Monthly Archives: December 2014


n this appendix we describe the derivation of the neoclassical vintage model, the solution methods for the dynamic model, details of the econometric procedure along with a complete description of the two-sector model used in section 5. At the end of this appendix we also provide complete tables for the moments of the neoclassical and putty-clay models with permanent technology shocks.

Derivation of the Neoclassical Vintage Model:

For the purpose of comparison, we construct a neoclassical model of vintage capital, initially introduced by Solow (1962). In this model, the restriction that ex post capital-labor ratios are fixed is removed. The two models are otherwise identical. Let It-j denote aggregate investment in period t—j: and define the following capital


For the quarterly version of the model, M = 40 implies capital goods completely depreciate within 10 years, which seems to be an unrealistically short lifespan. Thus, following Gilchrist and Williams (1998a), we use polynomial distributed leads and lags to approximate the M = oo leads and lags of variables. For example, for some variable и and coefficient sequence we approximate the sum ajut-j by the polynomial distributed lag (or lead) щц, where B(L) = Ьо—Ь\Ь—Ь2Ь2 —.. .—bpD* and pis finite.

For the putty-clay model we use p = 1 and chose values corresponding to bo and b\ that minimize the weighted squared deviations between the PDL representation and the original lag or lead structure; this approximations yields virtually no loss in accuracy for model simulations. This adds 8 equations to our model and reduces the maximum lead and lag from M to 1, thus drastically reducing the size of the companion form of the model. The solution time for this approximate model is trivial. speedy payday loan


Relative to GDP, the output and hours series exclude government and farm output as well as the imputed output obtained from owner-occupied housing. The output and hours series are thus defined in a mutually consistent manner. With the exception of agricultural investment in structures and machinery, the investment series is also consistent with the output and hours series. Both the output and the investment series are deflated using 1997 chain weighted-deflators.

After first removing a linear time trend from the hours series, we assume that the first difference of the log of output, the log of the investment/output ratio and the log of hours, [Ayt^it —yt, Ы] can be represented using a two-lag stationary VAR representation. Defining


For к = 1 these moments are the unconditional moments considered in section 6.
The second set of moments computes regression coefficients and correlations between the predictable components of Ац^, Aht}k and the predictable component of Ayt^- According to Rotemberg and Woodford, these measures of the underlying dynamic response of the system when away from steady state. Intuitively, these statistics capture the strength and magnitude of the expected comovements among output, investment and hours.

By varying fc, we vary the horizon over which the comovements between forecastable components are computed. The second set of moments also includes the ratio of the variance of the predictable component of Ayt,k relative to the total variance of Ayt,fc- Again, Rotemberg and Woodford view this statistic as providing a good indicator of the degree to which the model contains a propagation mechanism. Thus the second set of moments may be written as: