Skip to main content Accessibility help
Hostname: page-component-65dc7cd545-jbgjn Total loading time: 0.331 Render date: 2021-07-25T17:00:49.912Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }


Published online by Cambridge University Press:  25 June 2018

Sule Alan
University of Essex
Kadir Atalay
University of Sydney
Thomas F. Crossley
University of Essex and Institute for Fiscal Studies
Rights & Permissions[Opens in a new window]


Consumption Euler equations are important tools in empirical macroeconomics. When estimated on micro data, they 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, linearization, in turn, may induce serious approximation bias. We numerically solve and simulate six different life-cycle models, and then use the simulated data as the basis for a series of Monte Carlo experiments in which we evaluate the performance of linearized Euler equation estimation. We sample from the simulated data in ways that mimic realistic data structures. The linearized Euler equation leads to biased estimates of the EIS, but that bias is modest when there is a sufficient time dimension to the data, and sufficient variation in interest rates. However, a sufficient time dimension can only realistically be achieved with a synthetic cohort. Estimates from synthetic cohorts of sufficient length, while often exhibiting small mean bias, are quite imprecise. We also show that in all data structures, estimates are less precise in impatient models.

Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © Cambridge University Press 2018


K. Atalay acknowledges the support of the Australian Research Council (Grant #DP150101718). T. F. Crossley acknowledges support from the ESRC through the ESRC-funded Centre for Microeconomic Analysis of Public Policy at the Institute for Fiscal Studies (reference RES-544-28-5001) and through the Research Centre on Micro-Social Change (MiSoC) at the University of Essex, (reference ES/L009153/1). We also thank seminar participants at the University of Cambridge, University of Sydney and participants in the Journal of Applied Econometrics Workshop, and especially Anastasia Burkovskaya, Garry Barrett, Hamish Low, Simon Kwok, and Hashem Pesaran for helpful comments. All errors are our own.


Adams, A., Cherchye, L., De Rock, B., and Verriest, E. (2014) Consume now or later? Time inconsistency, collective choice, and revealed preference. American Economic Review 104 (12), 41474183.CrossRefGoogle Scholar
Andrews, Donald W. K. and Stock, J. H. (2005) Inference with Weak Instruments. Cowles Foundation discussion paper 1530.CrossRefGoogle Scholar
Alan, S., Attanasio, O., and Browning, M. (2009) Estimating Euler equations with noisy data: Two exact GMM estimators. Journal of Applied Econometrics 24, 309324.CrossRefGoogle Scholar
Alan, S and Browning, M. (2010) Estimating intertemporal allocation parameters using simulated residual estimation. Review of Economic Studies 77, 12311261.CrossRefGoogle Scholar
Alan, S., Browning, M., and Ejrneas, M. (2016) Income and consumption: A micro semistructural analysis with pervasive heterogeneity. Journal of Political Economy (forthcoming).Google Scholar
Attanasio, O. P. and Weber, G. (1993) Consumption growth, the interest rate, and aggregation. Review of Economic Studies 60, 631649.CrossRefGoogle Scholar
Attanasio, O. P. and Weber, G. (1995) Is consumption growth consistent with intertemporal optimization? Evidence from the consumer expenditure survey. Journal of Political Economy 103 (6), 11211157.CrossRefGoogle Scholar
Attanasio, O. P., Banks, J., Meghir, C. and Weber, G. (1999) Humps and bumps in lifetime consumption. Journal of Business and Economic Statistics 17 (1), 2235.Google Scholar
Attanasio, O. P. and Low, H. (2004) Estimating Euler equations. Review of Economic Dynamics 7 (2), 405435.CrossRefGoogle Scholar
Benito, A. and Mumtaz, H. (2009) Excess sensitivity, liquidity constraints, and the collateral role of housing. Macroeconomic Dynamics 13 (3), 305326.CrossRefGoogle Scholar
Blundell, R., Browning, M., and Meghir, C. (1994) Consumer demand and the life-cycle allocation of household expenditures. Review of Economic Studies 61, 5780.CrossRefGoogle Scholar
Browning, M., Deaton, A., and Irish, M. (1985) A profitable approach to labor supply and commodity demands over the life-cycle. Econometrica 53, 503544.CrossRefGoogle Scholar
Bond, S. and Meghir, C. (1994) Dynamic investment models and the Firm's financial policy. Review of Economic Studies 61 (2), 197222.CrossRefGoogle Scholar
Carroll, C. (2001) Death to the log-linearized consumption Euler equation! (and very poor health to the second-order approximation). Advances in Macroeconomics 1 (1), 10031003.CrossRefGoogle Scholar
Chamberlain, G. (1984) Panel data. In Griliches, Z. and Intriligator, M. D. (eds.), Handbook of Econometrics, vol. II, pp. 12471318. Amsterdam: Elsevier North-Holland.CrossRefGoogle Scholar
Crossley, T. F., Low, H., and Wakefield, M. (2009) The economics of a temporary VAT cut. Fiscal Studies 30 (1), 316.CrossRefGoogle Scholar
Davidson, R. and MacKinnon, J. G. (2004) Econometric Theory and Methods. New York: Oxford University Press.Google Scholar
Deaton, A. (1985) Panel data from time series of cross sections. Journal of Econometrics 30, 109126.CrossRefGoogle Scholar
Deaton, A. (1991) Saving and liquidity constraints, Econometrica 59 (5), 12211248.CrossRefGoogle Scholar
Dogra, K. and Gorbachev, C. (2016) Consumption volatility, liquidity constraints and household welfare. Economic Journal 126, 20122037.CrossRefGoogle Scholar
Druedahl, J. and Jorgensen, T. H. (2016) Estimating Dynamic Economic Models with Non-Parametric Heterogeneity. Mimeo.Google Scholar
Dynan, K. E. (1993) How prudent are consumers? Journal of Political Economy 101 (6), 11041113.CrossRefGoogle Scholar
Gayle, W. R. and Khorunzhina, N. (2016) Micro-level estimation of optimal consumption choice with intertemporal nonseparability in preferences and measurement errors,” Journal of Business & Economic Statistics (just-accepted).CrossRefGoogle Scholar
Gomes, F. and Issler, J. (2017) Testing consumption optimality using aggregate data. Macroeconomic Dynamics 21 (5), 11191140.CrossRefGoogle Scholar
Hahn, J., Hausman, J., and Kuersteiner, G. (2004) Estimation with weak instruments: Accuracy of higher order bias and MSE approximations. Econometrics Journal 7 (1), 272306.CrossRefGoogle Scholar
Hall, R. E. (1978) Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence. Journal of Political Economy 86, 971987.CrossRefGoogle Scholar
Hansen, L. P. and Singleton, K. J. (1982) Generalized instrumental variables estimation of nonlinear rational expectations models. Econometrica 50 (5), 12691286.CrossRefGoogle Scholar
Huang, K., Liu, K. X. D., and Zhu, J. C. (2015) Temptation and self-control: Some evidence and applications. Journal of Money, Credit and Banking 47, 581615.CrossRefGoogle Scholar
Ludvigson, S. and Paxson, C. (2001) Approximation bias in linearized Euler equations. Journal of Economics and Statistics 83 (2), 242256.Google Scholar
Mazzocco, M. (2007) Household intertemporal behaviour: A collective characterization and a test of commitment. Review of Economic Studies 74 (3), 857895.CrossRefGoogle Scholar
Mehra, R. and Prescott, E. C. (1985) The equity premium: A puzzle. Journal of Monetary Economics 15 (2), 145161.CrossRefGoogle Scholar
Moulton, B. (1986) Random group effects and the precision of regression estimates, Journal of Econometrics 32, 385397.CrossRefGoogle Scholar
Mudit, K. and Ravi, S. (2016) Elasticity of intertemporal substitution in consumption in the presence of inertia: Empirical evidence from a natural experiment. Management Science (forthcoming).Google Scholar
Mulligan, C. (2004) What do aggregate consumption Euler equations say about the capital-income tax burden? American Economic Review 94 (2), 166170.CrossRefGoogle Scholar
Office of National Statistics (2017) Consumer trends, UK; Quarter 4(Oct to Dec) 2016, released 31 March 2017 and accessed at: Scholar
Runkle, D. E. (1991) Liquidity constraints and the permanent income hypothesis. Journal of Monetary Economics 27, 7398.CrossRefGoogle Scholar
Shapiro, M. D. (1984) The permanent income hypothesis and the real interest rate: Some evidence from panel data Economic Letters 14 (1), 93100.CrossRefGoogle Scholar
Stock, J. H. and Yogo, M. (2005) Testing for weak instruments in linear IV regression. In Andrews, D. W. K. and Stock, J. H. (eds.), Identification and Inference for Econometric Models. Essays in Honor of Thomas Rothenberg, pp. 80108. New York: Cambridge University Press.CrossRefGoogle Scholar
Yogo, M. (2004) Estimating the elasticity of intertemporal substitution when instruments are weak. The Review of Economics and Statistics 86 (3), 797810.CrossRefGoogle Scholar
Supplementary material: PDF

Alan et al. supplementary material

Online Appendix

Download Alan et al. supplementary material(PDF)
PDF 570 KB
You have Access
Open access
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *