Question

In the credit market model with limited commitment, suppose that a consumer's collateral constraint is binding, and suppose that the consumer's current taxes fall, with an increase in future taxes that leaves lifetime wealth unchanged for the consumer. How does this affect the consumer's behavior? Explain.

Answer 1

For explanation, let us take the housing market itself. Since the consumer's collateral constraint is binding, we can infer that the interaction of house prices with borrowing and spending decisions has a pronounced effect (first order) on the macroeconomy, especially during a crisis when monetary policy is incapable of adjusting the interest rate, thus ultimately declines the consumption rate. So, what's a consumer behavior taking into consideration this fact? You might have guessed: a consumer has multiple thoughts on buying a house and ultimately opts not to invest in them. This aspect is seen from a perspective wherein the wealth remains unchanged as given in the question itself. This is the fact that contributes to no shocks in the investment. In short the consumer spending also takes a toll.

In order to propose an equilibrium model for binding collateral constraints, we take the linearized system of various necessary conditions as following...

A1EtXt+1 + A0Xt + A-1Xt-1 + But = 0

where A1, A0, and A-1 are matrices of coefficients conformable with the vector X collecting the model variables in deviation from the steady state withj binding constraints; and where u is the vector collecting all shock innovations (and B is the corresponding conformable matrix)

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