Probit with heteroscedasticity: an application to Indian poverty analysis

Abstract

This study argues that in limited dependent variable models, when there is heteroscedasticity, a probit model with a heteroscedastic structure should be estimated. The problem is illustrated using unit record data from the Indian National Sample Survey to analyse the determinants of poverty at household level. It is found that these biases are large even with large number of observations because in the limited dependent variable case, the bias does not vanish asymptotically when the assumption of homoscedasticity breaks down. Both regression coefficients and marginal effects differ widely between probit and hetprobit models in this study.

Acknowledgements

The 50th Round data were made available under the collaborative arrangement between the National Sample Survey Organisation, Government of India, and the Overseas Development Group, School of Development Studies, of the University of East Anglia. The authors’ work on this study was funded in part by SSRC Grant No R8256 of the UK Department of International Development, which also funded access to the 55th Round data. We would also like to acknowledge useful contributions from our colleagues in R8256, Dr Richard Palmer-Jones, of the School of Development Studies, University of East Anglia and Dr Amaresh Dubey, Department of Economics, North East Hills University, Shillong, India.

Notes

¹ The study presents estimates of standard probit approach and random effects model but there was no mention of heteroscedasticity with respect to standard probit model.

² Deaton and Tarozzi (2000) have pointed out that a limitation of the official poverty lines is that the price indices used to update these poverty lines are based on fixed commodity ‘weights’ that have become outdated over time. They have proposed an alternative set of poverty lines based on unit values and quantities consumed obtained from the NSS expenditure surveys themselves. However, a drawback of the Deaton–Tarozzi poverty lines is that they are not available for all states and Union territories in India. Furthermore, in the present case, the limitation of the official poverty lines is of less importance as poverty is not compared over time.

³ The large standard errors and large coefficients or vice versa might suggest that the assumption of heteroscedasticity leads to a considerable distortion of the results and that could be deceiving. However, marginal effects do not have sign reversals in any of the results.