¹ For example, in John Wilson, “The Myth of Candidate Partisanship: The Case of Waterloo South,” Journal of Canadian Studies 3 (1968), 21–31,CrossRefGoogle Scholar it is suggested that “candidate partisanship” had less effect than had been thought and probably motivated roughly 10 per cent of the electorate. Robert Cunningham, “The Impact of the Local Candidate in Canadian Federal Elections,” this JOURNAL 4 (1971), 287,Google Scholar also derives an average influence for local candidates of about 10 per cent. More recently, it is suggested by Clarke, H. D.Jenson, JaneLeDuc, LawrencePammett, Jon(Political Choice in Canada) [Toronto: McGraw-Hill Ryerson, 1979], 346)Google Scholar that the maximum influence directly attributable to local candidate effects is 5 per cent. Drummond, R. J.Fletcher, F. J. (“Political Communication and Orientation to Legislators among Ontario Voters, ”Google Scholar in Clarke, H. D.Campbell, ColinQuo, R. Q.Goddard, Arthur [ed.], Parliament, Policy and Representation [Toronto: Methuen, 1980], chap. 6)Google Scholar suggested that local candidate effects are small but significant; when asked an open question on what affected their votes, only 20 percent mentioned something connected to local candidates.

² for example Collie, M. P. (“Incumbency, Electoral Safety and Turnover in the House of Representatives, 1952–76,” American Political Science Review 75 [1981], 119)Google Scholar takes issue with the generally held view that incumbency has had increasing electoral value since the 1960s. The article also has a good bibliography of recent American work on incumbency. Some of the literature arguing for an increased incumbency effect is summarized in Patterson, S. C.“The Semi-Sovereign Congress,” in Anthony King (ed.), The New American Political System (Washington: American Enterprise Institute, 1980), 125Google Scholar. Patterson also observes that there “is no reason to believe that the high rate of return of incumbents to Congress sharply distinguishes it from parliaments in most other countries” (Ibid.., 143), and quotes evidence suggesting that incumbency was worth about 6 to 7 percent of the vote between 1966 and 1974 (Ibid., 144).

³ This type of model is described technically in Hildreth, C., Houck, J. p. “Some Estimators for a Linear Model with Random Coefficients,” Journal of the American Statistical Association 63 (1968), 584.Google Scholar This interpretation of the model was suggested to us by one of the anonymous referees of this JOURNAL.

⁴ Note that b_j and a_j do not vary within the subgroup to which j belongs. That is, the bars above these parameters indicate the expected value (mean) of the b³and a³, respectively, within a subgroup.

⁵ The error terms in equation (11) are independent with mean zero and variance equal to

If we assume that then the variance in expression (lla) becomes

Further, if we know, or assume, a value for c, then the problem reduces to one of heteroscedasticity which can be corrected by appropriately transforming the data. In this case, the transformation is to divide all variables including the constant term by the square root of the contents of the square brackets in expression (1lb). The sensitivity of our results to the assumption that c = 1 will be tested in the next section.

It was suggested earlier that a³ and ³ are likely to move together. If we drop the assumption that v and w are independent, but assume instead that they are perfectly correlated and each have the same standard deviation, then the error term in equation (11) has mean zero and variance , returning us to Model 1.

⁶ Equation (1) might have been written

where Z^j₁ and Z^j₂ are the votes for each of the other two parties in riding j (ignoring independents and minor parties) and ^c and d^j are the proportion of voters for each of those parties who defect to the party in question in the next election in ridingjThe aggregation being discussed implies that

where Thus b^j is a weighted average of c^j and d^j , where the weights are the relative votes of the other two parties which, of course, vary among ridings. Aggregation is only appropriate if c³ and d³are equal. In fact, the signs expected on c³ and d³ will likely depend on the relative position of the parties. For a discussion of this issue see, for example, Duff Spafford, “Electoral Systems and Voters' Behavior,” Comparative Politics 5 (1972), 129–34.

⁷ Model 2 is estimated using the adjustment described in footnote 5 with c =1.

⁸ The 1975 election was omitted because a major redistribution between 1971 and 1975 changed riding boundaries and altered the number of ridings in the province. The data used in this study are those published by the Chief Electoral Officer of Ontario.

⁹ Since by-elections invariably generate a new incumbent, it is not clear whether to use the by-election or the previous general election for P³_{x, i-1}. The special nature of these cases argued in favour of omitting them from the sample.

¹⁰ See, for example, Maddala, G. S.Econometrics (New York: McGraw-Hill, 1977), 259.Google Scholar

¹¹ Note that the sum of our dependent variable in each riding across all candidates must equal zero. This would imply that, if we estimated the equations as a system, the covariance matrix of the true disturbances would be singular, resulting in a nonestimatable system. We circumvent this problem by estimating equation by equation. While this may result in less efficient estimators, it does not alter the unbiasedness of the estimators.

¹² The Model 1 results are available from the authors on request.

¹³ In this paper, the term statistically significant means that the null hypothesis (generally that the coefficient is zero) is rejected at the .05 level.

¹⁴ See footnote 5 for a discussion of how the relative size of the variances affects the GLS adjustment. The relative variance (the term c in footnote 5) was changed within the range 0.25 to 4 with no significant change in the incumbency coefficient. For example, in the 1981 NDP equation, as c was increased from 0.25 to 4, the estimated coefficient on incumbency increased from 0.119 (standard error 0.019) to 0.124 (standard error 0.030).

¹⁵ In 1981, for example, there were 120 seats that had not had by-elections since 1977 (or were not in some other way special); of these, 107 had incumbents seeking re-election.

¹⁶ See Drummond and Fletcher, “Political Communication,” 104–06.

¹⁷ See Maddala, Econometrics, 198.

¹⁸ Recall that the significance level is assumed to be .05.

¹⁹ See Drummond and Fletcher, “Political Communication,” 103.