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August 26, 2010

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The Relationship Between Nominal Interest Rates and Inflation: Should Jaws be Dropping?

Posted: 26 Aug 2010 12:33 AM PDT

I'm getting some pushback on my post entitled "Jaws are Dropping," which is derived from a statement in one of the links I provided in the post. I think it must be either the title of the post or, when correcting a typo, the afterthought I added about the right answer to the question of whether a low federal funds rate eventually leads to a fall in inflation that has some people so worked up (good to see that Williamson has taking a break from his exhibitions of Krugman Derangement Syndrome, bashing Krugman seems to be the main point of his blog lately). It can't be anything else I said since my main point was that I didn't have time to say much about the whole controversy due to an impending deadline.

The main issue revolves around this statement from Minnesota Fed President Narayan Kocherlakota:

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation

I think the assertion that it "must" lead to that outcome is unsupportable, there are models where that isn't true, but he means "must" in terms of a very specific model of how the economy works, including an assumption of the super neutrality of money (which is asserted as an uncontroversial assumption, but I'd quarrel with that). So, yes, it's possible to write down a very specific model that has this as an implication, but does that make it generally true? Not to me.

In any case, here's an email from a friend of Narayana defending his statements:

Hi:

I rarely comment on posts on blogs, since most of the discussion seems to be most interested in scoring political points than in economic analysis. However today I will make an exception since Kocherlakota's words come directly from any standard treatment of monetary theory, and hence, they should have been anything except controversial.

In a large class of monetary models, the Euler equation of intertemporal maximization is:

FFR = (1/beta) *(u'(ct)/u'(ct+1))*inflation

where u'(.) is the marginal utility of consumption, FFR is the federal funds rate, and beta is the discount factor (see, for instance, equation 1.21 in page 71 of Mike Woodford's Interest and Prices for a derivation in a simple context).

Let us take first the case where money is neutral, probably an implausible case but a good starting point. In this situation, the ratio of marginal utilities is unaffected by the change in inflation or the FFR. Thus, a lower FFR means lower inflation. Otherwise, there are arbitrage opportunities left on the table. What is more, in such a world, the Fed can control inflation by controlling the FFR, so the relation is causal in a well-defined sense.

Now, let's move to the much more empirically relevant case of a New Keynesian model (here I am thinking about the standard NK model people use these days to analyze policy in the style of Mike Woodford, Larry Christiano or Martin Eichenbaum, with a lot of nominal and real rigidities, so I will not discuss the assumptions in detail).

Imagine that the Fed is targeting the FFR and decides to lower the long run target from, let's say 4% to 2%. What happens? Well, in the very short run, nominal rigidities imply that we will have a transition where inflation might (but not necessarily, it depends on details of the model) be temporarily higher but, after the necessary adjustments in the economy had occurred (adjustments that can be quite painful, generate large unemployment, and might reduce welfare by a considerable amount), we settle down in the lower inflation path. Again, the reason is that in most New Keynesian models, the ratio of marginal utilities is independent of the FFR (this will happen even in many models with long-run non-neutralities) and the Euler equation will reassert itself: the only way we can have a real interest rate of 3% when the target FFR is 2% is with a 1% deflation.

Hence, in the long run, as Kocherlakota's speech explicitly says:

"To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation."

An alternative way to see this is to think about a Taylor rule of the form:

Rt/R = (πt/π)γ

where γ>1 (here I am eliminating extra terms in the rule for clarity) where Rt is the FFR, R is the long run target for the FFR, πt is inflation, and π is the long run target for inflation. In a general equilibrium model, the Fed can only pick either R or π but not both. If it decides to pick a lower R, the only way the rule can work is through a fall in π.

While one may disagree with many aspects of modern monetary theory (and I have my own troubles with it), one must at least acknowledge that Kocherlakota's treatment of this issue or the relation between the FFR and inflation in the long run is what would appear in any standard macro model.

Thanks

Jesus Fernandez-Villaverde
And, he sends along an update:
One thing I forgot to mention: I guess that the intuition that most people have (and that reacts in a somewhat surprised way to Narayana's words) comes from a New Keynesian model, where lowering the FFR with respect to what the Taylor rule indicates (what we call a "monetary shock") increases inflation in the short run. But here we are not talking about the effects on inflation of a transitory monetary shock, but, as Narayana clearly says in his speech, about the long run effects of a change in the target of the FFR.

If you commit to a single class of models and the interpretation of the shocks within them, the kind of models and interpretations that Narayan Kocherlakota has questioned, at least in their standard forms, and if you buy all the embedded assumptions that are needed to obtain the result, not all of which are easy to defend (e.g. the assumption of long-run neutrality), then yes, "must" is correct. But "must" must be interpreted in a rather limited context, and in a more general setting it's not at all clear that this result will hold.

However, my real problem with this defense is that it doesn't deal with the assertion that if real rates normalize and the Fed doesn't raise its target rate in response, it will lead to deflation., i.e. it doesn't address Nick Rowe's point. If the target real rate is below the normal real rate, how does that cause deflation? That's the part that caused the objection in the first place, and the part that still leaves me puzzled. Here's Nick:

"To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation."

That could be interpreted two ways: a wrong way, and maybe, just maybe, a right way.

"When real returns are normalized, inflationary expectations could well be negative, and there may still be a considerable amount of structural unemployment. If the FOMC hews too closely to conventional thinking, it might be inclined to keep its target rate low. That kind of reaction would simply re-enforce the deflationary expectations and lead to many years of deflation."

Nope. He definitely meant it the wrong way. If the economy returns to normal, and the natural rate of interest rises, the Fed must raise its target rate of interest. (So far so good). If it doesn't, the result would be....deflation. ("Inflation" would be the right answer).

I also wonder if a permanent shock is the right way to think about this type of a policy, but I'll leave that as a question since I don't want to distract from Nick's point.

Update: Here's more from Nick:

What standard monetary theory says about the relation between nominal interest rates and inflation, by Nick Rowe: This is what I understand "standard" monetary theory to say about the relation between inflation and nominal interest rates.

I want to distinguish two cases.

In the first case the central bank pegs the time-path of the money supply. The money supply is exogenous. The nominal interest rate is endogenous. Standard monetary theory says that a permanent 1 percentage point increase in the growth rate of the money supply will (in the long run) cause both the nominal interest rate and the rate of inflation to rise by 1 percentage point. The Fisher relation holds as a long-run equilibrium relationship. The real interest rate is unaffected by monetary policy in the long run.

In the second case the central bank pegs the time-path of the nominal rate of interest. The nominal interest rate is exogenous. The money supply is endogenous. Start in equilibrium (never mind how we got there). Standard monetary theory says that if the central bank pegs the time-path of the nominal interest rate permanently 1 percentage point higher, this will cause the price level, and the rate of inflation, and the stock of money, to fall without limit. The Fisher relation will not hold, because there is no process that will bring us to a new long run equilibrium. The real interest rate will rise without limit.

These two cases are very different, because a different variable is assumed exogenous in each case.

I am assuming super-neutrality of money, in long-run equilibrium. The Fisher relation is a long run equilibrium relationship. We never get to the new long-run equilibrium in the second case, and so the Fisher relation does not hold.

Fire at the Fire Station

Posted: 26 Aug 2010 12:24 AM PDT

This must have been embarrassing:

Rural fire engine burns in Alvadore, by Emily Gillespie, The Register-Guard: The Santa Clara fire station responded to a fire at the Alvadore fire station near Junction City at around 8:45 p.m. on Tuesday night where a fire engine was burning. The 1980s-era vehicle was lost in the fire and is also presumably the cause of the fire...

"Inequality and the High-End Bush Tax Cuts"

Posted: 26 Aug 2010 12:15 AM PDT

Chuck Marr of the Center on Budget and Policy Priorities on the relationship between tax policy and inequality:

Inequality and the High-End Bush Tax Cuts, Off the Charts, CBPP: As I've said before, from the standpoint of economic efficiency there's a clear-cut case for letting the Bush tax cuts for people over $250,000 expire on schedule in December. Sunsetting the high-income tax cuts makes just as much sense from the standpoint of equity. Recent data from the Congressional Budget Office (CBO) show a stunning shift in income away from the middle class and towards the highest-income people in the country over the last three decades:

  • In 1979, the middle fifth of Americans took home 16.5 percent of the nation's total after-tax income. By 2007, after several decades of stagnant incomes in the middle and surging incomes at the top, the middle fifth's share had dropped to 14.1 percent. Over the same period, the top 1 percent's share more than doubled, from 7.5 percent of total after-tax income to 17.1 percent (see graph below). So by 2007, the top 1 percent had a bigger slice of the national income pie than the middle 20 percent.

  • If the distribution of after-tax incomes had remained unchanged between 1979 and 2007, the after-tax income of the average family in the middle would have been $9,000 (16 percent) higher in 2007 than it actually was. Instead of an income of $55,300, this typical family would have had $64,700 (see table below). ...

Here's how that income shift looks in graph form:

Tax policy is one of the best tools we have to help offset the troubling trend of growing inequality. Unfortunately, the Bush tax cuts have had the opposite effect, providing much larger benefits — both in dollar terms and as a percentage of income — to people at the very top than to middle- and lower-income people. People making more than $1 million get an average of about $124,000 each year in tax cuts, according to the Urban-Brookings Tax Policy Center. The main reason, of course, is the large tax cuts targeted specifically at high-income households.

So this fall, when policymakers decide whether to extend the high-end tax cuts, they should keep in mind just how unequal incomes in the United States have become. As former Federal Reserve Vice Chairman Alan Blinder wrote recently in the Washington Post, is the rationale for extending these tax cuts "that America needs more income inequality? Seems to me we have enough." To me, too.

"Fed to Outline Future Actions"

Posted: 26 Aug 2010 12:08 AM PDT

Is Ben Bernanke about to "stake out a public position"?:

Fed to Outline Future Actions Friday, by Sewell Chan, NY Times: With fresh signs that the housing market is weakening,... Ben S. Bernanke, on Friday will offer his outlook on the economy, explain the Fed's recent modest move to halt the slide and possibly outline other actions. ...
It is not known what Mr. Bernanke will say, but some insight may come from an episode in his past: his concern, soon after he became a Fed governor, that the economy was at risk of deflation as the nation gradually recovered from the dot-com bust a decade ago.
Mr. Bernanke's worry then is similar to what troubles the Fed now, and his views will have no small bearing on the Fed's course of action. ... Whether policy makers should take big steps to tackle the economic doldrums — by printing even more money and buying even more assets — [is] the dominant question...
Within the central bank, several officials are alarmed at the threat of the economy falling into a dangerous cycle of declining demand, wages and prices not experienced since the Depression. They say that a deflationary, double-dip recession is unlikely, but want to formulate concrete steps to ward it off.
Other officials contend the economic indicators, while dismaying, do not represent an immediate threat, and worry that additional monetary stimulus by the Fed could erode the already shaky confidence of the markets, or even backfire by eventually spurring uncontrolled inflation. ...

The risks are not symmetric. An extended period of stagnation is a highly undesirable outcome, and the Fed needs to take steps to try to prevent this from happening.

links for 2010-08-25

Posted: 25 Aug 2010 11:01 PM PDT

Does the Recovery Depend on Housing?

Posted: 25 Aug 2010 04:39 PM PDT

The Room for Debate asks:

Can the economy recover without a turn-around in home sales? Many say that job improvement has to come first, but the bad news on housing sales has put a new gloom on expectations of a recovery. Does the housing market have to lead the way out of the hole? If so, why?

The 800 word version of my response is below, but if you prefer, the edited, less wordy 400 word version, it is here along with responses from Jennifer H. Lee, Jeffrey Frankel, Patrick Newport, and Dean Baker [all responses]. Among other things, I wish I'd talked more about employment:

The bad news for recovery seems to be nonstop lately, with new home sales, which were at a record low in July, and durable goods orders, which came in far below expectations, continuing the trend. What does this say about the prospects for recovery?

It's useful to break down the economy into four major sectors — households, businesses, government, and the foreign sector — and consider how each will affect both long-run and short-run prospects for growth.

Household consumption, which excludes the purchase of new homes (more on this in a moment), is unlikely to be the engine of growth that it has been in recent decades. Consumption before the crash was largely debt fueled, based on the false promise of continuously rise housing prices, and therefore unsustainable.
It's widely believed that consumers will move to a lower level of consumption and a higher level of savings after the recession. During this transition, lower consumption growth will be a substantial drag on the economy — this would be on top of the decline in consumption caused by the recession itself. So while growth may return to normal in the long-run, it's unlikely that this sector will lead the way to recovery.

If consumption by households isn't the answer, what about investment? In the national income accounts, the purchase of new homes is counted as part of investment. Can investment by businesses or home purchases pick up the slack?
While housing will some day grow normally again, the large excess inventory of homes, poor sales, and other problems right now means that day is far, far away. In the short-run, looking to housing to lead the recovery is likely to lead to disappointment.

Business investment does not provide much hope either (the weak report durable goods orders on Wednesday is no comfort). Business investment might pick up some once there are signs of improvement in the economy, and if the Fed lowers long-term interest rates through quantitative easing, but this sector will follow the expectation of better times, it won't lead them.
As for foreign exports, which is one of our best hopes for growth in the long-run, it hard to see that sector leading the recovery since the rest of the world is having troubles too.

So there's very little besides government that can provide the needed boost to the economy in the immediate future. If government can provide the bridge across our short-run problems, then the other sectors can take over and generate long-run growth, and the hope is that the growth will be as robust as before the recent crash. But there's guarantee that hope will be realized.

Jaws are Dropping

Posted: 25 Aug 2010 11:38 AM PDT

Minnesota Fed President Narayan Kocherlakota recently argued that low interest rates will eventually cause inflation deflation (sorry for the typo, it's hard to write the wrong answer). I'm trying to understand why people at the Fed are so reluctant to do more to help the economy, what the reasoning is, etc., but I have to meet a deadline and need to stop using the blog as a distraction. So let me just note that there is a lot of "jaw dropping" over Kocherlakota's claim. See, for example, Andy Harless, Nick Rowe, and Robert Waldmann.  [Please see the update to this post.]

A Wake-Up Call for Policymakers?

Posted: 25 Aug 2010 09:50 AM PDT

More bad news about the economy. New home sales were at a record low during July:

Sales of new single-family houses in July 2010 were at a seasonally adjusted annual rate of 276,000, according to estimates released jointly today by the U.S. Census Bureau and the Department of Housing and Urban Development. This is 12.4 percent (±10.8%) below the revised June rate of 315,000 and is 32.4 percent (±8.7%) below the July 2009 estimate of 408,000.

And durable goods orders also came in well below expectations:

New orders for manufactured durable goods in July increased $0.6 billion or 0.3 percent to $193.0 billion, the U.S. Census Bureau announced today. This increase followed two consecutive monthly decreases including a 0.1 percent June decrease. Excluding transportation, new orders decreased 3.8 percent.

I wonder if the people at the Fed who are standing in the way of more help for the economy will revise their belief that the recovery is underway and, although it is proceeding slower than they'd like to see, nothing needs to be done, nothing more can be done, to help? I doubt they will, instead they'll find a way to fit this into the narrative they want to believe in. I'd ask a similar question about Congress, fiscal policy is likely to be more effective than monetary policy in a severe recession, but I gave up on them long ago.

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