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

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• Estimation commands
• truncreg, tobit,
• heckman, heckprobit,
• treatreg, ivreg
• Other useful commands
• ivprobit, ivtobit
• Useful option in the estimation commands
• pweights

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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)

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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)

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tobit

• Tobit first type (consumption of a good)
• tobit y x1 x2 xk , ll(0)
• tobit y x1 x2 xk , ul(c)

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cnreg

• Tobit first type
• Ex. minimum wage with different levels in
  different years
• cnreg y x1 x2 xk censored(d)

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intreg

• Interval data regression (ExBracket 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,
  (30000,8 say (ai, bi

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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 income Example Example y 5980 y in (a,b) (5000, 15000 (30000, 8 y 5980 a 5000 30000 y 5980 b 15000 .
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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

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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)

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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
• yy1 d y0 (1-d)
• yx? ? d?
• dz ? u where dl(dgt0)
• We have a selection problem because of the
  correlation
• between u and ?. This implies that d is not
  independent of ?.

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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(dz1 z2 zs)
• Ex Sample of graduated students with and without
  a master degree
• ylog earnings, d1 if master degree, 0 otherwise
• x age, age square, d, sex, type first degree
• z mothers level of education, fathers level
  of education, sex, type first degree

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How to use weights in Stata

• 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 sigma2/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.

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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
  observations
• regress y x1 x2 xk pweightp
• 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 invprop1/prop
• reg y x1 x2 xk pweightinvprop

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For complex survey design it is better to use

• svyset pweightp
• svy regress y x1 x2 xk
• svyset have options for cluster sampling designs
  or other complex design
• Declare survey design for dataset
• svyset pweightp, strata(stratid)

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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
• yx? ? d?
• Problem d and ? are correlated
• Solution 1 IV estimation ( IVz 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 (dz1 z2 zs)

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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/.aaba
  die.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

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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

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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.