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To evaluate the policy effects and net out the possible confounding effects of cyclical and seasonal factors on the composition of separations, we developed a set of time series regressions, using the following as right hand side variables: seasonal dummies, measures of aggregate business conditions, and dummy variables for the different policy regimes affecting UI eligibility. In developing these models, we noted that the business cycle measures that we have are (potentially) closely related to the dependent variable. (Unemployment rates, for example, are clearly affected by the size and composition of separations.) For this reason, only lagged business cycle variables, rather than contemporaneous ones, were used to avoid simultaneity bias. The measures employed as independent variables are Statistics Canada's Help Wanted Index (HWI), always divided by 10, and the age-specific unemployment rate derived from the Labour Force Survey.

All of the times series used were tested for zero frequency unit roots, using augmented Dickey-Fuller tests with Phillips-Perron provisions for autocorrelation. A set of monthly dummy variables to account for the seasonality was also included. Following Davidson and MacKinnon (1993, p. 705), since these monthly dummy variables are non-stochastic and of the same order as the constant, their inclusion does not change the asymptotic distribution of the test statistics. Most of the series strongly reject the null of a unit root, although one of the ROE series has a test statistic that is very close to the critical value at the 10% level but which cannot reject the null hypothesis. This is not unexpected, given the large number of series tested. All of the series are taken to be stationary.¹³

In order to allow individuals to respond less than instantaneously to business cycle conditions and UI policy changes and to account for autocorrelation in the residuals, we included lagged dependent variables which can be interpreted as partial adjustment effects. Given all these considerations, we selected an autoregressive distributed lag model of the form:

View Formula

as the base from which to test down to the final model. In addition to t- and F-tests, the Akaike (1973) and Schwarz (1978) information criteria are used in model selection. We never tested for p or r larger than 3 and q or s larger than 15 for the lagged dependent (y) or business cycle (x) variables. The use of dummy variables, as opposed to seasonal differencing, is discussed in Harvey (1981). The policy variable approach is what Mills (1990, chaps. 12 and 13) terms intervention analysis; each policy indicator is set to 1 in its policy interval and is zero elsewhere. The summations of j and l, starting at 12, in equation (7) capture the monthly nature of our data and permit the most flexibility in reducing the parameters set.¹⁴ In contrast, to facilitate comparisons, we wanted to use the same specification across similar equations where feasible and, therefore, include business cycle variables beyond the minimum number in some of the regressions.

A linear time trend (t) is retained in all of the regressions. As might be expected, given the potentially high partial correlation between a step function and a time trend, its inclusion affects the policy variables. While the Akaike and Schwarz criteria reject the trend for some of the series, it is maintained in all of the regressions to facilitate comparability.

Substantial testing for autocorrelation was carried out since; in the presence of lagged dependent variables, inconsistency would result had it been present. A variety of Breusch (1978) - Godfrey (1978) type tests using artificial regressions were conducted; those for residuals lagged once and 12 times are presented for each equation. Breusch and Pagan's (1980) Lemieux-MacLeod (LM) tests for autocorrelation (not shown) of various orders were also checked. While a small number of these test statistics are significant at the 10% level, this is considered to be normal, given that 24 lags were tested for each regression. We are satisfied that autocorrelation is not a problem. Testing, however, did reveal heteroskedasticity in many of the regressions. Heteroskedasticity-consistent estimates of the error terms have therefore been used throughout the paper, since the series are sufficiently short to make us reluctant to model the heteroskedasticity directly.

In equations with lagged dependent variables, the independent variables can be interpreted as having both long- and short-run effects (e.g. Johnston 1984, p. 350). The short-run effect is the coefficient on the variable. Because of the autoregressive nature of the equation, the long-run equilibrium is approached asymptotically. The specification is, however, restrictive in that all of the right-hand-side variables are forced to have the same adjustment process. Further, the policy variables affect relatively few observations and are less numerous and less significant than the business cycle variables. The magnitude of the long-run effects of the policy variables should, therefore, only be viewed with caution.

Footnotes

13

This is consistent with Lee and Siklos (1991), who find no unit roots in the raw Canadian quarterly unemployment rate at either the zero or seasonal frequencies.

14

A common parsimonious specification of the lag structure on either the dependent or independent variable is: (1-B)p(1-B 12), where B is the lag operator. Our specification captures this intuition, but allows us to drop higher order lags (the interactions of the lags from the first term with B12) if they are rejected by our information criteria. Conserving degrees of freedom is important in this application, since our series are relatively short.