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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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    References listed on IDEAS

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    Cited by:

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    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.
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    5. Thomas H. Jørgensen, 2016. "Euler equation estimation: Children and credit constraints," Quantitative Economics, Econometric Society, vol. 7(3), pages 935-968, November.
    6. Striani, Fabrizio, 2023. "Life-cycle consumption and life insurance: Empirical evidence from Italian Survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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    More about this item

    Keywords

    Euler Equations; Measurement Error; Instrumental Variables; GMM.;
    All these keywords.

    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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