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Estimation taking account of sample selection with Stata

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Estimation taking account of sample selection with Stata

Cheti Nicoletti

ISER, University of Essex

2009

- Estimation commands:
truncreg, tobit,

heckman,heckprobit,

treatreg, ivreg

- Other useful commands:
ivprobit, ivtobit

- Useful option in the estimation commands:
pweights

- 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)

- 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 first type (consumption of a good)
tobit y x1 x2 … xk , ll(0)

tobit y x1 x2 … xk , ul(c)

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

- cnreg y x1 x2 … xk censored(d)

- 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]

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

intreg y1 y2 x1 x2 … xk

- 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 yx1 x2 … xk, select(z1 z2 … zs)

heckman yx1 x2 … xk, select(d = z1 z2 … zs)

heckman yx1 x2 … xk, select(z1 z2 … zs) twostep

- The heckman command is used to estimate a probit model with selection (option twostep does not exist because inconsistent)
heckprobit px1 x2 … xk, select(z1 z2 … zs)

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 .

- 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 yx1 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

- Most Stata commands can deal with weighted data. Stata allows four kinds of weights:
- fweights, or frequency weights, are weights that indicate the number of duplicated observations.
- 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.
- 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.
- iweights, or importance weights, are weights that indicate the "importance" of the observation in some vague sense.

- 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 observations
regress 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 prop

gen invprop=1/prop

reg y x1 x2 … xk [pweight=invprop]

- 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)

- 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 correlated

Solution 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)

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, 358-377http://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

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- 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.
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