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Random walk model of consumption

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 Title: Random walk model of consumption Author: World Heritage Encyclopedia Language: English Subject: Collection: MacRoeconomics Publisher: World Heritage Encyclopedia Publication Date:

Random walk model of consumption

The random walk model of consumption was introduced by economist Robert Hall. 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.

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

Background

Hall introduced his famous random walk model of consumption in 1978. 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.

Model

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})

(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}

(2)

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

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

(3)

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.