### Inflation Targets, NGDP Targets, Woodford, and Liquidity Traps

**Matthew Martin**9/15/2013 03:26:00 PM

Tweetable

Some background: the Federal Reserve sets the nominal interest rate on short-term interbank loans, known as the FedFunds rate, which in turn affect all the other interest rates in the economy. The Fed Funds rate is inherent to monetary policy--that is, the Fed is setting this interest rate no matter what it does or doesn't do with monetary policy. The question, then, is what kind of decision rule should the Fed follow to determine how it will set interest rates? There are several candidates. An old Friedman-era answer was that the Fed should target the M2 measure of money supply, setting interest rates in a manner that would stabilize the path of M2. This proved untenable, as we kept overshooting the M2 target, generating "stagflation." Friedman's system collapsed in a spectacular double-dip recession in 1979-1982, and afterwards most of the developed world switched to an inflation target of around 2 percent per year. The US Fed did not formally announce this target until 2012, but economists have suspected they were secretly targeting 2 percent since the early 1980s (this has appeared in every version of the Taylor Rule I have ever seen). The 2 percent inflation target seems to have produced a "Great Moderation" which eliminated most, but not all, recessions (recession frequency declined from once every 4 years 1945-1981 to just once every 9 years after 1981).

More recently, especially since the start of the "Great Recession," many economists have noticed a flaw in the inflation targeting scheme:

It appears that maintaining a 2 percent inflation target requires long-run declining interest rates. This isn't the "balanced-growth" equilibrium we wanted. Now, not everyone seems to feel that a long-run decline in interest rates is a problem. I'd point to John Taylor as an example of a macroeconomist who basically doesn't believe anything changes at the zero-lower-bound. Taylor tweeted this yesterday:

Valerie Ramey reports http://t.co/TD0FaMwKlu at Bob Hall Fest yesterday that multiplier is not larger at zero lower bound for interest rateBut, if you're a rational economist, you'd be paying close attention to all the research showing that (yay! they're all ungated!) the zero-lower-bound poses huge macroeconomic problems. The problem is that, at the zero-lower-bound, the Fed is unable to lower the nominal interest rate any further, so in the event of a negative demand shock, or even a positive supply shock, output will contract in order to equilibrate the economy.

— John B. Taylor (@EconomicsOne) September 14, 2013

The essential problem here is that an optimal monetary policy rule cannot naively target a fixed inflation rate, because it must also be chosen to minimize the probability of hitting the zero lower bound.

One suggestion to do exactly that has been the NGDP target. Because bouts at the zero lower bound involve slow or negative growth in real GDP, then an NGDP target automatically implies a higher inflation rate in such instances. By the Fisher equation $$nominal~interest~rate=inflation+real~interest~rate$$ higher inflation implies a higher nominal interest rate for any given real interest rate (or put differently, if inflation rises at the zero lower bound but the Fed keeps nominal interest rates at zero, then the real interest rate falls, causing aggregate demand to rise).

There are a lot of ways to criticize NGDP targeting. For one thing, the NGDP target is just an arbitrary choice, not the result of an optimization procedure, and therefore has essentially zero probability of actually being optimal for a given model. Even if an economist specified a model and derived the NGDP target that produced the highest aggregate welfare (something I've not seen in any pro-NGDP papers), we'd still have to ask why he constrained the policy rule to only linear NGDP targets. By excluding non-linear policy rules from the analysis, we are excluding all most all of the potential policies that the Fed could take, and then claiming that one of the very few policies that are left is somehow "optimal." Its a lot like claiming that mashed potatoes are the "best" food at KFC, if you exclude all the menu items with chicken in them.

Additionally, there's no guarantee that an NGDP target is even possible. The problem is that an NGDP doesn't call for higher inflation until we hit the zero lower bound and start seeing contractions in output. Theoretically, if we can communicate higher inflation expectations, this is sufficient to actually produce the requisite inflation. But, announcing an NGDP target may not be sufficient to produce expectations of higher inflation for several reasons. For one an NGDP target is subject to the "taper" problem--as soon as output recovers, the NGDP target predicts inflation goes back to normal--this is not the expectation of higher-than-normal future inflation that Krugman and Woodford have argued for. Since monetary policy is ineffective at the zero lower bound (something most New Keynesian models agree on), this means that the NGDP target can produce higher contemporaneous inflation only if people think it will produce higher contemporaneous inflation--something they have no intrinsic reason to believe. Quite simply, the NGDP target may fail simply because it is not credible.

So, I partially agree with Andolfatto when he says

"what more does the NGDP crowd expect from an official NGDP target? Seems to me that they are just asking for more price inflation"The NGDPers have simply noticed that the optimal inflation target is higher when we are at risk of hitting the zero lower bound and that an NGDP target would call for higher inflation when we hit the zero lower bound. I suspect that the mostly unstated reason they support the NGDP target rather than, say, Woodford's "output gap adjusted price level target" is simply because they think it more politically feasible to get people to accept a mysterious NGDP target than tell them the truth--that you want to raise inflation rates whenever their incomes fall.

Nick Rowe9/15/2013 05:01:00 PMAn NGDP *level-path* target acts as an automatic stabiliser, relative to IT, because people will expect *temporarily* higher inflation and/or real income growth to get back to the target path, which both increase demand for a given nominal interest rate.

That means the probability of hitting the ZLB is reduced, for the same average inflation rate and average RGDP growth rate, as an inflation target.

A price level path target would also act as an automatic stabiliser in the same sense, but it's less reliable than an NGDP level path target, because it only operates if P falls below path, rather than if P.Y falls below path.

Matthew Martin9/15/2013 09:15:00 PMI generally agree that the NGDP level-path target would be an improvement over current policy, but it is still unlikely to be optimal simply because the rule is still arbitrary. The optimal rule could easily call for higher than trend NGDP level following a bout at the ZLB if the optimal response function is highly non-monotonic. Or, as Andolfatto has suggested, the optimal policy could be monotonic (which is usually the case for most things in DSGE models), in which case the optimal path of NGDP is to stay below trend for an adjustment period following a bout at the ZLB (if inflation is costly, we run the risk of welfare reducing "over-correction").

Matthew Martin9/15/2013 09:20:00 PMNick Rowe9/16/2013 06:36:00 AMSometimes, the best is the enemy of the good.

One practical complaint about Woodford's proposal is that central banks don't have a clue about potential output in real time. Simon van Norden did some research on this, and found the Bank of Canada's first estimates of potential output and output gaps had very little correlation with final revised estimates, looking back with the benefit of hindsight.

Even leaving that aside, Woodford didn't really convince me at a theoretical level. I'm sceptical of "divine coincidence", even if we ignore the ZLB.

Nick Rowe9/16/2013 06:43:00 AMMatthew Martin9/16/2013 04:25:00 PMI know John Taylor and others are trying to emphasize the importance of simplicity in monetary rules, but I don't quite buy it. I don't think that a simplistic formula like a linear taylor rule or NGDP target provides any better guidance than simply a graph of what the Fed predicts interest rates, prices, and output will do under it's policy. So, I believe in "rules-based policy" in the sense that I think the Fed should use the data and theory to derive an optimal policy function. But I differ with Taylor in that I don't see any extra benefits from the analytical simplicity of the policy function.