Control Function Methods in Applied Econometrics

Article Figures & Data

Table 1

Estimates of the log(wage) Equation

Explanatory Variable	1 OLS	2 2SLS	3 2SLS	4 CF	5 CF
educ	0.0747 (0.0036)	0.157 (0.052)	0.161 (0.054)	0.153 (0.048)	0.151 (0.048)
exper	0.0848 (0.0068)	0.119 (0.023)	0.120 (0.024)	0.116 (0.021)	0.115 (0.021)
exper²	−0.0023 (0.0003)	−0.0024 (0.0004)	−0.0024 (0.0005)	−0.0022 (0.0003)	−0.0022 (0.0003)
black	−0.119 (0.018)	−0.123 (0.051)	−0.121 (.062)	−0.107 (0.048)	−0.105 (0.048)
	—	—	−0.0008 (0.0408)	0.018 (0.006)	0.019 (0.006)
	—	−0.082 (0.048)	—	−0.082 (0.048	−0.106 (0.050)
	—	—	—	—	0.0019 (0.0010)
intercept	4.62 (0.07)	3.24 (0.88)	3.17 (0.91)	3.31 (0.81)	3.33 (0.81)
Observations	3,010	3,010	3,010	3,010	3,010

Notes: (i) Each equation contains dummy variables for living in an SMSA and living in the South. In addition, they include regional dummies for where the man was living in 1966 and an indicator of whether the man lived in an SMSA in 1966.
(ii) Standard errors for OLS and 2SLS are robust to heteroskedasticity.
(iii) In Column 2, the 2SLS estimates are equivalent to the CF estimates.
(iv) The standard errors for the CF estimates in Columns 4 and 5 are based on 1,000 bootstrap replications.

Table 2

Estimates of the math12 Equation

Explanatory Variable	1 OLS	2 2SLS	3 CF	4 2SLS	5 CF	6 CF
cathhs	1.49 (0.39)	2.36 (1.25)	1.59 (1.07)	2.06 (1.63)	2.30 (1.19)	−0.95 (1.75)
motheduc	0.714 (0.062)	0.713 (0.062)	0.714 (0.062)	0.620 (0.077)	0.714 (0.064)	0.709 (0.062)
fatheduc	0.893 (0.056)	0.887 (0.057)	0.893 (0.057)	0.908 (0.071)	0.886 (0.058)	0.876 (0.058)
Ifaminc	1.84 (0.14)	1.82 (0.14)	1.84 (0.14)	1.87 (0.18)	1.90 (0.15)	1.86 (0.15)
	—	—	—	1.61 (0.73)	−0.077 (0.262)	−0.085 (0.262)
	—	—	—	−0.198 (0.684)	0.089 (0.235)	0.184 (0.238)
	—	—	—	−0.688 (2.082)	−1.10 (0.61)	−0.691 (0.634)
	—	—	−0.061 (0.594)	—	−0.290 (0.632)	−1.52 (0.80)
	—	—	—	—	—	3.31 (1.31)
intercept	11.20 (1.25)	11.45 (1.29)	11.23 (1.28)	11.87 (1.62)	10.72 (1.37)	11.18 (1.38)
Observations	7,444	7,444	7,444	7,444	7,444	7,444

Notes: (i) Standard errors for OLS and 2SLS are robust to heteroskedasticity.
(ii) The standard errors for the CF estimates are based on 1,000 bootstrap replications.
(iii) Using the estimates from Column 6, the average treatment effect on the treated is 3.99 (t = 2.96) and the average treatment effect on the untreated is –1.27 (t = –0.73).

Table 3

Estimates of the inlf Equation

Explanatory Variable	1 Linear OLS	2 Linear 2SLS	3 Probit MLE	4 Probit CF	5 Probit CF	6 Probit CF
nwifeinc	−0.0033 (0.0002)	−0.0014 (0.0010)	−0.0091 (0.0010)	−0.0042 (0.0026)	−0.0001 (0.0028)	−0.0025 (0.0028)
educ	0.0350 (0.0026)	0.0300 (0.0035)	0.100 (0.008)	0.087 (0.010)	0.088 (0.010)	0.090 (0.010)
exper	0.0033 (0.0024)	0.00067 (0.00273)	0.0080 (0.0072)	0.0011 (0.0081)	0.0007 (0.0081)	0.0003 (0.0081)
exper²	−0.00023 (0.00005)	−0.00019 (0.00006)	−0.00062 (0.00006)	−0.00051 (0.00017)	−0.00049 (0.00017)	−0.00047 (0.00017)
kidlt6	−0.180 (0.016)	−0.183 (0.016)	−0.520 (0.045)	−0.512 (0.046)	−0.339 (0.064)	−0.346 (0.064)
	—	—	—	—	−0.000046 (0.000018)	−0.00029 (0.00012)
kidlt6 · nwifeinc	—	—	—	—	−0.0061 (0.0016)	−0.0058 (0.0016)
	—	—	—	−0.0052 (0.0027)	−0.0055 (0.0027)	−0.0273 (0.0072)
	—	—	—	—	—	−0.00052 (0.00013)
	—	—	—	—	—	0.00075 (0.00024)
intercept	0.333 (0.045)	0.371 (0.048)	−0.494 (0.130)	−0.390 (0.140)	−0.474 (0.141)	−0.422 (0.143)
	−0.0033 (0.0002)	−0.0014 (0.0010)	−0.0033 (0.0002)	−0.0015 (0.0009)	−0.00097 (0.00010)	−0.0015 (0.0010)
Observations	5,634	5,634	5,634	5,634	5,634	5,634

Notes: (i) Standard errors for OLS and 2SLS are robust to heteroskedasticity.
(ii) The standard errors for the CF estimates are based on 1,000 bootstrap replications.
(iii) is the estimated derivative-based average partial effect of nwifeinc, where the individual APEs are averaged across the entire sample.

Table 4

Average Partial Effects of nwifeinc at Different Quartiles

Notes: (i) Column 1 is for the probit estimates reported in Column 4 of Table 3, Column 2 corresponds to Column 5 in Table 3, and Column 3 corresponds to Column 6 in Table 3.
(ii) All standard errors are obtained from 1,000 bootstrap replications.