The Lalonde Data

For all of our examples, we use data from the job training program analyzed in Lalonde (1986) and Dehejia & Wahba (1999). A subsample of the data consisting of the National Supported Work Demonstration (NSW) treated group and the comparison sample from the Population Survey of Income Dynamics (PSID) is included in MATCHIT, and the full dataset is available at http://www.columbia.edu/~rd247/nswdata.html.⁵

The variables in this dataset are in Table 1 below. One causal effect of interest is the impact that participation in the job training program, treat==1, had on real earnings in 1978, re78, for those that participated in the program, i.e., the average treatment effect on the treated (ATT):

$$E( ( =1) \vert =1)\; - \; E( ( =0) \vert =1),$$ (1)

where re78(treat=1) represents the potential outcome under the treatment of the job program, and re78(treat=0) under control. To be clear, note that the first term (inside the expectation) in Equation 1 is observed, whereas the second term is the unobserved counterfactual of real earnings if participants had not participated. The nature of causal inference is that one of the two terms in the difference will always be unobserved. The same expression of the ATT, in mathematical notation is:

$$E(Y_{1i} \vert t_i=1 ) \; - \; E(Y_{0i} \vert t_i=1).$$ (2)

Table 1: Description of Lalonde data

Name	Description
Outcome ($Y$)
re78	Real earnings (1978)
Treatment Indicator ($T$)
treat	Treated in job training program from March 1975-June 1977 (1 if treated, 0 if not treated)
Pre-treatment Covariates ($X$)
age	Age
educ	Years of education
black	Race black (1 if black, 0 otherwise)
hispan	Race hispanic (1 if Hispanic, 0 otherwise)
married	Marital status (1 if married, 0 otherwise)
nodegree	High school degree (1 if no degree, 0 otherwise)
re74	Real earnings (1974)
re75	Real earnings (1975)