an institutional structure that limits access to the policy process and supported by a powerful policy image (Baumgartner & Jones 1993, 7). From time to time, these monopolies are successfully challenged by outsiders and replaced by a new institutional structure supported by a new dominant policy image. Later, Jones and Baumgartner introduced the model of disproportionate information processing, where the concepts of images and subsystems are generalized to a generic decision-making theory about information processing and friction in the policy-making process (Jones & Baumgartner 2005). Yet, the dynamic picture about how the understanding of policy issues changes over time remains a central characteristic to the model. Similar to the two other theories about policy change, Jones and Baumgartner’s model 6 is founded on a micro level of bounded rationality. The same was claimed by scholars of incrementalism, but according to Jones and Baumgartner the incremental approach failed to see that the serial processing capacities of the decision makers, which in periods of stability serve to prevent policy change, also ensure increased focus on new issues and perspectives to the exclusion of others once the focus of the policy makers shifts. Thus, government attention is not only selective, it also shifts among perspectives and objectives of attention. As True (2002, 177-180) argues in his application of the PET to the domain of U.S. national security policy: “The relationship between Soviet capabilities and U.S. defense spending was a complicated one, and it appears to have been episodic [...] At some times Soviet spending may have been important to U.S. budget decision making, and at other times it was not [...] In understanding national security and in explaining policy decisions over time, no one logic and no single frame of reference lasts forever.” Over time, according to PET, most policy areas may be subject to such a change in focus. From the perspective of this paper, the three theoretical approaches share an important and theoretically rather uncontested implication about the time-varying importance of causal factors. Examples of such time-varying relationships can be found in qualitative applications of the theories (for overviews, see Baumgartner et al. 2014; Jenkins-Smith et al. 2014), but the implication has not been examined in time-series analyses of policy change (two partial exceptions are True 2002, Jones, Baumgartner & True 1998). None of the theories offers point predictions about when the parameters will change, and across theories there is no consensus about whether such change will be gradual or punctuated. A crucial first step to approaching these questions, however, is to begin to model such transformative changes. In the next section, we motivate the adoption of a flexible approach to time-series analysis that can uncover time-varying relationships. 7 Studying dynamic relationships This study is the first to attempt a broad and systematic empirical test for the presence of dynamic relationships in macro-level policy outcomes. However, there is a large research literature examining such time-varying relationships in other contexts. The econometric problem of estimating changing relationships between variables is challenging and has inspired a variety of solutions. Ideally, we might estimate a model that allows the parameter for the effect of x on y to vary by time periods: yt = β0 + xt β1t + This model, however, is non-identifiable without additional assumptions. For example, with a large enough cross-section and interaction terms or hierarchical levels we could estimate how β1 changes with t. The assumption required is that the cases in the cross-section are sufficiently similar that β1 describes the relationship across cases. For a single time series, the required assumptions become still more demanding. One option is to split the single series into meaningful time periods and estimate β1 in separate regressions by time period or via interactions for time periods. This approach has been used in the only other work to previously test for the presence of dynamics in relationships between macro-level policy outcomes (True 2002). True’s (2002) results are suggestive that dynamics are present, as theorized. However, this approach to estimating variation in effect parameters suffers two weakness that are common to several other approaches that might also be applied. The first, and lesser, issue relates to statistical power. Subdividing the time series necessarily weakens the strength of our inferences by working with smaller samples, increasing the risk of both Type I and Type II errors. Low statistical power is also a difficulty for CUSUM and CUSUMSQ plots as tests for parameter stability (Wood 2000, Baltagi 2011). These plot functions of cumulative sums of residuals in order to identify breaks that may signal structural shifts in the parameters. 8 The passage of time and therefore the lengthening of our data on policy change ameliorates this issue to some degree though it cannot eliminate it altogether. The second, and potentially more challenging, difficulty is that subdividing a time series requires the analyst to identify and motivate the choice of relevant time periods a priori. Although a principled method of selecting time periods may be available for a given test, it does not translate into a methodology that can be more widely applied. Furthermore, this still forces the analyst to assume that effect parameters are constant within periods. The same difficulty with motivating a priori information applies to the Chow test, which can reveal if a shift in an effect parameter occurs at a particular point (Wood 2000). For a more systematic test, then, we should favor estimation methods that are flexible with regard to the timing of shifts and require as little a priori information as possible from the analyst. Dynamic conditional correlations (DCC) have been proposed for this purpose (Lebo & Box-Steffensmeier 2008). DCC dynamically estimates the covariance of two time series using a framework adapted from generalized autoregressive conditional heteroskedasticity modeling. This is a powerful method for identifying a certain type of dynamics, but it requires quite large data sets, the method works only for bivariate relationships, and some debate is ongoing with regard to the econometric properties of DCC (Caporin & McAleer 2013). Therefore, we turn to a class of modeling techniques for our test that are quite flexible with regard to detecting the timing of changes, can handle multivariate models, and demand minimal assumptions with regard to the form of dynamic relationships. These are the methods of flexible least squares (Wood 2000) or dynamic linear models using Kalman filtering (Shumway & Stoffer 2010, Mcavoy 2006, Kim & Nelson 2000). These approaches have been shown to be algebraically equivalent approaches to modeling dynamic coefficients (Montana, Triantafyllopoulos & Tsagaris 2009). For simplicity, we adopt the dynamic linear modeling with Kalman filter framework - i.e. state space modeling. Returning to our idealized model above, this approach can recover estimates of the timevarying effect coefficients, β1t , provided some scaffolding of additional assumptions. The key 9 one is that β1t is a realization of an observed and underlying “state” that varies as a Markov chain over time, with each new estimate at time t diverging from its previous realization at time t − 1 to improve the model’s predictive accuracy in the new period. Predictive accuracy is balanced against the magnitude of divergence from β1t−1 by a cost function. This means that the model can flexibly return a time-constant coefficient estimate where appropriate or detect the presence of dynamics where appropriate. The disadvantages of state space modeling are minimized in our application. One of the chief potential drawbacks to consider is that the model weights observations equally that is, observations in the distant past have an influence on parameter estimates at time t equal to that of the observation at time t − 1 (Lebo & Box-Steffensmeier 2008). This is true because the logic underlying the model is essentially Bayesian. At each period, t, all of the information about past observations is summarized in the distribution of the parameter at time t − 1, which is updated each period as new information is introduced. Since our largest application uses a time series of several decades of policy outputs, we avoid a situation in which estimates are influenced by the very distant past. Furthermore, this feature of the modeling technique means that changes in parameters must reach a threshold of distinctiveness to be detected. This makes it less likely that potentially minor or random fluctuations from period to period will cause us to incorrectly identify the presence of dynamics. A further potential drawback lies in the state space model’s assumptions regarding the distributions of the time-varying coefficients (Wood 2000). With regard to these issues, we are less concerned. These models have been widely applied in engineering, economics, biology, genetics, finance and other fields with great success (Petris, Petrone & Campagnoli 2007, Shumway & Stoffer 2010). We have no reason to suspect that its assumptions are inappropriate for our applications. In the next section, we turn to a detailed explanation of our estimation strategy and then to summarizing the results of our analyses. 10 State space modeling We apply a Kalman filter and smoother to estimate dynamic linear models of the impact of various inputs to the policy process on public budgets. The model is structured as follows: yt = Xt βt + vt (1) vt ∼ i.i.d.(0, σv2 ) βt = βt−1 + wt (2) wt ∼ i.i.d.(0, Q) The first line is the measurement equation. The inputs to the policy-making process in vector Xt influence the realization of the public budget, yt , via the vector of time-varying effect coefficients, βt . The disturbances, vt , are independent Gaussian white noise with variance σv2 . The third line, equation 2, is the state equation. The effect coefficients, β, are modeled as an unobserved state varying in a random walk over time. The state disturbances, in vector wt , are also Gaussian white noise with covariance matrix Q and are uncorrelated to vt . The model is estimated recursively. At each time t, βt−1 is our expectation of this period’s new value of βt , conditional on the information observed up to time t − 1. Based on this conditional expectation for βt , we calculate a prediction for the outcome in time t: ŷt . The error in this prediction, yt − ŷt , is used to update our final estimate of βt , such that larger errors provoke larger shifts in the coefficient estimates. This recursive estimation process means that at any time, t, all of the past information about the underlying state is summarized in their point estimates and covariance matrix at time t − 1. Shifts in the coefficient estimates each period are moderated by the ratio of uncertainty regarding the estimates of β to the total overall estimation uncertainty in the model (including that from β). Where uncertainty about β is a larger share of overall model uncertainty, 11 this ratio - named the Kalman gain - is closer to one. Updates to the coefficients become more responsive to that period’s prediction error as the Kalman gain approaches one. A formal definition of the Kalman gain and detailed estimating equations are provided in appendix C. The final step in the estimation of the model is to apply a smoother to the time-varying state estimates. The Kalman smoother utilizes the same approach as the filter, but run in reverse. Recall that when filtering at each time period, t, all information about the unobserved states up to that period is summarized in the point estimates and associated uncertainty of last period’s state estimates: βt−1 . The smoother, by running in reverse from time T back to time 1, updates again each period’s estimate of βt conditional on all information in the entire model. This smooths out some variation in the time-varying state estimates by using information from the full time series. Our final effect coefficient estimates are these smoothed time-varying coefficients. The recursive estimation procedure is identified conditional on a starting value for β, β0 , and estimates of Q, σv2 , and the starting value of the covariance matrix of innovations, Σ0 . These are estimated via maximum likelihood. The process begins with initial values for each of these latter parameters, and then the βt s are estimated using the Kalman filter. After this, maximum likelihood is used to re-estimate the other parameters conditional on the estimates of βt . This process is repeated until all the parameter estimates stabilize. In the next section, we outline a series of empirical settings in which we apply this methodology to test for the presence of transformative policy changes. Testing for transformative policy change The first setting in which we apply our state space model is to test for dynamic relationships between inputs to the policy process and policy outputs is in replicating the tentative positive results reported by True (2002). His test examined U.S. defense spending over several decades and found that the relationship between prior spending, international tensions and wars, and 12 Soviet spending showed evidence of changing over time. We collected similar data for the period 1948-2006. Unfortunately, lagged Soviet defense spending is only available between 1965 and 2006 (with Russian defense spending substituted following the collapse of the Soviet Union), which leaves too short a time series to apply our preferred modeling technique. Nevertheless, we continue with analyzing the rest of the model and will return to this problem with a version of the state space model augmented for dealing with missing data. The response variable is the percentage annual change in U.S. defense spending. Key explanatory variables include a lag of the national unemployment rate, the constant U.S. dollar level of the government’s international support spending (i.e. international aid), an indicator variable for presidential election years in which an incumbent is competing, and indicator variables for periods of war or heightened international tensions. This final set of variables was recoded into a single indicator for our analysis. Since the state space model can detect changes in the effect of the single indicator over time, and we have no theoretical reason to distinguish among periods of war or tension, we have collapsed them into a single indicator. The variable takes on a value of 1 during periods of war or tension, including: the Korean War, the Vietnam War, the Reagan buildup, the first Gulf war, and from 2001 onward following the attacks of September 11th and the wars in Afghanistan and Iraq. Finally, we also include the lagged constant U.S. dollar value of defense spending as a control. In our first model, we include all of these variables. In a second specification, we remove some of the variables with insignificant effects and add in an indicator for public opinion on defense and a measure of the partisan ideology of the U.S. House of Representatives. Our public opinion measure comes from Gallup’s annual estimate of the proportion of the U.S. population stating that defense is an important problem. House ideology is measured by averaging the DW-NOMINATE scores of all members of Congress during a given session.1 Positive values on this measure are associated with conservative political ideology, 1 Data is found on the website: http://www.voteview.com/. For details on DW-NOMINATE, see Poole & Rosenthal (1997) 13 and negative values are associated with liberal ideology. For this latter specification, data is only available from 1959-2006. Summary statistics for all variables in both models can be found in appendix A. Our additional variables were chosen to broaden the range of explanatory factors captured by the model. Whereas the occurrence of a war or international tension constitutes a feature of the environment facing policy makers that likely influences defense spending, the first model does not capture public opinion and only barely addresses partisan politics. However, public attention and partisan politics are two other theoretically important factors that likely influence policy change. Therefore, we capture public attention with the most important problem measure. Although the election year indicator does capture some aspects of politics, it is not explicitly partisan. Therefore, we add in an estimate of the ideology of the House of Representatives. Transformative change in any of these variables is likely to reflect that policy makers are learning, policy frames are changing, or that core beliefs about policy have evolved. Results Dynamic coefficient estimates from our first model specification are plotted in figure 1. There is some initial evidence here that inputs to the policy process do not have constant effects over time. Periods of war and international tension are not consistently related to increases in defense spending, for example. Furthermore, election years appear to be associated either with greater or lesser spending. The bubble-shaped confidence intervals on these two coefficients occur during periods in which the variable takes on a value of 0. The rest of the estimates from the model, however, shows little evidence of transformative changes. The lagged level of spending is consistently negative, such that higher levels of spending last year are associated with negative adjustments to this year’s budget. The effects of both international support spending and lagged unemployment are basically constant and 14 statistically indistinguishable from zero. Intercept Coefficient 0.4 Coefficient War/Tension 1.0 0.2 0.5 0.0 −0.5 0.0 1950 1960 1970 1980 1990 2000 1950 1960 Lag Defense Spending 1970 1980 1990 2000 Lag Unemployment 0.02 1e−06 Coefficient Coefficient 5e−07 0e+00 −5e−07 0.01 0.00 −1e−06 −0.01 1950 1960 1970 1980 1990 2000 1950 1960 International Support 1980 1990 2000 1990 2000 Election Year 0.001 0.2 0.000 Coefficient Coefficient 1970 −0.001 0.0 −0.2 −0.002 −0.4 −0.003 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 Figure 1: Estimated time-varying coefficients from model one Note: Effect coefficients are plotted over time. The solid line indicates the point estimate for the coefficient each period, while gray areas are 95% confidence intervals. The dashed horizontal line indicates zero. Where the gray area overlaps the dashed line, estimates are not statistically significant by conventional standards. We turn now to a revised model specification. Since the relatively short time series and numerous parameters being estimated places high demands on our limited amount of data, we can improve our estimates if we can eliminate unimportant information from the model. In our second model specification, plotted in figure 2, we replace unemployment and international support spending with public opinion and Congressional ideology and rerun the model on the time period from 1959-2006. The results in this second model specification are estimated with greater certainty and further sharpen up some of the trends glimpsed in the first. Here, we see again that lagged 15 Intercept House Ideology 0.4 Coefficient Coefficient 2 0.3 0.2 0 0.1 −2 0.0 1960 1970 1980 1990 2000 1960 1970 Lag Defense Spending 1980 1990 2000 Public Opinion 0e+00 Coefficient Coefficient 0.6 −5e−07 0.4 0.2 −1e−06 0.0 1960 1970 1980 1990 2000 1960 1970 War/Tension 1980 1990 2000 Election Year Coefficient Coefficient 0.04 0.2 0.0 −0.2 0.02 0.00 −0.02 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 Figure 2: Estimated time-varying coefficients from model two Note: Effect coefficients are plotted over time. The solid line indicates the point estimate for the coefficient each period, while gray areas are 95% confidence intervals. The dashed horizontal line indicates zero. Where the gray area overlaps the dashed line, estimates are not statistically significant by conventional standards. spending is associated with a fall in the percentage change in defense spending and the constant positive intercepts suggests a generally positive trend over time. This model’s time series commences after the negative effect estimated for election years in model one. However, in this model, the election year effect has essentially disappeared as the coefficient is constant never reaches statistical significance.2 Periods of war and international tension are even more clearly inconsistently related to changes in defense spending. Whereas the Vietnam era clearly saw higher spending associated with the war, by the Gulf War the estimated effect had reversed and in the 2 As a check on the within sample predictive accuracy of the two models, appendix B contains plots of predicted values from each model against the actual values of the response variable. 16 period of the Afghanistan and second Iraq wars there is no clear association between the crises and changes in defense spending. Instead, from around the Reagan era onward, strong public sentiment that defense is an important problem is positively associated with spending changes. This positive relationship is consistent with previous eras, but the relationship between public opinion and defense spending is barely statistically insignificant prior to this. Finally, House ideology shows dramatic transformations. Left-right ideology in the House has a positive association with changes in defense spending until the Reagan era, at which point is becomes indistinguishable from zero. In the early 1990s this association reverses briefly and becomes negative, and then it moves toward positive again though it is statistically insignificant from the mid-90s onward. The coefficient on House ideology reaches its lowest point in 1989, at which time a one standard deviation increase in ideology (i.e. a shift toward being more conservative) would be associated with a predicted 11.5% decrease in defense spending. This is in contrast to 1959, when the coefficient was at its highest point and a one standard deviation increase in ideology would have been associated with a predicted 16.2% increase in defense spending. The shifts in the impact of war and international tension are almost as pronounced. In 1966, after the major escalation of U.S. involvement in Vietnam following the Gulf of Tonkin Resolution, the war was associated with an estimated 7% increase in defense spending. However, in 1991 during the first Gulf War, that conflict was associated with an estimated almost 5% drop in defense spending. It is worth noting that these effects are not only statistically significant in that they differ from the null of zero, but these shifts are also statistically significantly different from one another. That is, the shifts we observe in the coefficients are significant and substantively large changes. 17 Conclusion We take these initial results as compelling evidence in support of the most important implication of our strongest theories of policy change: relationships are dynamic in the policymaking process. Testing the exact nature and mechanisms of these transformative changes is beyond the scope of this paper, but the econometric evidence is strongly suggestive that the key inputs to defense spending changes we have analyzed do not have constant relationships to policy output. Rather, their impacts on policy change over time. This opens up multiple possibilities for future theoretical and empirical research. Chiefly, there is a dearth of theoretical expectations regarding the timing and nature of transformative policy changes. With the empirical tools to test these expectations in hand, deriving such theoretical expectations is a promising way forward. Furthermore, the different causal mechanisms underlying the general theoretical expectation of transformational policy change provide a launching point for generating new hypotheses that can be tested using the framework we advocate. The planned next steps for this paper are to run comparable analyses across a large set of budgetary categories and to implement versions of the current analysis augmented for handling missing data in order to expand the time frames we can analyze. The modeling framework we have advocated can also generalize to handle non-normally distributed response variables, allowing us to examine policy outputs other than budget changes and other plausibly normally distributed phenomena. 18 References Baltagi, Badi. 2011. Econometrics. Springer Texts in Business and Economics. Baumgartner, Frank R. & Bryan D. Jones. 1993. Agendas and Instability in American Politics. Chicago, IL: University of Chicago Press. Cairney, Paul & Tanya Heikkila. 2014. 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Woodbury. 1986. “U.S. Defense Spending, Electoral Cycles, and Soviet-American Relations.” The Journal of Conflict Resolution 30(3):445–468. 21 A Appendix: Summary statistics Year % Change in defense spending Lagged defense spending International support spending War/Tension Lagged unemployment Election year Min Max Mean Std Dev Obs 1948 2006 - 59.00 -0.28 0.88 0.03 0.15 59.00 82334.00 510603.00 311106.83 93948.39 59.00 62.00 17711.00 4441.44 3455.43 59.00 0.00 1.00 0.39 0.49 59.00 0.00 9.71 5.53 1.65 59.00 0.00 1.00 0.17 0.38 59.00 Table A.1: Summary Statistics for Model 1 Year % Change in defense spending Lagged defense spending War/Tension House Ideology % Defense most important prob. Election year Min Max Mean Std Dev Obs 1959 2006 - 48.00 -0.12 0.17 0.02 0.07 48.00 238744.00 510603.00 339319.00 70873.23 48.00 0.00 1.00 0.40 0.49 48.00 -0.13 0.15 -0.02 0.08 48.00 0.00 0.47 0.15 0.14 48.00 0.00 1.00 0.17 0.38 48.00 Table A.2: Summary Statistics for Model 2 22 B Appendix: Within-sample predictions from models The following plots show the predictive accuracy of the two models. Both figures plot two lines. In solid black, we see the actual values of the response variable: percentage annual change in defense spending. The dashed line is the model’s prediction for each period, with its 95% confidence interval in gray. The predictive accuracy of model 2 is stronger, with the black line depicting actual change in defense spending being within the confidence interval for the prediction most of the time. Predicted and actual spending changes 1.0 0.5 0.0 −0.5 1950 1960 1970 1980 1990 2000 Figure A.1: Model 1: Predicted and actual values of change in defense spending Note: The solid black line is the actual value of the response variable. The dashed line is the model’s prediction of the response for each period, with its 95% confidence interval in gray. 23 Predicted and actual spending changes 0.2 0.1 0.0 −0.1 1960 1970 1980 1990 2000 Figure A.2: Model 2: Predicted and actual values of change in defense spending Note: The solid black line is the actual value of the response variable. The dashed line is the model’s prediction of the response for each period, with its 95% confidence interval in gray. 24 C Appendix: Model details The model exposition we adopt is that outlined in Shumway & Stoffer (2010). Their work provides a general version of the specific approach we utilize. The estimation of the timevarying covariates is recursive, starting at time one and progressing to time t. This entire recursive estimation is repeated with each of the maximum likelihood estimates of the additional parameters of the model, beginning with their initially chosen starting values and ending with the stable final estimates. The process proceeds as follows: 1. Select initial values for the parameters: β0 , Q, σv2 , and the covariance matrix of innovations (or prediction errors) Σ0 . 2. Run the Kalman filter to obtain values for the innovations (prediction errors) from the model, v, and their covariance. 3. Use the estimates obtained from the Kalman filter to estimate β0 , Q, σv2 , and Σ0 using maximum likelihood. 4. Repeat step 2 using the estimates from step 3 in place of the starting values selected in step 1. 5. Repeat step 4 until the estimates of β0 , Q, σv2 , and Σ0 or the likelihood stabilizes. The recursion for the Kalman filter proceeds as follows. At time 0, the following two steps are unique and take the place of steps one and two in the next list: 1. Calculate an expectation of β1 , conditional on β0 . We assume that β follows a random walk, therefore our initial expectation about next period is simply our current estimate: βt|t−1 = βt−1|t−1 . Likewise: β1|0 = β0 2. Calculate an expectation of the covariance of innovations to β1 , conditional on Σ0 and Q. We refer to this as P : P1|0 = Σ0 + Q. From time 1 through time t, the following steps are taken: 1. βt|t−1 = βt−1|t−1 2. Pt|t−1 = Pt−1|t−1 + Q 3. Calculate the predicted value of y conditional on expectations from time t − 1: yt|t−1 = Xt βt|t−1 4. Calculate the prediction error in time t: ηt|t−1 = yt − yt|t−1 5. Calculate the Kalman gain for period t, i.e. the proportion of uncertainty in each parameter in βt attributable to uncertainty regarding the parameter relative to the full uncertainty in the model: Kt = Pt|t−1 Xt0 Xt Pt|t−1 Xt0 + σv2 25 6. Update estimate of effect coefficients, βt|t , based on prediction error and Kalman gain: βt|t = βt|t−1 + Kt ηt|t−1 The value of βt|t is our estimate of βt . 7. Update expectation of the covariance of parameters, Pt|t , based on Xt and σv2 : Pt|t = Pt|t−1 − Pt|t−1 Xt0 Xt Pt|t−1 Xt Pt|t−1 Xt0 + σv2 This can also be expressed as: Pt|t = [I − Kt Xt ]Pt|t−1 26