Due February 19 Economics 2010d Spring 2014

Problem Set 3

1. In a classic paper in the 1989 American Economic Review, Blanchard and Quah proposed a

method for estimating the effects of supply and demand shocks without writing down a specific economic model. They argued that their method would work regardless of the model describing the economy, as long as the model satisfied two properties: (1) that supply shocks would have a permanent effect on output, and (2) that demand shocks would not have a permanent effect on output. This paper introduced the use of long-run identifying assumptions in Structural VARs (SVARs) to macroeconomics.

Assess Blanchard and Quahs method of identifying supply and demand shocks using a

benchmark RBC model. For the purposes of this question, interpret supply shocks as technology shocks, and demand shocks as shocks to government purchases.

(a) Begin by writing down a benchmark RBC model. Your model must have the following properties: (i) A representative consumer who maximizes discounted utility from consumption and leisure over an infinite horizon. Assume that each period the utility function is ln lnt tC H H

(ii) A representative firm that is perfectly competitive and maximizes profits, with the production function 1( )t t t tY K Z H

(iii) Government purchases, financed by lump-sum taxes. (iv) A closed economy with capital accumulation, so t t t tY C I G . (v) Variable technology (i.e., Z changing over time). Write down the consumer and firm optimization problems and the equilibrium condition(s) for the economy. Derive the key first-order conditions.

(b) Suppose there is a permanent shock to technology. Will this shock have a permanent effect on output? Explain your answer and the economics at work as thoroughly and rigorously as you can.

(c) Suppose there is a permanent shock to government purchases. Will this shock have a permanent effect on output? Explain your answer and the economics at work as thoroughly and rigorously as you can.

(d) Does the model you wrote down in part (a), if driven by permanent technology and government purchase shocks, satisfy the two identifying assumptions made by Blanchard and Quah? Explain your answer.

(e) If the model does satisfy the Blanchard-Quah assumptions, then suggest some modifications to the model or assumptions about the shock processes that would cause it to violate their

identifying assumptions. If it does not satisfy their assumptions, then suggest some modifications to the model or assumptions about the shock processes that would make the model predictions consistent with the identifying assumptions.

2. In an important paper in the 1999 American Economic Review, Jordi Gal proposed a

method for estimating the effects of technology and non-technology shocks without writing down a specific economic model. He argued that this method would work regardless of the model describing the economy, as long as the model satisfied two properties: (1) that technology shocks would have a permanent effect on labor productivity (output per hour worked), and (2) that non-technology shocks would not have a permanent effect on labor productivity.

Thus, relative to Blanchard and Quah, Gals paper introduced the idea of examining the long-run response of labor productivity rather than output.

Assess Gals method of identifying supply and demand shocks using the closed-economy RBC model you developed in the previous question.

(a) Suppose there is a permanent shock to technology. Will this shock have a permanent effect

on labor productivity?

(b) Suppose there is a permanent shock to government purchases. Will this shock have a permanent effect on labor productivity?

(c) Does the model you wrote down in Question 1, if driven by permanent technology and government purchase shocks, satisfy the two identifying assumptions made by Gal? Explain your answer.

(d) Suppose there are permanent technology shocks and transitory government purchase shocks. Does Gals method identify the technology shocks properly?

(e) What if the model is driven by both permanent and transitory technology shocks? Does Gals method still identify the technology shocks properly?

3. Solving the Standard RBC Model with Different Labor Supply Assumptions The representative household maximizes:

0

,st t s t ss

E U C H ,

and faces the budget constraint:

1 1t t t t t t t t tK K R K W H C G ,

with standard notation. Government purchases are assumed to be pure waste. A profit-maximizing competitive firm produces all output using the technology

1( )t t t tY K Z H .

The national income accounting identities for a closed economy imply:

t t t t t t t t tY C I G R K W H .

The log-linearized laws of motion for the two shocks are:

1

1

Zt Z t t

Gt G t t

Z Z

G G

a) First assume that 1, log1

tt t t

HU C H C

. Derive all the relevant first-order conditions for the consumer and the firm. What is the Frisch elasticity of labor supply in this case?

b) Log-linearize all the equations needed to solve the model numerically. Suppose the parameter values are: = 0.33, = 0.25, = 0.99, = 0.025, Z = 0.99, G = 0.90, sC = 0.65 and sG = 0.20. c) Put the calibrated log-linear model into Dynare. Find the impulse responses to a 1/sG percent

shock to G and a 1/(1 ) percent shock to Z. Compare them to the impulse responses obtained for the model in section, where the utility function was log log .t tC H H

d) Now let the utility function be 1

log1

tt

HC

(a particular case of a specification proposed

by Greenwood, Hercowitz and Huffman (1988)), with still 0.25. Solve for the impulse responses to the same shocks and calibration given the new utility specification. Explain the economics driving the differences that you find. Are they due to differences in the Frisch labor supply elasticity?

e) Are both preference specifications consistent with steady-state growth? Explain.

f) Suppose we let go to zero in both part (c) and (d). Are the impulse responses well-behaved

in both cases? Explain why or why not.