A New Method to Estimate the Low Income Proportion: Monte Carlo Simulations

Authors: Encarnación Álvarez, Rosa M. García-Fernández, Juan F. Muñoz

Abstract:

Estimation of a proportion has many applications in economics and social studies. A common application is the estimation of the low income proportion, which gives the proportion of people classified as poor into a population. In this paper, we present this poverty indicator and propose to use the logistic regression estimator for the problem of estimating the low income proportion. Various sampling designs are presented. Assuming a real data set obtained from the European Survey on Income and Living Conditions, Monte Carlo simulation studies are carried out to analyze the empirical performance of the logistic regression estimator under the various sampling designs considered in this paper. Results derived from Monte Carlo simulation studies indicate that the logistic regression estimator can be more accurate than the customary estimator under the various sampling designs considered in this paper. The stratified sampling design can also provide more accurate results.

Keywords:

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1096541

References:

[1] E. A´ lvarez, R.M. Garc´ıa-Ferna´ndez, J.F. Mun˜oz and F.J. Blanco- Encomienda, "On estimating the headcount index by using the logistic regression estimator”. International Journal of Mathematical, Computational, Physical and Quantum Engineering, 8(8),pp. 1039–1041, 2014.
[2] J. Chen and R.R. Sitter, ”A pseudo empirical likelihood approach to the effective use of auxiliary information in complex surveys”. Statistica Sinica, 9, pp. 385-406, 1999.
[3] E. Crettaz and C. Suter, ”The impact of Adaptive Preferences on Subjective Indicators: An Analysis of Poverty Indicators”. Social Indicators Research, 114, pp. 139-152, 2013.
[4] J.C. Deville and C.E. S¨arndal, ”Calibration estimators in survey sampling”. Journal of the American Statistical Association, 87, pp. 376-382, 1992.
[5] P. Duchesne, ”Estimation of a proportion with survey data”. Journal of Statistics Education, 11, pp. 1-24, 2003.
[6] F. Giambona and E. Vassallo, ”Composite Indicator of Social Inclusion for European Countries”. Social Indicators Research, 116, pp. 269-293, 2014.
[7] D.G. Horvitz and D.J. Thompson, ”A generalization of sampling without replacement from a finite universe”. Journal of the American Statistical Association, 47, pp. 663-685, 1952.
[8] R.Lehtonen and A. Veijanen, ”On multinomial logistic generalized regression estimators”, Survey Methodology, 24, pp. 51-55, 1998.
[9] M. Medeiros, ”The Rich and the Poor: the Construction of an Affluence Line from the Poverty line”. Social Indicators Research, 78, pp. 1-18, 2006.
[10] I. Molina and J.N.K. Rao, ”Small area estimation of poverty indicators”, The Canadian Journal of Statistics, 38, pp. 369-385, 2010.
[11] J. Navicke, O. Rastrigina and H. Sutherland, ”Nowcasting Indicators of Poverty Risk in the European Union: A Microsimulation Approach”. Social Indicators Research, doi: 10.1007/s11205-013-04918. 2013
[12] J.N.K. Rao, J.G. Kovar and H.J. Mantel, ”On estimating distribution function and quantiles from survey data using auxiliary information”. Biometrika, 77, pp. 365-375, 1990
[13] C.E. S¨arndal, B. Swensson and J. Wretman, Model Assisted Survey sampling, Springer Verlag, 1992.
[14] P.L.D. Silva and C.J. Skinner, ”Estimating distribution function with auxiliary information using poststratification”. Journal of Official Statistics, 11, pp. 277-294, 1995.
[15] S. Singh, Advanced sampling theory with application: how Michael selected Amy, Kluver Academic Publisher, 2003.