From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Subject: Re: RBC Modelling
Reply-To: thompson@atlas.socsci.umn.edu
Organization: Economics Department, University of Minnesota
Date: Wed, 2 Sep 1992 16:10:51 GMT

jmo@stokes.princeton.edu (Mike Orszag) writes:

>The RBC models use assumptions based on observed macroeconomic
>data (Cobb-Douglas production function, etc.) and are calibrated
>with macroeconomic data. It would be very surprising if such
>models did not match the data very closely.

>There is no indication that the "technological shocks" of RBC models
>have anything to do with real technological innovation; I think
>they are connected with various real rigidities which are in any
>case indistinguishable from technological shocks even at the
>microeconomic level.

For those of you who haven't seen these models, the basic idea behind "technology shocks" is something like this:

Y = real output per worker
K = real capital per worker

Assumed production function:

         Y = T * f(K)

where T is an unobserved variable (discussed below), and f( ) is some
function fixed up to a possible unknown parameter.  Typically it is
assumed that

          f(K) = alpha * (K ** beta)      (Fortran notation here)

where alpha and beta are unknown but fixed coefficients satisfying
alpha > 0 and 0 < beta < 1.  This is the Cobb-Douglass form.  It is
chosen for convenience, not because it is "based on macroeconomic
data".

Substituing and taking logs we get

	log Y = log alpha + beta*log(K) + log T

We may assume without losing any generality that log(T) has zero mean
(or any other convenient normalization) since it appears linearly with
log(alpha) and both are unobserved.  The parameters alpha and beta are
fit to data by some means (the "calibration" refered to by Mr. Orszag,
although other methods, statistical estimation for example, are
conceivable).  log(T) is the "technology shock" of the model.

Interpretation: log T represents the difference between log Y and log
f(K).  If we think of f(K) as representing a "long run" or "average"
production function, then this difference is essentially the deviation
(in logs) between actual output and the output predicted by the long
run production function.  This difference may represent temporary
changes in productivity.  Hence the name "technology shock".  It may
also represent many other things, however, including the inability of
the _assumed_ form for f(K) to capture the actual relationship between
inputs and outputs.  It may also be capturing the errors that are
introduced by working with aggregate data rather than modelling the
complex underlying market structures directly.

So Mr. Orszag is quite right when he warns that the "technology
shocks" in these models are not necessarily related to measured
changes in real technology or productivity.

Note: The above should be regarded as an interpretation of one
equation in one kind of real business cycle model currently employed
in active research.  Before you flame it, keep in mind that you are
only looking at one piece of a model, and context is often important
for proper interpretation.
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209