Some estimators for dynamic panel data sample selection models *

Transcription

1 Some estmators for dynamc panel data sample selecton models * Serg Jménez-Martín, Unversat Pompeu Fabra, Barcelona GSE and FEDEA a José María Labeaga, UNED and UNU-MERIT, Unversy of Maastrcht María Engraca Rochna-Barrachna, Unversdad de Valenca and ERI-CES February, 2014 Very prelmnary Frst draft Abstract Due to the ncreasng avalably of longudnal data sets for mcroeconomc agents, s beng common to use econometrc approaches to address endogenous sample selecton problems. Snce s lkely that these methods are gong to be used more frequently n the future, we thnk that s mportant to hghlght advantages and problems n the performance of the dfferent estmators and to draw researchers' attenton to potental pfalls n usng them n appled studes. Ths s the man goal of our study. We examne the propertes of exstng approaches n several drectons. We present Generalzed Method of Moments (GMM) estmators for panel data sample selecton models where the regresson equatons are dynamc and s allowed for the exstence of endogenous regressors and correlated ndvdual unobserved heterogeney. To see the performance of the proposed estmators we perform a Monte Carlo study of the fne sample propertes of the proposed methods. We also evaluate the performance of our proposed methods n a female labour supply equaton adjusted n a sample took from the PSID. Our Monte Carlo results suggest that n many standard cases s not necessary to correct the model for sample selecton. Ths s true n general for the purely autorregresve model and the dynamc model wh exogenous regressors, and more questonable when the regressor s endogenous (and we do not dspose of external nstruments). In the latter case a more general correcton of the sample selecton problem s requred. In the case of observed data, we detect that s not necessary to correct for selectvy when the model s estmated by System-GMM even n the case the model contans an endogenous varable. However, these results should be vewed wh cauton due to potental msspecfcaton of the model. Keywords: Panel data, sample selecton, treatment effects, generalzed method of moments JEL Class.: J52, C23, C24 * We are grateful to ECO C03-02 and ECO C05-01 (Spansh Mnstry of Scence and Technology) for fnancal support. Usual dsclamers apply. a Correspondng author: Serg Jménez-Martín, Department of Economcs, UPF, Barcelona, Span. e-mal: serg.jmenez@upf.edu 1

2 1. Introducton The ncreasng avalably of longudnal data has provded the possbly of dong both theoretcal and emprcal papers n several economc felds. As s well know, panel data offers researchers several advantages both wh respect to cross-secton and tme seres. The man advantage s that panel data methods can account for unobserved heterogeney. As a counterpart, whle n lnear models s normally easy to estmate the parameters the same s not true n the case of non-lnear models. Moreover, the problems of self-selecton, nonresponse and attron are usually worse n panels than n cross-sectons (see Baltag, 2005). In applcatons, these problems ental the necessy to estmate the models on unbalanced panels. Many tmes, we should frst answer the queston about the reason why the panel becomes unbalanced and s que common that appears because of endogenous attron or endogenous selecton. There are a number of studes dealng at the same tme wh unobserved heterogeney and selectvy. Most of them do under strct exogeney assumptons. For nstance, Verbeek and Njman (1992) proposed tests of selecton bas (varable addon and Hausman type tests) n ths context, eher wh or whout allowng for correlaton between the unobserved effects and explanatory varables. These authors do not suggest, however, the way of estmatng the parameters of the model when the hypothess of absence of endogenous selecton s rejected. Wooldrdge (1995) also proposed varable addon tests for selecton bas and he gves procedures for estmatng the model after correctng for selectvy. Kyrazdou (1997) proposes correctng for selecton bas by usng a semparametrc approach based on a condonal exchangeably assumpton. Rochna- Barrachna (1999) also proposes estmators for panel data sample selecton models where the correcton terms are more complex than n Wooldrdge (1995) because the model s estmated n tme dfferences. On the other hand, Kyrazdou (2001) extends the methods to dynamc models wh selecton. Hu (2002) constutes a recent example for the case of dynamc censored panel data models. The dfferent methods proposed n the prevous papers have been appled to a number of emprcal economc studes. Charler, Melenberg and van Soest (2001) apply them to estmate housng expendure by households. Jones and Labeaga (2004) select out the 2

3 sample of non-smokers usng the varable addon tests of Wooldrdge (1995) and then they estmate tob type models on the sample of smokers and potental smokers usng GMM and Mnmum Dstance methods. González-Chapela (2004) uses GMM when estmatng the effects of recreaton goods on female labour supply. Wnder (2004) uses nstrumental varables to account for endogeney of some regressors when estmatng earnngs equatons for females. Jménez-Martín (2006) estmates and tests the possbly of dfferent wage equatons for strkers and non-strkers n a dynamc context. Dustmann and Rochna-Barrachna (2007) estmate females' wage equatons and, fnally, Semykna Wooldrdge (2005, 2008) both propose new two-stage methods for estmatng panel data models n the presence of endogeney and selecton and apply them to estmate earnngs equatons for females. Snce s lkely that these approaches are gong to be used more frequently n the future, we thnk that s mportant to hghlght advantages and problems n the performance of the dfferent estmators and to draw researchers' attenton to potental pfalls n usng them n appled studes. Ths s the man goal of our study. We examne the propertes of exstng approaches n several drectons. We present estmators for panel data sample selecton models where the regresson equatons are dynamc and s allowed for the exstence of endogenous regressors and correlated ndvdual unobserved heterogeney. The type of methods presented are dfferent Generalzed Method of Moments (GMM) estmators for dynamc panel data sample selecton that may combne estmaton of the models both n frst dfferences and levels. Therefore, we consder the possbly of applyng System- GMM estmators for dynamc panel data to the case of sample selecton. Dependng both on estmaton n levels or frst dfferences the correcton terms present dfferent degrees of complexy. Some of ths complexy can be smplfed f we are wllng to mpose statonary assumptons, exchangeably condons, and/or lack of ndvdual heterogeney n the selecton equatons, although we also look at the general case that does not mpose the prevous assumptons. In a suaton where the correcton term can show small tme varaton (see Kyrazdou, 1997) ncreasng the specfcaton wh equatons n levels of the varables could be very mportant for the results of the selecton tests. We explore the possbly of usng standard software for estmatng the models. We assume a typcal model for the outcome of nterest and we allow the selecton equaton 3

4 to be statc or dynamc. Ths model s confronted to Monte Carlo smulatons allowng dfferent schemes of correlaton between heterogeneous effects and varables n both equatons, to the potental endogeney of a regressor and a smple correcton for selectvy based on estmates derved n typcal bnomal probs models for each cross-secton. Ths exercse provdes a general pcture mplyng the non-necesy to correct for selectvy even when we allow for a large share of censorng. We also confront our methodology to a sample of women taken from the Panel Study of Income Dynamcs for perod In secton 2 of the paper we present the general model and the estmaton methods. To see the performance of the proposed estmators we conduct n secton 3 a Monte Carlo study of the fne sample propertes of dfferent Generalzed Method of Moments (GMM) estmators for dynamc panel data sample selecton models. Ths exercse s carred out for a small to medum sample sze and two very unbalanced regmes: a hgh probably regme and a low probably one. The latter assumpton s not strctly necessary but s often the case n realy. The results of the experments are n general satsfactory, n terms of small bases, for the pure autoregressve model or the model wh addonal exogenous regressor(s). These small bases are mantaned when the addonal regressor(s) s(are) correlated wh the term capturng ndvdual heterogeney, although the bases ncrease n some cases when allowng also for correlaton wh the tme varyng componen of the error term error provded the nstrument are poor. In secton 4 we present the results of the estmaton of a female labor supply equaton wh seven waves of data from the PSID and an average degree of censorng of 55 percent. Our results suggest no need to correct for selectvy n dynamc models estmated by System-GMM even when the specfcaton contans an endogenous varable. These results should be vewed by cauton because the autocorrelaton tests detect msspecfcaton of the model. Fnally, secton 5 concludes. 2. The model Consder we have nterest n an outcome varable y, whch s related to an endogenous bnary ndcator d or treatment and other varables ncluded n the vector x. Consder that the model for y s by nature dynamc. In partcular, consder that the sngle equaton model s gven by: 4

5 y = y 1 x for 1,, N, t 1, T (1) Where x s a vector of regressors (that also ncludes a constant term) and s an ndvdual heterogeney component ndependent of, the error term., are the correspondng parameters of the model. We consder that x can be correlated wh both the ndvdual effect and the error term. Fnally, note that our model nests two specal cases: () when =0 we get the statc model; and, () when 0 we have the purely autorregresve model wh ndvdual effects. However, the varable of nterest s not always observable. A model for d * drves the observably of y. We can thnk at least n two alternatves for modelng d * : eher a statc (selecton model A) or a dynamc one (selecton model B). The statc verson s gven by: d * whle the dynamc one s gven by: * = z u ; d 1[ d 0] (2a) d * * = d z u ; d 1[ d 0] (2b) 1 Where s a term capturng unobserved ndvdual heterogeney, z (that also ncludes a constant term) s a vector of strctly exogenous regressors once we allow for z to be correlated wh, and u s an error term. The vector z may nclude all the varables n the vector x that are exogenous and also other varables. Furthermore, n general, u and are correlate. However n case they are not correlated we are n the case of random selecton. Alternatvely, when the correlaton s dfferent from zero, there s endogenous selecton. Note that after selecton of the observatons, the vald sample s formed by those observatons for whch: 5

6 y = y x for t s. t. d, d1 1 1 Gven we allow for endogeney of x, n case of dsposng of the necessary contemporaneous nstruments, the estmaton sample concdes wh the above sample ( d, 1 1). However, when usng nternal nstrument (lagged at least twce), the sample d s condonal to observng the outcome for at least three consecutve perods ( 1 2 d, d, d 1) Estmaton of the outcome equaton There are varous possbles to consstently estmate dynamc panel data equatons for large N and small T cases. Among them, the most popular ones among practconers are the Generalzed Method of Moments (GMM) of Arellano and Bond (1991) and the System- GMM proposed by Arellano and Bover (1995) and Blundell and Bond (1998). After prelmnary exploraton of the results we have decded to concentrate the analyss n the performance of the System-GMM method. Ths s so because outperforms other GMM methods, n a large majory of the cases consdered. The system estmator nvolves the estmaton of both combned levels and frst dfferences equatons of the model. In case of endogenous sample selecton and assumng statonary of the selecton process (Jménez et al, 2009) both equaton needs to be corrected for the potental selecton bas. However the correcton needed dffers by equaton. For example for the levels equatons y = y x E( / z, d, d1 1) for t s. t. d, d1 1 1 We need to control the expectaton of the error condonal on consecutve outcomes of the selecton process. And for the frst dfferenced equatons y = y x E( / z, d, d1, d2 1) for t s. t. d, d1, d2 1 1 We need to control the expectaton of the error condonal on three consecutve outcomes. Howevere, n our frst approxmaton to the problem we approxmated these correcton 6

7 terms by ntroducng the lambda obtaned from a year-by-year prob (n levels for the equatons n levels and frst dfferenced for equatons n dfferences). The procedure, followng Wooldrdge (1995), may be stated as follows. Frst, we estmate T decson equatons usng standard dscrete choce models. After estmaton of the model we perform a varable addon test for selecton bas. A more general soluton to the correcton of the bas can be found n Jménez et al (2009, mmeo). Under a farly standard statonary condon of the selecton process, they fnd that estmaton usng standard software (for example, the stata xtabond2) gets complcated snce the correcton of equatons n levels mples two regressors,,,,,,,, that are obtaned from a bvarate prob n perods t, t-1. Lkewse, equatons n frst dfferences ncorporate two regressors,,,,,,,,,,,,,,,,, }, and,,,,,,,,, both of them obtaned from a trvarate prob n perods t, t-1 and t-2. [Work n progress] 3. Montecarlo experment In accordance wh the prevous secton we consder the followng data generatng processes. For the selecton equaton we assume two dfferent optons: A. d B d * a z u *. d a [0.5d 1 ] z u 1 ( d * 0) where a s set so p ( d * 0) The outcome of nterest s generated as follows (we mantan the statc and dynamc versons of the model): * y = (2 x ) /(1 ) t 1 * * y = 2 y1 x t 2,, T y * y f d 1 We set 1 and let vary between 0.25, 0.50 and The purely autoregressve model s obtaned by settng 0. T can vary between 17 and 20 and the frst 13 observatons are 7

8 dropped to be able to assume that nal condons do not matter. Regardng the errors, we consder the followng structure for them: ~ N(0, ), u ~ N(0, ), 0 0 u 0.25, 0.25u 1, 1 u 0 0 ~ N(0, ), ~ N(0, ), 1 1 Note that the mpled correlaton between the errors derved from these assumptons s corr(, u ) 0.25/ the regressor(s): In addon we consder the followng process for x x x x x 0 = (.5 )/2 x t 1 =.5 0.5x1. t 1 ~ N (0, x x0 x ), 0.25, x 1 x0 x 0 N (0, x 0 ), x 0 1 where s a parameter that controls whch partcular relatonshp x has wh the error n the model. We consder two cases: 0 (exogenous x) and (endogeneous). In sum, we have a two equaton model n whch we allow for varaton n the dynamcs of the outcome varable, the exogenous-endogenous nature of the regressor and the varous correlaton parameters of the model Descrpton of the experments For each experment 500 uns are consdered. For each un, up to 20 tmes seres observatons are drawn. However, the nal 13 observaton are dscarded to dmnsh the nfluence of the nal condons. Thus, we end up havng a small T (from 4 to 7) panel data sample as s usual n the emprcal lerature. After the realzaton of the selector, the selected panels are formed. At least three consecutve observatons of the same regme are needed n order to form an observaton of the selected panel. For each combnaton of the parameters we made 500 replcatons. In cases where x s not exogenous, we select the nstruments as follows. For frst dfferences equatons we use lags from t 2 backwards, although we also compare the 8

9 performance of the estmates wh a restrcted set of nstruments. 1 For the level equaton we use frst dfferences of the regressors. Should be decded about the exogeney of x we carry out, n a prevous step, a Grlches and Hausman (1986) type of test. In all cases, we present three System-GMM estmators of the model. The frst one s obtaned under the assumpton of exogenous selecton and evaluates the general performance of the estmator. The other two are obtaned under the assumpton of endogenous sample selecton. The second one does not correct for sample selecton (and thus evaluates the necessy of addng a sample selecton correcton) and the last one correct wh a year-by-year prob (Wooldrdge, 1995) Smulaton results for the pure autorregresve model Table 1 presents the results for the pure autorregresve model, for three values of the autorregresve parameter: 0.25, 0.50 and 0.75 and = We smulate two alternatve selecton models: statc (selecton model A) and dynamc (selecton model B). In each case, we report three alternatve estmates: the estmate obtaned under the assumpton of exogenous selecton (benchmark estmator), endogenous selecton whout correcton, and corrected wh a year-by-year correcton. The results whout correcton have very strong mplcatons. In all cases and for both models, the bas never exceeds one percent (average bas dvded by the true value of the coeffcent) and n many cases s smaller. Addng a smple correcton (based on a yearby-year prob) reduces the small bas by about 10 percent and also reduces the standard errors of the model. The average sgnfcance test of the null hypothess that the coeffcent of lambda s zero s estmated at about (selecton model A) and 0.02 (selecton model B). Alternatvely the mpled rejecton frequency s estmated at about 0.90 for model A and 0.88 for model B, somewhat below the expected value of In summary, the evdence seems to suggests that the need to correct for sample selecton bas n autorregresve dynamc panel models s small. 1 In fact, GMM could theoretcally mply that we should use as many nstruments as possble, although could affect the performance of the estmaton method, power of the tests and degrees of freedom remanng. 9

10 Table 1. Average bas n the pure autoregressve model. = 0.25, N=500, R=500. System-GMM estmator No Endogenous selecton No Year by correcton Year correcton Endogenous selecton Lambda testng delta stat bas bas bas sgnf ERF model (0.25) 1 av s.e (0.50) 1 av s.e (0.75) 1 av s.e (0.25) 2 av s.e (0.50) 2 av s.e (0.75) 2 av s.e Notes. 1. Sgnf. = average(1-normal(abs(coef(lambda)/sgma(lambda)))) 2. Erf=sgnf<alpha= Smulaton results for the dynamc model wh eher exogenous or endogenous regressor Table 2 presents the results for the dynamc outcome model wh a regressor that can be eher exogenous or endogenous, for three values of the autorregresve parameter: 0.25, 0.50 and 0.75 and = As before, we smulate two alternatve selecton models: statc (selecton model A) and dynamc (selecton model B). In each case, we report three alternatve estmates: the estmate obtaned under the assumpton of exogenous selecton (benchmark estmator), endogenous selecton whout correcton, and corrected wh a yearby-year correcton. The results wh any value of and an exogenous regressor are n lne wh those descrbed n the pure autorregressve model. The mpled bas of the endogenous selecton model wh correcton s even smaller than n the AR(1) for and s estmated at about 1 per cent for 10

11 the coeffcent of x. The results wh an endogenous regressor are, as expected, worse than those obtaned wh an exogenous regressor. The results regardng the bas of pont to a moderate bas that gets reduced as we ncrease the value of alpha (the bas goes from 3.5% to 1.0% as we ncrease from 0.25 to 0.75 percent. The results regardng the coeffcent of s pont to a small bas of about 2-3 percent. In both cases the bas dsappears n case we use an exogenous nstrument correlated wh both y and x. The average sgnfcance test of the null hypothess that the coeffcent of s zero s estmated at about Alternatvely the mpled rejecton frequency s estmated at about 0.5 for model A and for model B, well below the expected value of Thus, n ths model the test of fals to reject exogenous selecton. Table 2. Dynamc model wh a tme varyng regressor, = 0.25, N=500, R=200 No Endogenous selecton Endogenous selecton No Year by Year Lambda w X stat correcton Correcton Testng 0 Sgnf. ERF 0 A. Statc selecton equaton (0.25) exog bas s.e endog bas s.e (0.50) exog bas s.e endog bas s.e (0.75) exog bas s.e endog bas s.e B. Dynamc selecton equaton (0.25) exog bas s.e endog bas s.e (0.50) exog bas s.e endog bas s.e (0.75) exog bas s.e

12 endog bas s.e Notes. 1. Sgnf. = average(1-normal(abs(coef(lambda)/sgma(lambda)))). 2. Erf=sgnf<alpha=0.05 In summary the results pont to some need to correct sample selecton n models wh endogenous regressors. We explore more general correcton strateges for ths case n secton 3.4 (work n progress) Sensvy analyss In ths secton we comment on varous departures from the basc set of assumptons. At ths stage we have consdered the followng cases: (a) varyng the longudnal dmenson; (b) Increasng sample selecton (from 0.15 to 0.25); (c) Two correlated regressors; (d) The x regressor s not autocorrelated; and, (e) ncreasng the rato of the varances ( / =2). a. Varyng the longudnal dmenson We have expermented from T = 4 to T = 7. The effect on bas of ths varaton n the longudnal dmenson of the data s almost neglgble. Alternatvely, ncreases the estmated varance. b. Increasng the degree of sample selecton Increasng sample selecton does not affect much the bas of the autorregresve parameter when x s exogenous. Alternatvely the bas ncreases when x s endogenous. c. Two (or more) correlated regressors Increasng the number of regressors mproves the estmated bas of the estmated coeffcent for both cases, x endogenous and x exogenous. Furthermore, mproves the estmated varance. So, ths case does not mply any addonal problem to the ones ponted above. On the contrary more regressors, some of the correlated wh the endogenous one may help dentfcaton of the model. 12

13 d. The x regressor s not autocorrelated Snce we do not need any extra nstrument for dentfcaton, when x es exogenous we do not detect any addonal problem. Alternatvely, when x s endogenous we have a serous dentfcaton problem snce we do not have good nstrument for x. Agan, the presence of other regressors correlated wh x helps dentfcaton. e. Increasng the rato of the varances ( / =2) When the rato of varances of the outcome equaton ncreases dentfcaton becomes easer. For example when = 0.25, the average bas gets reduced consderably (less than 1 percent for alpha and about 0.1 percent for x) for the case n whch x s endogenous. Alternatvely the ERF of the test of the coeffcent of correcton term does not mprove sgnfcantly. 3.4 Bvarate and trvarate sample selecton correctons [work n progress] 4. Emprcal applcaton We apply the method proposed to the estmaton of a labor supply equaton for women usng data from the Panel Study of Income Dynamcs (PSID). We select seven years and bult subsamples to avod problems of attron and to have a comparable tme sample sze to the one used n the Monte Carlo experment. We have selected several subsamples correspondng to dfferent perods n order to provde robustness to the results. We present n ths paper the results correspondng to the a subsample of women for the perod but we have appled the method to alternatve subsamples (wh the same tme dmenson) to provde robustness to our resutls, whch are avalable upon request. We select the sample attendng the followng crera - Famles are restrcted to have a male head, some wfe present each year and usable age varables for the wfe and the head 13

14 - The wfe s age was restrcted to be between 30 and 65 n The composon of the famly should reman stable,.e. no change n the head or the wfe whn the famly beng contnuously marred - All observatons from the non-random low ncome sample are excluded - Non-whes are excluded - Answer for the labour force partcpaton queston of the wfe s requred - If there are nconsstences between partcpaton and labour ncome of the wfe, the observatons are excluded. (Inconsstences are, for nstance, a posve number of hours worked assocated wh zero wages) - Observatons wh wfe s educaton or experence erroneous are excluded. - Observatons of hours worked by the wfe greater than 5000 a year are excluded. After applyng these crera to the orgnal data we end up wh a sample of 508 women (smlar ndvdual sample sze to the one used n the Monte Carlo exercses) and a sample sze sample. = Table 3 presents the basc descrptve statstcs obtaned from the Table 3. Descrptves statstcs Mean St. Dev. Partcpaton (1975) Hours (1975) Log wages (1975) Partcpaton (1976) Hours (1976) Log wages (1976) Partcpaton (1977) Hours (1977) Log wages (1977) Partcpaton (1978) Hours (1978)

15 Log wages (1978) Partcpaton (1979) Hours (1979) Log wages (1979) Partcpaton (1980) Hours (1980) Log wages (1980) Partcpaton (1981) Hours (1981) Log wages (1981) D D Notes. () Log wages s log of the hourly wage. () D 1 = 1 f at least one chld less that 6 years old s present. () D 2 = 1 f at least one chld older than 5 and younger than 10 years old s present. Our estmatng strategy s explaned s the prevous secton. We adjust a statc prob model for each year (as n equaton 2a) and we use the estmates to compute the nverse of the Mll rato. Once we stack the lambda for the seven perods, we nclude as an addonal varable for adjustng an hours equaton (as n equaton 1). The prob model s estmated ncludng only the log wage or ncludng a specfcaton wh famly composon varables, age and age square of the wfe and the log wage. We estmate a statc hours equaton ncludng only the wage, the two famly composon varables reported n Table 2 and the selecton term by Generalzed Least Squares (GLS) or usng Least Squares Dummy Varables (whn-groups regresson). In both cases we are assumng that the log wage s exogenous. Eher when the prob only ncludes the wage or when also ncludes the demographcs, the selecton term s hghly sgnfcant (values of the coeffcent vary between -370 and -300 and t-ratos vary between 9.6 and 13.2, dependng on the specfcaton of the prob model and on the method used for estmatng the equaton of nterest). Moreover, when we consder the wage s exogenous n ths statc model and we 15

16 estmate the hours equaton by GMM, the selecton term s (t-rato 4.78) n the general prob specfcaton and (t-rato 3.95) n the restrcted one. We then move to estmate equaton (1),.e. a dynamc hours equaton and we also consder the log wage as endogenous. We estmate ths model usng System-GMM and we present our results n Table 4 for the two specfcatons of the selecton equaton. Condonal to the valdy of the results, we can observe that there s no need to correct for selecton once we nstrument the lag of hours and log wages usng System-GMM. However, the results for the two models of the table suggest that once the dynamc structure of the hours s taken nto account, there s no need for addonal determnants of the hours suppled. Although the Sargan test margnally valdates the nstrument set, we should be careful because whle the model should detect frst order correlaton n the resduals snce s estmate n frst dfferences, m 2 suggest some msspecfcaton problem. 2 Table 4. Hours equaton for a sample of women rom the PSID Model 1 Model 2 h t (3.49) Log wages (0.29) D (0.23) D (0.72) Lambda (0.48) 0.64 (3.47) (0.05) (0.31) (0.31) (1.04) m m Sargan test (10) (0.09) (0.08) Notes. 2 In the model estmated n frst dfferences, we only nclude wages and famly composon varables because they vary enough to be ncluded n the specfcatons whle other varables do not. However, we do not nclude non-labor ncome and can be an mportant determnant both at the extensve and ntensve margns of female labor supply. 16

17 () Model 1 corresponds to the general prob specfcaton and Model 2 to the restrcted one. () m 1 and m 2 are the test for frst and second order seral correlaton of Arellano and Bond (1991). () Sargan test s the overdentfyng restrcton test (degrees of freedom n parenthess). (v) Robust t-statstcs n parenthess. (v) D 1 = 1 f at least one chld less that 6 years old s present. (v) D 2 = 1 f at least one chld older than 5 and younger than 10 years old s present. 5. Concludng remarks In ths paper we have analyzed the esmaton of dynamc panel data models subject to sample selecton from the pont of vew of practconers. We analyze the performance of GMM estmators n a very general case: a panel data sample selecton model where the regresson equatons s dynamc and s allowed for the exstence of endogenous regressors and correlated ndvdual unobserved heterogeney. In partcular we evaluate the performance of the estmator n three suatons: no endogeneous selecton, and endogenous selecton controllng and not controllng for sample selecton. To see the performance of the proposed estmator we perform a Monte Carlo study of the fne sample propertes of the proposed methods. We also face our proposed methods to a sample taken from the PSID for the adjustment of female labour supply equatons. Our Monte Carlo results suggest that n many standard cases s not necessary to correct the model for sample selecton. Ths s true n general for the purely autorregresve model and the dynamc model wh exogenous regressors, and more questonable when the regressor s endogenous (and we do not dspose of external nstruments). In the latter case a more general correcton of the sample selecton problem s requred. Prelmnary work wh a more general correcton suggest that a substantal fracton of the bas s removed. The estmates obtaned n the emprcal exercse bascally confrm the results of the Monte Carlo experment but the test detect some potental msspecfcaton and they should be vewed wh cauton. 17

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19 References Arellano, M. and Bond, S. (1991), "Some tests of specfcaton for panel data: Monte Carlo Evdence and an applcaton to employment equatons," Revew of Economc Studes, 58, Arellano, M. and Bover O. (1995): "Another look at the nstrumental-varable estmaton of error-components models" Journal of Econometrcs, 68, Baltag, B. (2005): Econometrc Analyss of Panel Data, John Wley and Sons, Chchester Blundell, R. and Bond, S. (1998) "Inal condons and moment restrctons n dynamc panel data models", Journal of Econometrcs, 87, Charler, E., Melenberg, B. and van Soest, A. (2001), "An analyss of housng expendures usng semparametrc methods and panel data", Journal of Econometrcs, 101, Dustman, C. and Rochna-Barrachna, M. R. (2002) "Selecton correcton n panel data models: An applcaton to labour supply and wages", IZA WP 162. Gonzalez-Chapela, J. (2004), On the prce of recreaton goods as a determnant of female labor supply, mmeo. Grlches, Zv & Hausman, Jerry A., "Errors n varables n panel data," Journal of Econometrcs, Elsever, vol. 31(1), pages , February. Heckman, J.J. (1976), "The common structure of statstcal models of truncaton, sample selecton and lmed dependent varables as a smple estmator for such models," Annals of Economc and Socal Measurement, 5, Hu, L. (2002), "Estmaton of a censored dynamc panel data model", Econometrca Jménez Martín, S. (2006), "Strke outcomes and wage settlements", Labour, 20, Jménez Martín, S Labeaga, JM and Rochna M (2009) Some estmators for dynamc sample selecton panel data models, mmeo. Jones, A. and Labeaga, J. M. (2004), "Indvdual heterogeney and censorng n panel data estmates of tobacco expendures", Journal of Appled Econometrcs, 18, Kyrazdou, E. (1997), "Estmaton of a panel data sample selecton model", Econometrca 65, Kyrazdou, E. (2001), "Estmaton of dynamc panel data sample selecton models", Revew of Economc Studes 68, Mundlak, Y. (1978), "On the poolng of tme seres and cross secton data", Econometrca 46, Semykna, A. and Wooldrgde, J.M. (2005), "Estmatng panel data models n the presence of endogeney and selecton: Theory and applcaton," mmeo. Vella, F. and Verbeek, M. (1998) "Two-step estmaton of panel data models wh censored endogenous varables and selecton bas", Journal of Econometrcs, 90, Verbeek, M., and Njman, T. (1992), " Testng for selectvy bas n panel data models," Internatonal Economc Revew 33, Wndmejer, Frank, "A fne sample correcton for the varance of lnear effcent two-step GMM estmators," Journal of Econometrcs, 126,

20 Wooldrgde, J.M. "Selecton Correctons for Panel Data under Condonal Mean Independence Assumptons," Journal of Econometrcs, 68 (1995): Wooldrgde, J.M. (2002), Econometrc Analyss of Cross-secton and Panel Data, The MIT Press, Cambrdge: Boston. 20