LATE

Local average treatment effect is an approach to estimating treatment effects that acknowledges that the standard instrumental variable approach requires very strong and non-credible assumptions. As shown here, in order to estimate the average treatment effect we need to assume that the instrument is independent of the unobserved characteristics that determine both the policy variable and the outcome variable of interest. In addition, we need to assume that the effect of the instrument on the policy variable is constant across the population being studied.

This second requirement may not be credible. Consider the problem of estimating returns to schooling using an instrument associated with proximity to a college. David Card assumes that students who live close to a college will be more likely to attend college. The assumption requires that proximity to college has exactly the same impact on each student. This seems unlikely. In the LATE approach, students are broken up into four groups: compliers, always-takers, never-takers, and defiers. Compliers behave as we hope, they are students that do not go to college if they live far from a college and attend college if they live close to a college, always-takers attend college no matter where they live, never-takers do not attend college even it they live close by and defiers do exactly the oppose of what we hope, they go to college when they live far away and do not go to college when they live close by.

Splitting the students in this way, is not an assumption, but it has important implications. Consider the "intent-to-treat" analysis we did here. We looked at whether students who live close to college earn more than student who live far away. We can think of this as a "change" in proximity to college and we can think of the measured effect as occurring through a "change" in the likelihood of a student going to college. If we then look at our groups, we note that two of them do not "change." The only groups that change their behavior with changes in proximity to college are the compliers and defiers.

Now for the assumptions.

The first assumption is that there are no defiers. This is an economic or behavioral assumption. It is implied by the "law of demand." If we think of closeness to college as a "price" of attending college then students should not increase their demand when prices increase.

The second assumption is that the effect of the instrument on the policy variable is constant across the population of compliers. We cannot get away from this type of assumption. However, the hope is that it is more reasonable if we limit it to just the compliers. In our example it states that when a student goes from being far from a college to being close to a college (and they are a complier) then they go to college. You have to read this last sentence a couple of times to even notice the assumption. If the instrument and the policy variable are both discrete or yes/no variable like in our example, then the assumption seems pretty reasonable.

Given these assumptions we can use our intent-to-treat estimation and estimates on the difference in college attendance between those that live close to a college and those far from a college, to estimate the average treatment effect of attending college on "compliers."

Using this method we can estimate that college increasing earnings by about 10% per year of college for compliers (using the NLS 66 data, see below). Note that the IV estimates using proximity to college are higher than the estimate from simply using the observed difference income.

The LATE estimates still rely on assumptions about the causal mechanism. It is assumed that the observed difference in income for those that live close to college is due to fact that they attend college and not due to other differences between students that live close and far away from colleges.

While LATE is not the average treatment effect, there some argument that it is a more relevant measure. The problem with using the average treatment effect to evaluate policy is that most policies do not require the whole population to change treatment. If the FDA approves a new drug for AIDS, it may not be the case that every AIDS patient switches to the new drug. This means that the outcome of the policy change may be quite different from the outcome predicted by measuring the average treatment effect. A nice feature of the LATE estimate is that has a built in assumption that we are only looking at the impact of people likely to change their treatment.

Cameron, A.C. and P.K. Trivedi, 2005, Microeconometrics: methods and applications.

Card, D, 1995, "Using Geographic Variation in College Proximity to Estimate the Returns to Schooling, inn L.N. Christofides, E.K. Grant, and R. Swidinsky, editors, Aspects of Labor Market Behaviour: Essays in Honour of John Vanderkamp.

Imbens, G, 2010, "Better LATE Than Nothing: Some Comments on Deaton (2009) and Heckman and Urzua (2009)," in American Economic Review.

R Code

# load data in from proximity.zip

# http://davidcard.berkeley.edu/data_sets.html

x <- read.delim("nls.dat",sep="",header=FALSE, stringsAsFactors = FALSE) #SAS file

y <- read.csv("names.csv",stringsAsFactors = FALSE,header = FALSE) # created a file from the log file with the variable names.

colnames(x) <- as.vector(y$V1)

x$lwage76 <- as.numeric(x$lwage76)

E0 <- mean(x[x$nearc4==0,]$lwage76,na.rm = TRUE)

E1 <- mean(x[x$nearc4==1,]$lwage76,na.rm = TRUE)

P0 <- mean(ifelse(x$nearc4==0,1,0),na.rm = TRUE)

P1 <- mean(ifelse(x$nearc4==1,1,0),na.rm = TRUE)

LATE <- (E1 - E0)/(P1 - P0)

LATE/4 # to compare to standard estimates of an extra year of education.

# Comparing incomes of students who went to college and those that didn't.

(mean(x[x$ed76>12,]$lwage76,na.rm = TRUE) - mean(x[x$ed76<13,]$lwage76,na.rm = TRUE))/4