Panel Data Methods For Microeconomics Using Stata

Panel data methods for microeconometrics using Stata
A. Colin Cameron Univ. of California - Davis

Prepared for West Coast Stata UsersGroup Meeting Based on A. Colin Cameron and Pravin K. Trivedi, Microeconometrics using Stata, Stata Press, forthcoming.
October 25, 2007
A. Colin Cameron
Univ. of California - Davis (Prepared Panel formethods West Coast for Stata Stata UsersGroup Meeting Based October on 25, A. Colin 2007 Cameron 1 / 39 and
1. Introduction
Panel data are repeated measures on individuals (i ) over time (t ). Regress yit on xit for i = 1, ..., N and t = 1, ..., T . Complications compared to cross-section data:
1
Inference: correct (inate) standard errors. This is because each additional year of data is not independent of previous years. Modelling: richer models and estimation methods are possible with repeated measures. Fixed eects and dynamic models are examples. Methodology: dierent areas of applied statistics may apply dierent methods to the same panel data set.
A. Colin Cameron
This talk: overview of panel data methods and xt commands for Stata 10 most commonly used by microeconometricians. Three specializations to general panel methods:
1
Short panel: data on many individual units and few time periods. Then data viewed as clustered on the individual unit. Many panel methods also apply to clustered data such as cross-section individual-level surveys clustered at the village level. Causation from observational data: use repeated measures to estimate key marginal eects that are causative rather than mere correlation. Fixed eects: assume time-invariant individual-specic eects. IV: use data from other periods as instruments. Dynamic models: regressors include lagged dependent variables.
A. Colin Cameron
Outline
1 2 3 4 5 6 7 8 9 10 11 12
Introduction Linear models overview Example: wages Standard linear panel estimators Linear panel IV estimators Linear dynamic models Long panels Random coe cient models Clustered data Nonlinear panel models overview Nonlinear panel models estimators Conclusions
A. Colin Cameron
2.1 Some basic considerations

1 2
6 7
Regular time intervals assumed. Unbalanced panel okay (xt commands handle unbalanced data). [Should then rule out selection/attrition bias]. Short panel assumed, with T small and N ! . [Versus long panels, with T ! and N small or N ! .] Errors are correlated. [For short panel: panel over t for given i , but not over i .] Parameters may vary over individuals or time. Intercept: Individual-specic eects model (xed or random eects). Slopes: Pooling and random coe cients models. Regressors: time-invariant, individual-invariant, or vary over both. Prediction: ignored. [Not always possible even if marginal eects computed.] Dynamic models: possible. [Usually static models are estimated.]
A. Colin Cameron
2.2 Basic linear panel models

Pooled model (or population-averaged)
0 yit = + xit + uit .
(1)
Two-way eects model allows intercept to vary over i and t

0 yit = i + t + xit + it .
(2)
Individual-specic eects model

0 yit = i + xit + it ,
(3)
for short panels where time-eects are included as dummies in xit . Random coe cients model allows slopes to vary over i
0 yit = i + xit i + it .
A. Colin Cameron
(4)
2.2 Fixed eects versus random eects
0 + ( + ). Individual-specic eects model: yit = xit i it
Fixed eects (FE):

i is possibly correlated with xit regressor xit can be endogenous (though only wrt a time-invariant component of the error) can consistently estimate for time-varying xit (mean-dierencing or rst-dierencing eliminates i ) cannot consistently estimate i if short panel prediction is not possible = E[yit ji , xit ]/xit
A. Colin Cameron
Random eects (RE) or population-averaged (PA)

i is purely random (usually iid (0, 2 )). regressor xit must be exogenous corrects standard errors for equicorrelated clustered errors prediction is possible = E[yit jxit ]/xit
Fundamental divide
Microeconometricians: xed eects Many others: random eects.
A. Colin Cameron
2.3 Robust inference
Many methods assume it and i (if present) are iid. Yields wrong standard errors if heteroskedasticity or if errors not equicorrelated over time for a given individual. For short panel can relax and use cluster-robust inference.
Allows heteroskedasticity and general correlation over time for given i . Independence over i is still assumed.
Use option vce(cluster) if available (xtreg, xtgee). This is not available for many xt commands.
then use option vce(boot) or vce(cluster) but only if the estimator being used is still consistent.
A. Colin Cameron
2.4 Stata linear panel commands
Panel summary
xtset; xtdescribe; xtsum; xtdata; xtline; xttab; xttran Pooled OLS regress Feasible GLS xtgee, family(gaussian) xtgls; xtpcse Random eects xtreg, re; xtregar, re Fixed eects xtreg, fe; xtregar, fe Random slopes xtmixed; quadchk; xtrc First dierences regress (with dierenced data) Static IV xtivreg; xthtaylor Dynamic IV xtabond; xtdpdsys; xtdpd
A. Colin Cameron
Univ. of California - Davis (Prepared Panel formethods West Coast for Stata Stata UsersGroup Meeting October Based on 25, A. 2007 Colin Cameron 10 / 39 and
3.1 Example: wages
PSID wage data 1976-82 on 595 individuals. Balanced. Source: Baltagi and Khanti-Akom (1990). [Corrected version of Cornwell and Rupert (1998).] Goal: estimate causative eect of education on wages. Complication: education is time-invariant in these data. Rules out xed eects. Need to use IV methods (Hausman-Taylor).
A. Colin Cameron
3.2 Reading in panel data
xt commands require data to be in long form. Then each observation is an individual-time pair. Original data are often in wide form. Then an observation combines all time periods for an individual, or all individuals for a time period. Use reshape long to convert from wide to long. xtset is used to dene i and t .
xtset id t is an example allows use of panel commands and some time series operators.
A. Colin Cameron
3.3 Summarizing panel data
A. Colin Cameron
describe, summarize and tabulate confound cross-section and time series variation. Instead use specialized panel commands:
xtdescribe: extent to which panel is unbalanced xtsum: separate within (over time) and between (over individuals) variation xttab: tabulations within and between for discrete data e.g. binary xttrans: transition frequencies for discrete data xtline: time series plot for each individual on one chart xtdata: scatterplots for within and between variation.
A. Colin Cameron
4.1 Standard linear panel estimators

1 2 3
Pooled OLS: OLS of yit on xit . Between estimator: OLS of y i on xi . Random eects estimator: FGLS in RE model. b i ) on (xit b Equals OLS i xi ); p of (yit i y 2 2 i = 1 / ( Ti + 2 ) . Within estimator or FE estimator: OLS of (yit First dierence estimator: OLS of (yit Implementation:
xtreg does 2-4 with options be, fe, re xtgee does 3 (with option exchangeable) regress does 1 and 5.
4 5
y i ) on (xit on (xit xi ,t
xi ).
1 ).
yi ,t
1)
Only 4. and 5. give consistent estimates of in FE model.

A. Colin Cameron Univ. of California - Davis (Prepared Panel formethods West Coast for Stata Stata UsersGroup Meeting October Based on 25, A. 2007 Colin Cameron 15 / 39 and
4.2 Example
Coe cients vary considerably across OLS, FE and RE estimators. Cluster-robust standard errors (su x rob) larger even for FE and RE. Coe cient of ed not identied for FE as time-invariant regressor.
4.3 Fixed eects versus random eects

Use Hausman test to discriminate between FE and RE.
If xed eects: FE consistent and RE inconsistent. If not xed eects: FE consistent and RE consistent. So see whether dierence between FE and RE is zero. i 1 0h e b e b e d [ H= Cov ] 1 ,RE 1 ,FE 1 ,RE 1 ,FE 1 ,RE
where 1 corresponds to time-varying regressors (or a subset of these).
b 1 ,W ,
Problem: hausman command assumes RE is fully e cient. But not the case here as robust se s for RE dier from default se s. So hausman is incorrect. Instead implement Hausman test using suest or panel bootstrap or Wooldridge (2002) robust version of Hausman test.
A. Colin Cameron
5.1 Panel IV
Consider model with possibly transformed variables: yit = + xit0 + uit , where yit = yit or yit = y i for BE or yit = (yit yit = (yit i y i ) for RE. OLS is inconsistent if E[uit jxit ] = 0. y i ) for FE or
So do IV estimation with instruments zit satisfy E[uit jzit ] = 0. Command xtivreg is used, with options be, re or fe. This command does not have option for robust standard errors.
A. Colin Cameron
5.2 Hausman-Taylor IV estimator
Problem in the xed eects model

If an endogenous regressor is time-invariant Then FE estimator cannot identify (as time-invariant).
Solution:
Assume the endogenous regressor is correlated only with i (and not with it ) Use exogenous time-varying regressors xit from other periods as instruments
Command xthtaylor does this (and has option amacurdy).
A. Colin Cameron
6.1 Linear dynamic panel models
Simple dynamic model regresses yit in polynomial in time.

e.g. Growth curve of child height or IQ as grow older use previous models with xit polynomial in time or age.
Richer dynamic model regresses yit on lags of yit .
A. Colin Cameron
6.2 Linear dynamic panel models with individual eects
Leading example: AR(1) model with individual specic eects yit = yi ,t

1
0 + xit + i + it .
Three reasons for yit being serially correlated over time:

True state dependence: via yi ,t 1 Observed heterogeneity: via xit which may be serially correlated Unobserved heterogeneity: via i
Focus on case where i is a xed eect

FE estimator is now inconsistent (if short panel) Instead use Arellano-Bond estimator
A. Colin Cameron
6.3 Arellano-Bond estimator

First-dierence to eliminate i (rather than mean-dierence)
(yit
yi ,t
1)
= (yi ,t
yi ,t
2 ) + (xit
xi0 ,t
1 )
+ (it
i ,t i ,t
1 ). 1)
OLS inconsistent as (yi ,t 1 yi ,t 2 ) correlated with (it (even under assumption it is serially uncorrelated). But yi ,t 2 is not correlated with (it i ,t 1 ), so can use yi ,t 2 as an instrument for (yi ,t 1 yi ,t
2 ).
Arellano-Bond is a variation that uses unbalanced set of instruments with further lags as instruments. For t = 3 can use yi 1 , for t = 4 can use yi 1 and yi 2 , and so on. Stata commands
xtabond for Arellano-Bond xtdpdsys for Blundell-Bond (more e cient than xtabond) xtdpd for more complicated models than xtabond and xtdpdsys.
7.1 Long panels
For short panels asymptotics are T xed and N ! . For long panels asymptotics are for T !
A dynamic model for the errors is specied, such as AR(1) error Errors may be correlated over individuals Individual-specic eects can be just individual dummies Furthermore if N is small and T large can allow slopes to dier across individuals and test for poolability.
A. Colin Cameron
7.2 Commands for long panels
Models with stationary errors:

xtgls allows several dierent models for the error xtpcse is a variation of xtgls xtregar does FE and RE with AR(1) error
Models with nonstationary errors (currently active area):

As yet no Stata commands Add-on levinlin does Levin-Lin-Chu (2002) panel unit root test Add-on ipshin does Im-Pesaran-Shin (1997) panel unit root test in heterogeneous panels Add-on xtpmg for does Pesaran-Smith and Pesaran-Shin-Smith estimation for nonstationary heterogeneous panels with both N and T large.
A. Colin Cameron
8.1 Random coe cients model
Generalize random eects model to random slopes. Command xtrc estimates the random coe cients model
0 yit = i + xit i + it ,
where (i , i ) are iid with mean (, ) and variance matrix and it is iid. No vce(robust) option but can use vce(boot) if short panel.
A. Colin Cameron
8.2 Mixed or multi-level or hierarchical model
Not used in microeconometrics but used in many other disciplines. Stack all observations for individual i and specify yi = Xi + Zi ui + i where ui is iid (0, G) and Zi is called a design matrix. Random eects: Zi = e (a vector of ones) and ui = i Random coe cients: Zi = Xi . Other models including multi-level models are possible. Command xtmixed estimates this model.
A. Colin Cameron
9.1 Clustered data
Consider data on individual i in village j with clustering on village. A cluster-specic model (here village-specic) species
0 yji = i + xji + ji .
Here clustering is on village (not individual) and the repeated measures are over individuals (not time). Use xtset village id Assuming equicorrelated errors can be more reasonable here than with panel data (where correlation dampens over time). So perhaps less need for vce(cluster) after xtreg
A. Colin Cameron
9.2 Estimators for clustered data
If i is random use:
regress with option vce(cluster village) xtreg,re xtgee with option exchangeable xtmixed for richer models of error structure
If i is xed use:
xtreg,fe
A. Colin Cameron
10.1 Nonlinear panel models overview

General approaches similar to linear case
Pooled estimation or population-averaged Random eects Fixed eects
Complications
Random eects often not tractable so need numerical integration Fixed eects models in short panels are generally not estimable due to the incidental parameters problem.
Here we consider short panels throughout. Standard nonlinear models are:

Binary: logit and probit Counts: Poisson and negative binomial Truncated: Tobit
A. Colin Cameron
10.2 Nonlinear panel models

A pooled or population-averaged model may be used. This is same model as in cross-section case, with adjustment for correlation over time for a given individual. A fully parametric model may be specied, with conditional density
0 f (yit ji , xit ) = f (yit , i + xit , ),
t = 1, ..., Ti , i = 1, ...., N , (5)
where denotes additional model parameters such as variance parameters and i is an individual eect. A conditional mean model may be specied, with additive eects
0 E[yit ji , xit ] = i + g (xit )
(6)
or multiplicative eects E[yit ji , xit ] = i

A. Colin Cameron
0 g (xit ).
(7)
10.3 Nonlinear panel commands
Counts Pooled poisson negbin GEE (PA) xtgee,family(poisson) xtgee,family(nbinomial) RE xtpoisson, re xtnegbin, fe Random slopes xtmepoisson FE xtpoisson, fe xtnegbin, fe plus tobit and xttobit.
Binary logit probit xtgee,family(binomial) link(logit xtgee,family(poisson) link(probit xtlogit, re xtprobit, re xtmelogit xtlogit, fe
A. Colin Cameron
11.1 Pooled or Population-averaged estimation

Extend pooled OLS
Give the usual cross-section command for conditional mean models or conditional density models but then get cluster-robust standard errors Probit example: probit y x, vce(cluster id) or xtgee y x, fam(binomial) link(probit) corr(ind) vce(cluster id)
Extend pooled feasible GLS

Estimate with an assumed correlation structure over time Equicorrelated probit example: xtprobit y x, pa vce(boot) or xtgee y x, fam(binomial) link(probit) corr(exch) vce(cluster id)
A. Colin Cameron
11.2 Random eects estimation

Assume individual-specic eect i has specied distribution g (i j). Then the unconditional density for the i th observation is f (yit , ..., yiT jxi 1 , ..., xiT , , , ) Z h i T = f ( y j x , , , ) g (i j)d i . it it i t =1
(8)
Analytical solution:
For Poisson with gamma random eect For negative binomial with gamma eect Use xtpoisson, re and xtnbreg, re
No analytical solution:
For other models. Instead use numerical integration (only univariate integration is required). Assume normally distributed random eects. Use re option for xtlogit, xtprobit Use normal option for xtpoisson and xtnegbin
A. Colin Cameron
11.2 Random slopes estimation
Can extend to random slopes.

Nonlinear generalization of xtmixed Then higher-dimensional numerical integral. Use adaptive Gaussian quadrature
Stata commands are:

xtmelogit for binary data xtmepoisson for counts
Stata add-on that is very rich:

gllamm (generalized linear and latent mixed models) Developed by Sophia Rabe-Hesketh and Anders Skrondal.
A. Colin Cameron
11.3 Fixed eects estimation
In general not possible in short panels. Incidental parameters problem:

N xed eects i plus K regressors means (N + K ) parameters But (N + K ) ! as N ! Need to eliminate i by some sort of dierencing possible for Poisson, negative binomial and logit.
Stata commands
xtlogit, fe xtpoisson, fe (better to use xtpqml as robust se s) xtnegbin, fe
Fixed eects extended to dynamic models for logit and probit. No Stata command.
A. Colin Cameron
12. Conclusion
Stata provides commands for panel models and estimators commonly used in microeconometrics and biostatistics. Stata also provides diagnostics and postestimation commands, not presented here. The emphasis is on short panels. Some commands provide cluster-robust standard errors, some do not. A big distinction is between xed eects models, emphasized by microeconometricians, and random eects and mixed models favored by many others. Extensions to nonlinear panel models exist, though FE models may not be estimable with short panels. This presentation draws on two chapters in Cameron and Trivedi, Microeconometrics using Stata, forthcoming.
Book Outline
For Cameron and Trivedi, Microeconometrics using Stata, forthcoming. 1. Stata basics 2. Data management and graphics 3. Linear regression basics 4. Simulation 5. GLS regression 6. Linear instrumental variable regression 7. Quantile regression 8. Linear panel models 9. Nonlinear regression methods 10. Nonlinear optimization methods 11. Testing methods 12. Bootstrap methods
Book Outline (continued)
13. Binary outcome models 14. Multinomial models 15. Tobit and selection models 16. Count models 17. Nonlinear panel models 18. Topics A. Programming in Stata B. Mata
A. Colin Cameron
Econometrics graduate-level panel data texts

Comprehensive panel texts
Baltagi, B.H. (1995, 2001, 200?), Econometric Analysis of Panel Data, 1st and 2nd editions, New York, John Wiley. Hsiao, C. (1986, 2003), Analysis of Panel Data, 1st and 2nd editions, Cambridge, UK, Cambridge University Press.
More selective advanced panel texts

Arellano, M. (2003), Panel Data Econometrics, Oxford, Oxford University Press. Lee, M.-J. (2002), Panel Data Econometrics: Methods-of-Moments and Limited Dependent Variables, San Diego, Academic Press.
Texts with several chapters on panel

Cameron, A.C. and P.K. Trivedi (2005), Microeconometrics: Methods and Applications, New York, Cambridge University Press. Greene, W.H. (2003), Econometric Analysis, fth edition, Upper Saddle River, NJ, Prentice-Hall. Wooldridge, J.M. (2002, 200?), Econometric Analysis of Cross Section and Panel Data, Cambridge, MA, MIT Press.

Panel Data Methods For Microeconomics Using Stata

Uploaded by

Copyright:

Available Formats

Panel Data Methods For Microeconomics Using Stata

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Panel Data Methods For Microeconomics Using Stata

Uploaded by

Copyright:

Available Formats

Panel data methods for microeconometrics using Stata

A. Colin Cameron Univ. of California - Davis

October 25, 2007

2.1 Some basic considerations

2.2 Basic linear panel models

Two-way eects model allows intercept to vary over i and t

Individual-specic eects model

2.2 Fixed eects versus random eects

0 + ( + ). Individual-specic eects model: yit = xit i it

Fixed eects (FE):

Random eects (RE) or population-averaged (PA)

2.3 Robust inference

2.4 Stata linear panel commands

3.1 Example: wages

3.2 Reading in panel data

3.3 Summarizing panel data

4.1 Standard linear panel estimators

Only 4. and 5. give consistent estimates of in FE model.

4.3 Fixed eects versus random eects

where 1 corresponds to time-varying regressors (or a subset of these).

5.2 Hausman-Taylor IV estimator

Problem in the xed eects model

Command xthtaylor does this (and has option amacurdy).

6.1 Linear dynamic panel models

Simple dynamic model regresses yit in polynomial in time.

Richer dynamic model regresses yit on lags of yit .

6.2 Linear dynamic panel models with individual eects

Leading example: AR(1) model with individual specic eects yit = yi ,t

Three reasons for yit being serially correlated over time:

Focus on case where i is a xed eect

6.3 Arellano-Bond estimator

7.1 Long panels

7.2 Commands for long panels

Models with stationary errors:

Models with nonstationary errors (currently active area):

8.1 Random coe cients model

8.2 Mixed or multi-level or hierarchical model

9.1 Clustered data

9.2 Estimators for clustered data

10.1 Nonlinear panel models overview

Here we consider short panels throughout. Standard nonlinear models are:

10.2 Nonlinear panel models

t = 1, ..., Ti , i = 1, ...., N , (5)

or multiplicative eects E[yit ji , xit ] = i

10.3 Nonlinear panel commands

11.1 Pooled or Population-averaged estimation

Extend pooled feasible GLS

11.2 Random eects estimation

11.2 Random slopes estimation

Can extend to random slopes.

Stata commands are:

Stata add-on that is very rich:

11.3 Fixed eects estimation

In general not possible in short panels. Incidental parameters problem:

Book Outline (continued)

Econometrics graduate-level panel data texts

More selective advanced panel texts

Texts with several chapters on panel