It is hard to identify treatment effects when individuals do not comply with their assigned treatment—when there are unobservable characteristics that determine whether the treatment was actually taken. But sometimes, we are fortunate. We know the assigned treatments or have information on what motivates individuals to be treated, an instrument. lateffects leverages this instrument to provide meaningful causal effects. This feature is a part of StataNow™.

lateffects estimates a local average treatment effect (LATE), a causal effect for a subpopulation. We would prefer to identify an effect for the entire population, but in many instances, this is not feasible. We cannot identify a treatment effect for the population because of unobservable differences between treated units and untreated units. Unaccounted for, unobservable differences confound any causal effect we would like to identify. However, in an experimental setting, we may know the treatment to which each individual was randomly assigned. Or in an observational setting, we may have a binary exogenous variable that encourages individuals to take a treatment. With such a variable that splits the population into treated and untreated units as if they were randomly assigned, we can identify a treatment effect for those that comply with the treatment assignment, a LATE. Because the effect is identified only for compliers, the estimand is sometimes referred to as a complier average treatment effect.

Without covariates, one can estimate a LATE using two-stage least squares. But when covariates are incorporated into the model, the equivalence breaks. In other words, using two-stage least squares may not give you the causal effect you want. lateffects gives you a LATE with and without covariates.

Let's see it work

We would like to study how participating in an elementary school program that targets reading ability, participate, affects the scores of a high school state exam used in college admissions, score. Enrollment in the program is voluntary. Therefore, participation is not randomized, which will confound the effects we are measuring.

Fortunately, there was a lottery that selected some individuals within schools to participate in the program and some to be controls. The lottery gave more weight to children in low-income households. Families of selected students received a small one-time cash transfer if they decided to participate. The binary variable selected is 1 for those selected to participate. Of course, not all that were selected by the lottery participated in the program, and some students participated regardless of the lottery outcome.

If the lottery had selected students randomly, we could use selected as an instrument and estimate the LATE. However, because we know that the lottery was based on income, we need to specify a model so that after adjusting for covariates, the selection is as if it were random. We conjecture that once we control for whether an individual lives in a rural area, rural—which are poorer than urban areas for our population—and for whether they live in a low-income zone, lowinc, the instrument is as good as randomly assigned. Using lateffects, we can fit a model to obtain a LATE of participating in the program on the exam score for those that complied with the treatment assignment. We type

. lateffects kappa (score) (participate) (selected i.lowinc i.rural)

We chose the normalized kappa weighted estimator for illustration. The first set of parentheses corresponds to the outcome, the second to the treatment, and the last to the instrument propensity-score model.

We obtain the following result:

. lateffects kappa (score) (participate) (selected i.lowinc i.rural)

Iteration 0:  EE criterion = 2.683e-19
Iteration 1:  EE criterion = 5.025e-31

Local average treatment effect                           Number of obs = 2,134
Estimator:       Normalized kappa
Outcome model:   Weighted Mean
Treatment model: Weighted Mean
IV pscore model: Logit



             
 
               Robust                                           
       score 
 
 Coefficient  std. err.      z    P>|z|     [95% conf. interval]
 
 
 
LATE         
 
                                                                
 participate 
 
                                                                
   (1 vs 0)  
 
   .8205241   .2101326     3.90   0.000     .4086717    1.232376

The LATE is 0.82. This means that for the subpopulation of students that comply with the lottery, scores on the state exam would be 0.82 higher on average if they all participate in the reading program than if none of them participates. Scores are measured on a continuous scale from 1 to 10.

Suppose that we believe it is important to consider a student's grade point average (GPA) in 2005, gpa2005, to model both the treatment and the outcome. To model treatment or outcome, we need the inverse-probability-weighted regression adjustment (IPWRA) estimator. We type

. lateffects ipwra (score gpa2005) (participate gpa2005) (selected i.lowinc i.rural)

Iteration 0:  EE criterion = 3.126e-19
Iteration 1:  EE criterion = 5.159e-31

Local average treatment effect                           Number of obs = 2,134
Estimator:       IPW regression adjustment
Outcome model:   Linear
Treatment model: Logit
IV pscore model: Logit


             
 
               Robust                                           
       score 
 
 Coefficient  std. err.      z    P>|z|     [95% conf. interval]
 
 
 
LATE         
 
                                                                
 participate 
 
                                                                
   (1 vs 0)  
 
    1.07929   .1433535     7.53   0.000     .7983219    1.360257

The LATE is larger when we account for GPA. However, in both cases, it is around 1 point.

After lateffects, we can inspect whether the treatment assignment is as if it were random after controlling for covariates. We may type

. latebalance summarize

Covariate balance summary


 Number of observations 
 
        Raw    Weighted
 
 
 
                  Total 
 
      2,134       2,134
  Assigned to treatment 
 
        612   1,066.896
    Assigned to control 
 
      1,522   1,067.104




                
 
Standardized differences          Variance ratio
                
 
        Raw    Weighted           Raw   Weighted
 
 
 
         lowinc 
 

             1  
 
   .3099247    .0001318      1.710866   1.000252
                
 

          rural 
 

             1  
 
   .2250566    .0002798      1.346618   1.000404

In the first table of the output, we see that after weighting by the probabilities of being assigned to treatment or control, the treatment and control groups are roughly balanced relative to the sample, which has 612 observations assigned to treatment and 1,522 assigned to be controls. Similarly, we see that the standardized differences after weighting are close to 0 and the variance ratios are close to 1. This suggests that after controlling for covariates, treatment assignment is as if it were random. This provides support for our modeling choices.

There is much more we can do. Above, we fit a linear model. When we have a binary, count, or fractional outcome, we can fit probit, logit, Poisson, fractional probit, or fractional logit models. We can also further check assumptions. We could verify that the overlap assumption is satisfied using lateoverlap. Additionally, we could look at the mean of covariates for the compliers to characterize the complier subpopulation using estat compliers.