Palgrave Handbook of Econometrics: Applied Econometrics

92 How much Structure in Empirical Models?

0.2

–0.0

–1.00

–0.75

0.75

1.00

Shock 1

Output

Unemployment

Shock 2

–0.50

0.50

–0.25

0.25

0.00

–0.2

–0.4

–0.6

–0.8

–1.0

05

0 05

0.00

0.02

0.00

–0.02

–0.04

–0.06

–0.08

–0.10

0.25

0.50

0.75

1.00

1.25

1.50

5

05

Tr u e

VAR(1)

VAR(4)

Figure 2.5 Responses in the Blanchard and Quah model

and the resource constraint is:

ct+kt+gt=ktη− 1 N^1 t−ηzt+( 1 −δ)kt− 1 , (2.21)

wherectis consumption andφis the risk aversion coefficient,Ais a constant
andNtare hours worked;ztis a first-order autoregressive process with persistence

ρz, steady-state valuezssand varianceσz^2 ;gtis a first-order autoregressive pro-

cess with persistenceρg, steady-state valuegssand varianceσg^2 ;kt− 1 is the current
capital stock;ηis the share of capital in production, and δthe depreciation rate
of capital. Using the method of undetermined coefficients, and letting output be
yt≡kηt− 1 Nt^1 −ηzt, and investment beit =kt−( 1 −δ)kt− 1 , the aggregate deci-
sion rules for(kt,ct,Nt,yt,rt,it), wherertis the real rate, imply standard dynamics
in response to the two shocks. In particular, asztincreases, hours, consumption,
output, the real rate and investment increase contemporaneously while the dynam-
ics of the capital stock have a hump-shaped pattern. On the other hand, asgt
increases, consumption falls, hours, output, the real rate and investment increase
contemporaneously and the capital stock has a hump-shaped pattern.
What would the dynamics induced by the two shocks in a system which includes
only the interest rate and investment look like? That is, what would happen if we
integrate out the effect of the shocks on the other four variables? Figure 2.6 plots
the responses of the two variables of interest to the two shocks in the full and the