Estimation taking account of sample selection with Stata

Cheti NicolettiISER, University of Essex

2009

• Estimation commands:

truncreg, tobit,

heckman, heckprobit,

treatreg, ivreg

• Other useful commands:ivprobit, ivtobit

• Useful option in the estimation commands:

pweights

truncreg• The truncreg command is useful to estimate regression

models with a truncated sample• Ex: Health insurance claims observed only when amount

claimed is higher than a fixed threshold.

truncreg y x1 x1 x2 … xk , ll(c)

),0( 2* Niidxy

xc)YE(Y that soc y*ifonly * yobserve we

Normal Truncated yobserve We ~** cyy

xc

and where

1

tobit

• The tobit command is useful to estimate regression models with a censored dependent variable (deterministic censure)

• 3 Different types of models:Tobit with fixed censoring value (tobit)Censored regression with varying censoring

value (cnreg)Regression with interval data (intreg)

tobit• Tobit first type (consumption of a good)

tobit y x1 x2 … xk , ll(0)

tobit y x1 x2 … xk , ul(c)

),0( 2* Niidxy

0if 0

0if*

**

y

yyy

cyc

cyyy

*

**

2 if

if

cnreg

• Tobit first type Ex. minimum wage with different levels in different years

• cnreg y x1 x2 … xk censored(d)

),0( 2* Niidxy

index individual the is if

ifi

cyc

cyyy

iii

ii

i *

**

otherwise

if

1

0 *

ii

i

cyd

intreg• Interval data regression (Ex:Bracket information on

income for people refusing to give the exact value)

• Whet yi* is not declared we observe the range to which yi* belong

(0, 5000], (5000,15000], (15000,30000], (30000,+∞] say (ai, bi]

otherwise0

declared is of valued exact the if *1 yd

n

i

d

ii

d

ii

ii

abxyL

1

12

2

*

2

1exp

2

1

),0( 2* Niidxy

Estimating the regression with interval data in Stata

The command intreg needs two variables to define the dependent variable, say y1 and y2

intreg y1 y2 x1 x2 … xk

Individuals giving y1 y2

An exact value of their income

Example

A range for their incomeExample

Example

y*

5980

y* in (a,b)(5000, 15000]

(30000, +∞]

y*

5980

a5000

30000

y*

5980

b15000

.

heckman• The heckman command is used to estimate Generalized Tobit or

Tobit of the 2nd type using ML estimation (default option) or the two-step estimation (option [twostep])

heckman y x1 x2 … xk, select(z1 z2 … zs)

heckman y x1 x2 … xk, select(d = z1 z2 … zs)

heckman y x1 x2 … xk, select(z1 z2 … zs) twostep

),0( 2* Niidxy )1,0(* Niidvwherevzd

otherwise0if 0

srespondentfor 0if1

otherwise .

0if*

***

d

dd

dyy

heckprobit• The heckman command is used to estimate a probit

model with selection (option twostep does not exist because inconsistent)

heckprobit p x1 x2 … xk, select(z1 z2 … zs)

)1,0(* Niidvwherevzd

otherwiseif

responds th-i individual if if

otherwise

if

00

01

.

0*

***

d

dd

dpp

otherwise

if

0

0*1*)1,0(*

ypNiidxy

i

d

i

dp

ii

p

iiiiii ZZXZXL 11

22 )(),,(),,(

Impact of an endogenous dummy Homogenous treatment effect

y1= earnings for trained people

y0= earnings for non-trained people

d dummy indicating participation to the training program

y=y1 d +y0 (1-d)

y=x+ d+

d*=z +u where d=l(d*>0)

We have a selection problem because of the correlation

between u and . This implies that d is not independent of .

1

,0

0 2

uNiidu

treatreg

• The treatreg command is used to evaluate the effect of a endogenous binary variables (treatment, program, …) on a continuous variable of interest (see previous slide).

treatreg y x1 x2 … xk , treat(d=z1 z2 … zs)• Ex: Sample of graduated students with and without a

master degree • y=log earnings, d=1 if master degree, 0 otherwise• x = age, age square, d, sex, type first degree• z = mother’s level of education, father’s level of

education, sex, type first degree

How to use weights in Stata• Most Stata commands can deal with weighted data. Stata

allows four kinds of weights:1. fweights, or frequency weights, are weights that

indicate the number of duplicated observations.2.pweights, or sampling weights, are weights that

denote the inverse of the probability that the observation is included due to the sampling design and or nonresponse.

3.aweights, or analytic weights, are weights that are inversely proportional to the variance of an observation; i.e., the variance of the j-th observation is assumed to be sigma^2/w_j, where w_j are the weights.

4. iweights, or importance weights, are weights that indicate the "importance" of the observation in some vague sense.

Option pweights• Usually sample surveys provide weights to take account of sampling

design and nonresponse. • Let p be individual weight• Then we can run a regression with weighted observationsregress y x1 x2 … xk [pweight=p]

• Let us assume to have a sample with a sample selection problem (due to observables), then we can use propensity score weighting

• A possible “simplified” way to estimate your own weights is described in the following:

probit d z1 z2 … zs

predict propgen invprop=1/propreg y x1 x2 … xk [pweight=invprop]

For complex survey design it is better to use

• svyset [pweight=p]

• svy: regress y x1 x2 … xk

• svyset have options for cluster sampling designs or other complex design

• Declare survey design for dataset

• svyset [pweight=p], strata(stratid)

ivreg

• The ivreg command is used to estimate regression model by using instrumental variables for potential endogenous explanatory variables.

• Evaluation of the impact of years of schooling on earnings

y=x+ d*+ Problem: d* and are correlatedSolution 1: IV estimation ( IV=z: parental interest in the

child education, bad financial shock of the family when the child is age 11-16, presence of older siblings, Blundell et al 2003)

ivreg y x1 x1 x2 … xk (d*=z1 z2 … zs)

STATA program for evaluation

Abadie A., Drukker D., Herr J.L., Imbens G.W. (2001), Implementing Matching Estimators for Average Treatment Effects in Stata, The Stata Journal, 1, 1-18 http://ksghome.harvard.edu/~.aabadie.academic.ksg/software.html

Becker S.O., Ichino A. (2002), Estimation of average treatment effects based on propensity scores. The Stata Journal, 2, 358-377 http://www.lrz-muenchen.de/~sobecker/pscore.html

Sianesi B. (2001), Implementing Propensity Score Matching Estimators with STATA, UK Stata Users Group, VII Meeting London, http://ideas.repec.org/c/boc/bocode/s432001.html

Text Book References:• Amemiya T. (1985), Advanced Econometrics, Basil Blackwell,

Oxford. • Gourieroux C. (2000),  Econometrics of Qualitative Dependent

Variables, Cambridge University Press, Cambridge. • Greene W.H. (2000), Econometric Analysis, Third edition, Prentice-

hall, London. • Maddala G. S. (1983), Limited-Dependent and Qualitative Variables

in Econometrics, Cambridge University Press, Cambridge.• Wooldridge J.M. (2002), Econometric Analysis of Cross-Section and

Panel Data, MIT press• Lee M. (2005) Micro-Econometrics for policy, program and

treatment effects. Advanced Text in Econometrics. Oxford University Press, Oxford

Survey Articles:• Angrist J. (2001), Estimation of Limited-Dependent Variable Models with Binary

Endogenous Regressors: Simple Strategies for Empirical Practice,” Journal of Business and Economic Statistics, 19, 2-28.

• Angrist J.D., Krueger A.B. (1999), Empirical strategies in labor economics, published as working paper Princeton University, 401, and in O. Ashenfelter and D. Card, eds., Handbook of Labor Economics, Volume 3A, Amsterda,, 1277-1366.

• Blundell R., Costa-Dias M. (2002), Alternative approaches to evaluation in empirical microeconomics', published as IFS, Cemmap working paper, 10, and in Portuguese Economic Journal, Vol.1, 91-115, 2002.

• Blundell R., Powell J.L. (2001), Endogeneity in nonparametric and semiparametric regression models, IFS, Cemmap working paper, CWP09/01, Chapter 8 in Advances in Economics and Econometrics , M. Dewatripont, Hansen, L. and S. J. Turnsovsky (eds.), Cambridge University Press, ESM 36, pp 312-357,2003.

• Heckman J.J., Ichimura H., Smith J.A., Todd P. (1998), Characterization of Selection Bias Using Experimental Data, Econometrica, 66, 1017-1098.

• Heckman J.J., LaLonde R.J., Smith J.A. (2000), The economics and econometrics of active labor market programs, in O. Ashenfelter and D. Card, (eds.), Handbook of Labor Economics, vol. 3, North Holland, Amsterdam.

• Moffitt R. (2004), An introduction to the symposium of matching econometrics, Review of Economics and Statistics, vol. 1, a collection of articles on matching by various authors.

• Vella F. (1998), Estimating models with sample selection bias: a survey', The Journal of Human Resources, vol. 3, 127-169.