World Library  
Flag as Inappropriate
Email this Article

Random walk model of consumption

Article Id: WHEBN0026828614
Reproduction Date:

Title: Random walk model of consumption  
Author: World Heritage Encyclopedia
Language: English
Subject: Life-cycle hypothesis, Absolute income hypothesis, Relative income hypothesis, Consumption (economics), Macroeconomics
Collection: MacRoeconomics
Publisher: World Heritage Encyclopedia

Random walk model of consumption

The random walk model of consumption was introduced by economist Robert Hall.[1] This model uses the Euler equation to model consumption. He created his consumption theory in response to the Lucas critique. Using Euler equations to model the random walk of consumption has become the dominant approach to modeling consumption.[2]


  • Background 1
  • Model 2
  • Advantages 3
  • Criticisms 4
  • References 5


Hall introduced his famous random walk model of consumption in 1978.[3] His approach is differentiated from earlier theories by the introduction of the Lucas critique to modeling consumption. He incorporated the idea of rational expectations into his consumption models and sets up the model so that consumers will maximize their utility.


Consider a two-period case. The Euler equation for this model is

E_{1}u'(c_{2})=\left(\frac{1 + \delta}{1 + r}\right) u'(c_{1})






where \delta is the subjective time preference rate, r is the constant interest rate, and E_{1} is the conditional expectation at time period 1.

Assuming that the utility function is quadratic and \delta=r, equation (1) will yield

E_{1} c_{2} = c_{1}






Applying the definition of expectations to equation (2) will give:

c_{2} = c_{1}+\epsilon_{2}






where \epsilon_{2} is the innovation term. Equation (3) suggests that consumption is a random walk because consumption is a function of only consumption from the previous period plus the innovation term.


Use of the Euler equations to estimate consumption appears to have advantages over traditional models. First, using Euler equations is simpler than conventional methods. This avoids the need to solve the consumer's optimization problem and is the most appealing element of using Euler equations to some economists.[4]


Controversy has arisen over using Euler equations to model consumption. Applying the Euler consumption equations has trouble explaining empirical data.[5][6] Attempting to use to Euler equations to model consumption in the United States has led some to reject the random walk hypothesis.[7] Some argue that this is due to the model's inability to uncover consumer preference variables such as the intertemporal elasticity of substitution.[8]


  1. ^ Hall (1978)
  2. ^ Chao, Hsiang-Ke (2007). "A Structure of the Consumption Function". Journal of Economic Methodology 14 (2): 227–248.  
  3. ^  
  4. ^ Attanasio, Orazio; Low, Hamish. "Estimating Euler Equations". Review of Economic Dynamics 7: 405–435.  
  5. ^ Molana, H. (1991). "The Time Series Consumption Function: Error Correction, Random Walk and the Steady-State". The Economic Journal 101 (406): 382–403.  
  6. ^ Canzoneri, M. B.; Cumby, R. E.; Diba, B. T. (2007). "Euler equations and money market interest rates: A challenge for monetary policy models". Journal of Monetary Economics 54 (7): 1863.  
  7. ^ Jaeger, Albert (1992). "Does Consumption Take a Random Walk?". The Review of Economics and Statistics 74 (4): 607–614.  
  8. ^ Carroll, Christopher D. (2001). "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)". Advances in Macroeconomics 1 (1). 
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.