Table 3 Female participation rate regressed on the lagged unemployment rate, and male discouraged worker rate regressed on the lagged male unemployment rate, long-term, ECM and asymmetric ECM estimate results
Female participation rate (45+) | Male discouraged worker rate (45+) | |||
|---|---|---|---|---|
Coefficient | Standard error | Coefficient | Standard error | |
Long-term relationship | ||||
unemployment rate−10 | −0.129b | 0.025 | ||
unemployment rate−5 (males 45+) | 0.039b | 0.009 | ||
\( {\overline{R}}^2 \) | 0.360 | 0.286 | ||
LM (p value) | 41.295 (0.00) | 14.94 (0.00) | ||
ADF (p value) | −2.172 (0.03) | −3.290 (0.00) | ||
Error correction model | ||||
Δunemployment rate | 0.240a | 0.100 | ||
Δunemployment rate−3 (males 45+) | −0.081a | 0.035 | ||
\( {\widehat{\varepsilon}}_{t-1} \) | −0.267b | 0.080 | −0.449b | 0.108 |
\( {\overline{R}}^2 \) | 0.247 | 0.280 | ||
LM (p value) | 2.281 (0.12) | 1.065 (0.35) | ||
ADF (p value) | −5.951 (0.00) | −6.214 (0.00) | ||
Error correction model—long-term asymmetry | ||||
Δunemployment rate | 0.324b | 0.109 | ||
Δunemployment rate−3 (males 45+) | −0.077a | 0.036 | ||
\( {\widehat{\varepsilon}}_{t-1}^{+} \) | −0.104 | 0.123 | −0.376a | 0.154 |
\( {\widehat{\varepsilon}}_{t-1}^{-} \) | −0.404b | 0.112 | −0.521b | 0.152 |
\( {\overline{R}}^2 \) | 0.280 | 0.271 | ||
LM (p value) | 2.00 (0.15) | 0.769 (0.47) | ||
ADF (p value) | −7.30 (0.00) | −6.352 (0.00) | ||
Wald test long-term asymmetry (p value) | 1.71 (0.095) | 0.669 (0.51) | ||
Error correction model—short-term and long-term asymmetry | ||||
Δunemployment rate+ | −0.214 | 0.238 | ||
Δunemployment rate− | 0.636b | 0.161 | ||
\( \varDelta \mathrm{unemployment}\ {\mathrm{rate}}_{-3}^{+}\ \left(\mathrm{males}\ 45+\right) \) | −0.068 | 0.058 | ||
\( \varDelta \mathrm{unemployment}\ {\mathrm{rate}}_{-3}^{-}\ \left(\mathrm{males}\ 45+\right) \) | 0.013 | 0.233 | ||
\( {\widehat{\varepsilon}}_{t-1}^{+} \) | 0.108 | 0.144 | −0.263 | 0.194 |
\( {\widehat{\varepsilon}}_{t-1}^{-} \) | −0.651b | 0.144 | −0.536b | 0.159 |
\( {\overline{R}}^2 \) | 0.361 | 0.206 | ||
LM (2 lags) (p value) | 1.003 (0.38) | 0.109 (0.90) | ||
ADF (p value) | −6.697 (0.00) | −6.792 (0.00) | ||
Wald test short-term asymmetry (p value) | −2.514 (0.02) | −0.983 (0.33) | ||
Wald test long-term asymmetry (p value) | 3.080 (0.00) | 1.080 (0.29) | ||