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Table 10 Estimates of divorce parameters, standard deviations, and marginal effects (average treatment effects of the treated) when correlation is restricted in the bivariate probit model

From: Effects of Parental Divorce on Teenage Children’s Risk Behaviors: Incidence and Persistence

  1995 2001
ρ Unrestricted –0.90 0.00 0.90 Unrestricted –0.90 0.00 0.90
Males
 Binge drinking 0.80
(0.44)
[0.07]
1.69**
(0.03)
[0.07]
0.23**
(0.05)
[0.08]
–1.24*
(0.03)
[0.05]
0.33
(0.53)
[–0.01]
1.26**
(0.03)
[0.01]
–0.02
(0.05)
[–0.01]
–1.34**
(0.04)
[–0.02]
 Alcohol consumption –0.02
(0.61)
[0.11]
1.58**
(0.03)
[0.13]
0.28**
(0.05)
[0.11]
–1.15**
(0.03)
[0.09]
–0.13
(0.46)
[–0.02]
1.21**
(0.04)
[–0.01]
–0.07
(0.05)
[–0.02]
–1.43**
(0.04)
[–0.02]
 Tobacco use 1.27**
(0.26)
[0.05]
1.77**
(0.04)
[0.03]
0.22**
(0.05)
[0.06]
–1.24**
(0.04)
[0.04]
0.23
(0.61)
[0.09]
1.64**
(0.03)
[0.09]
0.24**
(0.05)
[0.09]
–1.22**
(0.03)
[0.07]
 Marijuana use 0.98**
(0.26)
[0.06]
1.83**
(0.04)
[0.05]
0.27**
(0.05)
[0.07]
–1.22**
(0.04)
[0.05]
0.36
(0.45)
[0.09]
1.70**
(0.03)
[0.09]
0.26**
(0.05)
[0.09]
–1.20**
(0.03)
[0.07]
 Hard drug use 0.88**
(0.34)
[0.01]
1.89**
(0.05)
[0.00]
0.12
(0.07)
[0.01]
–1.40**
(0.05)
[0.01]
–0.21
(1.37)
[0.01]
1.79**
(0.05)
[0.00]
0.05
(0.06)
[0.01]
–1.41**
(0.04)
[–0.01]
Females
 Binge drinking 1.13**
(0.28)
[0.10]
1.80**
(0.04)
[0.09]
0.35**
(0.05)
[0.11]
–1.16**
(0.03)
[0.08]
0.69
(0.44)
[0.05]
1.46**
(0.03)
[0.06]
0.13**
(0.05)
[0.05]
–1.27**
(0.03)
[0.02]
 Alcohol consumption 0.92**
(0.30)
[0.11]
1.61**
(0.03)
[0.13]
0.26**
(0.05)
[0.10]
–1.24**
(0.03)
[0.08]
–0.15
(0.43)
[0.04]
1.46**
(0.03)
[0.06]
0.13**
(0.05)
[0.04]
–1.45**
(0.03)
[0.05]
 Tobacco use 0.89**
(0.33)
[0.08]
1.89**
(0.04)
[0.06]
0.35**
(0.05)
[0.08]
–1.17**
(0.04)
[0.06]
0.96*
(0.39)
[0.11]
1.73**
(0.03)
[0.11]
0.32**
(0.05)
[0.11]
–1.17**
(0.03)
[0.08]
 Marijuana use 1.03**
(0.25)
[0.06]
1.91**
(0.04)
[0.05]
0.32**
(0.05)
[0.07]
–1.21**
(0.04)
[0.05]
0.88**
(0.27)
[0.06]
1.77**
(0.04)
[0.05]
0.23**
(0.05)
[0.06]
–1.25**
(0.03)
[0.03]
 Hard drug use 0.88**
(0.32)
[0.01]
1.94**
(0.06)
[–0.01]
0.10
(0.07)
[0.01]
–1.46**
(0.06)
[0.00]
0.43
(0.34)
[0.01]
1.88**
(0.05)
[0.00]
0.09
(0.07)
[0.01]
–1.44**
(0.05)
[0.00]
  1. ρ is the restricted correlation coefficient
  2. Standard errors in parentheses
  3. Marginal effects (average treatment effects of the treated) in brackets
  4. The average treatment effects of the treated are calculated as
  5. \( TE = P(risk|x,divorce = 1) - P(risk|x,divorce = 0) = \frac{{\Phi_{2} \left( \bar{x}'\hat{\alpha },\,\bar{x}'\hat{\beta }\,+\,\hat{\delta },\,\rho \right)}}{{\Phi \left( {\bar{x}'\hat{\alpha }}\right)}} - \frac{{\Phi_{2} \left( - \bar{x}'\hat{\alpha },\,\bar{x}' \hat{\beta },\,-\rho \right)}}{{1 - \Phi \left( {\bar{x}'\hat{\alpha }} \right)}},\) where Φ2 is the CDF of the bivariate normal, Φ is the CDF of the normal, x’ are the mean of the variables used in both the divorce and risk equations, αˆ are the estimated parameters in the divorce equation, βˆ are the estimated parameters in the risk equation, δˆ is the estimated divorce parameter in the risk equation
  6. p < 0.05; ** p < 0.01