### Forecasts of Output Growth and Inflation under Hawkish, Intermediate, and Dovish Monetary Policies

To give you some idea how economists might investigate alternative monetary policies, I estimated a simple econometric model and then simulated three different possible monetary policies to see how inflation and output growth would react.

More specifically, I estimate a two lag vector autoregressive (VAR) model with the variables output growth, inflation, and the federal funds rate. Rates of change are measured as year over year. You can think of these models as very general reduced form equations where all of the endogenous variables are functions of exogenous or predetermined variables. For example, the output growth equation is:

y_{t} = b_{0} + b_{1}y_{t-1} + b_{2}y_{t-2
+ }b_{3}inf_{t-1} + b_{4}inf_{t-2} + b_{5}ff_{t-1}
+ b_{6}ff_{t-2 }+ e_{t}

The other two equations would be the same except the left-hand side variable
would be either inf_{t} or ff_{t }instead of output growth, y_{t}, and the coefficients would differ. Because every variable in the
system depends upon lags of every other variable, these models are fairly
general (contemporaneous values on the right-hand side can be
substituted for to get the lagged specification).

I estimated this model using data from 1960Q1 through 2006Q1, then simulated three monetary policies over the next two years:

Dove: Increase to 5.0 in 2006Q2 (as was done), and stay at 5.0 thereafter.

Intermediate: Increase to 5.0 in 2006Q2, then to 5.5 in 2006Q3, then hold at 5.5.

Hawk: Increase to 5.0 in 2006Q2, then to 5.5 in 2006Q3, then to 6.0 in 2006Q4, then hold at 6.0.

Graphically, here are the three policies since 2000Q1. The graph shows actual policy through 2006Q1, and the simulated policies through 2008:1. Note that these policies continue to increase the federal funds rate at the smae measured pace as in recent quarters (the changes are in increments of .5 rather than .25 in both the historical data and in the simulations because there are approximately two meetings per quarter):

*Click on figure to enlarge*

Here are the outcomes of the simulations. In these two graphs, actual values are shown through 2006Q1 along with the forecasts for the three different policy scenarios:

*Click on figures to enlarge*

Focusing first on output in the top graph, initially the path of output growth is very similar for the three policies, so much so that only the red line is visible on the graph. However, after peaking at around 4.1% in either 2006Q3 or Q4 depending on the policy, output growth then falls until the end of the forecast period at 2008Q1. The differences in output growth at 2008Q1 are 3.41% for the hawkish policy, 3.58% for the intermediate, and 3.76% for the dovish policy. So, there is approximately a one third of a percentage point difference in output growth between the hawkish and dovish scenarios.

The second graph brings up a problem with this class of models. In these simple VAR models, changes in policy have very little effect on inflation and, to the extent that policy does have an effect, it is perverse. Inflation is higher, though not by much, when policy is tighter and this is one reason the results should be interpreted with caution. For example, after two years, inflation is forecast to be 3.47% under the hawkish policy, 3.44% under the intermediate policy, and 3.41% for the dovish policy, values that are perverse but unlikely to be statistically distinct. The solution to the "price puzzle" is to add more variables, commodity price indexes are one way to reverse the sign, but explaining the movement in inflation through time (and hence inflation expectations) remains problematic generally and some recent work has moved toward solutions based upon imposing structural restrictions, or explanations that use theoretical results involving indeterminacy (multiple equilibria).

Finally, I should add that the results do not change much if a measure of the output gap (the deviation of output from a quadratic trend) is used instead of output growth, or if PCE less food and energy is used instead of PCE. Not perfect, but enough for now...

Posted by Mark Thoma on Monday, June 26, 2006 at 01:22 AM in Economics, Inflation, Macroeconomics, Methodology, Monetary Policy, Unemployment |
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