Shapiro and Watson (1988) estimated a structural VAR imposing long-run constraints.

Replicate a simplified version of their model. Take the quarterly series hoanbs (hours worked, nonfarm business sector), gdpc1 (real GDP), and gdpctpi (GDP deflator) from FRED-QD. Transform the first two to growth rates and for the third (GDP deflator) take the second difference of the logarithm (differenced inflation). Shapiro and Watson estimated a structural model imposing the constraints that labor supply hours are long-run unaffected by output and inflation and GDP is long-run unaffected by demand shocks. This implies a recursive ordering in the variables for a long-run restriction.

(a) Write down the matrix C as in (15.24) imposing the identifying constraints as defined above.

(b) Is the model identified?

(c) Use the AIC to select the number of lags for a VAR.

(d) Estimate the structural VAR. Report the estimated C matrix. Can you interpret the coefficients?

(e) Estimate the structural impulse responses of the level of GDP with respect to the three shocks.

Interpret the results.