Political parties in Canada: What determines entry,exit and the duration of their lives?

Introduction

While political scientists have long been interested in political parties that achieve success (Berrington, 1985; Lucardie, 2007), articles by Pedersen (1982) and those in Harmel (1985) initiated interest in the emergence of short-lived parties that have often been considered marginal to the political process. Indeed, the continuous arrival of new parties has sometimes been viewed as a threat to political stability, particularly in emerging, post-communist countries (Powell and Tucker, 2014; Travits, 2008). In established democracies, the entry of new parties is more often viewed favourably, with some authors arguing that entry is needed for effective political competition (Aldrich, 1995; Mulligan and Tsui, 2015). From this perspective, the policies embodied in entering parties and the threat they pose to established parties help ensure the responsiveness of the political process to the evolving wishes of the electorate. In general, new parties form to promote underrepresented parts of the political spectrum (Meyer and Miller, 2015) or to break from existing parties whose platforms, leadership, or regional representation is insufficiently the representative of subgroup aspirations (Lago and Martinez, 2011). But while the reasons for the formation of new parties may be diffuse and idiosyncratic, as are often the reasons for ultimate success or failure, ¹ the times and circumstances under which new parties enter or exit the political area may exhibit greater commonality. In this article, we explore whether the lives of political parties in Canada have exhibited any such pattern. More particularly, we ask whether the entry, exit, and duration of Canadian political parties respond systematically to measurable characteristics of the political and/or economic environment. ²

The successful coexistence and electoral dominance of two founding political parties—the early coalitions that evolved into the Liberal and Conservative Parties of Canada—may suggest that the entry of new parties into the Canadian electoral process has been both infrequent and unsuccessful. Indeed, Canada’s adoption of a first-past-the-post plurality voting system is often thought to have made the emergence of new parties largely problematic. ³ However while the success of new parties is often fleeting, virtually all Canadian elections have experienced one or more entrant, with some having considerable success. Over the post Confederation period (1867 onward), there have been roughly three attempts per election to establish a foothold on the Canadian political landscape. Many have achieved moderate success, with three succeeding to form the official opposition. ⁴

The motivation for entry into the political system is perhaps too easily explained. The dimensionality of the issue space relative to the set of policies that any political party can hold makes it is unlikely that existing parties will generate the policy mix desired by all groups within the electorate. What is more difficult to explain is their choice to pursue group goals outside of the existing party system. With the arrival of new ideas, new leaders and an always changing social and economic landscape, groups wishing to promote change could choose to merge their proposals within the existing party structure. The choice to start their own party will in part be a function of the receptivity of established parties and the attention they can bring to the proposed cause versus the cost and likelihood of success as a new party dedicated to these ideas.

Cox (1997) provides the methodology most often used to explain entry. In this approach, a new party will enter the electoral arena if the expected benefit of seeking electoral support exceeds the expected cost of entry. Variables that can proxy participation benefits, entry costs, and likelihood of achieving threshold political support are then used to test the entry/exit hypothesis. In application, empirical work on new party entry and longevity has featured cross-country analysis (Bolleyer, 2012; Harmel, 1985; Hug, 2000; Nishikawa, 2010). Here institutions—differences in election rules, threshold requirements, entry conditions, and registration costs/subsidies—provide the primary observables used to explain why entry occurs more often in one country than another. ⁵ More recently, a specialized branch has focused on “excessive” entry rates in post-communist emerging economies (Powell and Tucker, 2014; Sikk, 2005; Travits, 2008). In this article, we take a time series approach and follow authors like Happy (1989), Chhibber and Kollman (1998), and Lucardie (2007) to apply the Cox analysis within a single country that has had a fundamentally unchanged political institutional structure.

Our analysis then tests and compares the relative strength of hypotheses advanced to explain political party life over Canada’s long 145-year (42 elections) history. In the following two sections, we analyze the party’s extensive margin—the decision whether to enter or exit the electoral process and extend that analysis to its net effect on party turnover or churning. ⁶ In the fourth, we look to characterize the hazard facing new political parties and the extent to which political and economic factors affect their life span or duration. The article concludes by summarizing our most important findings.

Setup and proposed test of a micro model of new party entry and exit

Following Cox (1997), a potential party chooses to enter the electoral process if the expected net benefit of entering an election as a new political party, ENB (entry), is positive. More formally, a new party will register as an entrant into the political process if

If each election presents a flow of potential party entrants with varying values of participation and probabilities of success, the existence of common setup and participation costs will divide the set potential entrants such that the marginal entrant is the one whose expected benefit just exceeds expected cost. It follows that if there were an increase (decrease) in the likelihood of new party electoral success or a fall (rise) in the cost of participation, the number of new parties entering would be expected to rise (fall). This forms the theoretical basis for the empirical test described below.

Once a party enters the electoral arena, however, the decision to continue will involve an optimal stopping rule. ⁷ That is, a party will continue to participate in elections only as long as the expected benefit of continuing exceeds its marginal cost of participating. Hence, the optimal stopping rule is to exit at the time when

Note that the exit decision differs from the entry decision not only because the perception of the benefit from participation may be more fully clarified only after entry but also because entry involves an additional set of once-and-for-all setup and registry costs. Once an entrant achieves success, entry costs become sunk so that the cost of continuation falls below the cost of entry. It follows that continuation can often be supported even if the realized benefits of continuation are lower than those needed to motivate initial entry. ⁸

While the two decision rules seem intuitively plausible, the hypotheses become testable only if we can identify factors whose change will alter the probability of success, the expected benefit of participation, and setup or continuation costs. The fact that the perceived benefits of electoral participation are typically unobservable means that operationalizing a time series test requires finding a set of variables that both span the entire time period and provide suitable measures of the other three components. In what follows, we discuss a set of measurable proxies in terms of four broad categories: the heterogeneity of the electorate, the rules and/or conventions that can affect party entry and/or exit, the cost of entering relative to continuing in the electoral process, and the role of economic circumstance.

We begin with the size and heterogeneity of the electorate as key determinants of the demand for political representation. One metric that has often been used to represent the relative size and heterogeneity of the voting pool is the proportion of the population with the right to vote (Berrington, 1985). In Canada, the right to vote has been continuously expanded, with each extension of the franchise broadening the characteristics of the voting pool, thus creating opportunities for new parties to cater to voter interests not previously reflected in party programs. ⁹ A similar measure of scale and diversity is the turnout rate where larger voter turnout typically reflects a broader set of interests. In the empirical work below, we proxy these dimensions of voter heterogeneity by the electoral participation rate, defined as the fraction of the population registered to vote (the franchise) times the fraction of eligible voters who choose to vote (the turnout rate). Higher participation rates are expected to increase entry and decrease exit.

Religious diversity has also been used as a measure of heterogeneity (Kotler-Berkowitz, 2001), reflecting the varying support given to different political parties. Canada is not an exception in this regard (Wilkins-Laflamme, 2016). The measure of religious diversity used in our empirical work is the inverse of a Herfindahl index of denominational shares, interpolated between censuses and averaged over the previous governing period. The hypothesis is that an increase in religious diversity will increase entry and diminish exit.

A third measure of heterogeneity—the proportion of recent immigrants in the population—has proven to be more controversial. On the one hand, the diversity introduced by new immigrant values can be viewed as increasing the scope for political representation outside of established parties. For this reason, higher immigration levels would be expected to increase entry (Ordeshook and Shvetsova, 1994). On the other hand, recent immigrants tend to locate in the same area, be concerned with the same fundamental issues, and often have a greater concern for political stability. This compactness often allows immigrant groups to acquire political leverage with a particular established party. ¹⁰ A more immediate impact can also come from the fear that immigration can arouse in nonimmigrant voters. A concern with the social and economic costs of integrating new arrivals, together with a fear of increased competition for lower skilled jobs, may lead to compositional shift in the vote toward the more conservative established parties and away from parties offering newer, less familiar programs (Mayda et al., 2018). Should the latter cases dominate, immigration will be associated with less entry and more exit.

Berrington (1985) among others points to institutions as factors that can make the electoral process more or less conducive to entry/exit. One such feature of Westminster parliamentary governments is the possibility of electing a minority government. Because such periods reflect a lack of consensus among voters for the policies of any existing party, the anticipation of minority government may open a window for new parties to enter while encouraging less successful parties to exit. ¹¹ This hypothesis is tested through a dummy variable (1 for elections featuring minority outcomes and 0 otherwise). A second type of political convention that has governed Canadian election practice has been the relaxation and/or suppression of electoral competition between the two main political parties during world wars (Berrington, 1985: 447). This reduction of regular party competition would be expected to increase the opportunity for new parties to capture disaffected voters. We test for this wartime effect on entry by including a dummy variable (1 vs. 0) for those elections held surrounding the two world wars.

When we turn from factors that influence the likelihood of success to the cost side, significant effects on entry/exit can be expected from changes to the rules that disadvantage entrants relative to incumbents and marginal versus established parties. ¹² One institutional change stands out in particular. In 1974, Canada introduced public funding for federal political parties by eliminating in stages party reliance on corporate and union contributions in return for the subsidization of election expenses and the granting of tax credits to individual contributors. ¹³ For a period, 2004–2011, subsidization also included a per-vote subsidy. However to qualify for public support, a party had to be registered and have received at least 2% of the vote in the preceding general election or 5% of the votes in districts in which it had a candidate (Jensen and Young, 2011). Political parties also received parliamentary research and staffing support but only if they maintained party status (which required them to hold a minimum of 12 seats in the House of Commons). It follows that by subsidizing more established political parties, the introduction of public funding implicitly discriminated both against entrants (MacIvor, 1996) and smaller parties that were unable to achieve moderate size. To capture the effect of public funding on entry/exit, we used two financial reform variables: a dummy variable, funding1974, covering 1974 onwards and a second dummy, funding2004, that targeted specifically the 2004–2011 time period (featuring the per-vote subsidy). ¹⁴ The aggregate effect is the sum of these two effects over the common period.

Finally, it is often hypothesized that poor economic conditions reduce an incumbent’s chance of electoral victory (Lewis-Beck and Stegmaier, 2000). The question here is whether the same conditions influence entry and/or exit. If the demand for political diversity is a normal good, the cost of raising funds for parties promising new policies and programs should be lower when times are good. Similarly, the cost of maintaining relatively unsuccessful political activity will be more difficult in times of economic distress. Hence, entry should rise when times are good while exits should fall. We test for these effects using the growth rate of per capita income and the inflation rate averaged over the previous governing interval. ¹⁵

The entry and exit data used as dependent variables come from the Parliament of Canada website. Because our data set begins with Confederation in 1867, all parties were at one time new so that dependent variables consist of the population of newly registered parties in each election. Using the entry and exit data, party life spans were calculated. In the database, there are 125 different named parties registered as running for Canada’s federal parliament between 1867 and 2015. ¹⁶ The timing of their entrance and exit over the 42 federal elections is shown in Figure 1.

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Figure 1.

Parties entering and exiting by election and date: 1867–2015.

Economic conditions for the pre-1926 period were collected from Leacy, Urquhart and Buckley (1983) and Urquhart (1993) while post 1926 data come from the Statistics Canada database (CANSIM II) and averaged over the time period of the government immediately prior to the current election. A complete list of variables with their sources is presented in the Online supplemental appendix.

Because the number of new parties that arrives in any election is always discrete, the entry/exit analysis that follows uses a Poisson count regression to test for the significance of our proposed set of political, institutional, and economic conditions affecting entry/exit. The specific equation used to test the separate entry and exit decisions, together with their combined effect as turnover or churning, can be written as

where in election number t, the covariates are defined in the paragraphs above and E ( N t ) is in the first instance the mean count number of entrants, in the second, the mean count of exits, before finally becoming their sum (as churning).

New party entry, party exit, and political party churning: Empirical results

The marginal effects of the covariates of the Poisson regression model of political party entry and exit across the 41 federal elections since 1872 are presented as columns 1 and 2 of Table 1. ¹⁷ The marginal effects on the aggregate are presented in column 3. From the regression statistics reported at the end of each column, it can be seen that the set of hypotheses provides no evidence of model misspecification and a regression fit consistent with the shape of the Poisson distribution explains between 27 and 40% of the variation in entrants/exits. To facilitate a comparison of the empirical results with the model’s predictions, we include the hypothesized sign for each marginal effect as the first item in the appropriate variable box of the entry, exit, and churning equations.

By inspection, it can be seen that virtually all of the estimated marginal effects on entry and exit in columns 1 and 2 appear with their predicted sign, with most being significantly different from zero. Greater voter heterogeneity, as reflected in higher participation rates and greater religious diversity, is associated with significantly higher entry. From column 2, it can be seen that both measures of heterogeneity are also associated with significantly higher exit rates. The continued presence of the two major parties throughout the time suggests that greater heterogeneity is associated with greater turnover among smaller sized political parties.

Greater diversity arising through a higher immigration can be seen to be associated with a fall in party entry and the number of parties exiting. The former effect on entry is not significant, while the latter effect is highly significant. Together, the data strongly contradict the hypothesis that higher immigration flows support greater political diversity through a larger number of political parties. The results are more consistent with the hypothesis that higher immigration enhances established political parties at the expense of entrants and smaller parties. ¹⁸

The coefficient estimates on the two institutional features argued to enhance the opportunities for potential entrants versus established political parties—consolidation during the world wars and the absence of voter consensus in periods of minority government—are not inconsistent with their expected effect on entry. The reintroduction of political competition following the end of the two world wars and, to a much lesser extent, the expectation of opportunity offered by periods of minority government are both associated with higher levels of new party entry. The estimated effects on exit, however, are weaker and not significant. In combination, only the effect of the two world wars does provide evidence consistent with restrained competition, increasing the total number of political parties.

The hypothesized effect of the way that public funding was introduced in Canada appears strongly in the data. The introduction of public electoral funding is associated with lower levels of new party entry, over the entire 1974–2015 time period and slightly more so in the 2004–2015 interval associated with the per-vote subsidy. The corresponding exit coefficients in column 2 are both stronger and more significant. The continued presence of the two dominant parties implies that public funding has favored established parties over smaller marginal parties and independent candidates. By reducing both entry and exit, the combined effect is more consistent with the predictions of the “carteling hypothesis” of Katz and Mair (1995), where established parties collude to advantage themselves at the expense of the fringe of smaller sized parties. (See Young, 1998, for an alternative view).

Finally, the prior economic environment is found to have had a significant effect on party entry and exit. Lower inflation and higher per capita growth rates are associated with higher rates of new party entry in column 1, while lower inflation and higher growth rates in column 2 are associated with lower rates of exit. Inflation appears to have had a more significant effect on both entry and exit, while real growth rates are significant only with respect to entry.

Before leaving the consideration of the entry and exit decisions, it is important to recognize that our methodology assumes that the two decisions are independent so that the entry decision, for example, is not made in anticipation of the exit decisions being made at the same time. To test this hypothesis, we ran the two Poisson decision equations simultaneously as a generalized structural system. Here a latent variable (constrained to 1 in the exit decision to reflect the relative strength of the integration of the two decisions) is used to indicate the degree to which one decision impacts the other. The results are presented in Table 1A of Online supplemental appendix.

What the results indicate is that the presence of the latent variable adds nothing to the explanatory power of the entry/exit equations. The coefficient is both small (−0.013) and insignificant (z = 0.25), indicating the two decision processes are independent. ¹⁹ This can be seen by the fact that the coefficient estimates in the second set of equations that assume independence (without the latent variables) are virtually identical to the estimates that include the use of the latent variable. The former set is also the Poisson regression equations whose marginal effects have been discussed as columns 1 and 2 in Table 1.

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Table 1.

Marginal effects on the number of new party entrants and exits in Canadian federal elections: 1872–2015 (absolute value of t-statistic in parenthesis using robust standard errors).

Predicted	Number of new parties		Number of parties exiting		Churn = entrants + exits
	Poisson regression		Poisson regression		Poisson regression
	Sign	(1)	Sign	(2)	(3)
Electoral participation rate	(+)	0.088*** (3.29)	(±)	0.061*** (3.22)	0.154*** (3.89)
Religion index	(+)	2.14** (1.92)	(±)	2.16*** (3.20)	4.77*** (5.57)
Average immigration rate (in prior governing period)	(±)	−0.601 (1.18)	(±)	−0.902** (2.38)	−1.61** (2.12)
Minority government	(+)	0.872 (1.26)	(+)	−0.100 (0.23)	1.14 (1.56)
World War elections	(+)	4.47** (2.31)	(−)	0.597 (0.82)	4.23** (2.53)
Public election funding (1974 onwards)	(−)	−1.81* (1.89)	(−)	−2.63*** (5.46)	−4.93*** (5.37)
Additional per-vote subsidy (2004–2011)	(−)	−0.719 (1.21)	(−)	−1.178*** (2.97)	−1.95*** (4.07)
Average inflation rate (in prior governing term)	(−)	−0.210** (2.76)	(+)	0.099** (2.39)	−0.054 (0.81)
Average growth rate of per capita income (in prior governing term)	(+)	0.066* (1.88)	(−)	−0.045 (0.97)	−0.013 (0.22)
Regression equation statistics
1. Number of observations		41		41	41
2. Regression pseudo R 2		0.270		0.372	0.400
3. Linktest (t value)
_hat		3.04***		3.54***	3.25***
_hatsq		−0.39		0.12	−0.91
4. Goodness-of-fit
Pearson		32.77		37.25	32.29
Prob > χ 2 (32)		0.38		0.203	0.403

* Significantly different from zero at 10%; **Significantly different from zero at 5%; ***Significantly different from zero at 1%.

While the entry and exit decisions are choices made by individual parties, what may be more important for the health of the political process is the rate at which political parties turnover. In the industrial organization literature, Schumpeter’s hypothesis of creative destruction has been used to explain the economic role of churning—the aggregate of firm entry and exit in an industry. In that literature, increased churning has been found to indicate higher rates of product innovation, productivity growth, and improved overall performance (Bartelsman and Doms, 2000). Although much productivity growth arises from incremental innovation by industry incumbents, “more radical” ideas and innovations have come from entrants who survive by driving out complacent incumbents (Acemoglu and Cao, 2015). To the extent that significant innovation arises through a similar process of creative destruction in the political arena, greater churning among political parties may stand as a proxy for the degree of innovation and competitiveness of the political process.

In column 3 of Table 1, the marginal effects of our covariates on the churning of political parties are presented. In terms of individual hypotheses, the heterogeneity of the electorate stands out for its strong effect on churning. Both entry and exit are larger for higher electoral participation as well as greater religious diversity. Moreover, the fact that the two coefficient estimates are insignificantly different from each other implies that this heterogeneity increases turnover without changing the number of parties. The composition of the party pool becomes newer rather than larger. Higher immigration flows have similar contractionary effects but the strength of the exit effect dominates entry to reduce turnover significantly. This reinforces our earlier conjecture that the Canadian data are more consistent with the hypothesis that higher immigration flows enhance the position of established parties.

In contrast to the effects of heterogeneity, economic circumstance exerts its strongest effect on the number of political parties. Good times in a business cycle are associated with increases the number of political parties, while poorer times see a reduction in their numbers. To the extent that new ideas and innovative programs enter through new parties, the results suggest that political innovation arising from this source is more likely arise in the upswing or ongoing boom period of a business cycle than in the following period of contraction.

The third distinctive feature of the churning data is the already noticed effect produced by the way public funding has been introduced in Canada. Here, the individual results of public funding on entry and exit are both significantly negative, reinforcing each other in their overall effect on churning. The data suggest that public funding has produced a powerful negative effect on both turnover and the number of political parties.

The duration of political party life

When we turn from entry and exit to determine the best representation of a political party’s intensive margin, it becomes apparent that simple characterization of typical party life will be difficult. Our early overview suggested that Canada has at least two different types of political parties: the present Liberal and Conservative parties that have dominated the entire period of Canadian political life and the large remainder whose entry has been spread across time and for whom duration has been more limited. ²⁰ Only in the latter case do life spans vary widely, with a large majority lasting for only a few elections. ²¹ A second feature of the data is that a large number of parties (23 in 2015) continue to survive beyond the end of our sample period. Hence, the duration data are both heterogeneous (due to the presence of characteristics of success that are not easily quantified) and right censored.

Because all the models used adjust for the right censoring of party duration, we begin by presenting the output of a discrete hazard model with nonparametric finite mixtures. ²² This is done to address directly the possibility that we have two distinct party types in the data—those that entered at Confederation and last versus those that enter later and live shorter lives. Here, the use of a semi-parametric discrete time proportional hazard model, where heterogeneity is modelled nonparametrically and set to mimic the observed breaks in the empirical hazard, allows for the presence of two distinct types of heterogeneity across political parties. A semi-parametric discrete time hazard model that allows for a discrete mixture form of heterogeneity (with frailty) is then estimated and compared to the same model estimated without allowance for heterogeneity. The results are presented in Figure 2. The effect that allowing for frailty makes to the covariate analysis is then shown in Table 2. ²³

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Figure 2.

Discrete hazard model with and without heterogeneity adjustment.

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Table 2.

Discrete time proportional hazard models with and without frailty.

	Without frailty		With discrete mixture
Failed	Coefficient estimate	t	Coefficient estimate	t
Incumbent competitors	−0.1612	−1.13	−0.1800	−1.24
Average growth per capita	0.0597	1.08	0.0496	0.87
Minority government	−0.6562	−1.52	−0.5681	−1.32
World war elections	−0.4100	−0.80	−0.8188	−1.58
Average inflation rate	0.0762	1.24	0.1440**	2.25
Average growth of government	−0.0228**	−1.96	−0.0208*	−1.74
Electoral participation rate	0.0311	0.81	0.0429	1.09
Public funding (1974 onwards)	−2.1210***	−2.66	−1.9746**	−2.33
Average immigration ratio	−0.6535	−1.66	−0.7162*	−1.76
Proportion of labor force in agriculture	−0.0297	−1.25	−0.0308	−1.27
Religion index	1.8860*	1.77	1.8335	1.61
du1	−4.2816	−1.7	−6.8596**	−2.38
du2	−4.0752	−1.68	−6.9767**	−2.54
du3	−3.2632	−1.29	−6.0982**	−2.11
du4	−4.1128	−1.56	−7.1510**	−2.41
du5	−4.9737	−1.78	−7.9899**	−2.56
Log likelihood	−225.11		−206.37
			m1_cons ≡ 0
			m2 _cons 3.2249	3.54
			logitp2 _cons 2.2275	4.49
			Prob(Type1) 0.097308	2.23**
			Prob(Type2) 0.902692	20.7***

Note: du(i) indicates the timing of successive kinks in the empirical hazard of Figure 2. * Significantly different from zero at 10%; ** Significantly different from zero at 5%; *** Significantly different from zero at 1%.

In Figure 2, the two dashed lines in comparison with the single solid line capture visually the two distinct hazards present in the data and the cost of not distinguishing between them. With the vertical axis representing the hazard and survival time on the horizontal axis, the model that allows for heterogeneity (the dashed lines) has two distinct types: the 2 type 1 parties that face a likelihood of exit that is low with little variation and the 104 type 2 parties whose hazard appears as the highest dashed line. Type 2 parties face a hazard that begins quite high (almost 30%) and then falls to vary about 15% between the 3rd and 15th elections before rising rapidly again beyond the 16th election. What is also apparent is that the height of the hazard function without heterogeneity (the solid line) is intermediate and reflects almost entirely the pattern suggested by the 104 type 2 parties. The effect of combining the two types together is then to mute the magnitude of the hazard faced by those parties entering elections following Confederation.

In Table 2, we present the results of testing the two forms of the nonparametric discrete time hazard model (with and without frailty) against the data. The results reinforce the picture presented in Figure 2—the model allowing for party heterogeneity (with frailty) both reduces significantly the log likelihood function and indicates that the probability of a second distinct party type is quite high. In addition, while both models find that public funding and higher growth rates of government size increase significantly the longevity of established political parties, allowing for frailty also results in the effects of inflation and immigration on exit risk now becoming significant.

The ability to distinguish two distinct party types in the data allows us to partition the data and focus solely on the type of hazard function that best describes the life spans of the 104 parties that have entered and will likely exit the electoral process. By dealing exclusively with a more homogenous set of parties, we have more confidence in the identification possibilities of standard parametric and semi-parametric hazard models. An additional benefit of having tested for two distinct party types is that we can provide a purely statistical basis of support for the existence of a Duverger-type dominant two-party system in Canada. ²⁴ The ability to isolate a separate grouping of two parties with virtually infinite life spans from a surrounding fringe of parties with varying degrees of finite electoral success reinforces the Duverger conjecture that in a first-past-the-post parliamentary system such as Canada’s expected number of parties that will survive in the long run will converge toward two.

To test whether a discrete or continuous survival time model can best describe the newly partitioned data, we first looked at models that are fully parametric before turning to models that are semi-parametric (in the sense that the baseline hazard can be nonparametrically identified). Figure 3 summarizes the results of applying all our different hazard specifications to the data by giving a visual representation of their ability to capture the actual hazard pattern present in the data (the solid-line empirical hazard in Figure 3).

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Figure 3.

Alternative representations of the hazard function.

As Figure 3 demonstrates that the empirical hazard function is non-monotonic, beginning high and falling dramatically before varying both up and down as survival time increases. Figure 3 also shows that the best fitting parametric model—the continuous (Gompertz)—cannot adequately capture the time pattern dictated by the empirical hazard. Because nonparametric estimation permits greater flexibility to encompass non-monotonic shapes, we turned to continuous and discrete semi-parametric model specifications of the baseline hazard. The plots in Figure 3 illustrate this feature. In relative terms, however, the continuous semi-parametric (Cox) hazard model can be seen to dominate its discrete counterpart (the c_log_log) in terms of its ability to capture the initial sharp downturn and overall shape of the empirical hazard.

Using the baseline estimate of the Cox model as our best representation of the survival hazard faced by a new party entrant, the plot confirms the earlier observation that duration dependence will not be monotonic. Survival risk is highest initially with continued survival encountering a hazard that falls continuously through the sixth election. Given survival until the sixth election, duration dependence then rises and falls before beginning a long continuous climb through the 13th election. Once the party survives into its 13th election, the hazard again falls. ²⁵ The pattern described suggests that to some extent success will breed success. For an entering party, initial acceptance is difficult but the risk of failure will fall once an election presence is established. The varying but rising hazard between the 6th and 13th elections suggests an interval during which voters determine which party is likely to be a long-term survivor and the party must decide whether its message still resonates with voters or has been absorbed by one of the major parties. Not all will be successful. ²⁶

The effects of the covariates in shifting the baseline hazard in our four performing hazard models are presented in Table 3. In interpreting these results, it is important to recognize that the β_i coefficient estimates in the first three columns measure proportional changes relative to the baseline hazard. Hence, a coefficient estimate significantly greater (smaller) than one is needed to indicate an increase (decrease) in the overall hazard. In the fourth column (for the c-log-log discrete hazard model), the hazard itself is estimated so that more conventionally a significant positive (negative) coefficient estimate will indicate an increase (decrease) in the likelihood of exit, given survival to that point.

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Table 3.

Hazard of party exit in Canadian federal elections: 1867–2011. (robust standard errors in parenthesis).

	Parametric (Gompertz) continuous hazard ratio (1)	Parametric (Weibull) continuous hazard ratio (2)	Semi-parametric (Cox) continuous hazard ratio (3)	Semi-parametric discrete hazard model hazard (4)
Incumbent competitors	0.848*** (0.049)	0.860*** (0.045)	0.879** (0.048)	−0.141* (0.076)
Electoral participation rate	1.036* (0.022)	1.033 (0.022)	1.024 (0.018)	0.039 (0.025)
Average immigration rate (prior governing period)	0.669* (0.150)	0.646** (0.142)	0.636** (0.136)	−0.367 (0.292)
Minority	1.008 (0.247)	0.943 (0.226)	1.182 (0.304)	−0.078 (0.030)
Average inflation rate (prior governing period)	1.021 (0.028)	1.017 (0.029)	1.024 (0.024)	0.037 (0.040
Average income growth rate per capita (prior governing period)	1.012 (0.044)	1.022 (0.044)	0.999 (0.045)	0.031 (0.052)
Average growth rate of government size (prior governing period)	0.989* (0.006)	0.987** (0.006)	0.992 (0.006)	−0.019** (0.009)
Public funding 1974	0.361*** (0.119)	0.315*** (0.107)	0.385*** (0.116)	−1.316*** (0.390)
Censored	4.687*** (2.15)	4.606*** (2.20)	4.279*** (1.873)	1.899*** (0.659)
Constant	0.640 (0.399)	0.534 (0.352)		−1.382* (0.746)
	/γ = −0.117	/ln_p = −0.078
		p = 0.925
		1/p = 1.081

* Significantly different from one at 10%; **Significantly different from one at 5%; ***Significantly different from one at 1%.

Despite the differences in their ability to capture the shape of the empirical hazard, the results for the effects of the covariates on the baseline hazard are broadly consistent across all four models. In particular, the impact of the incumbent competitors on the exit hazard is highly significant in all models. The intermediate-sized hazard ratio estimate of 0.860 (in column 2) indicates that the time to exit following an increase of one incumbent competitor is shortened by 16%. Of the two measures of voter heterogeneity, religious diversity and electoral participation, only electoral participation is found to be marginally significant and in only one of the four cases. However, the similar size of the coefficient estimates and their proximity to significance does suggest that greater electoral participation may increase the hazard of exit for small- to medium-sized parties. This would reinforce our earlier finding on the intensive margin, where greater electoral participation was shown to increase both party entry and exit rates.

All models concur in finding that periods of minority government, world wars, and the two measures of economic circumstance, inflation and per capita income growth rates, had no significant effect on average party life span. While the latter two economic variables had success in helping to explain the timing of party entry and exit, economic circumstance in itself does not appear to be important in determining long-term survival. On the other hand, higher growth rates of government size are associated with long-lived parties, significantly decreasing the hazard of exit in three of our four cases.

The two variables that stand out most prominently in the table are immigration flows during the previous governing period and the period following introduction of public election funding in 1974. Higher immigration rates are associated with a significant decrease in the hazard ratio in three of our cases. This is consistent with our earlier conjecture that greater immigration flows reinforce the position of established parties, in this case by decreasing the exit hazard and thus increasing expected life spans. Using the estimate from the continuous semi-parametric model, a unit increase in the average immigration rate is shown to reduce the hazard of party exit by 56%. Even stronger is the estimated impact on the risk of exit from the introduction of public funding for established political parties. Established political parties that were exposed to the new public funding policy (from 1974 onward) found their risk of exit (compared to parties that were not previously exposed) reduced by over 160%.

Conclusion

In this article, we have considered a number of specific hypotheses advanced to explain the life characteristics of political parties in Canada in the context of Cox’s (1997) model of political party entry. Analysis of the extensive margin finds that most hypotheses perform as expected, but with several unexpected results. For example, greater voter heterogeneity in the form of higher participation rates and greater religious diversity has had significant positive effects on both entry and exit with the net effect increasing the rate of party turnover rather than the number of political parties. On the other hand, economic circumstance appears to produce its strongest effect on the number of parties rather than turnover rate, suggesting that the business cycle plays an important role in changing the number of active political parties. Perhaps, our two most interesting findings are responses to the introduction of public funding and recent immigration flows. The public funding of political parties in Canada following 1974 appears to not only have reduced the outflow of existing parties but to have discouraged the inflow of entrants. The combined effect has been to reinforce the dominance of the established parties at the expense of both smaller sized parties and potential entrants. The data similarly indicate that higher immigration flows are associated with fewer party entrants and exits. This in turn suggests that the established political parties in Canada have been more successful in capturing immigrant support or that the fear of job competition and social disruption has led voters to shift support to more conservative established parties.

To determine the representation of party duration, we analyzed a variety of hazard models. That analysis indicated the presence of two distinct party types with respect to length of stay, a group of two that is always present and a grouping of all others that have variable lengths of stay and whose duration experience drives the overall risk of party exit. Hence, from an entirely theoretical perspective, duration analysis reinforces a variation of Duverger’s law as relevant for Canada—a set of two parties that exchange periods of governing and a fringe of ever evolving parties whose size and duration respond to changes in political and economic circumstances. A look at the measurable characteristics that have most strongly influenced the length of stay finds that public funding of political parties and increases in immigration decrease the hazard of exit and impact positively the length of stay. As such, the duration findings reinforce the findings made with respect to the extensive margin.

To the extent that the Canadian experience is indicative of factors that can influence new party entry and turnover in other Westminster-type parliamentary systems, our results suggest two significant policy insights. First, the attempt to open political access to a broader range of party choices by eliminating corporate and union support and substituting in its place public funding may in fact achieve the opposite result. Unlike Mendilow’s (1992) representation of the Israeli case where low qualifying thresholds led to a proliferation of new parties, Canada’s experience has been more consistent with public support entrenching established parties. The fear that increased immigration may lead to political instability through the growth of newer parties with more radical programs appears similarly unfounded. In Canada’s case, the opposite may be a more significant fear. That is, increases in immigration have been associated more with a reduction in the number of parties and the consolidation of voter support among older more established political parties. This in turn may have unduly restricted the flow of new ideas, innovative programs, and practices that would otherwise have contributed to a more progressive and efficient political party system.

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