Do business cycle peaks predict election calls? 1

Transcription

1 Do business cycle peaks predict election calls? 1 by Marcel-Cristian Voia and J. Stephen Ferris Third Draft May 7, 2012 Department of Economics Carleton University Ottawa, Ontario, K1S 5B6 Abstract This paper examines the empirical regularity that business cycle peaks and federal elections tend to arise together in Westminster parliamentary democracies, particularly as it applies to Canadian data over the post Confederation time period (1870 onwards). We argue that the appearance of timing simultaneity and the proper identification of causality is possible only if the selection issue associated with observed events is addressed carefully. Our results suggest that it is business cycle peaks that lead federal elections rather than the other way around. While such a finding reinforces the hypothesis of strategic election timing, the result is also insightful because it helps to explain why the predicted presence of a political business cycle is harder to find in parliamentary governments where the date of the next election is under the control of the governing political party than in democratic systems where governing durations and election dates are fixed. Key Words: election timing, political business cycles, selection models, election hazard JEL categories: D72, D78, C41. 1 We would like to thank Hashmat Khan, Niklas Potrafke, Marcos Menchaca, Stan Winer and a referee from this journal for comments on earlier drafts of this paper. Earlier versions of this paper were given at the Public Choice Society Meetings in San Antonio, March 2011 and the Canadian Economic Association Meetings in Ottawa, June 2011.

2 1. Introduction The motivation for this paper is provided in Figure 1 below. There a diagram placing the dates of Canadian federal elections against the dates on which the Canadian business cycle peaked suggests a remarkable coincidence in timing. Between the introduction of parliamentary democracy in Canada (Confederation in 1867) and the present there have been ten occasions when the year of a federal election and the year of a business cycle peak have coincided; in another thirteen cases, they arose within one year of each other. On the other hand, the diagram also shows some obvious exceptions: the 1931 election that arose in the heart of the Great Depression and the relatively long duration of current (post 1980) business cycles in comparison with more frequently arising federal elections. The latter highlights an asymmetry that arises between elections and business cycle peaks--there have been 40 general elections since Confederation as compared to 32 business cycles. 2 All in all, however, the appearance of synchronization seems close enough to pose the question of whether or not there is a meaningful empirical relationship arising between the two. Our purpose in this paper is then to inquire into the relationship between business cycle peaks and elections in Canada and, to the extent a significant statistical relationship can be found, to ask whether one occurrence is the cause of the other. Of particular interest is whether business cycle peaks lead elections and thus whether the data is consistent with the hypothesis of strategic election timing versus the alternatives that the two events arise from common causes or because the election stimulates the economy thus contributing to the business cycle peaking. To investigate this problem we organize the paper as follows: Section 2 describes the methodology followed, Section 3 presents the results of the independent probit models, and Section 4 presents the results of the bivariate probit models. Section 5 discusses causal identification and robustness tests while Section 6 presents the policy implications of the analysis. Section 7 concludes. 2 Canada is a parliamentary democracy where the governing political party is determined by the majority political party elected in a general, first-past-the-post constituency election. Over our time period, , there was set constitutionally a five year maximum term within which the governing party typically could chose the date of the next federal election. The constitutional limit may have restricted artificially the duration of governments relative to business cycle, a feature that will influence the choice of our estimation procedure below. 1

3 -- insert Figure 1 about here Methodology To identify the relationship between business cycle peaks and federal elections in Canada we use a methodology that builds through a sequence of steps. In the first step we model the probability that the two events arise separately by identifying the factors that are exogenous to each event. After doing so we test for whether there exists a correlation between these two events without making any special correction for simultaneity. If no correlation can be identified, we then ask whether simultaneity could be present and first assume that that simultaneity is due to common unobservables missing from the two equations. To do this we estimate a bivariate model that assumes correlated unobservables. When we find that the apparent correlation is not due to unobservables, we next ask whether there is a selection issue that needs to be addressed. To test this we estimate a bivariate model with selection that we expect will capture the correlation between the two events. If a correlation can be identified, we then proceed to establish the proper direction of causation by estimating two selection models (one that conditions the election call on peaks, the other that conditions the peaks on the election). Opposite signed significant correlations, we argue, establishes the appropriate direction of causation between the two events. To quantify the effect of this correlation we first generate the risk measure associated with the event that drives the correlation. This, we argue, is the hazard of a business cycle peak, the risk that a business cycle peak will arise given that it has not yet occurred. This estimated measure of risk is then re-introduced into the original election probability equation as a generated regressor that corrects for selection effects and is so used in both linear and nonlinear versions of the probability model. Because the generated risk measure is the equivalent of an Inverse Mills ratio, a generated variable that corrects for selection in linear models, we expect a stronger effect on the probability measure that is linear. As an additional test, we consider the effect of this generated risk measure on the log-duration of the event at risk. This last model is equivalent to an accelerated 2

4 failure hazard model in linear form. Such a linear specification of the hazard is helpful because it correctly captures the selection effect and therefore the correlation arising between the two events. Proceeding more formally, our task is to estimate parsimonious models that characterize the probabilities of having a business cycle peak and having an election. To begin, we characterize the observation of an election as a binary variable,, where { (1) The realization of is then used to define a latent utility measure of an election call,. Given the available data, the latent utility of an election call can be modeled as:, (2) where represents a set of political variables, a set of macro variables, a set policy variables that may be relevant for an election call. We assume that the error term,, is normally distributed with mean zero and constant variance,. Under the assumption of normalcy and together with the observed election calls,, as the outcome, the model represented in (2) becomes a probit model. The probability of observing an election can then be estimated using the reduced form model: ( ), (3) where ( ) is the cumulative density function (CDF) associated with the normal distribution. For the second case, we characterize the observation of a peak in the business cycle in year t,, as the binary variable: { (4) 3

5 The realization of the business cycle, is in turn used to define a latent utility measure of the probability of realizing a peak in. Given the available data, we use the following model to estimate that latent utility as (5) where is an international indicator of cyclical activity closely associated with the Canadian business cycle, is a set of relative prices, a set of policy variables thought to be associated with real output growth in Canada, and is a random error. Again we assume that the error term in the latent utility model is normally distributed so that together with the observed cycle peaks as the outcome, the model in (5) becomes a probit model. The probability of observing a peak in the business cycle can then be estimated using the following reduced form: ( ) (6) where ( ) is the CDF of a normal distribution. The latter arises because of the assumption made with respect to, i.e. ( ). Before moving to the stage of joint determination, the models in (3) and (6) are tested for specification error, endogeneity, and fit. To anticipate our findings, the tests suggest that the two chosen models are well specified with the results that present no evidence of endogeneity bias and generate a good fit with the data. Our structuring of the problem has thus far focused on finding models that explain the two events when the two events are treated separately. Here the observed coincidence in timing would arise from the timing of the underlying factors, some of which the two relationships may have in common. After finding models that provide the best possible fit for these two independent events, we turn in the second stage of our analysis to the additional possibility that the two observed events are correlated through unobservables. Hence our focus becomes whether there is independent correlation arising between the two events is actually present and, if present, what generates this correlation. Does the correlation arise because important but unobservable 4

6 variables influence both equations or does the correlation arise because there is an important selection issue that links the two events. Our first test for correlation between the two models considers the possibility that the two models are seemingly unrelated but correlated. To account for this correlation, we consider a bivariate model of the form: { (7) where and are correlated with ( ) and where the two sets of covariates may include some of the same together with additional covariates that are important for one model but not the other. If the error of the bivariate model is normally distributed with correlation, we can estimate (7) using a bivariate probit model with bivariate probability: ( ) ( ( ) ( ) ), (8) where ( ) and ( ). Identification is achieved in part through specification of the function form of our test (nonlinear for both equations and the correlation parameter, ) and because the two models have only a few regressors in common and are treated as seemingly unrelated. There is one important reason why the seemingly unrelated specification above would not measure the true degree of correlation arising between the two errors. This is when the selection of one of the events is due to the realization of the other. Hence to account for this selection possibility, we consider a Heckman-type selection model based on the two separate probit models where the disturbances are correlated in the same spirit as in the seemingly unrelated regression model but where the realization of one is conditional on the realization of the other. Note that in general either of the two events could be the triggering mechanism. In our case a business cycle peak could precipitate an election call or an election could trigger a peak in the business cycle. This means that the two forms of the specification test can be used as a single test for which event leads the other. In particular, if a business cycle peak leads an election call, then the unexpected arrival of a business 5

7 cycle peak should increase unexpectedly the probability of an election. The two equation residuals should be positively correlated. At the same time, however, if a business cycle peak truly led an election call then an unexpected election call should not increase the likelihood of a business cycle peak. Rather the business cycle peak should now be less likely. This implies that the residuals of the Heckman specification test should be negatively correlated when the election call is used to condition a business cycle peak. It follows that the two Heckman selection possibilities can be used to test for the ordering of the relationship between elections calls and business cycle peaks. If event A conditions the occurrence of event B, then the correlation among the residuals of the Heckman specification test should be positive when conditioned by A and negative when conditioned by B. To capture selection bias by conditioning on business cycle peaks, the following model is constructed: ( ), together with where and are correlated with ( ). If have a bivariate normal distribution with mean zero and correlation, the model can be written as a bivariate censored probit and specified as { ( ) (9) The new model assumes that the probability of an election call is tied to the business cycle peaking such that its realization,, adds information relevant to the observation of an election. Equation (9) is then estimated as a bivariate probit censored model of the Heckman type. To capture the alternative form of selection bias we condition on elections. Here the same procedure is followed with conditioning in the second probit equation. Maddala (1983) argues that in absence of exclusion restrictions on the exogenous variables, the same regressors cannot be used in the two equations. However, Wilde (2000) showed that identification can be achieved when each equation contains independently varying exogenous regressors. Hence under the method 6

8 we adopt, identification can arise under two conditions. First as long as the joint normality of the error terms is satisfied, identification is achieved. On the other hand, if normalcy is not satisfied, identification will be weak and an exclusion restriction in the separation equation will be needed. It follows that when the necessary parameterization is in question, the use of instruments will be particularly helpful. Consequently we use additional regressors in both parts of our model, regressors that are important for an election call but not for economic growth and vice versa. 3 These additional regressors define the exclusion restrictions used for identification in the bivariate probit model. The significance of these additional variables (shown in the empirical section below) implies that our exclusion restrictions have worked. Our data has the additional complication of having the potential triggering event arise infrequently relative to the other event. This unbalancing arises because the time between elections in Canada is limited constitutionally while business cycles have no similar truncation. It follows that the number of conditioning events is relatively small and that elections and business cycle peaks cannot be matched symmetrically. In partial response and as a robustness test of our initial findings, we redo the timing convention for the dating of our events. Whereas our original test would count an October election as arising in the following year, our redating procedure gives a weight of 1/4 to the current year and 3/4 to the following year. A similar adjustment is made for the dating of the business cycle peak. Doing so both increases the number of years in which elections and business cycle peaks arise and makes their appearance in time more symmetric. The results of these specifications (and an alternative linearized version of the model) identify a positive correlation between the two models when conditioned on business cycle peaks, reinforced by a negative correlation when the models are conditioned on an election call. Hence our tests encourage us to believe that causation runs from business cycle peaks to elections rather than the other way round. To further assess 3 These include the fraction of seats won by the winning political party (Seats) and whether or not the winning political party had a minority government or not (Minority) as regressors for the probability of an election call but not a business cycle peak. The dating of US business cycle peaks (BCP_US) and detrended farm (Farm_deviation) and export prices (exp_deviation) are variables determining the likelihood of a business cycle peak but not an election call. These variables form our exclusion restrictions. 7

9 causality and reinterpret the negative findings for interconnection at the start of the paper, we develop a single equation alternative to the Heckman selection model that conditions the probability of an election arising by an equivalent of the Inverse Mills Ratio (which in our case is the hazard of having a business cycle peak arise). A significant coefficient on that hazard confirms the presence of selection in an election call based on business cycle peaks and thus the hypothesis that the expectation of a cycle peaking has an important causal role to play in explaining the likelihood of a federal election. In addition, the marginal effect associated with its inclusion allows us to quantify the impact of the risk of a cycle peak on an election call. Finally, we consider the effect of this generated measure of risk on the hazard of an election. As both the Cox model and semi-parametric versions of the accelerated failure hazard model (AFT) model are models that leave the baseline hazard (or, equivalently, the baseline survival distribution) unspecified, we rely on the similarities of the two models to do our test on the hazard of an election. An extension of the AFT model to incorporate correlated survival data can be done by including random effects in the regression expression as in a classical linear mixed model. The proposed test uses the later specification of the AFT model. This version of the AFT model takes a linear specification of the form: log(t) = -x + log(u), where t is the length of a governing duration and u is the error term. This last model illustrates dramatically that the risk of a business cycle peaking (given that it has not yet peaked) decreases the length of the election cycle. This linear specification of the hazard is helpful in capturing the selection effect correctly and therefore the appropriate degree of correlation between the two events. In an appendix we show that the choice used for our estimated risk measure does indeed provide the best fit for our true risk measure. 4 4 The appropriate corrections of the standard errors are made when the generated regressor is used in all the specifications above. We also emphasize that the generated regressor of the risk measure should be a consistent estimate 8

10 3. Results: The Independent Probit Models We begin with the probit equation explaining election calls. To derive this relationship we follow our earlier papers, Ferris and Voia (2010, 2011), where the time duration of a federal government is modelled as the outcome of an optimal stopping rule. 5 There the governing political party is assumed to choose the date of the next election to maximize the likelihood of re-election and the predictions of that model are tested against Canadian data. Our starting point here is the set of variables found predictive in that analysis. A complete description of the data used in our tests is provided in the Data appendix together with a Table describing their statistical properties. The data run from 1870 to 2008 and cover 38 federal elections. A key feature of that table is that all variables are I(0) or stationary. In column (1) of Table 1 we present the result of using these variables in a probit model. The results imply that a Canadian federal election in year t (Elyear) was more likely the smaller was the size of the electoral victory by the winning political party (Seats, interpreted as the competitiveness of the political process) and even more likely if the governing party did not have a parliamentary majority (Minority). The optimal stopping rule characteristic itself predicts that an election will be more likely the higher is the current rate of growth of real per capita income (Growth). However, the minimum growth rate needed to trigger an election will fall as the governing party s time in office approaches its constitutional limit (Exp_weighted _growth). Finally, the probability of an election call could depend on the macroeconomic policies adopted by the government at that time. For example, opportunistic theories of the political business cycle imply that the likelihood of an election call is larger the larger is the increase in government of the true risk measure. In an appendix we provide a test that shows that our choice for the estimated risk measure is the best fit of the true risk measure. 5 There is a large literature in political science that models governing durations as optimal stopping rules. Recent examples include: Kayser (2005), Berlinski, Dewan and Dowding (2007), and Huber and Martinez-Gallardo (2008). 9

11 spending (Dlngsize), the decrease in taxes (Dlntaxsize), and the increase in monetary growth (Growthmb). 6 Our results suggest that none of these policy variables has played that role. While the coefficients on these policy variables all have the sign expected for opportunism, none are significantly different from zero. 7 The sub-tables attached to Table 1 provide a test of the appropriateness of this specification and a measure of fit. In the first table, fit is measured by comparing the mean and standard deviation of actual election calls over our time period against the corresponding moments implied by the estimated model. The results indicate a close match between these two distributions. The two means differ by only two percent (.281 versus.275). The table that follows provides a test of misspecification error for our model. This test regresses the link function of the outcome variable (in this particular case, the probability function) on the predicted probability and predicted probability squared. The intuition behind the test is that the predicted probability function should be statistically significant unless the model is misspecified. Proper specification of the model also implies that the square predicted probability should not have predictive power. If the square predicted probability is significant it means either that we have omitted an important variable from the model or that our link function is not correctly specified. The link test finds that the linear prediction is significant and the squared prediction is not, thus providing no evidence of misspecification insert Table 1 about here ---- In columns (2) and (3) we present the result of testing for evidence of a connection between an election call and a peaking of the business cycle by first adding the actual occurrence of a Canadian business cycle peak, Canpeaks, and then adding the probability of a business cycle peak arising, Prob(Canpeaks), as a determinant of the likelihood of an election. 8 Inspection of the results at the bottom of columns (2) and (3) indicates that neither coefficient estimate is significantly different from zero. Neither does their inclusion 6 There is also no evidence of a (Liberal) partisan effect on election calls or Canadian business cycle peaks. 7 This remains true in all versions of our tests. 8 The derivation of Prob(Canpeaks) is described in the following paragraph. 10

12 improve the overall equation fit with the data. It follows that adding the actual occurrence of a business cycle or the probit estimate of that likelihood as a determinant of Canadian elections does not capture the apparent interconnection suggested by Figure 1. The hypothesis that the occurrence of a business cycle peak triggers a federal election call is supported by neither of these single equation estimates. When we turn to establish a probit equation for the likelihood of realizing a Canadian business cycle peak, we find much less help in the economic literature. For Canada, however, there has been considerable work done comparing the characteristics of Canadian and U. S. business cycles (Hay 1966, Cross 1996, and Gregory et al. 1997). The overwhelming conclusion of that literature is that there is a strong interconnection between the two business cycles. Since the direction of causality is unlikely to go from Canada to the US, we use the peak in the US business cycle (BCP_US, as provided by the NBER) as an indicator of the set of unobserved common factors determining a peak in the Canadian business cycle. 9 We supplement that with the hypothesis that as a small open economy, the Canadian economy will experience periods of more rapid growth, and thus be more likely to experience a business cycle peak when export prices generally and commodity prices in particular are relatively high. For Canada, forestry, oil and mineral prices would be the most appropriate commodity prices, but as a class we can find only export and farm product prices to span our entire time period. Over time, relative export prices and relative farm prices have both been trend stationary (downward) so that their deviations from their time trend were used as regressors in our empirical work (exp_deviation and farm_deviation). Because of a more general concern with the intersection of business cycles and economic policy, we include as a final set of considerations federal government economic policies. Hence we include as potential determinates the same set of policy variables used to estimate the likelihood of an election call (Dlngsize, Dlntaxsize and Growthmb). 9 The United States is by far Canada s largest trading partner. For example, in 2006 the United States took roughly eighty percent of Canada s exports versus its next most important trading partner, the United Kingdom, at 2.5 percent. 11

13 The results reported in column (1) of Table 2 suggest that the peaking of the U.S. business cycle (BCP_US) is the key determinant of observing a Canadian business cycle peak. Export prices become significant only if we extend the confidence interval to 10 percent and fiscal expenditures appear counter to expectations. However, this initial impression is misleading. When only BCP_US is included in the probit, the equation as a whole does not fit the data well, generating a distribution mean of.530 as compared to the actual value of.230. When the two commodity price ratios are included along with the policy variables, the overall equation does perform well. First the fit with the data becomes much better, resulting in a mean likelihood of an cycle peak of.274 as compared to the actual likelihood of.230. In addition the link test finds that the linear prediction is highly significant while the squared prediction and constant are not, thus giving no evidence of specification error. The model suggests that increases in relative export prices are somewhat successful as an indicator of a business cycle peak and it is non-farm prices, rather than farm prices, that are more likely to have had a positive effect on business cycle peaks. Finally note that the coefficient signs on the policy variables directly contradict the hypothesis that economic policy is a potential cause of the business cycle peak. Rather the set of coefficient signs and the significance of government spending are consistent with the hypothesis that economic policy is counter-cyclical, a finding complementary to recent findings on the relationship of policy to the Canadian business cycle (Winer and Ferris, 2008) insert Table 2 about here ---- In columns (2) and (3) of Table 2 we present the results of adding first the realization of an election, Elyear, and then the estimated probit value of an election arising, Prob(Elyear), as explanatory variables for the likely emergence of a business cycle peak. Here the public choice hypotheses would be that either the election itself or its expectation may stimulate the economy (Frey and Schneider, 1978) so increasing the likelihood of a business cycle peak. As was the earlier case for the likelihood of an election call, however, neither variable has had a significant effect on the likelihood of a business cycle peak. Neither does their 12

14 inclusion improve the overall model fit. It follows that in neither of our single equation election or business cycle cases does the addition of the actual or expected value of the other give any ground for believing that a relationship arises between these two events. 4. The Results: Bivariate Probit Models While the individual probit models explaining federal election calls and business cycle peaks appear to work well enough individually, the equation standard error estimates will be misspecified if the error terms in the two equations are correlated and the bias cannot be identified. As importantly, system estimation that allows for an interrelationship between the two events may better reveal what we suspect to be important regressors (such as the relative prices). To allow for the possibility of correlated unobservables, we re-estimate the two probit equations as a seemingly unrelated system. The results are shown in Table 3. In that table it can be seen that simultaneous estimation improves somewhat the significance of export and farm prices but is unsuccessful in identifying any significant correlation among the equation residuals. That is, while the seemingly unrelated results suggest the possibility of a positive correlation between the two distributions ( ), the results are not strong enough to identify such a correlation at standard levels of significance. There is only a twenty percent chance that. Accounting for unobservables also improves somewhat the significance of the government policy variables in the business cycle peak probit. However, the significant coefficient signs on both fiscal expenditures and monetary policy are inconsistent with the original hypothesis that policy helps to produce the emergence of a business cycle peak (but are supportive of counter-cyclical government policy government spending and monetary growth falling in the most expansionary stage of the business cycle). Combining these observations, the sign of improvement in coefficient estimates when estimated simultaneously, together with the inability of the seemingly unrelated method to account for the apparent correlation arising between our two events, suggests the possibility that a simultaneous model that allows for selection bias may be more appropriate. 13

15 ---- insert Table 3 about here ---- As discussed earlier, a selection model can be conditioned either on the realization of an election call or on the emergence of a business cycle peak and the ability to do both allows us to better identify the appropriate conditioning event. That is, if one event truly triggers the other, the matched residuals should not be symmetric. Rather conditioning on the event that is triggering should result in correlations among residuals that are positive, while conditioning on the following event should produce residuals that are negative. The unbalanced nature of the two events means that it may be more meaningful to begin the search for the triggering event by conditioning selection on business cycle peaks, since each peak allows for the possibility of a corresponding election call (whereas the reverse does not). In addition, we note that the observation that Canpeaks = 0 is difficult to interpret in terms of its economic effect. That is, while the nonobservance of a business cycle peak is easy enough to understand, the non-emergence of a peak could be associated either with a period of ongoing real growth or with a period of contraction, each having a quite different effect on the likelihood of an election call. Hence restricting our attention to the sample of periods when the business cycle has peaked means that we do not have to deal with the interpretation of exactly what Canpeaks = 0 will imply. In column (1) of Table 4a we present the results of a test of the selection hypothesis that the emergence of an election depends upon the realization of a business cycle peak. In moving to this alternative, the log likelihood function rises in value from to As importantly, by conditioning on the periods when a business cycle peak has arisen, the Heckman-type selection model does uncover strong evidence of a correlation arising among the model residuals. The selection model implies that unexpected shocks arising to Canada s business cycles are virtually perfectly correlated with unexpected election calls. The probability that the two equations are independent, that the correlation among the model residuals is zero, has fallen below 2 percent. 14

16 ---insert Table 4 about here --- It should be noticed that accounting for the interconnection between the two events in terms of a selection criteria does diminish somewhat the significance of the factors found previously to have influenced the likelihood of an election call. While the likelihood of an election call is still inversely related to the size of the winning party s majority, the effect of minority governments is now found to be insignificant. It is perhaps not surprising that conditioning on the emergence of a business cycle peak would reduce the separate importance of the growth rate as a determinant of an election call; however as before, the data remains consistent with the hypothesis that the growth rate falls in importance as the political party s term in office approaches its constitutional limit. Finally, as was the case before, the policy variables remain insignificant in their effect on the likelihood of an election call. On the other hand, conditioning on the emergence of a business cycle peak does increase generally the significance of those factors influencing the likelihood of a business cycle peak. While the occasion of a US business cycle peak significantly raises the likelihood of the Canadian equivalent, the selection method appears to better isolate the estimated effect of relative prices and policy variables. For elections to follow a business cycle peak the second part of our test requires the residuals of the two equations to be correlated negatively when the initial Heckman test is reversed and the probability of a business cycle peak is made conditional on the occurrence of an election. The results of this test are shown in column (1) of Table 4b. There the estimated rho is found to be significantly negative (-.806). The same pattern of coefficient findings is found for the other variables with again the finding that while the policy variables have their expected effect on elections (but are statistically insignificant) the signs of their effect on business cycle peaks are more consistent with the adoption of counter-cyclical policy. Overall the Heckman selection model with system estimation conditional on the realization of a business cycle peak does provides formal support for the observations that began this paper. The empirical relation 15

17 found in the data is consistent with the hypothesis that Canadian business cycle peaks precipitate federal elections. In the next section we examine the robustness of this finding and examine what more can be said about the direction of causality running between these two events. 5. Causal Identification and Robustness Tests In the models estimated thus far we have assumed that the error terms were normally distributed in order to use probit and bivariate probit system estimation. In addition we have argued that while the distribution of our error terms is unknown, our exclusion restrictions will allow identification even if the equation errors are not normally distributed. In this section we first report the results of re-estimating the system of equations reported above using the linear probability model. By imposing linearity in the probability, the test relaxes somewhat the restriction on the form of the distribution of error terms but at the cost of misspecifying the support of the probability measure. A linear probability measure will also help identify causality if the equivalent of an Inverse Mills Ratio is used for identification. For this reason we subsequently test for causality by using an appropriate generated regressor that replaces the Inverse Mills Ratio under a linear specification and also test whether the same regressor can capture causality in a nonlinear probability model (probit in our case). As our first robustness test, then, we re-estimated the entire set of probit equations reported above in the form of a linear probability model. Without including all of these results we can report that the results were broadly similar in almost all instances, indicating the same pattern of associations and correlations across equation residuals reported above. Because of their importance for our argument, we report, as column (2) in Tables 4a and 4b, the results of redoing the Heckman specifications reported in column (1). By inspection it can be seen that while the linear form of the test results in a decrease in the significance of some of the individual variables, the positive correlation found among the equation residuals in Table 4a remains very strong and significantly different from zero. In the opposite conditioning of the Heckman test, the expected negative 16

18 relationship is not found, the rho estimated there found to be insignificantly different from zero. In at least one version of the specification test, the linear probability model confirms our previous finding that business cycle peaks lead election calls. A second empirical issue arises because, in order to maximize the number of elections calls and business cycle peaks, a long time series is required and data limitations over a long time horizon restrict the data frequency to annual versus quarterly or monthly data. This implies that when elections and business cycle peaks arise at different points during the year, they are assigned more or less arbitrarily to one year or another. Hence as a second robustness test, we re-estimate the system using a weighted dating system where the yearly weights were the fraction of each year in which the election or business cycle peak took place. In the case of elections, if the election arose in July, then the election weight applied to the current year would be 5/12 while the remaining weight of 7/12 would be applied to the year that followed. For the business cycle peak we used as a weight the fraction of the year leading into the peak. Re-estimation on this basis is presented as column (3) in Tables 4a and 4b. Here the results are exactly opposite to the linear probability case reported in column (2). The positive correlation expected among the residuals of the two equations in Table 4a was found to be insignificantly different from zero, but the expected negative correlation in Table 4b was found and found to be significantly different from zero. While the individual predictions fit the data less well with this dating of events, in both of these cases the general pattern of correlations among the models residuals is consistent with the hypothesis that business cycle peaks trigger elections. We turn next to the question of causality in terms of the single probit equations that began our empirical analysis. Capturing this successfully would allow us an estimate of the importance of the triggering event. From Tables 1 and 2 where we have already shown that when each probit equation is estimated separately, neither the addition of the realized outcome nor the addition of the estimated probit of the other event has a significant effect on the likelihood function. Hence neither appears to have any significant effect on 17

19 the likelihood of realizing the other. On the other hand, our analysis of the system of probit equations has revealed that selection is an important issue and, when selection is an issue, the use of an unconditional probability both to estimate the causal effect and to correct for selectivity bias is not appropriate. With selection, the hazard of a business cycle peak or the hazard of an election can be shown to be an equivalent measure of the Inverse Mills Ratio that can control for the selection effect and identify causality properly. That is, when looking for the event that triggers selection, we are interested in what is happening in the very near future following that selection event. Because the hazard is a probability conditional in time that addresses specifically what happens in the very next period, the hazard better answers this question. The probit probability, on the other hand, is constructed independent of time and thus is less informative with respect to causality. Thus to the extent that an event triggering causality is indicated, we are more likely to find evidence of its effect through the use of the appropriate hazard specification. In our case this can be shown to be the Cox hazard (see Appendix B). In Table 5 we report the results of adding the two Cox hazards to the single equation models of Tables 1 and The upper half of Table 5 reports the model of business cycle peaks estimated first as a probit model and then as a linear probability model; the lower half of the table reports election model also estimated first as a probit model, then as a linear probability model. What is quite striking is that unlike the case when using the unconditional probit, the Cox hazard of a business cycle peak works well as an explanatory variable in both the election probit and the linear election probability model. The likelihood that the business cycle will peak this period given that it has not yet peaked is marginally significant in its effect on the likelihood of an election in the probit model (at 90 percent), but is highly significant in the alternative linear probability model (at 99 percent). While testing for causality with an equivalent Inverse Mills Ratio is more appropriate for linear models, our results suggest that using the same measure in a nonlinear (probit) model can capture the selection effect. 10 The Cox election hazard is constructed in Ferris and Voia (2010) and used in a test of the political business cycle in Canada in Ferris and Voia (2011). Our construction of the hazard of a business cycle peak is the subject of the separate note included as Appendix B below. 18

20 The electoral importance of the risk of a business cycle peak in generating an election call can be found from its marginal effect on the probit and the linear probability models. In both cases the estimated marginal effects are quite similar, for its marginal effect on the probit and for its marginal effect on the linear probability. The marginal effects can be interpreted as implying that a 1 percent increase in the hazard of a business cycle peak will increase the probability of an election by almost 6 percent. As argued earlier, reversing the conditioning should show evidence of a negative relationship between the likelihood of a business cycle peak conditional on the hazard risk that an election will arise this year given that an election has not yet arisen. Because a high value of the election hazard most often indicates a time period towards the end of a governing mandate when an election has not yet been called, the likelihood that a business cycle peak will be experienced in the immediate future is now less rather than more likely. The negative coefficient in the probit equation for business cycle peak hazard then provides additional support for the hypothesis that business cycle peaks drive elections rather than the other way around and reinforces our earlier findings. The effect and significance of the arrival of a business cycle peak on the likelihood of an election call can be seen most clearly diagrammatically. In Figure 2 the Cox election hazard is plotted for the two cases when a business cycle peak has arisen and when it has not. What stands out in that diagram is that the likelihood of having an election call given that one has not yet been made jumps dramatically when a business cycle peak arises in the middle years of a party s governing tenure. If the business cycle peak arises either very early or very late in a governing term, the arrival of a business cycle peak has no significant effect on the timing of an election call. However, if the business cycle peak arises before the necessity of calling another election, the arrival of a business cycle peak does influence strongly and positively the likelihood of an election call. ---insert Figure 2 about here--- As a final robustness test of our findings we estimate a log-linear accelerated failure hazard model. The results are reported in Appendix C and repeat the same general pattern as that found in the probit equations. In 19

21 particular, business cycle peaks can be seen to have no effect on the duration of an election cycle unless we correct for selection by using the risk of hazard in a business cycle peak. In the final table of the appendix it is shown that the Cox hazard of a business cycle peak accelerates dramatically the ending of a governing duration and the quantitative impact on the log duration implies a 5.6 percent marginal effect. A one percent increase in the hazard of a business cycle peak leads to a reduction in the duration of the governing cycle of about 6 percent. 6. Implications for Policy In the Public Choice literature it is sometimes argued that elections, particularly electoral surprises, have a positive effect on economic growth and so generate a political business/policy cycle (Nordhaus, 1975; and Frey and Schneider, 1978). Others within the same literature have argued that the desire to remain in office means that economic policy can and will be used to signal competence and so influence the probability of re-election (Rogoff and Sibert, 1988; Shi and Svensson, 2006). Still others argue that even without deliberate manipulation, the governing political party in a parliamentary democracy has an incentive to monitor economic performance and so optimally time its election call (Balke, 1990; Kayser, 2005; Berlinski, Dewan and Dowding, 2007; and Ferris and Voia, 2010). The significance of this paper is that for Canada over our time period evidence is found for only one of these hypotheses, namely the hypothesis of election timing. While the results are not inconsistent with some effect of elections on the business cycle and perhaps even with a role for monetary policy in relation to the business cycle, the data is most consistent with the hypothesis that a business cycle peak is a stronger determinant of an election call than vice versa. While the data is supportive of the hypothesis that business cycle peaks drive election calls, the establishment of a selection linkage between these events may also help to explain why public choice economists have had difficulty finding evidence of opportunism and/or a political business cycle (Drazen 2000; Persson and Tabellini, 2003). To see this note that in Canada since Confederation, fiscal policy been 20

22 always been countercyclical and increasingly so since Keynes (Winer and Ferris, 2008). This is consistent with our findings that business cycle peaks are consistently associated with lower levels of government spending and money growth and higher levels of taxation. Hence to the extent that political parties engage in opportunism and elections are timed to take advantage of the peaking of a business cycle, evidence of opportunistic spending may become lost in the aggregate through the countercyclical spending and tax changes that are changing in the opposite direction. The coincidence of elections and cycle peaks means that clear evidence of opportunism in parliamentary countries where elections times are not predetermined will be much harder to come by. In our case this may explain why the signs of the policy coefficient estimates are consistent with opportunism in the election equations but are not found to be significantly different from zero. 7. Conclusion In this paper we have argued that what appears to be a coincidence in the timing of business cycle peaks and election calls in Canada arises neither because the two events are generated by a similar set of causes nor because the two events are correlated because of common but unobserved covariates. Rather the two events appear together in time because the outcomes are sequenced in a specific way. To test whether it is business cycle peaks that lead election calls or elections that precipitate cycles peaking we use Heckman specification tests. The results suggest that it is the expectation of a business cycle peaking (given that the cycle has not yet peaked) that triggers an election call by the governing political party. Moreover the effect of a cycle peak is quantitatively significant, with a 1 percent increase in the hazard of a cycle peaking leading to a more than five times greater increase in the probability of an election arising. This effect is in addition to the way that higher growth rates have usually been thought to (positively) influence election calls. While the results are not inconsistent with elections having some influence on policy choices and hence on economic outcomes, the results are also insightful in explaining why evidence of a political budget cycle is 21

23 often hard to come by in countries with parliamentary governments. Because in such jurisdictions elections can be timed to take advantage of such advantageous circumstances as the arrival of a business cycle peak, evidence of opportunism in the spending, taxation or monetary expansion in government policy will tend to be lost as such policies encounter directly the normal constraint imposed by countercyclical policy arising at the top of the business cycle. 22