¹ Burnham, Walter Dean, ‘The Changing Shape of the American Political Universe’, American Political Science Review, LIX (1965), 7–28CrossRefGoogle Scholar; Converse, Philip E., ‘Change in the American Electorate’, in Campbell, Angus and Converse, Philip E., eds, The Human Meaning of Social Change (New York: Sage, 1972), pp. 263–337Google Scholar; and Burnham, Walter Dean, ‘Theory and Voting Research’, American Political Science Review, LXVIII (1974), 1002–23.CrossRefGoogle Scholar

² Converse, , ‘Change in the American Electorate’, p. 288.Google Scholar

³ Converse, , ‘Change in the American Electorate’, p. 263.Google Scholar

⁴ For examples, see Abramson, Paul R. and Aldrich, John H., ‘The Decline of Electoral Participation in America’, American Political Science Review, LXXVI (1982), 502–21CrossRefGoogle Scholar; and Shaffer, Stephen D., ‘A Multivariate Explanation of Decreasing Turnout in Presidential Elections, 1960–1976’, American Journal of Political Science, XXV (1981), 68–95.CrossRefGoogle Scholar

⁵ See Clausen, Aage, ‘Response Validity: Vote Report’, Public Opinion Quarterly, XLI (1968), 56–64Google Scholar; Traugott, Michael W. and Katosh, John P., ‘Response Validity in Surveys of Voting Behaviour’, Public Opinion Quarterly, XLIII (1979), 359–77CrossRefGoogle Scholar; and Katosh, John P. and Traugott, Michael W., ‘The Consequences of Validated and Self-Reported Voting Measures’, Public Opinion Quarterly, XLV (1981), 519–35.CrossRefGoogle Scholar

⁶ As in Campbell, Angus, ‘Surge and Decline: A Study of Electoral Change’, in Campbell, Angus, Converse, Philip E., Miller, Warren E. and Stokes, Donald E., Elections and the Political Order (New York: John Wiley, 1960), p. 42.Google Scholar

⁷ See Campbell, , ‘Surge and Decline’Google Scholar and DeNardo, James, ‘Turnout and the Vote: The Joke's on the Democrats’, American Political Science Review, LXXIV (1980), 406–20.CrossRefGoogle Scholar

⁸ Here we ignore the fact that elections occur at discrete intervals and regard turnout as a continuous function of time. This simplifies the exposition of ideas without altering the essential features of the problem. The same results can be derived straightforwardly using more cumbersome difference equations.

⁹ It is necessary to entertain some range of values for θ_C because it is not clear how often ‘personal calamities’ prevent core regulars from reaching the polls. As a rough guide, we can use the self-reported rate of turnout among ‘strong partisans’ in the Michigan surveys, which is typically about 85 per cent. Of course, it is important to remember that the groups of ‘strong’ self-identifiers and core regulars need not be, and probably are not, equivalent. Nor is the measurement taken in the survey beyond suspicion.

¹⁰ The solutions involve non-linear combinations of the regression coefficients and the assumed value of

¹¹ Converse, Philip E., The Dynamics of Parly Support: Cohort Analyzing Party Identification (Beverly Hills, Calif.: Sage, 1976), p. 31.Google Scholar

¹² Converse, , The Dynamics of Party Support, pp. 71–2.Google Scholar

¹³ See Cavalli-Sforza, L. L. and Feldman, M. W., Cultural Transmission and Evolution: A Quantitative Approach (Princeton, N.J.: Princeton University Press, 1981).Google ScholarPubMed

¹⁴ Observe that this model is specified in the form of Equations 2a and 6.

¹⁵ See Draper, N. and Smith, H., Applied Regression Analysis, 2nd edn (New York: John Wiley, 1981), pp. 458–517.Google Scholar

¹⁶ Malinvaud, E., Principles of Econometrics (Amsterdam: North Holland, 1966), pp. 290–9.Google Scholar

¹⁷ Extensive experimentation with these models suggests that estimates that stray out of bounds or otherwise misbehave would be the more likely result of such misspecifications.

¹⁸ Abramson, and Aldrich, , ‘The Decline of Electoral Participation in America’.Google Scholar

¹⁹ It is noteworthy that the tables of Abramson and Aldrich (particularly Table 1) show the rates of turnout among ‘strong’ partisan identifiers to have been rock steady between 1960 and 1980 while those of weak and leaning identifiers declined. See Abramson, and Aldrich, , ‘The Decline of Electoral Participation in America’, p. 506.Google Scholar

²⁰ The estimated value of θ_c also goes badly out of bounds for the models of pure dealignment when the sample is extended to include the election of 1982 or those before 1964. Our methods therefore corroborate the findings of survey researchers whose evidence suggests that 1964 and 1980 mark the endpoints of the recent dealignment. For further information, see Wattenberg, Martin P., The Decline of American Political Parties, 1952–1980 (Cambridge, Mass.: Harvard University Press, 1984)Google Scholar and Converse, , The Dynamics of Party Support.Google Scholar

²¹ For corroborating evidence, see Brody, Richard A., ‘The Puzzle of Political Participation in America’, in King, Anthony, ed., The New American Political System (Washington, DC: American Enterprise Institute, 1978).Google Scholar

²² Any number of plausible variations of the contaminated model yield essentially similar (albeit even more volatile) results. Indeed, the only thing that is not volatile about these models is the consistency with which the contamination parameter turns up with the wrong sign. Details on numerous linear and non-linear versions of the contaminated model are available on request. In general, it is fair to say that these models press our small sample of cases to its limit for information about effects whose magnitude appears small in relation to the noise in the time series. In settings where there are more cases available or the effects of contamination are more pronounced, these models could be far more useful and instructive than they prove to be here.