RDP 9801: Labour Market Adjustment: Evidence on Interstate Labour Mobility Appendix A: Unit Root and Cointegration Tests

Table A1 presents single equation tests of cointegration between state and national unemployment rates using the two step procedure suggested in Engle and Granger (1987). Table A2 applies the Johansen (1988) procedure to test for the number of cointegrating relations between the vector of state unemployment rates. Results from these tests are discussed in more detail in Section 4.

Table A3 presents stationarity tests on the variables in Section 5 of the paper. Unit root tests are conducted based on the methodology in Dickey and Fuller (1979, 1981).

The methodology of the panel unit root test is based on Im, Pesaran and Shin (1995). Their approach involves estimating an augmented Dickey-Fuller (ADF) regression for each variable and state, and comparing a statistic based on the average t-statistic on the lagged level variable against a critical value, to test the null hypothesis of a unit root. The authors present Monte-Carlo evidence which suggests this approach has good power in finite samples compared to alternative panel unit root tests.

The test employs the following test statistic (Im, Pesaran and Shin 1995, Equation 59 p. 16).

where N is the number of time series in the panel, is the average t-statistic from a series of univariate ADF tests on each variable (where the number of lags in the regression is determined using the Schwarz criterion), and a_NT and b_NT are the expected small sample mean and variance of the distribution of t-statistics under the null hypothesis of non-stationarity (found through Monte-Carlo simulation). This statistic is asymptotically distributed as a standard normal variable. The appropriate hypothesis is a one-sided test of z = 0 against the alternative z < 0.