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GMM Estimation of a Maximum Distribution With Interval Data

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  • Wu, Ximing
  • Perloff, Jeffrey M.

Abstract

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

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    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. 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.
    3. Wu, Ximing & Perloff, Jeffrey M., 2004. "China's Income Distribution Over Time: Reasons for Rising Inequality," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt9jw2v939, Department of Agricultural & Resource Economics, UC Berkeley.
    4. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    5. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    6. Wu, Ximing & Perloff, Jeffrey M., 2004. "China's Income Distribution Over Time: Reasons for Rising Inequality," Institute for Research on Labor and Employment, Working Paper Series qt9jw2v939, Institute of Industrial Relations, UC Berkeley.
    7. Jeffrey M. Perloff & Ximing Wu, 2004. "China's Income Distribution and Inequality," Econometric Society 2004 North American Summer Meetings 316, Econometric Society.
    8. Ximing Wu & Thanasis Stengos, 2005. "Partially adaptive estimation via the maximum entropy densities," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 352-366, December.
    9. Dalén, Jörgen, 1987. "Algebraic bounds on standardized sample moments," Statistics & Probability Letters, Elsevier, vol. 5(5), pages 329-331, August.
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    Cited by:

    1. Piao Wang & Shahid Hussain Gurmani & Zhifu Tao & Jinpei Liu & Huayou Chen, 2024. "Interval time series forecasting: A systematic literature review," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(2), pages 249-285, March.
    2. 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.
    3. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.

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    Keywords

    Income Distribution;

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