*! version 2.0.0 Kenneth Houngbedji 14jan2016

Title

absdid -- Semiparametric Difference-in-Difference Estimator
of Abadie (2005)

Syntax

absdid depvar [if] [in] [,
tvar(varname)
xvar(varlist)
options
]

Heterogeneity
yxvar(varlist) list of variables which can modify the treatment
effect

Propensity score
sle set a logistic function to estimate the propensity score

order(#) set order of the polynomial function used to estimate the
propensity score

csinf(#) drop the observations of which the propensity score
is less than #

csup(#) drop the observations of which the propensity score is
greater than #

xvar(varlist) and yxvar(varlist) may contain factor variables
and interactions terms;
see fvvarlist.

Description

absdid implements the semiparametric difference-in-difference estimator of
Abadie (2005).

The estimator compares depvar (the change of the outcome of interest between
baseline and follow-up) across the treated (tvar(varname) == 1)
and the untreated (tvar(varname) == 0) groups. To address non-random
selection into treatment groups, the estimator adjusts for observable differences
between treatment groups at the baseline based on the list xvar(varlist)
of control variables.

Options

Mandatory

tvar(varname) is the binary treatment variable. It is required and should
be coded as 0 or 1, with 0 indicating an untreated observation
and 1 indicating a treated observation.

xvar(varlist) specifies the variables for the selection into treatment
equation. It is an integral part of the semiparametric difference-in-difference
estimator and is required. The selection equation should contain at least one
variable.

Heterogeneity

yxvar(varlist) specifies the variables which can modify the treatment effect.
By default the treatment effect is assumed to be constant.

Propensity score

sle forces to use a logistic specification to estimate the propensity score
(see Hirano et al.(2003)). This ensures for instance
that the estimated propensity score is always greater than 0 and less than 1. By
default the propensity score is estimated with a linear regression.

order(#) indicates the order of the polynomial function to be used to
estimate the propensity score. By default it is equal to 1.

csinf(#) troncates the observations of which the propensity score
is less than #. The default is csinf(0).

csup(#) troncates the observations of which the propensity score
is greater than #. The default is csup(1).

Example: Union-wage premium

Setup

. use "http://www.parisschoolofeconomics.eu/docs/houngbedji-kenneth/absdid.dta", clear

Estimate the union-wage premium

. absdid dlwage, tvar(union97) xvar(age black hispanic married i.grade)

Union-wage premium with the sle option

. absdid dlwage, tvar(union97) xvar(age black hispanic married i.grade) sle

Union-wage premium when the probability to be treated varies between 0.01 and 0.99

. absdid dlwage, tvar(union97) xvar(age black hispanic married i.grade) csinf(0.01) csup(0.99)

Union-wage premium using a polynomial function of order 4 to estimate the propensity score

. absdid dlwage, tvar(union97) xvar(age black hispanic married i.grade) order(4)

Variation of union-wage premium across age and education

. absdid dlwage, tvar(union97) xvar(age black hispanic married i.grade) yxvar(age hschool college)

Interaction terms

. absdid dlwage, tvar(union97) xvar(c.age##c.age black hispanic married i.grade) yxvar(c.age##c.age hschool college)

Stored results

absdid stores the following in e():

Scalars

e(N) number of observations

Macros

e(cmd) absdid

e(depvar) name of dependent variable

e(properties) b V

Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

Functions

e(sample) marks estimation sample

References

Abadie, A. 2005. Semiparametric Difference-in-Differences Estimators. Review of Economic Studies 72: 1--19

Hirano, K., Imbens, G.W. and Ridder, G. 2003.
Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score.
Econometrica 71(4): 1161--1189

Author

Kenneth Houngbedji,
Paris School of Economics, Paris, France. email: kenneth.houngbedji@psemail.eu.