In an email concerning my discussion on Econolog regarding lags in monetary policy I was asked about the relationship between changes in the federal funds rate and subsequent changes in the inflation rate. A paper in the February 2005 issue of the Journal of Political Economy by Lawrence J. Christiano and Martin Eichenbaum of Northwestern University, the NBER, and Federal Reserve Bank of Chicago, and Charles L. Evans of the Federal Reserve Bank of Chicago entitled “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy” provides evidence on this issue:
Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy, JPE [subscription link only]: This paper seeks to understand the observed inertial behavior of inflation and persistence in aggregate quantities. To this end, we formulate and estimate a dynamic, general equilibrium model that incorporates staggered wage and price contracts … the model does a very good job of accounting quantitatively for the estimated response of the U.S. economy to a policy shock. … Specifically, the model generates an inertial response in inflation and a persistent, hump-shaped response in output after a policy shock. In addition, the model generates hump-shaped responses in investment, consumption, employment, profits, and productivity, as well as a small response in the real wage. Also, the interest rate and the money growth rate move persistently in opposite directions after a monetary policy shock. A key finding of the analysis is that stickiness in nominal wages is crucial for the model's performance. Stickiness in prices plays a relatively small role.
Here’s Figure 1 from the paper displaying how output, inflation, and other variables respond after a shock to the federal funds rate:
Model- and VAR-based impulse responses. Solid lines are benchmark model impulse responses; solid lines with plus signs are VAR-based impulse responses. Grey areas are 95 percent confidence intervals about VAR-based estimates. Units on the horizontal axis are quarters. An asterisk indicates the period of policy shock. The vertical axis units are deviations from the unshocked path. Inflation, money growth, and the interest rate are given in annualized percentage points (APR); other variables are given in percentages.
For those of you who aren't used to reading graphs like these the exercise is fairly simple. Start with an economy at equilibrium, then hit it with a single shock, in this case a federal funds rate shock, and see how the economy responds. The diagrams show two models, one is an estimated model (called a VAR model in the diagram) with a very flexible form that allows it to match actual data fairly well. The other is a simulated theoretical model called the benchmark theoretical version (benchmark because other version are investigated with varying degrees of price and wage stickiness, different policy rules, and different assumptions regarding price setting behavior). We are mostly interested in the VAR results for this discussion, but what the diagram shows is that the benchmark theoretical model does a fairly good job of matching actual patterns in U.S. data.
Let’s now turn to the question about lags in the response of inflation to changes in the federal funds rate. Here’s their summary of the results:
The results suggest that after an expansionary monetary policy shock,
- output, consumption, and investment respond in a hump-shaped fashion, peaking after about one and a half years and returning to preshock levels after about three years;
- inflation responds in a hump-shaped fashion, peaking after about two years;
- the interest rate falls for roughly one year;
- real profits, real wages, and labor productivity rise; and
- the growth rate of money rises immediately.
To me, it’s always surprising how long the effects of a monetary shock last; the peak effect on inflation takes two years to unfold and the effect on output peaks after a year and a half. Let me add one more note. In his spare time, when he’s not blogging, David Altig also looks into these issues (from the citations in the paper):
Altig, David, Lawrence J. Christiano, Martin Eichenbaum, and Jesper Linde. 2003. "The Role of Monetary Policy in the Propagation of Technology Shocks." Manuscript, Northwestern Univ.
An updated version of the paper is available as a Cleveland Fed Working Paper "Firm-Specific Capital, Nominal Rigidities, and the Business Cycle"
Update: In the comments, CR asks a good question:
But what is a "monetary policy shock"? It would seem that rate increases at a 'measured pace' would almost not qualify. Sure the accumulated changes would matter to the economy, but ...
I was thinking of Prof. Hamilton's argument that the high price of oil hasn't impacted the economy as much as some would expect because of the gradual nature of the demand driven price increase as opposed to a rapid rise in prices due to a supply shock.
How did the author's define a monetary shock? Just some thoughts ...
I should have made this clear. The monetary policy rule is ff = g(I) + shock where I is the information set available when the ff is set (e.g. a Taylor rule would have deviations of output and inflation from their target values in g(I)). The shock cannot be predicted given the information available. The stabilization question asks which type of feedback rule g(I) minimizes the variation of output around its optimal value in the presence of monetary and other shocks that hit the economy. Is inflation targeting the best? If so, what type of targeting rule? Should we use expected future output and inflation, today's values, yesterday's values, what's the best policy model? Should a lagged value of the ff rate be included (this is called smoothing)? How should variables such as inflation and output be measured? Should we look at core inflation, the CPI, etc., and should asset prices be included in our index? In looking at these questions is it better to use “real-time” or revised data? How important is the smoothing term in providing stability? The Christiano, Eichenbaum, and Evans paper looks at how well various versions of the benchmark model match U.S. data so that we will know what types of models to use in assessing what an optimal policy rule might look like. Other research simulates models under a variety of policy rules in an attempt to settle some of these questions.