Archive for the 'Tyler Cowen' Category

The Well-Defined, but Nearly Useless, Natural Rate of Interest

Tyler Cowen recently posted a diatribe against the idea monetary policy should be conducted by setting the interest rate target of the central bank at or near the natural rate of interest. Tyler’s post elicited critical responses from Brad DeLong and Paul Krugman among others. I sympathize with Tyler’s impatience with the natural rate of interest as a guide to policy, but I think the scattershot approach he took in listing, seemingly at random, seven complaints against the natural rate of interest was not the best way to register dissatisfaction with the natural rate. Here’s Tyler’s list of seven complaints.

1 Knut Wicksell, inventor of the term “natural rate of interest,” argued that if the central bank set its target rate equal to the natural rate, it would avoid inflation and deflation and tame the business cycle. Wicksell’s argument was criticized by his friend and countryman David Davidson who pointed out that, with rising productivity, price stability would not result without monetary expansion, which would require the monetary authority to reduce its target rate of interest below the natural rate to induce enough investment to be financed by monetary expansion. Thus, when productivity is rising, setting the target rate of interest equal to the natural rate leads not to price stability, but to deflation.

2 Keynes rejected the natural rate as a criterion for monetary policy, because the natural rate is not unique. The natural rate varies with the level of income and employment.

3 Early Keynesians like Hicks, Hansen, and Modigliani rejected the natural rate as well.

4 The meaning of the natural rate has changed; it was once the rate that would result in a stable price level; now it’s the rate that results in a stable rate of inflation.

5 Friedman also rejected the natural rate because there is no guarantee that setting the target rate equal to the natural rate will result in the rate of money growth that Freidman believed was desirable.

6 Sraffa debunked the natural rate in his 1932 review of Hayek’s Prices and Production.

7 It seems implausible that the natural rate is now negative, as many exponents of the natural rate concept now claim, even though the economy is growing and the marginal productivity of capital is positive.

Let me try to tidy all this up a bit.

The first thing you need to know when thinking about the natural rate is that, like so much else in economics, you will become hopelessly confused if you don’t keep the Fisher equation, which decomposes the nominal rate of interest into the real rate of interest and the expected rate of inflation, in clear sight. Once you begin thinking about the natural rate in the context of the Fisher equation, it becomes obvious that the natural rate can be thought of coherently as either a real rate or a nominal rate, but the moment you are unclear about whether you are talking about a real natural rate or a nominal natural rate, you’re finished.

Thus, Wicksell was implicitly thinking about a situation in which expected inflation is zero so that the real and nominal natural rates coincide. If the rate of inflation is correctly expected to be zero, and the increase in productivity is also correctly expected, the increase in the quantity of money required to sustain a constant price level can be induced by the payment of interest on cash balances. Alternatively, if the payment of interest on cash balances is ruled out, the rate of capital accumulation (forced savings) could be increased sufficiently to cause the real natural interest rate under a constant price level to fall below the real natural interest rate under deflation.

In the Sraffa-Hayek episode, as Paul Zimmerman and I have shown in our paper on that topic, Sraffa failed to understand that the multiplicity of own rates of interest in a pure barter economy did not mean that there was not a unique real natural rate toward which arbitrage would force all the individual own rates to converge. At any moment, therefore, there is a unique real natural rate in a barter economy if arbitrage is operating to equalize the cost of borrowing in terms of every commodity. Moreover, even Sraffa did not dispute that, under Wicksell’s definition of the natural rate as the rate consistent with a stable price level, there is a unique natural rate. Sraffa’s quarrel was only with Hayek’s use of the natural rate, inasmuch as Hayek maintained that the natural rate did not imply a stable price level. Of course, Hayek was caught in a contradiction that Sraffa overlooked, because he identified the real natural rate with an equal nominal rate, so that he was implicitly assuming a constant expected price level even as he was arguing that the neutral monetary policy corresponding to setting the market interest rate equal to the natural rate would imply deflation when productivity was increasing.

I am inclined to be critical Milton Friedman about many aspects of his monetary thought, but one of his virtues as a monetary economist was that he consistently emphasized Fisher’s  distinction between real and nominal interest rates. The point that Friedman was making in the passage quoted by Tyler was that the monetary authority is able to peg nominal variables, prices, inflation, exchange rates, but not real variables, like employment, output, or interest rates. Even pegging the nominal natural rate is impossible, because inasmuch as the goal of targeting a nominal natural rate is to stabilize the rate of inflation, targeting the nominal natural rate also means targeting the real natural rate. But targeting the real natural rate is not possible, and trying to do so will just get you into trouble.

So Tyler should not be complaining about the change in the meaning of the natural rate; that change simply reflects the gradual penetration of the Fisher equation into the consciousness of the economics profession. We now realize that, given the real natural rate, there is, for every expected rate of inflation, a corresponding nominal natural rate.

Keynes made a very different contribution to our understanding of the natural rate. He was that there is no reason to assume that the real natural rate of interest is unique. True, at any moment there is some real natural rate toward which arbitrage is forcing all nominal rates to converge. But that real natural rate is a function of the prevailing economic conditions. Keynes believed that there are multiple equilibria, each corresponding to a different level of employment, and that associated with each of those equilibria there could be a different real natural rate. Nowadays, we are less inclined than was Keynes to call an underemployment situation an equilibrium, but there is still no reason to assume that the real natural rate that serves as an attractor for all nominal rates is independent of the state of the economy. If the real natural rate for an underperforming economy is less than the real natural rate that would be associated with the economy if it were in the neighborhood of an optimal equilibrium, there is no reason why either the real natural rate corresponding to an optimal equilibrium or the real natural rate corresponding to the current sub-optimal state of economy should be the policy rate that the monetary authority chooses as its target.

Finally, what can be said about Tyler’s point that it is implausible to suggest that the real natural rate is negative when the economy is growing (even slowly) and the marginal productivity of capital is positive? Two points.

First, the marginal productivity of gold is very close to zero. If gold is held as bullion, it is being held for expected appreciation over and above the cost of storage. So the ratio of the future price of gold to the spot price of gold should equal one plus the real rate of interest. If you look at futures prices for gold you will see that they are virtually the same as the spot price. However, storing gold is not costless. According to this article on Bloomberg.com, storage costs for gold range between 0.5 to 1% of the value of gold, implying that expected rate of return to holding gold is now less than -0.5% a year, which means that the marginal productivity of real capital is negative. Sure there are plenty of investments out there that are generating positive returns, but those are inframarginal investments. Those inframarginal investments are generating some net gain in productivity, and overall economic growth is positive, but that doesn’t mean that the return on investment at the margin is positive. At the margin, the yield on real capital seems to be negative.

If, as appears likely, our economy is underperforming, estimates of the real natural rate of interest are not necessarily an appropriate guide for the monetary authority in choosing its target rate of interest. If the aim of monetary policy is to nudge the economy onto a feasible growth path that is above the sub-optimal path along which it is currently moving, it might well be that the appropriate interest-rate target, as long as the economy remains below its optimal growth path, would be less than the natural rate corresponding to the current sub-optimal growth path.

Can We All Export Our Way out of Depression?

Tyler Cowen has a post chastising Keynesians for scolding Germany for advising their Euro counterparts to adopt the virtuous German example of increasing their international competitiveness so that they can increase their exports, thereby increasing GDP and employment. The Keynesian response is that increasing exports is a zero-sum game, so that, far from being a recipe for recovery, the German advice is actually a recipe for continued stagnation.

Tyler doesn’t think much of the Keynesian response.

But that Keynesian counter is a mistake, perhaps brought on by the IS-LM model and its impoverished treatment of banking and credit.

Let’s say all nations could indeed increase their gross exports, although of course the sum of net exports could not go up.  The first effect is that small- and medium-sized enterprises would be more profitable in the currently troubled economies.  They would receive more credit and the broader monetary aggregates would go up in those countries, reflating their economies.  (Price level integration is not so tight in these cases, furthermore much of the reflation could operate through q’s rather than p’s.)  It sometimes feels like the IS-LM users have a mercantilist gold standard model, where the commodity base money can only be shuffled around in zero-sum fashion and not much more can happen in a positive direction.

The problem with Tyler’s rejoinder to the Keynesian response, which, I agree, provides an incomplete picture of what is going on, is that he assumes that which he wants to prove, thereby making his job just a bit too easy. That is, Tyler just assumes that “all nations could indeed increase their gross exports.” Obviously, if all nations increase their gross exports, they will very likely all increase their total output and employment. (It is, I suppose, theoretically possible that all the additional exports could be generated by shifting output from non-tradables to tradables, but that seems an extremely unlikely scenario.) The reaction of credit markets and monetary aggregates would be very much a second-order reaction. It’s the initial assumption–  that all nations could increase gross exports simultaneously — that is doing all the heavy lifting.

Concerning Tyler’s characterization of the IS-LM model as a mercantilist gold-standard model, I agree that IS-LM has serious deficiencies, but that characterization strikes me as unfair. The simple IS-LM model is a closed economy model, with an exogenously determined price level. Such a model certainly has certain similarities to a mercantilist gold standard model, but that doesn’t mean that the two models are essentially the same. There are many ways of augmenting the IS-LM model to turn it into an open-economy model, in which case it would not necessarily resemble the a mercantilist gold-standard model.

Now I am guessing that Tyler would respond to my criticism by asking: “well, why wouldn’t all countries increase their gross exports is they all followed the German advice?”

My response to that question would be that the conclusion that everybody’s exports would increase if everybody became more efficient logically follows only in a comparative-statics framework. But, for purposes of this exercise, we are not starting from an equilibrium, and we have no assurance that, in a disequilibrium environment, the interaction of the overall macro disequilibrium with the posited increase of efficiency would produce, as the comparative-statics exercise would lead us to believe, a straightforward increase in everyone’s exports. Indeed, even the comparative-statics exercise is making an unsubstantiated assumption that the initial equilibrium is locally unique and stable.

Of course, this response might be dismissed as a mere theoretical possibility, though the likelihood that widespread adoption of export-increasing policies in the midst of an international depression, unaccompanied by monetary expansion, would lead to increased output does not seem all that high to me. So let’s think about what might happen if all countries simultaneously adopted export-increasing policies. The first point to consider is that not all countries are the same, and not all are in a position to increase their exports by as much or as quickly as others. Inevitably, some countries would increase their exports faster than others. As a result, it is also inevitable that some countries would lose export markets as other countries penetrated export markets before they did. In addition, some countries would experience declines in domestic output as domestic-import competing industries were forced by import competition to curtail output. In the absence of demand-increasing monetary policies, output and employment in some countries would very likely fall. This is the kernel of truth in the conventional IS-LM analysis that Tyler tries to dismiss. The IS-LM framework abstracts from the output-increasing tendency of export-led growth, but the comparative-statics approach abstracts from aggregate-demand effects that could easily overwhelm the comparative-statics effect.

Now, to be fair, I must acknowledge that Tyler reaches a pretty balanced conclusion:

This interpretation of the meaning of zero-sum net exports is one of the most common economic mistakes you will hear from serious economists in the blogosphere, and yet it is often presented dogmatically or dismissively in a single sentence, without much consideration of more complex or more realistic scenarios.

That is a reasonable conclusion, but I think it would be just as dogmatic, if not more so, to rely on the comparative-statics analysis that Tyler goes through in the first part of his post without consideration of more complex or more realistic scenarios.

Let me also offer a comment on Scott Sumner’s take on Tyler’s post. Scott tries to translate Tyler’s analysis into macroeconomic terms to support Tyler’s comparative-statics analysis. Scott considers three methods by which exports might be increased: 1) supply-side reforms, 2) monetary stimulus aimed at currency depreciation, and 3) increased government saving (fiscal austerity). The first two, Scott believes, lead to increased output and employment, and that the third is a wash. I agree with Scott about monetary stimulus aimed at currency depreciation, but I disagree (at least in part) about the other two.

Supply-side reforms [to increase exports] boost output under either an inflation target, or a dual mandate.  If you want to use the Keynesian model, these reforms boost the Wicksellian equilibrium interest rate, which makes NGDP grow faster, even at the zero bound.

Scott makes a fair point, but I don’t think it is necessarily true for all inflation targets. Here is how I would put it. Because supply-side reforms to increase exports could cause aggregate demand in some countries to fall, and we have very little ability to predict by how much aggregate demand could go down in some countries adversely affected by increased competition from exports by other countries, it is at least possible that worldwide aggregate demand would fall if such policies were generally adopted. You can’t tell how the Wicksellian natural rate would be affected until you’ve accounted for all the indirect feedback effects on aggregate demand. If the Wicksellian natural rate fell, an inflation target, even if met, might not prevent a slowdown in NGDP growth, and a net reduction in output and employment. To prevent a slowdown in NGDP growth would require increasing the inflation target. Of course, under a real dual mandate (as opposed to the sham dual mandate now in place at the Fed) or an NGDP target, monetary policy would have to be loosened sufficiently to prevent output and employment from falling.

As far as government saving (fiscal austerity), I’d say it’s a net wash, for monetary offset reasons.

I am not sure what Scott means about monetary offset in this context. As I have argued in several earlier posts (here, here, here and here), attempting to increase employment via currency depreciation and increased saving involves tightening monetary policy, not loosening it. So I don’t see how fiscal policy can be used to depreciate a currency at the same time that monetary policy is being loosened. At any rate, if monetary policy is being used to depreciate the currency, then I see no difference between options 2) and 3).

But my general comment is that, like Tyler, Scott seems to be exaggerating the difference between his bottom line and the one that comes out of the IS-LM model, though I am certainly not saying that IS-LM is  last word on the subject.


About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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