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GMM Estimation of a Maximum Distribution With Interval Data


  • Wu, Ximing
  • Perloff, Jeffrey M.


We develop a GMM estimator for the distribution of a variable where summary statistics are available only for intervals of the random variable. Without individual data, once cannot calculate the weighting matrix for the GMM estimator. Instead, we propose a simulated weighting matrix based on a first-step consistent estimate. When the functional form of the underlying distribution is unknown, we estimate it using a simple yet flexible maximum entropy density. our Monte Carlo simulations show that the proposed maximum entropy density is able to approximate various distributions extremely well. The two-step GMM estimator with a simulated weighting matrix improves the efficiency of the one-step GMM considerably. We use this method to estimate the U.S. income distribution and compare these results with those based on the underlyign raw income data.

Suggested Citation

  • Wu, Ximing & Perloff, Jeffrey M., 2005. "GMM Estimation of a Maximum Distribution With Interval Data," Institute for Research on Labor and Employment, Working Paper Series qt7jf5w1ht, Institute of Industrial Relations, UC Berkeley.
  • Handle: RePEc:cdl:indrel:qt7jf5w1ht

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    References listed on IDEAS

    1. Golan, Amos & Judge, George & Perloff, Jeffrey M, 1996. "Estimating the Size Distribution of Firms Using Government Summary Statistics," Journal of Industrial Economics, Wiley Blackwell, vol. 44(1), pages 69-80, March.
    2. Jeffrey M. Perloff & Ximing Wu, 2004. "China's Income Distribution and Inequality," Econometric Society 2004 North American Summer Meetings 316, Econometric Society.
    3. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    4. Thanasis Stengos & Ximing Wu, 2005. "Partially Adaptive Estimation via Maximum Entropy Densities," University of Cyprus Working Papers in Economics 6-2005, University of Cyprus Department of Economics.
    5. Dalén, Jörgen, 1987. "Algebraic bounds on standardized sample moments," Statistics & Probability Letters, Elsevier, vol. 5(5), pages 329-331, August.
    6. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    7. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
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    Cited by:

    1. Lee, Jongchul, 2013. "A provincial perspective on income inequality in urban China and the role of property and business income," China Economic Review, Elsevier, vol. 26(C), pages 140-150.

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    Income Distribution;


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