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Euler Equation Estimation on Micro Data

Author

Listed:
  • Sule Alan

    () (Koc University and University of Cambridge)

  • Kadir Atalay

    (University of Sydney)

  • Thomas F. Crossley

    (Koc University, University of Cambridge and Institute for Fiscal Studies, London)

Abstract

First order conditions from the dynamic optimization problems of consumers and firms are important tools in empirical macroeconomics. When estimated on micro-data these equations are typically linearized so standard IV or GMM methods can be employed to deal with the measurement error that is endemic to survey data. However, it has recently been argued that the approximation bias induced by linearization may be worse than the problems that linearization is intended to solve. This paper explores this issue in the context of consumption Euler equations. These equations form the basis of estimates of key macroeconomic parameters: the elasticity of inter-temporal substitution (EIS) and relative prudence. We numerically solve and simulate 6 different life-cycle models, and then use the simulated data as the basis for a series of Monte Carlo experiments in which we consider the validity and relevance of conventional instruments, the consequences of different data sampling schemes, and the effectiveness of alternative estimation strategies. The first-order Euler equation leads to biased estimates of the EIS, but that bias is perhaps not too large when there is a sufficient time dimension to the data, and sufficient variation in interest rates. A sufficient time dimension can only realistically be achieved with a synthetic cohort. Estimates are unlikely to be very precise. Bias will be worse the more impatient agents are. The second order Euler equation suffers from a weak instrument problem and offers no advantage over the first-order approximation.

Suggested Citation

  • Sule Alan & Kadir Atalay & Thomas F. Crossley, 2012. "Euler Equation Estimation on Micro Data," Koç University-TUSIAD Economic Research Forum Working Papers 1221, Koc University-TUSIAD Economic Research Forum.
  • Handle: RePEc:koc:wpaper:1221
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    File URL: http://eaf.ku.edu.tr/sites/eaf.ku.edu.tr/files/erf_wp_1221.pdf
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    References listed on IDEAS

    as
    1. Shapiro, Matthew D., 1984. "The permanent income hypothesis and the real interest rate : Some evidence from panel data," Economics Letters, Elsevier, vol. 14(1), pages 93-100.
    2. Guvenen, Fatih, 2006. "Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1451-1472, October.
    3. Thomas F. Crossley & Hamish Low & Matthew Wakefield, 2009. "The Economics of a Temporary VAT Cut," Fiscal Studies, Institute for Fiscal Studies, vol. 30(1), pages 3-16, March.
    4. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    5. Attanasio, Orazio P & Weber, Guglielmo, 1995. "Is Consumption Growth Consistent with Intertemporal Optimization? Evidence from the Consumer Expenditure Survey," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1121-1157, December.
    6. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
    7. Sule Alan & Martin Browning, 2003. "Estimating Intertemporal Allocation Parameters using Simulated Residual Estimation," CAM Working Papers 2003-03, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    8. Altug, Sumru & Miller, Robert A, 1990. "Household Choices in Equilibrium," Econometrica, Econometric Society, vol. 58(3), pages 543-570, May.
    9. Sule Alan & Orazio Attanasio & Martin Browning, 2009. "Estimating Euler equations with noisy data: two exact GMM estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 309-324, March.
    10. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, June.
    11. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
    12. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
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    Cited by:

    1. repec:bla:obuest:v:79:y:2017:i:5:p:717-746 is not listed on IDEAS
    2. Bram De Rock & Bart Capéau, 2015. "The implications of household size and children for life-cycle saving," Working Paper Research 286, National Bank of Belgium.
    3. Keshav Dogra & Olga Gorbachev, 2016. "Consumption Volatility, Liquidity Constraints and Household Welfare," Economic Journal, Royal Economic Society, vol. 126(597), pages 2012-2037, November.
    4. Thomas H. Jørgensen, 2017. "Life-Cycle Consumption and Children: Evidence from a Structural Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 717-746, October.
    5. Thomas H. Jørgensen, 2016. "Euler equation estimation: Children and credit constraints," Quantitative Economics, Econometric Society, vol. 7(3), pages 935-968, November.
    6. Daria Pignalosa, 2018. "The Role Of The Utility Function In The Estimation Of Preference Parameters," Departmental Working Papers of Economics - University 'Roma Tre' 0235, Department of Economics - University Roma Tre.

    More about this item

    Keywords

    Euler Equations; Measurement Error; Instrumental Variables; GMM.;

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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