Abstract
This paper proposes a parametric approach to estimating a dynamic binary response panel data model that allows for endogenous contemporaneous regressors. Such a model is of particular value for settings in which one wants to estimate the effects of an endogenous treatment on a binary outcome. In order to demonstrate the usefulness of the approach, we use it to examine the impact of rural-urban migration on the likelihood that households in rural China fall below the poverty line. In this application, it is shown that migration is important for reducing the likelihood that poor households remain in poverty and that non-poor households fall into poverty. Furthermore, it is demonstrated that failure to control for unobserved heterogeneity would lead the researcher to underestimate the impact of migrant labor markets on reducing the probability of falling into poverty.
- 1
With a structural binary outcome model that allows for unobserved effects, one must be concerned that bias could be introduced through a systematic relationship between an unobserved effect and the initial value of the dependent variable. This is known as the initial conditions problem.
- 2
We follow Chay and Hyslop (2000) in classifying models requiring no assumption on unobservable effects or initial conditions as fixed effect models, and refer to random effect models as those in which one specifies a distribution of unobserved effects and initial conditions given exogenous explanatory variables.
- 3
More details on this approach and potential drawbacks can be found in Wooldridge (2010, p. 267).
- 4
The specification of this density in Wooldridge’s method is motivated by Chamberlain’s (1980) approach, which models the distribution of the unobserved effect conditional on the strictly exogenous variables.
- 5
Generally, model (1) can contain a random vector of endogenous covariates y2it. Modification of our approach discussed in this section to accommodate a random vector of endogenous regressors is straightforward assuming we have sufficient number of instrumental variables.
- 6
In other words, we assume that the vector z2it contains at least one element.
- 7
An additional advantage of the Mundlak device is that it might be easier to apply in the context of unbalanced panels. See Wooldridge (2009) and Abrevaya (2012) for a related discussion.
- 8
Generally, when a probit model contains a binary endogenous regressor, full maximum likelihood estimation of the bivariate probit model of interest can be used instead of a two-stage CF approach. Traditional two stage least square estimates of a corresponding linear model of interest can provide another option for approximating the average partial effects.
- 9
An alternative method for estimating π,
is the minimum distance estimator, described in detail by Chamberlain (1984). Cappellari (1999) has developed a code that conveniently implements this method in Stata.
- 10
See Wooldridge (2010) for details.
- 11
See chapter 12.8.2 in Wooldridge (2010) for more details.
- 12
Referral through one’s social network is a common method of job search in both the developing and developed world. Carrington, Detragiache, and Vishnawath (1996) explicitly show that in a model of migration, moving costs can decline with the number of migrants over time, even if wage differentials narrow between source communities and destinations. Survey-based evidence suggests that roughly 50% of new jobs in the US are found through referrals facilitated by social networks (Montgomery 1991). In a study of Mexican migrants in the US, Munshi (2003) shows that having more migrants from one’s own village living in the same city increases the likelihood of employment.
- 13
One shortcoming of the survey is the lack of individual-level information. However, we know the numbers of working-age adults and dependents, as well as the gender composition of household members.
- 14
Our approach to valuing consumption follows the suggestions of Chen and Ravallion (1996) for the NBS Rural Household Survey, and is explained in more detail in appendix A of Benjamin, Brandt, and Giles (2005).
- 15
The cross-sections used were the rural samples of the 1993, 1997 and 2000 China Health and Nutrition Survey (CHNS) and a survey conducted in 2000 by the Center for Chinese Agricultural Policy (CCAP) with Scott Rozelle (UC Davis) and Loren Brandt (University of Toronto).
- 16
From follow up interviews with village leaders, it is apparent that registered residents living outside the county are unlikely to be commuters and generally live and work outside the village for more than 6 months of the year.
- 17
Wooldridge (2002) shows that when the assumption of strict exogeneity of the regressors fails in the context of the standard FE estimation the inconsistency of the instrument is of order T–1.
- 18
We do not know village small group membership in the RCRE survey prior to 2003 when a new survey instrument was introduced. If we regress land per capita on village dummy variables in 2003, we obtain an R2 of 0.503, while if we run a regression of land per capita on small group dummy variables, we obtain an R2 of 0.616. A Lagrange Multiplier test for whether the small group effects add anything significant over the village effects, which is effectively a test of whether small group coefficients are constant within villages, yields an LM statistic of 310.67, which has a p-value of 0.0000.
- 19
Regressing a dependent variable (such as the endogeneous village-level measure of migration) on independent variables at a lower level of aggregation is not new in empirical research. A recent paper by Olken (2009), for example, estimates such a model using cross-sectional data looking at how the number of channels (measured at the sub-district level) vary with village characteristics (which are at a lower level of aggregation).
- 20
Since the RCRE survey was not conducted in 1992 and 1994, we estimate the dynamic model with 2-year spacing from 1989 to 2001.
- 21
When applying the CF approach, we detect serial correlation in the first-stage residuals (p-value = 0.000). Thus, on the second stage, we use the first-stage residuals free of serial correlation. To obtain the latter, we first estimate the slope coefficient from an AR(1) regression of the first-stage residuals using OLS. Second, knowing the consistent slope estimate, we employ the Cochrane-Orcutt transformation to get the residuals free of serial correlation.
- 22
We employ the Hausman test for endogeneity to formally assess the need to control for endogeneity of migration share. The t-statistic for the significance of the first-stage residuals in the pure RE probit model is 3.08 with p-value of 0.002, which suggests there is enough evidence to reject the null hypothesis that the share of village out-migrants is exogenous. For the correlated RE probit, the t-statistic for the first-stage residuals is 2.93 with p-value of 0.003. Thus, for the correlated RE model, we also reject the null hypothesis that the share of migrants is exogenous.
- a
The paper has benefited from helpful comments and conversations with Alan de Brauw, Ana Maria Herrera, Martin Ravallion, Peter Schmidt, David Tschirley, Adam Wagstaff, Jeffrey Wooldridge, from seminar participants at Ohio State University, University of South Carolina, George Washington University and conference participants at the June 2007 UNU-WIDER Conference on Fragile States held in Helsinki and the September 2009 Midwest Econometrics Group Annual Meeting. We also would like to thank the co-editor, Jason Abrevaya, and two anonymous referees for valuable comments and suggestions. We gratefully acknowledge financial support for data collection from the National Science Foundation (SES-0214702) and support for work on this paper from the Knowledge for Change Trust Fund at the World Bank (RF-P111846-RESE-TF092861 and RF-P116739-RESE-TF094568). The research discussion and conclusions presented in this paper reflect the views of the authors and should not be attributed to the World Bank or to any affiliated organization or member country.
References
Abrevaya, J. 2012. “The Projection Approach for Unbalanced Panel Data.” Econometrics Journal forthcoming.10.1111/j.1368-423X.2012.00389.xSearch in Google Scholar
Adren, T. 2007. “The Persistence of Welfare Partipation.” IZA Discussion Paper 3100 (October 2007).Search in Google Scholar
Bane, M. J., and D. T. Ellwood. 1986. “Slipping into and Out of Poverty: The Dynamics of Spells.” The Journal of Human Resources 21 (1): 1–23.10.2307/145955Search in Google Scholar
Benjamin, D., L. Brandt, and J. Giles. 2005. “The Evolution of Income Inequality in Rural China.” Economic Development and Cultural Change 53 (4): 769–824.10.1086/428713Search in Google Scholar
Biewen, M. 2009. “Measuring State Dependence in Individual Poverty Status: Are There Feedback Effects to Employment Decisions and Household Composition?” Journal of Applied Econometrics 24 (7): 1095–1116.10.1002/jae.1081Search in Google Scholar
Cai, F., A. Park, and Y. Zhao. 2008. “The Chinese Labor Market.” chapter prepared for China’s Great Economic Transition, edited by Loren Brand and Thomas Rawski, Cambridge University Press.Search in Google Scholar
Cappellari, L. 1999. “Minimum Distance Estimation of Covariance Structures.” 5th UK Meeting of Stata Users.Search in Google Scholar
Carrington, W., E. Detragiache, and T. Vishnawath. 1996. “Migration with Endogenous Moving Costs.” American Economic Review 86 (4): 909–930.Search in Google Scholar
Chamberlain, G. 1980. “Analysis of Covariance with Qualitative Data.” Review of Economic Studies 47: 225–238.10.2307/2297110Search in Google Scholar
Chamberlain, G. 1984. “Panel Data.” In Handbook of Econometrics, edited by Z. Griliches and M. D. Intriligator, 1247–1318. Vol. 2. Amsterdam: North Holland.10.1016/S1573-4412(84)02014-6Search in Google Scholar
Chan, K. W., and L. Zang. 1999. “The Hukou System and Rural-Urban Migration in China: Processes and Changes.” China Quarterly 160: 818–855.10.1017/S0305741000001351Search in Google Scholar
Chay, K. Y., and D. R. Hyslop. 2000. “Identification and Estimation of Dynamic Binary Response Models: Empirical Evidence Using Alternative Approaches.” mimeo.Search in Google Scholar
Chen, S., and M. Ravallion. 1996. “Data in Transition: Assessing Rural Living Standards in Southern China.” China Economic Review 7 (1): 23–56.10.1016/S1043-951X(96)90018-8Search in Google Scholar
Chiappori, P., and B. Salanie. 2000. “Testing for Asymmetric Information in Insurance Markets.” Journal of Political Economy 108: 56–78.10.1086/262111Search in Google Scholar
de Brauw, A., and J. Giles. 2008a. “Migrant Opportunity and the Educational Attainment of Youth in Rural China.” Policy Research Working Paper 4585, The World Bank (February 2008).10.1596/1813-9450-4526Search in Google Scholar
de Brauw, A., and J. Giles. 2008b. “Migrant Labor Markets and the Welfare of Rural Households in the Developing World: Evidence from China.” Policy Research Working Paper 4526, The World Bank (April 2008).10.1596/1813-9450-4585Search in Google Scholar
Devicienti, D., and A. Poggi. 2007. “Poverty and Social Exclusion: Two Sides of the Same Coin or Dynamically Interrelated Processes?.” LABORatorio R. Revelli Working Papers Series 62, LABORatorio R. Revelli, Centre for Employment Studies.Search in Google Scholar
Du, Y., A. Park, and S. Wang. 2005. “Migration Helping China’s Poor?” Journal of Comparative Economics 33 (4): 688–709.10.1016/j.jce.2005.09.001Search in Google Scholar
Giles, J. 2006. “Life More Risky in the Open? Household Risk-Coping and the Opening of China’s Labor Markets.” Journal of Development Economics 81 (1): 25–60.10.1016/j.jdeveco.2005.04.006Search in Google Scholar
Giles, J., and K. Yoo. 2007. “Precautionary Behavior, Migrant Networks and Household Consumption Decisions: An Empirical Analysis Using Household Panel Data from Rural China.” Review of Economics and Statistics 89 (3): 534–551.10.1162/rest.89.3.534Search in Google Scholar
Hahn, J., and G. Kuersteiner. 2002. “Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects When Both n and T Are Large.” Econometrica 70: 1639–1657.10.1111/1468-0262.00344Search in Google Scholar
Hansen, J., and R. Wahlberg. 2009. “Poverty Persistence in Sweden.” Review of the Economics of the Household 7 (2): 105–132.10.1007/s11150-009-9054-9Search in Google Scholar
Heckman, J. J. 1981. “The Incidental Parameters Problem and the Problem of Initial Conditions in Estimating a Discrete Time - Discrete Data Stochastic Process.” In Structural Analysis of Discrete Data with Econometric Applications, edited by C.F. Manski and D. McFadden, 179–195. MIT Press: Cambridge, MA.Search in Google Scholar
Heckman, J. J., and R. J. Willis. 1977. “A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women.” Journal of Political Economy 85: 27–58.10.1086/260544Search in Google Scholar
Honoré, B. E., and E. Kyriazidou. 2000. “Panel Data Discrete Choice Models with Lagged Dependent Variables.” Econometrica 68: 839–874.10.1111/1468-0262.00139Search in Google Scholar
Hyslop, D. R. 1999. “State Dependence, Serial Correlation and Heterogeneity in Intertemporal Labor Force Participation of Married Women.” Econometrica 67 (6): 1255–1294.10.1111/1468-0262.00080Search in Google Scholar
Jalan, J., and M. Ravallion. 1998. “Transient Poverty in Post-Reform Rural China.” Journal of Comparative Economics 26 (2): 338–357.10.1006/jcec.1998.1526Search in Google Scholar
Jalan, J., and M. Ravallion. 2002. “Geographic Poverty Traps? A Micro Model of Consumption Growth in Rural China.” Journal of Applied Econometrics 17 (4): 329–346.10.1002/jae.645Search in Google Scholar
Liang, Z., and Z. Ma. 2004. “China’s Floating Population: New Evidence from the 2000 Census.” Population and Development Review 30 (3): 467–488.10.1111/j.1728-4457.2004.00024.xSearch in Google Scholar
Mallee, H. 1995. “China’s Household Registration System Under Reform.” Development and Change 26 (1): 1–29.10.1111/j.1467-7660.1995.tb00541.xSearch in Google Scholar
Meng, X. 2000. “Regional Wage Gap, Information Flow, and Rural-Urban Migration,” In Rural Labor Flows in China, edited by Yaohui Zhao and Loraine West, 251–277. Berkeley: University of California Press.Search in Google Scholar
Montgomery, J. D. 1991. “Social Networks and Labor-Market Outcomes: Toward an Economic Analysis.” American Economic Review 81 (5): 1407–1418.Search in Google Scholar
Mundlak, Y. 1978. “On the Pooling of Time Series and Cross Section Data.” Econometrica 46: 69–85.10.2307/1913646Search in Google Scholar
Munshi, K. 2003. “Networks in the Modern Economy: Mexican Migrants in the U.S. Labor Market.” Quarterly Journal of Economics 118 (2): 549–599.10.1162/003355303321675455Search in Google Scholar
Olken, B. A. 2009. “Do TV and Radio Destroy Social Capital? Evidence from Indonesian Villages.” American Economic Journal: Applied Economics 1 (4): 1–35.Search in Google Scholar
Papke, L. E., and J. M. Wooldridge. 2008. “Panel Data Methods for Fractional Response Variables with an Application to Test Pass Rates.” Journal of Econometrics 145: 121–13310.1016/j.jeconom.2008.05.009Search in Google Scholar
Ravallion, M. 1996. “Issues in Measuring and Modeling Poverty.” The Economic Journal 106: 1328–1343.10.2307/2235525Search in Google Scholar
Ravallion, M., and S. Chen. 2007. “China’s (Uneven) Progress Against Poverty.” Journal of Development Economics 82 (1): 1–42.10.1016/j.jdeveco.2005.07.003Search in Google Scholar
Rivers, D., and Q. H. Vuong. 1988. “Limited Information Estimators and Exogeneity Tests for Simultaneous Probit Models.” Journal of Econometrics 39: 347–366.10.1016/0304-4076(88)90063-2Search in Google Scholar
Rozelle, S., L. Guo, M. Shen, A. Hughart, and J. Giles. 1999. “Leaving China’s Farms: Survey Results of New Paths and Remaining Hurdles to Rural Migration.” The China Quarterly 158: 367–393.10.1017/S0305741000005816Search in Google Scholar
Smith, R., and R. Blundell. 1986. “An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply.” Econometrica 54: 679–685.10.2307/1911314Search in Google Scholar
Taylor, J. E., S. Rozelle, and A. de Brauw. 2003. “Migration and Incomes in Source Communities: A New Economics of Migration Perspective from China.” Economic Development and Cultural Change 52 (1): 75–101.10.1086/380135Search in Google Scholar
Wooldridge, J. M. 2000. “A Framework for Estimating Dynamic, Unobserved Effects Panel Data Models with Possible Feedback to Future Explanatory Variables.” Economics Letters 68: 245–250.10.1016/S0165-1765(00)00230-5Search in Google Scholar
Wooldridge, J. M. 2005. “Simple Solutions to the Initial Conditions Problem in Dynamic, Nonlinear Panel Data Models with Unobserved Heterogeneity.” Journal of Applied Econometrics 20: 39–54.10.1002/jae.770Search in Google Scholar
Wooldridge, J. M. 2009. “Correlated Random Effects Models with Unbalanced Panels.” Michigan State University, mimeo.Search in Google Scholar
Wooldridge, J. M. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed. MIT Press: Cambridge, MA.Search in Google Scholar
Zhao, Y. 2003. “The Role of Migrant Networks in Labor Migration: The Case of China.” Contemporary Economic Policy 21 (4): 500–511.10.1093/cep/byg028Search in Google Scholar
©2013 by Walter de Gruyter Berlin Boston
