Let's assume a simple model of consumption and demand in real balances described by max s.t. Eo

Let's assume a simple model of consumption and demand in real balances described by

 

Transcribed Image Text:

max s.t. Eo t=0 3² u (Cr₁ Ft) P¿C₂ + B₁ + M₁ = (1 + r²₁) B₁-1 + (1+1) Mt-11 where C, is real consumption at time t; M₁/P, is real money balances (M, is money holdings and P, is the price level); B, is bond holdings, which earn a gross rate of return (1+r); money holdings earn a gross rate of return (1+r). The representative household also enjoys utility from holding real money balances. In this economy, the household chooses sequences for consumption, {C}, and real money balances, {M/Po a. Obtain the first-order conditions for the maximization of the household problem (hint: divide the period-t budget constraint by P, before maximizing). b. Assume now that the utility function is Cobb-Douglas in consumption and real money balances, i.e., 1-a u(C₁)C(M)¹ where 0<a<1 You have data for real consumption, real money balances, the price level, and for the short-term interest rates on bonds and money balances. Your objective is to estimate 3 and a by GMM. Derive all the steps for the estimation, presenting the moment conditions and the objective function for the estimation. Discuss identification. max s.t. Eo t=0 3² u (Cr₁ Ft) P¿C₂ + B₁ + M₁ = (1 + r²₁) B₁-1 + (1+1) Mt-11 where C, is real consumption at time t; M₁/P, is real money balances (M, is money holdings and P, is the price level); B, is bond holdings, which earn a gross rate of return (1+r); money holdings earn a gross rate of return (1+r). The representative household also enjoys utility from holding real money balances. In this economy, the household chooses sequences for consumption, {C}, and real money balances, {M/Po a. Obtain the first-order conditions for the maximization of the household problem (hint: divide the period-t budget constraint by P, before maximizing). b. Assume now that the utility function is Cobb-Douglas in consumption and real money balances, i.e., 1-a u(C₁)C(M)¹ where 0<a<1 You have data for real consumption, real money balances, the price level, and for the short-term interest rates on bonds and money balances. Your objective is to estimate 3 and a by GMM. Derive all the steps for the estimation, presenting the moment conditions and the objective function for the estimation. Discuss identification.

Answer rating: 100% (QA)

A To obtain the firstorder conditions for the maximization of the household problem we need to set up the Lagrangian function and then differentiate it with respect to the choice variables Lets define ... View the full answer