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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

From: The impact of easy and early access to old-age benefits on exits from the labour market: a macro-micro analysis

  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)  
  1. Data seasonally adjusted. Dependent variable: quarterly female participation rate (45+) or male discouraged worker rate (45+)
  2. asignificant at the 5% level; bsignificant at the 1% level
  3. Source: authors’ calculations; data sources: LFS and Central Statistical Office Poland