What are the effects of monetary policy on output? Results from an agnostic identification procedure

TL;DR: The authors proposed to estimate the effects of monetary policy shocks by a new agnostic method, imposing sign restrictions on the impulse responses of prices, nonborrowed reserves and the federal funds rate in response to a monetary policy shock.

About: This article is published in Journal of Monetary Economics.The article was published on 2005-03-01 and is currently open access. It has received 2058 citations till now. The article focuses on the topics: Credit channel & Monetary hegemony.

Summary

1 Introduction

• In summary, this literature indeed reinforces the view emerging from the first simple look at the data as in figure 1.
• While theories with different implications can fairly easily be constructed, these assumptions may enjoy broad support and in any case, are usually tacitly assumed in most of the VAR literature: their aim is to bring them directly out into the open and to make them subject to debate.
• When imposing the sign restrictions, one needs to take a stand on for how long these restrictions ought to hold after a shock.
• “Contractionary” monetary policy shocks have an ambiguous effect on real GDP.

2 The Method

• There is not much disagreement about how to estimate5 VARs.
• The disagreement starts when discussing, how to decompose the prediction error ut into economically meaningful or “fundamental” innovations.
• Define the monetary policy impulse vector as that impulse vector a, which minimizes the total penalty Ψ(a) for prices, nonborrowed reserves and (after flipping signs) the federal funds rate at horizons k = 0, . . . , K, Ψ(a) = ∑ j∈ “GDP Deflator”, “Comm. Price Index”, “Nonborr. Reserves” “Federal Funds Rate”.
• As a drawback, the pure-sign-restriction is, in effect, simultaneously an estimation of the reduced-form VAR alongside the impulse vector: VAR parameter draws, which do not permit any impulse vector to satisfy the imposed sign restrictions, are discarded as “impossible”.

3 Results

• The authors present some results, using their method.
• The authors have employed the data set used in Bernanke and Mihov (1996a,b), which contains the GDP, the GDP deflator, a commodity price index, total reserves, nonborrowed reserves and the federal funds rate for the U.S. at monthly frequencies from January 1965 to December 1996.
• Here, the authors identify the monetary policy shock with the innovations in the Federal Funds Rate ordered last.
• The results are fairly “reasonable” in that they confirm conventional undergraduate textbook intuition.
• Without a good defense of the timing implicit in the particular Cholesky decomposition employed, the results of figure 2 may thus be tainted by the specification search described in the introduction.

3.1 Results for the pure-sign-restriction approach.

• I.e., the responses of the GDP price deflator, the commodity price index and nonborrowed reserves have been restricted not to be positive and the federal funds rate not to be negative for the six months k, k = 0, . . . , 5 following the shock.
• The results can be described as follows: 8A number of authors prefer two standard deviation bands, which would correspond to the 2.3% and the 97.7% quantiles.
• After one to two years, a reversal sets in with reserves eventually expanding by around 0.4 percent.
• The answer to the opening question is: the effects of monetary policy shocks on real output are ambiguous.

3.2 Results from the penalty-function approach.

• Figures 5 and 6 provide the same results, now using the penalty-function approach rather than the pure-sign-restriction approach.
• The magnitudes are slightly larger, and the confidence bands somewhat sharper, in particular immediately after the shock, compared to the pure-sign restriction approach.
• While the pure-sign-restriction approach is very agnostic about the size of the impulse response away from the sign restriction, a larger responses is “rewarded” by the penalty-function approach at least as long as this does not generate sign-violations elsewhere.
• Instead of a range of impulse vectors consistent with the sign restriction, the penalty function approach seeks a unique monetary policy impulse vector by searching e.g. for a large initial reaction of the Federal Funds Rate.
• Indeed, this seems to be the case: the 64% range for the real GDP response, for example, never seems to venture outside the ±0.2 percent error band around zero calculated for the pure-sign-restriction approach.

3.3 How much variation do monetary policy shocks explain?

• Having identified the monetary policy shock, it is then interesting to find out, how much of the variation these shocks explain.
• These questions are answered by figure 7 for the benchmark experiment, i.e. using a pure sign restriction approach with a 6-months restriction (K=5).
• The figure shows the fraction of the k−step ahead variance in the six variables explained by monetary policy shocks, with the variables ordered as in figure 3.
• The remaining variations in prices and interest rates may still be due to monetary policy, but then it needs to be due to the endogenous part of monetary policy: by systematically responding to shocks elsewhere, monetary policy may end up being responsible for 100% of the movements in prices.
• These results are rather similar to the results found in the empirical VAR literature so far, see the surveys cited in the introduction.

3.4 A summary.

• The results could be paraphrased as a new Keynesian-new classical synthesis: even though the general price level is sticky for a period of about a year (see also Blinder, 1994), monetary policy has ambiguous real effects.
• These observations largely confirm the results found in the empirical VAR literature so far, see in particular Leeper, Sims and Zha (1996), except for the ambiguity regarding the effect on output: this exception is, of course, a rather important difference.
• The authors also agree with these authors that it makes sense that variation in monetary policy accounts only for a small fraction of the variation in any of these variables: good monetary policy should be predictable policy, and from that perspective, monetary policy in the US during this time span has been successful indeed.

4 The Volcker recessions, which weren’t.

• In light of the well-known Lucas Critique (1976), one obviously needs to interpret the results with some caution.
• Rounding up the other usual suspects is something which the authors have explicitely not focussed on in this exercise.
• It is admittedly hard to also explain the large interest rate movements this way.
• The authors believe that the analysis here supports a “not guilty” verdict for monetary policy shocks as a cause for the 1980 recession, in contrast to the conventional consensus view, also known as Whatever the truth.

5 Conclusions

• This paper proposed to estimate the effects of monetary policy by a new “agnostic” method, imposing sign restrictions on the impulse responses of prices, nonborrowed reserves and the federal funds rate in response to a monetary policy shock.
• Monetary policy shocks accounts for probably less than twentyfive percent of the k-step ahead prediction error variance of real output, and may easily account for less than three percent.
• The commodity price index falls more quickly.
• They account for about one third of the variation in prices at longer horizons.
• While these observations confirm some of the results found in the empirical VAR literature so far, there are also some potentially important differences in particular with respect to their key question.

Figures

Figure 1: This figure contrasts movments in the Federal Funds Rate, shown as a thick, solid line with the scale on the left, with real GDP growth rates, shown as a thinner, dotted line with the scale on the right. To aid the visual comparison, the real GDP growth rates have been put “upside down”, i.e., peaks in the figure are actually particularly low values for the growth rate. “Eyeball econometrics” suggests a strong cause-and-effect from Federal Funds Rate movements to real GDP: whenever interest rates rise, growth rates fall (i.e. the dotted line rises) shortly afterwards. This is particularly visible for 1968 through 1983. It seems easy to conclude from this picture, that the question about the effects of monetary policy on output is answered clearly: contractionary monetary policy leads to contractions in real GDP.

Figure 5: Impulse responses to a contractionary monetary policy shock one standard deviation in size, using the penalty-function approach with K = 5. I.e., the responses of the GDP price deflator, the commodity price index, nonborrowed reserves and the negative of the Federal Funds Rate have been penalized for positive values and slightly rewarded for negative values in the months k, k = 0, . . . , 5 following the shock: the shock was identified by minimizing total penalties. The error bands are now much sharper than in figure 3. While the real GDP response is still within the ±0.2 error band around zero estimated before, there now seems to be a piece between one and 12 month, showing a conventional response.

Figure 4: Impulse responses of real GDP to a contractionary monetary policy shock one standard deviation in size, using the pure-sign-restriction approach. For the left column, K = 2 and K = 5 were used, whereas K = 11 and K = 23 have been used in the right column. Essentially, all of these figures show again an error band of ±0.2 percent around zero. As one moves from shorter to longer horizons K, that band seems to move up. Overall, the evidence in favor of the conventional view of a fall in output after a “contractionary” monetary policy shock seems to weak at best.

Figure 6: Impulse responses of real GDP to a contractionary monetary policy shock one standard deviation in size, using the penalty-function approach, imposing sign restriction for the months k = 0, . . . , K after the shock. For the left column, K = 2 and K = 5 were used, whereas K = 11 and K = 23 have been used in the right column. Compared to figure 4, the results are now sharper, but also more sensitive to variations in K. Only low values of K are fairly consistent with the conventional view of a decline in real GDP following a “contractionary” monetary policy shock.

Figure 7: These plots show the fraction of the k-step ahead forecast error variance explained by a monetary shock, using a pure-sign restriction approach with K = 5, as in figure 3. The three lines are the 16% quantile, the median and the 16% quantile of the posterior distribution. According to the median estimates, monetary policy shocks account for 10 percent of the variations in real GDP at all horizons, for up to 30 percent of the long-horizon variations in prices and for 25 percent of the variation in interest rates at the short horizon, falling off after that.

Figure 3: Impulse responses to a contractionary monetary policy shock one standard deviation in size, using the pure-sign-restriction approach with K = 5. I.e., the responses of the GDP price deflator, the commodity price index and nonborrowed reserves have been restricted not to be positive and the federal funds rate not to be negative for months k, k = 0, . . . , 5 after the shock. The impulse response for real GDP is a ±0.2 percent confidence band around zero: while consistent with the textbook view of declining output after a monetary policy shock, it is also consistent with e.g. monetary neutrality.

Figure 8: These plots compare the actual data for real GDP to a “counterfactual” experiment, in which it is assumed that there hadn’t been any monetary policy shocks after Volcker became the chairman of the Federal Reserve: all monetary policy shocks after August 1979 have been set to zero. For the top figure, the pure-sign-restriction approach has been used, whereas the penalty-function approach was taken for the middle figure, both with K = 5. The bottom figure has been calculated from a Cholesky decomposition with monetary policy shocks identified as innovations in the Federal Funds Rate ordered last. Note that certainly the 1980 recession does not disappear in any of these three plots.

Figure 2: Impulse responses to a contractionary monetary policy shock one standard deviation in size, identified as the innovation in the Federal Funds Rate ordered last in a Cholesky decomposition. This “conventional” identification exercise is provided for comparison. The three lines are the 16% quantile, the median and the 16% quantile of the posterior distribution. The first column shows the responses of real GDP, the GDP deflator and the commodity price index. The second column shows the responses of total reserves, nonborrowed reserves, and the Federal Funds Rate. This identification mostly generates “reasonable” results, but also the price puzzle: the GDP deflator rises first before falling.

Frequently asked questions

Q1. What have the authors contributed in "What are the effects of monetary policy on output? results from an agnostic identification procedure" ?

This paper proposes to estimate the effects of monetary policy shocks by a new “ agnostic ” method, imposing sign restrictions on the impulse responses of prices, nonborrowed reserves and the federal funds rate in response to a monetary policy shock. The authors provide a counterfactual analysis of the early 80 ’ s, setting the monetary policy shocks to zero after December 1979, and recalculating the data. 

Q2. How much of the k-step ahead prediction error variance of real output is a ?

Monetary policy shocks account for probably less than twentyfive percent of the k-step ahead prediction error variance of real output, and may easily account for less than three percent. 

Q3. What is the reason for the variation in prices and interest rates?

The remaining variations in prices and interest rates may still be due to monetary policy, but then it needs to be due to the endogenous part of monetary policy: by systematically responding to shocks elsewhere, monetary policy may end up being responsible for 100% of the movements in prices. 

Q4. How does the monetary policy shock affect real output?

A one-standard deviation monetary policy shock may leave output unchanged or may drive output up or down by up to 0.2 percent in most cases, thus possibly triggering fairly sizeable movements of unknown sign. 

Q5. How does the Federal Funds Rate react to a monetary policy shock?

4. The Federal Funds Rate reacts large and positively immediately, typically rising by 30 basis points, then reversing course within a year, ultimately dropping by 10 basis points. 

Q6. What is the average GDP price deflator?

The GDP price deflator reacts very sluggishly, with prices dropping by about 0.2 percent within a year, and dropping by 0.5 percent within five years. 

Q7. What is the impulse vector corresponding to monetary policy shocks?

To identify the impulse vector corresponding to monetary policy shocks, the authors impose, that a contractionary policy shock does not lead to an increase in prices or in nonborrowed reserves and does not lead to a decrease in the federal funds rate. 

Q8. What is the largest fraction of variation explained by monetary policy?

For interest rates, the largest fraction of variation explained by monetary policy is at the short horizon, providing further support to the view, that11monetary policy shocks are accidental errors by the Federal Reserve Bank, which are quickly reversed. 

Q9. What is the drawback of the pure-sign-restriction approach?

As a drawback, the pure-sign-restriction is, in effect, simultaneously an estimation of the reduced-form VAR alongside the impulse vector: VAR parameter draws, which do not permit any impulse vector to satisfy the imposed sign restrictions, are discarded as “impossible”. 

Q10. What is the simplest way to calculate the impulse response?

a is an impulse vector if and only if there are coefficients αi, i = 1, . . . ,m with5∑m i=1 α 2 i = 1, so thata = m∑ i=1 ( αi √ λi ) xi (3)Given an impulse vector a, it is easy to calculate the appropriate impulse response, see appendix B for details.