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Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?

An Erratum to this article was published on 29 March 2008

Abstract

This paper explores income distribution modeling approaches for poverty analysis in a CGE micro-simulation context. Income distribution functional forms such as the lognormal, Pareto, beta distribution and empirical methods are currently used in CGE models in parallel with the estimation of FGT poverty indices. The particular methods or functional forms used in this context are not always clearly defined and justified. In this paper, we investigate and provide better criteria for selecting a functional distribution for poverty analysis. To achieve this, we apply parametric estimation to seven functional forms and compare the results to a purely “empirical” method. The results showed that no single form is more appropriate in all instances or for all household subgroups. The choice of a modeling approach should be motivated by a search for best fit and should be based on appropriate statistical tests. Selecting inappropriate distributional forms can lead to biased results in terms of poverty analysis. Introducing functional forms in the empirical approach can also provide greater confidence in the results obtained.

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Abbreviations

AUE:

other urban educated

AUNE:

other-urban non-educated

BN:

basic needs

CDF:

cumulative density function

CES:

constant elasticity of substitution

CET:

constant elasticity of transformation

CGE:

computable general equilibrium

Champ:

Champernowne

DAD:

distributive analysis – analyse distributive

DAG:

Dagum

DKRE:

Dakar educated

DKRNE:

Dakar non-educated

E:

nominal exchange rate

EDF:

empirical distribution function

ESAM:

enquête sénégalaise auprès des ménages

FGT:

Foster, Greer and Thorbecke

Logn:

lognormal

Logn3:

displaced lognormal

OECD:

Organization for Economic Co-operation and Development

Pdf:

probability density function

r:

rental rate of capital

RE:

rural educated

RNE:

rural non-educated

w:

skilled wages;

SAE:

sum of absolute errors

SAM:

social accounting matrix

Sg:

government savings;

SM:

Singh–Maddala

wn:

unskilled wages;

SSE:

sum of squared errors

Yg:

Government income

Ytm:

total household income;

Va:

value-added

References

  1. 1.

    Aaberge, R.U., Colombino, E., Homøy, B. Strøm, Wennemo T.: Population aging and fiscal sustainability: an integrated micro–macro analysis of required tax changes, discussion paper no. 366, Statistics Norway, Oslo (2004)

  2. 2.

    Abdelkhalek, T., Chaoubi, A.: Distributions des dépenses de consommation des ménages au Maroc: une analyse paramétrique. Rev. Écon. Dév. 2, 85–106 (2004)

    Article  Google Scholar 

  3. 3.

    Adelman, I., Robinson, S.: Income distribution policy: a computable general equilibrium model of South Korea. In: Adelman, I (ed.) The Selected Essays of Irma Adelman. Volume 1. Dynamics and Income Distribution. Economists of the Twentieth Century Series, 256–89. Aldershot, UK (1979)

  4. 4.

    Aitchinson, J., Brown J.A.: The lognormal distribution. Cambridge University Press, Cambridge (1957)

    Google Scholar 

  5. 5.

    Aka, F.B.: Fiscal adjustment, poverty, inequality and welfare in Côte d’Ivoire DIAL, (mimeo), Paris (2003)

  6. 6.

    Ammon O.: Die Gesellschaftsordnung und ihre Natürlichen Grundlagen, Jena (1895)

  7. 7.

    Annabi, N, Cissé, F., Cockburn, J., Decaluwé, B.: Trade liberalisation, growth and poverty in senegal: a dynamic microsimulation CGE model analysis, Working paper 2005–07. CEPII, Paris, France (2005)

  8. 8.

    Armington, P.S.: A theory of demand for products distinguished by place of production. IMF staff paper no. 16, 159–176, (1969)

  9. 9.

    Bandourian R., McDonald, J.B., Turley, R.S.: A comparison of parametric models of income distribution across countries and over time. Luxembourg income study working paper no. 305, Luxembourg (2002)

  10. 10.

    Boccanfuso, D., Cabral, F., Cissé, F., Diagne, A., Savard L.: Un modèle CGE-Multi-Ménages Intégrés Appliqué à l’Économie Sénégalaise. Cahier du CIRPEE, no. 03-33, Québec City (2003)

  11. 11.

    Bordley, R.F., McDonald, J.B., Mantrala A.: Something new, something old: parametric models for the size distribution of income. J. Income Distrib. 6.1, 97–102 (1996)

    Google Scholar 

  12. 12.

    Bourguignon, F., Robilliard, A.-S., Robinson, S.: Representative versus real households in the macro-economic modeling of inequality. Working paper no. DT/2003-10, DIAL, Paris (2003)

  13. 13.

    Champernowne, D.G.: A model for income distribution. Econ. J. 53, 318–351 (1953a)

    Article  Google Scholar 

  14. 14.

    Champernowne, D.G.: The graduation of income distribution. Econometrica 20.4, 591–615 (1953b)

    Google Scholar 

  15. 15.

    Chia, N.C., Wahba, S., Whalley, J.: Poverty-reduction targeting programs: a general equilibrium approach. J. Afr. Econ. 3.2, 309–338 (1994)

    Google Scholar 

  16. 16.

    Cockburn, J.: Trade liberalization and poverty in Nepal: a computable general equilibrium micro-simulation analysis, Working paper no. 01-18, CREFA, Université Laval, Québec City (2001)

  17. 17.

    Cockburn, J.: Procedures for conducing poverty/distribution analysis of CGE simulation results with DAD. CIRPÉE, Université Laval, Québec City (2005)

  18. 18.

    Cogneau D., Robillard, A.S.: Income distribution, poverty and growth in Madagascar: micro simulations in a general equilibrium framework, IFPRI TMD Discussion paper no. 61, IFPRI, Washington (2000)

  19. 19.

    Cowell, F.A.: Measurement of inequality. In: Atkinson, A.B., Bourguignon, F. (eds.) Handbook of Income Distribution. North Holland, Amsterdam (2000)

    Google Scholar 

  20. 20.

    Cowel, F.A., Victoria Feser, M.P.: Robustness properties of inequality measures. Econometrica 64, 77–101 (1996)

    Article  Google Scholar 

  21. 21.

    Cowel, F.A., Victoria Feser, M.P.: Distribution free inference for welfare indices under complete and incomplete information. J. Econ. Inequality 1, 191–219 (2003)

    Article  Google Scholar 

  22. 22.

    D’Agostino R.B., Stephens, M.A.: Goodness-of-Fit Techniques. Marcel Dekker, New York (1986)

    Google Scholar 

  23. 23.

    Dagum, C.: A new model of personal income distribution: specification and estimation. Econ. Appl. 3.3, 413–437 (1977)

    Google Scholar 

  24. 24.

    Damuri Y.Z., Perdana, A.A.: The impact of fiscal policy on income distribution and poverty: a computable general equilibrium approach for Indonesia, CSIS working paper series no. 068, Jakarta (2003)

  25. 25.

    Decaluwé, B., Patry, A., Savard, L., Thorbecke, E.: Poverty analysis within a general equilibrium framework working paper 99-09, African Economic Research Consortium (1999a)

  26. 26.

    Decaluwé, B., Dumont, J.C., Savard, L.: How to measure poverty and inequality in general equilibrium framework, working paper no. 9920, Québec City, CREFA, Laval University (1999b)

  27. 27.

    Decaluwé, B., Savard, L., Thorbecke, E.: General equilibrium approach for poverty analysis: with an application to Cameroon. Afr. Dev. Rev. 17(2), 213–243 (2005)

    Article  Google Scholar 

  28. 28.

    de Janvry, A., Sadoulet, E., Fargeix, A.: Adjustment and Equity in Ecuador. OECD Development Center, Paris (1991)

    Google Scholar 

  29. 29.

    Dervis, K, de Melo, J., Robinson, S.: General Equilibrium Models for Development Policy, p 526. Cambridge University Press, London, (1982)

    Google Scholar 

  30. 30.

    de Souza Ferreira Filho, J.B., Horridge, M.: Economic integration, poverty and regional inequality in Brazil, working paper G-149, COPS/IMPACT, Monash University, Clayton (2004)

  31. 31.

    Duclos J.Y., Arrar, A., Fortin, C.: DAD 4.03: Distributional analysis/Analyse distributive, MIMAP Project, International Development Research Centre, Government of Canada (1999)

  32. 32.

    Fisk, P.R.: The graduation of income distribution. Econometrica 29.2, 171–185 (1961)

    Article  Google Scholar 

  33. 33.

    Flaichaire, E., Nunez O.: Estimation of income distribution and detection of subpopulations: an explanatory model, mimeo presented at the JMA, Montpellier (2003)

  34. 34.

    Foster, J., Greer, J., Thorbecke, E.: A class of decomposable poverty measure. Econometrica 52.3, 761–766 (1984)

    Article  Google Scholar 

  35. 35.

    Gibrat R.: Les Inégalités économiques. Paris, Sirely (1931)

  36. 36.

    Gordy, M.B.: A Generalization of the Generalized Beta Distribution. Board of Governors of the Federal Reserve System, Washington (1998)

  37. 37.

    Gørtz, M., Harrison, G., Neilsen, C., Rutherford, T.: Welfare gains of extending opening hours in Denmark Economic Working Paper B-00-03, Darla Moore School of Business, University of South Carolina, Columbia, South Carolina (2000)

  38. 38.

    Khan, H.A.: Using macroeconomic computable general equilibrium model for assessing poverty impact of structural adjustment policies. Discussion paper series no. 12, ADB Institute, Manila (2004)

  39. 39.

    Kirman, A.: Whom or what does the representative individual represent? J. Econ. Perspect. 6(2), 117–136 (1992)

    Google Scholar 

  40. 40.

    Kleiber, C.: Dagum vs. Singh–Maddala income distributions. Econ. Lett. 53(3), 265–268 (1996)

    Article  Google Scholar 

  41. 41.

    Luppino, M., Gajewski, G., Zohir, S.: Estimating the impact of the Jamuna Bridge on poverty levels in Bangladesh using SAM and CGE model: a comparative study, paper presented at the ECOMOD Input-Output and general equilibrium: data modeling and policy analysis conference, Brussels (2004)

  42. 42.

    Marron, J.S., Schmitz, H.P.: Simultaneous density estimation of several income distributions. Econom. Theory 8, 476–488 (1992)

    Google Scholar 

  43. 43.

    McDonald, J.B.: Some generalized functions for the size distribution of income. Econometrica 52, 647–663 (1984)

    Article  Google Scholar 

  44. 44.

    McDonald, J.B., Ransom, M.R.: Functional forms, estimation techniques and the distribution of income. Econometrica 47.6, 1513–1525 (1979)

    Article  Google Scholar 

  45. 45.

    McDonald, J.B., Xu Y.J.: A Generalization of the Beta distribution with application. J. Econom. 66.2, 152–204 (1995)

    Google Scholar 

  46. 46.

    Metcalf, E.C.: An econometric model of the income distribution. Markham, Chicago (1972)

    Google Scholar 

  47. 47.

    Montaud, J.M.: Dotations en capital et pauvreté des ménages au Burkina Faso : une analyse en équilibre général calculable. Rev. Rev. Écon. Dév. 1, 42–72 (2003)

    Google Scholar 

  48. 48.

    Mujeri, M., Khondker, B.: Poverty implication of trade liberalization in Bangladesh: a general equilibrium analysis. Globalization and Poverty Program DFID, mimeo, Karachi (2002)

  49. 49.

    Pareto, V.: Cours d’économie publique. Rouge, Lausanne (1897)

  50. 50.

    Parker, S.C.: The generalised Betas a model for the distribution of earnings. Econ. Lett. 62.2, 197–200 (1999)

    Article  Google Scholar 

  51. 51.

    Ravallion, M.: Poverty comparisons. Harwood, New York (1994)

    Google Scholar 

  52. 52.

    Rutherford, R.S.G.: Income distribution a new model. Econometrica 23, 277–294 (1955)

    Article  Google Scholar 

  53. 53.

    Sahota, G.: Theories of personal income distribution: a survey. J. Econ. Lit. 16, 1–55 (1978)

    Google Scholar 

  54. 54.

    Salem, A.B.Z., Mount, T.D.: A convenient descriptive model of income distribution. Econometrica 42, 1115–1127 (1974)

    Article  Google Scholar 

  55. 55.

    Savard L.: A segmented endogenous labor market for poverty, income distribution analysis in a CGE-Household MS model: a top–down/bottom–up approach, working paper no. 03-43, CIRPEE, Université Laval, Quebec City (2003)

  56. 56.

    Savard, L.: Poverty and inequality analysis within a CGE framework: a comparative analysis of the representative agent and microsimulation approaches. Dev. Policy Rev. 23.3, 313–332 (2005)

    Article  Google Scholar 

  57. 57.

    Silverman, B.W.: Density Estimation for Statistics and data analysis. Chapman and Hall, London (1986)

    Google Scholar 

  58. 58.

    Singh, S.K., Maddala, G.S.: A function for the size distribution of incomes. Econometrica 44, 963–973 (1976)

    Article  Google Scholar 

  59. 59.

    Stifel, D., Thorbecke, E.: A dual-dual CGE model of an archetype African economy: trade reform, migration and poverty. J. Policy Model. 25.3, 207–235 (2003)

    Article  Google Scholar 

  60. 60.

    Tadikamalla, P.R.: A look at the Burr and related distributions. Int. Stat. Rev. 48, 337–344 (1980)

    Article  Google Scholar 

  61. 61.

    Victoria-Feser, M.-P.: A general robust approach to the analysis of income distribution, inequality and poverty. Int. Stat. Rev. 68, 277–293 (2000)

    Article  Google Scholar 

  62. 62.

    Victoria-Feser, M.-P.:Robust estimation of personal income distribution models. DARP discussion paper no 4, STICERD, LSE (1993)

  63. 63.

    Zhang, Q.: DAD, an innovative tool for income distribu tion analysis. J. Econ. Inequality 1, 281–284 (2003)

    Article  Google Scholar 

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Correspondence to Luc Savard.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10888-008-9084-1

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Boccanfuso, D., Decaluwé, B. & Savard, L. Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?. J Econ Inequal 6, 149–184 (2008). https://doi.org/10.1007/s10888-007-9055-y

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Keywords

  • Computable general equilibrium models
  • Estimation
  • Measurement and poverty analysis
  • Personal income and wealth distribution

JEL Classification

  • I32
  • D31
  • C13
  • C68