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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. 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. 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.
    5. Dalén, Jörgen, 1987. "Algebraic bounds on standardized sample moments," Statistics & Probability Letters, Elsevier, vol. 5(5), pages 329-331, August.
    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. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    8. 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. 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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