Romer discusses this paper briefly in Section 6.10.
Don't be too worried about the simplicity of the AD curve. In logs, Lucas assumes that it has the form y = x - P, where x
is nominal GDP and is assumed to be constant along the AD curve. This
has become a pretty standard simplification in the literature. It
assumes that the effects on AD from the IS/LM model can be captured by
the single variable x and that the elasticity of aggregate
demand is negative one. This is obviously a simplification, but may not
do gross injustice to the empirical facts. His x variable is analogous to the m variable that we are using to represent AD in class.
The solution to his theoretical model on page 328-29 is broadly
similar to Romer's imperfect information model of Section 6.9. Lucas's
equation (13) is comparable to Romer's (6.92).
The key column in Lucas's Table 1 is the last one, which measures
each country's variance of aggregate demand (measured by nominal GDP
variance). This is analogous to Vmin Romer's equation (6.92).
Questions for analysis
Based on Lucas's equation (13) and Romer's (6.92), what relationship
would we expect between the elasticity of output (aggregate supply)
with respect to AD fluctuations and the variances of aggregate demand?
What is the intuition behind this result?
Comparing Tables 1 and 2, what relationship does Lucas observe? How strong is this relationship?
According to equations (13) and (6.92), the variance of "relative shocks" (Vz in Romer, τ2
in Lucas) should also affect the elasticity of aggregate supply. What
does Lucas assume about this variance in his test? Is this assumption
reasonable? Is it ideal? If you had access to the data, how might you
try to improve on it?
Looking at Lucas's Table 1, there is a substantial positive
correlation between the average level of inflation (second column) and
the variance of inflation. Highly variable inflation is strongly
associated across countries with high inflation. The average level of
aggregate demand growth Δx would be the sum of the first two
columns of Table 1. Is the average level of AD growth highly correlated
with the variance of AD growth? What, if any, relationship does Lucas's
model predict between the average level of AD growth and the
elasticity of the AS curve? What pattern shows up in his results? (This
is the basis for an extended test that we will examine in a couple of
weeks.)