NGDP targeting and the Taylor Rule

Chris Waller pointed out to me this morning that the NGDP target is formally equivalent to a special case of the Taylor rule. (Maybe this is generally known? I don't know.)

The argument goes as follows. Let R denote the nominal interest rate. Then the NGDP target proposes a monetary policy rule of the form:

R = R* + [log(NGDP) - log(NGDP*)]

where the starred variables denote targets.  So the rule above raises the interest rate when NGDP is above target and lowers the interest rate when NGDP is below target.

Of course, NGDP = PY, so log(NGDP) = log(P) + log(Y).

Thus, we may rewrite our policy rule in the following way:

R = R* + [log(P) +log(Y) - log(P*) - log(Y*)]

Now add and subract the lagged value of log(P) from the RHS of the equation above to get:

R = R* + [log(P) - log(P-) +log(Y) - log(P*) + log(P-) - log(Y*)]

or

R = R* + A*[log(P/P-) - log(P*/P-)]  + B*[log(Y) - log(Y*)]

So the NGDP targeting rule proposes to adjust the nominal interest rate in terms of the prevailing inflation and output gaps, with weights A = B = 1.

It seems surprising that the solution A=B=1 is generically robust. But maybe it is. In many models, A>1 is required for stability. This is the so-called Taylor principle. It is also a property of learning models; see Howitt 1992.

So maybe the NGDP targeting crowd is just saying that A should be lowered and B increased? Is that it? Have to rush off to a meeting...
 

The magic fairy NGDP wand

It's been a good day of blogging. And it seems like the day has not ended yet. Scott Sumner posts his most recent reply to me here: Second Reply to Andolfatto.

Alright, time to take a step back and put things in some perspective. What exactly is my beef with NGDP targeting anyway?

The somewhat surprising answer is: nothing, per se. I am, however, somewhat perplexed with many of those who strongly advocate NGDP targeting. I believe they are overstating the case for NGDP targeting. And in doing so, I believe that they are diverting attention away from the real economic and political forces that are potentially holding growth back. It may be comforting to believe that most of our major economic problems can be solved by having the Fed simply wave a magic fairy NGDP wand. Yes, well, I'm sorry, but I remain skeptical.

Back in April 2012, I asked David Beckworth to provide me with what he viewed as a theoretical foundation for NGDP targeting (see here). David pointed me to a very nice paper by Evan Koenig, which emphasized the role of nominal (unindexed) debt.

That led me to believe that the rationale for NGDP targeting rested on the idea that such a policy would smooth out shocks to the price-level in a way that inflation-targeting would not. This led me to write down a simple OLG model with nominal debt here and here. What I found was a case for stabilizing the price-level, but not necessarily the NGDP.

Now why did I find this result and why does it seem to contradict the prescription offered by Scott and others? I think I have traced the source of the discrepancy.

Scott et. al. like to organize their thinking around a static textbook AS-AD model. The friction is some sort of nominal price rigidity. Consider a negative AD shock. That has the effect of depressing the P and increasing the real debt burden (e.g., in the context of a sticky nominal wage, it increasing the real wage bill for the business sector, leading to layoffs, and a decline in Y). An NGDP target would stabilize NGDP by stabilizing both P and Y. O.K., good.

Now consider a negative AS shock. This causes P to rise and Y to fall. As NGDP (=PY) may not be very much changed, the policy would advocate little if any intervention. However, a strict PL target would require reducing P. Reducing P would mean increasing real debt burdens, which would further decrease Y. Conclusion: a PL target is destabilizing.

Now, I know that Scott finds mathematical models "annoying" (to me, this is like saying one finds musical scores annoying and that one can always play music better by ear). But please, go take a look at my model (academic economists should find it very simple and straightforward).

My model is explicitly dynamic--you know--kind of like the way reality is. The shock I consider does not fit easily into either the AS or AD category. The event is a "bad news" shock--a downward revision in the forecast of future capital return (or the after-tax return to capital). The impact effect of the shock is like a negative AD shock, because it depresses the demand for investment (and leads to a flight to government money/debt, which causes a surprise decline in P). The contemporaneous AS remains unaffected.

On the other hand, the decline in current capital spending manifests itself as a smaller future productive capital stock, so the that future real GDP is expected to decline. (Whether it actually declines depends on the realization of the shock: it may be either higher or lower than expected). So in this sense, my shock looks like a negative AS shock too.

Now, let's imagine that this bad news is persistent. Then absent intervention, P remains depressed and Y remains depressed. Moreover, because debt is not indexed, and because a surprise drop in P hurts the initial group of investors in my model, the amount of capital investment that occurs on impact is too low (relative to a world in which debt could have been indexed). The PL target rule corrects this inefficient reallocation of purchasing power (away from investors, toward consumers, in my model).

What is the effect of targeting NGDP in my model? To stabilize NGDP, capital spending has to be stabilized and, to the extent that future productivity is lower (in according with earlier expectation), capital spending has to be increased. We can obviously think of policies that achieve this result. In fact, my model is consistent with the proposition that higher inflation leads to higher output (via a Tobin effect). But whether such a policy is desirable is open to debate. In particular, is it really a good idea to encourage more investment in a sector (e.g., housing) in a sector where the returns have fallen? Moreover, people are heterogeneous (my model takes this into account). There would be winners and losers. I don't here very much talk about this prospect from the NGDP targeting crowd.

So there you have it. Please stop telling me that NGDP targeting is "obviously" and unambiguously a good thing. I agree that it is -- if you insist on organizing your thinking with Econ 101 tools. And you know what? Maybe this toolkit is the correct toolkit to use. But again, forgive me if I just do not see this as obvious. This is supposed to be science, not religion.

Finally, maybe someone can speak on the following issue (see here). There is a difference between wishing for a NGDP target before the crisis, and wishing for the policy to be implemented right now. I have some sympathy for the idea that it would have been nice to have the policy in place earlier (I think it would have largely been innocuous). But I am having a harder time seeing the benefits of such a policy imposed right now by the Fed with the tools it has available. In particular, even if "debt overhang" was a major drag on the economy following the end of the most recent recession, what evidence do we have that it is still a *major* force holding the recovery back (especially, as I pointed out in my earlier posts, the price level seems to be close to its long-run trend path). What is the mechanism that people have in mind?

Thanks very much to all of you who have commented and pointed me to readings. I don't always have the time to get to them, owing to the demands on my time here at work, but I do appreciate it! And thanks to Scott for his thoughtful replies to my posts. It's been a fun discussion.
 

A reply to Sumner

I figured that my previous post might stimulate an interesting debate on the relative merits of NGDP targeting. So far, I've only heard from Scott Sumner (see here). Scott thinks I'm wrong for many reasons. He lists 4, which I reply to here.

1. Government price indices don’t measure the prices that are of macroeconomic interest. For instance in the 6 years after the housing bubble peaked the US, BLS data shows housing prices rising by about 10%, while Case-Shiller showed a 35% decline. Housing is 39% of the core CPI. That’s a big deal.

The BLS data show housing prices rising by 10% after housing prices peaked? Not sure I understand this claim. I thought that the price of housing services entered into the CPI, not house prices directly. In any case, it would have been nice to have been provided with an alternative price index.

2. But even if the data were accurate, prices are the wrong variable, and models that suggest PLT is equivalent to NGDPLT are simply wrong. Indeed one of the strongest arguments for NGDPLT is that it does better when productivity growth is unstable. And productivity growth in America is unstable.

Scott, I hate to break this to you but: all models are wrong in the sense that they are abstract representations of reality. Perhaps you mean "wrong" in the sense that any model that displays such an equivalence necessarily does not fit the data? If so, what evidence do you have that supports this claim?

By the way, Miles Kimball, who has some kind words to offer your crowd, claims here that the NGDP target has to be adjusted for changes in productivity growth. But maybe you have some different model in mind? Where does this model live?

3. It’s also a mistake to draw a trend line on the assumption that the Fed is doing PLT at 2.09%, if it is not in fact doing PLT at 2.09%. Fitted trend lines trick the human eye, as I’ve discussed in previous posts. Do I have evidence that they were not doing PLT at 2.09%? Sure, lots of evidence. The Fed called for fiscal stimulus in late 2008 and early 2009, which would have been sheer madness if they had been doing PLT at 2.09%. As you can see from the graph, the price level was actually above target in 2008, suggesting an overheating economy. That strongly suggests the trend line is in the wrong place.

I am not sure why a call for "fiscal stimulus" in late 2008 and early 2009 would have been "madness." The PCE price-level peaked in July 2008 and fell sharply in late 2008 and early 2009 (largely reflecting the collapse in energy prices).

4. You might respond that the trend line sure looks accurate. Yes, but I could draw a different trend line that would look equally accurate from 1990 to 2008, and then show the price level below target after 2008. Who’s to say that’s not right? Indeed that trend line would be far more consistent with the Fed’s calls for fiscal stimulus, and complaints from Fed officials that demand has fallen short of their goals.

Unfortunately I don’t know how to add trend lines to St Louis Fred graphs. But here’s the graph I’m thinking of, from January 1990 to September 2008. If you assume the Fed was doing PLT during that period, and fit a trend line, I claim that the period after September 2008 would entirely lie below the trend line. That would be partly because the slope would be steeper, and partly because the trend PL would be higher in September 2008 than on Andolfatto’s graph.

Scott: here is the graph. First, I logged the data (natural log). Then I drew a trend line through the data beginning in Jan 2009 and ending in Jul 2008 (not Sep 2008 as you suggest, because I'm sure you meant Jul 2008, the month in which the PCE price level peaked). I then projected this trend line through the rest of the sample. Here is the result:

I can hardly see any difference.

If PLT and NGDPLT really were similar policies, then why does NGDP look far below trend since 2008, while the price level (according to Andolfatto, but I have my doubts) is right on trend?

That would be because the RGDP is below trend. And there are many reasons why RGDP may be below trend that are independent of the conduct of monetary policy.

U.S. price-level dynamics

Since some measure of "price-level stability" constitutes one half of the Fed's dual mandate, I thought it might be of some interest to document the behavior of various measures of the price-level and its components in the U.S. Some of what I report here will be familiar to some readers and maybe surprising to others. I conclude with a thought about NGDP targets and what they're supposed to accomplish over a price-level target.

Let me start with the consumer price index (CPI). The CPI is constructed by the Bureau of Labor Statistics. The CPI attempts to measure the dollar cost of a typical basket of consumer goods and services (to see which goods and service are included, click here).

The following figure plots the CPI, core CPI, food, and energy. The core CPI is defined as "all items excluding food and energy."

The two striking properties of this data are: (1) consumer goods and services prices (measured in dollars) have generally been rising, with an exceptionally rapid rise occurring in the 1970s; and (2) the dollar price of energy is relatively volatile, with its trend diverging from the other CPI components for a considerable length of time.

When people speak of "high inflation" these days, I think they are generally focused on the recent behavior of food and energy prices. As the diagram above shows, energy prices have increased by about 150% since 2000. Food prices have generally risen more rapidly than other CPI components since 2009, but only modestly so. But it's important to keep in mind that while food and energy are obviously important, together they account for only 25% of expenditures on consumer goods and services (in the CPI basket).

While many people appear to be focused on the rapid rise in energy prices, the data above suggest that it might be more interesting to ask why energy prices remained so low throughout much of the 1980s and 1990s. Economists like to stress the role of relative prices in coordinating the allocation of resources in an economy. The price of energy relative to other consumer goods and services fell significantly over the time period 1984-1999, and caught up with the rest of the basket only in 2004.

Why was energy so cheap from 1984-2004 and what implications (if any) did this have for resource allocation?

The next diagram plots the same data, but using a log scale. Transforming the data in this manner is convenient because the slopes of the curves can be interpreted as inflation rates.

This diagram highlights the effect of the energy price shocks that occurred in the early and late 1970s. The sharp spike in energy prices that occurred in 2008 is relatively small by comparison.

 

Let's take a look at the (log) CPI from 1990 onward and draw a linear trend line through the data. Here is what we get:

The CPI inflation rate since 1990 averaged 2.62% per annum. The current CPI inflation rate appears to be close to trend.

Of course, the Fed's official target of 2% inflation refers not to CPI inflation, but to the PCE inflation rate. PCE stands for "Personal Consumption Expenditures" price index; see here. The following diagram plots the PCE price index from 1959 onward, and decomposes the PCE into (1) durable goods, (2) nondurable goods, and (3) services.

It's interesting to see the price deflation in consumer durables since the early 1990s. The volatility in nondurable goods near the end of the sample is likely attributable to energy prices.

Now let's take a look at the (log) PCE from 1990 onward, together with linear trend:

The PCE inflation rate since 1990 averaged 2.09% per annum.

What's interesting about this diagram is that even though the Fed does not officially target the PCE price level, the data above suggests that the Fed is behaving as if it does.

As a price-level (PL) target is equivalent to a nominal GDP (NGDP) target in a wide class of macroeconomic models (especially under the assumption of constant productivity growth), then what more does the NGDP crowd expect from an official NGDP target? Seems to me that they are just asking for more price inflation and wishfully hoping that some of the subsequent rise in NGDP will take the form of real income.

Tell me I'm wrong (and why).

Whither the consumer?

Well, I'm back from my summer hiatus. I know you all missed me.

So, I'm looking at some graphs that my colleague, Fernando Martin, prepared relating to the behavior of the U.S. economy. First, let's take a look at real GDP. Actually, real GDP per capita, with the population defined as those aged 16-64 plus those aged 65+ and counted as part of the labor force (non-retired). The data (1948-2013) is logged and a linear trend is fit through the sub-sample (1955-2007). Here is what you get:

It is rather remarkable how well the linear trend fits the historical data despite the significant demographic changes that have occurred over this sample period. But, there you have it.

Of course, as the great Eugen Slutsky pointed out, the interaction of chance events could generate periodicity where none actually exists, see: The Summation of Random Causes as the Source of Cyclic Processes. In layman's terms: that linear trend you seen drawn through the data above might just be a figment of your imagination. So we should always be careful when interpreting deviations from statistical trend.

Having said that, there is something rather odd about the recent recovery dynamic. In the U.S., the business cycle is mostly about investment spending. Consumer spending (non-durables and services) is relatively stable. And in the typical recovery dynamic, consumption and investment tend to move together (this applies to booms as well).

The following figure plots (detrended) real per capita consumption (non-durables and services) and investment (includes consumer durables). With the onset of the 2008 recession, we see the sharp drop in consumption and the even sharper drop in investment. The decline in both series initially was not unusual--apart from the severity of the shock. What is unusual is the subsequent recovery dynamic: consumption and investment appear to be heading in different directions, relative to their historical trends.

Here's the same data, except with investment decomposed into residential and non-residential investment.

So, residential investment behaves largely like other forms of investment, except that it is considerably more volatile. In particular, the recovery dynamic for residential investment looks like what one might expect, given the large negative shock in that sector. And yet consumer spending continues to fall away from its historical trend, even as residential investment recovers (albeit, slowly).

Can someone point me to a theoretical model that generates this type of consumption-investment dynamic during a recovery?

Household deleveraging surely has to be a big part of the explanation here--see the following diagram (source). [It is curious to  note, however, that consumption seemed below trend even during the mid-2000s boom period--will have to think about that.]

These debt-service ratios are now at or close to their historical lows. Is the consumer now ready for a major comeback?

Selgin on Gorton

I learned a lot about financial crises from Gary Gorton's work in the area. His views on what went wrong during the recent crisis and what might be done to prevent similar events are views that should be taken seriously. Seriously, that is, but not uncritically. And this is where George Selgin provides a useful service: see Misunderstanding Financial History. 

Sadowski on Bullard (Guest Post)

About a year ago, Jim Bullard criticized the argument that that the Fed was missing on both sides of its dual mandate. Mark Sadowski (who should have his own blog, I think) has asked me to post his reply. I am most happy to do so.

=======================================

This is written in response to a question David Andolfatto posed in September in a blog post entitled “Is the Fed missing on both sides of its dual mandate?”

http://andolfatto.blogspot.com/2012/09/is-fed-missing-on-both-sides-of-its.html

David concluded that post with the following statement:

 “Bullard suggests that a non-monotonic transition path for inflation is unlikely to be part of any optimal path in a NK [New Keynesian] type model. The optimal path for inflation is unlikely to be part of any optimal path in a NK type model. The optimal transition dynamics are typically monotonic—think of the optimal transition path as a movement back up the PC [Phillips Curve] in the diagram above. If this is true, then the optimal transition path necessarily has the Fed missing on both sides of its dual mandate.

Of course, conventional NK models frequently abstract from a lot of considerations that many people feel are important for understanding the recent recession and sluggish recovery. The optimal monetary policy may indeed dictate "inflation overshooting" in a different class of models. Please feel free to put forth your favorite candidate. Tell me why you think Bullard is wrong.”

James Bullard, President of the St. Louis Fed, had just written an opinion piece for the Financial Times where he stated:

http://www.ft.com/intl/cms/s/0/168023d6-0243-11e2-b41f-00144feabdc0.html

“To argue against monotonic convergence now would imply that when unemployment is above the natural rate, monetary policy should aim for inflation above the Fed’s 2 per cent target. On the face of it, this does not make sense: the US has experienced periods when both inflation and unemployment have been above desirable levels. In the 1970s this phenomenon was labeled stagflation. Monetary policy has been regarded as poor during that period.”

At the time Scott Sumner mockingly responded:

http://www.themoneyillusion.com/?p=16344

“To argue for monotonic convergence now would imply that when unemployment is above the natural rate, monetary policy should aim for inflation below the Fed’s 2 per cent target. On the face of it, this does not make sense: the US has experienced periods when both inflation and employment have been below desirable levels. In the 1930s this phenomenon was labeled “The Great Depression.” Monetary policy has been regarded as poor during that period.”

Sumner is of course talking about the contractionary portion of the U.S. Great Depression. The subsequent 1933-37 recovery, during which real GDP grew at an average rate of 9.5%, is an excellent example of “oscillatory convergence” with unemployment high and falling and inflation higher than normal. And yes, monetary policy is generally regarded as excellent during that period.

Andolfatto’s, Bullard’s, and Sumner’s comments raise a great many questions. For example, what is the relationship between unemployment and inflation? How has this relationship changed over time, and why? How has this relationship been modeled over time? How should this relationship affect the conduct of monetary policy? For the moment, at least, I want to stay focused on Bullard’s remarks.

As evidence Bullard cited a paper by Frank Smets and Raf Wouters, “Shocks and Frictions in US Business Cycles – A Bayesian DSGE Approach” (American Economic Review, Vol. 97, No. 3, June 2007, pp. 566-606). In an essay published about a month later, “Monetary Policy and the Expected Adjustment Path of Key Variables” (Federal Reserve Bank of St. Louis Economic Synopses, 2012, No. 30), Bullard clarified his Financial Times comments:

http://research.stlouisfed.org/publications/es/article/9490

“Let’s consider the medium-sized macroeconomic framework of Smets and Wouters (2007). This is an important benchmark model; and, while we could argue about the details, I think it will serve to make my point. In the Smets and Wouters dynamic stochastic general equilibrium (DSGE) model there are many shocks, and there is a monetary policymaker that follows a Taylor-type monetary policy rule not unlike ones used in actual policy discussions. The authors estimate their model using postwar U.S. data, and they also report results for subsamples including the post-1984 data. Importantly, what the authors are estimating is a general equilibrium for the economy, which includes monetary policy.

How does the economy adjust in the Smets and Wouters model? The chart is Figure 2 from their paper.

http://research.stlouisfed.org/publications/es/12/ES_30_2012-10-12_chart.pdf

The authors plot the reaction of key macroeconomic variables to three types of shocks in their model that might be thought of as demand shocks. Variables are reported as deviations from a steady-state value, so that zero represents a return to normal. The variables include inflation and a labor market variable—hours worked. Time is measured in quarters. The shock is a positive one—output and hours go up in response—but the story is merely transposed for a negative shock (i.e., flip the figures upside down).

The reaction of all variables is essentially monotonic beyond the hump in these graphs, at least through year four. (That is, the adjustment does not show much of a tendency to oscillate about the long-run value.) For all three types of demand shocks, the Fed would be “missing on both sides of the dual mandate” almost all of the time as the economy recovers from the shock. If the shock were negative, hours would be too low (unemployment too high), and inflation would be too low every quarter for many years. Yet the monetary policy embedded in this general equilibrium is a Taylor-type policy rule that has often been argued to closely approximate the optimal monetary policy in frameworks such as this one. 2 It is in this sense that I do not think merely observing where inflation and unemployment are relative to targets or long-run levels at a point in time is telling us very much about whether the monetary policy in use is the appropriate one or not.”

Footnote 2 reads:

“One can investigate optimal-control monetary policy assuming credible commitment in this model, taking the non-policy parameters as estimated by Smets and Wouters. This type of monetary policy changes these impulse response functions but still leaves goal variables “missing on both sides of the mandate” in many situations. I thank Robert Tetlow for investigating this issue in response to an earlier draft.”

The monetary policy reaction function that is built into the Smets and Wouters (2007) model is the original rule John Taylor proposed in 1993 ("Discretion versus Policy Rules in Practice", Carnegie-Rochester Conference Series on Public Policy, Vol. 39, December 1993, pp. 195-214), namely a Taylor Rule that places equal weights on the inflation gap and the output gap. In 1999 Taylor discussed an alternative version of this rule that placed double the weight on the output gap than on the inflation gap, (“A Historical Analysis of Monetary Policy Rules”, Monetary Policy Rules, Chicago: University of Chicago Press, pp. 319-341). This is a point to which we shall return later. Thus the response of the economy to the demand shocks illustrated in Figure 2 is conditional on the Taylor Rule embedded in the model.

At this point it might be worth mentioning that one of the acknowledged shortcomings of medium-scale New Keynesian DSGE models is that typically there is no reference to unemployment. Bullard infers the impact of a demand shock on unemployment from its effect on hours worked. In particular, the Phillips Curve in the Smets-Wouters model is a hybrid New Keynesian type in which inflation depends on past inflation, expected future inflation, current price mark-up and a price mark-up disturbance. Apparently the only reference in the model to the output gap occurs in the model’s monetary policy reaction function (i.e. the Taylor Rule).

Bullard’s footnote on optimal control monetary policy is especially relevant in this context. What is “optimal control” monetary policy? Federal Reserve Vice Chair Janet Yellen spoke about optimal control techniques in speeches in April, June and November of last year. Here is how she introduced them in April:

http://www.federalreserve.gov/newsevents/speech/yellen20120411a.htm

“One approach I find helpful in judging an appropriate path for policy is based on optimal control techniques. Optimal control can be used, under certain assumptions, to obtain a prescription for the path of monetary policy conditional on a baseline forecast of economic conditions. Optimal control typically involves the selection of a particular model to represent the dynamics of the economy as well as the specification of a "loss function" that represents the social costs of deviations of inflation from the Committee's longer-run goal and of deviations of unemployment from its longer-run normal rate. In effect, this approach assumes that the policymaker has perfect foresight about the evolution of the economy and that the private sector can fully anticipate the future path of monetary policy; that is, the central bank's plans are completely transparent and credible to the public."

In that speech Yellen describes how projections generated by FRB/US, the Federal Reserve’s primary forecasting model, were adjusted to replicate the baseline outlook constructed using the distribution of FOMC participants' projections for unemployment, inflation, and the federal funds rate that were published in January of that year. A search procedure was used to solve for the path of the federal funds rate that minimized the value of a loss function. The loss function was equal to the cumulative sum from 2012:Q2 through 2025:Q4 of three factors: 1) the discounted squared deviation of the unemployment rate from 5-1/2 percent, 2) the squared deviation of overall PCE inflation from 2 percent, and 3) the squared quarterly change in the federal funds rate. She termed this path the “optimal control” path.

Yellen also used the FRB/US model to construct the federal funds rate path called for by the 1993 and 1999 versions of the Taylor Rule conditioned on the same illustrative baseline outlook used to generate the optimal control path. These paths, as well as the optimal control, and the various resulting paths for unemployment and inflation are depicted in Figure 8 of her speech:

 http://www.federalreserve.gov/newsevents/speech/yellen20120411-slide8.jpg

The 1993 Taylor Rule calls for the federal funds rate to begin rising in 2013Q2. The 1999 Taylor Rule calls for the federal funds rate to begin rising in 2015Q1. Optimal control calls for the federal funds rate to begin rising in 2015Q4. More importantly, note that whereas the paths for unemployment and inflation under the Taylor Rules converge monotonically, under optimal control they display oscillatory convergence, with both unemployment and inflation “overshooting” before converging to their long run values. 

Now, it’s true these results were generated with FRB/US and not the Smets-Wouters model. FRB/US is a somewhat older (1997), large-scale simultaneous equation macroeconometric model. But because expectations of future economic conditions are explicit in many of its equations, and adjustment of nonfinancial variables is delayed by frictions, it too is often described as New Keynesian. The dynamic adjustment of its aggregate price equation means that, like the Smets-Wouters model, inflation is dependent on past inflation, expected future inflation and the current price markup, as well as number of additional variables such as the unemployment rate, energy prices, etc. And the general effect of monetary policy shocks on output, inflation and interest rates is quite similar to the Smets-Wouters model.

Thus I expect were one to investigate optimal control monetary policy assuming credible commitment using the Smets-Wouters model, as Bullard mentions the possibility of in his footnote, one would probably find results similar to those generated with the FRB/US model assuming it were subject to the same loss function. To be more explicit, under the same assumptions, an optimal control path generated by the Smets-Wouters model would very likely exhibit the same oscillatory convergence pattern of unemployment and inflation as demonstrated with the FRB/US model.

Thus it seems to me that the primary issue here is not what type of model should be used, but what the goals of monetary policy should be. Should monetary policy be guided by simple rules, such as the Taylor Rules, because in the past, and under potentially very different conditions, they were considered optimal? Or should monetary policy be more explicitly guided by the mandates to which it is legally subject? Or, indeed, should monetary policy be guided by something else entirely?

Mark Sadowski