Wednesday, September 07, 2011

Nick Rowe, Confused

Nick Rowe comments on the Cambridge Capital Controversy in comments to this post:
"Don't take my answer as authoritative.

As far as I can see, the Cambridge-Cambridge Capital Controversy has had almost zero impact on modern macroeconomics. My guess is that not many have much knowledge of that debate. (I have *some* knowledge, through my own curiosity 30 years ago, but not much). The existence of a natural rate is treated as unproblematic. There is some possibility allowed that monetary policy might have some long-run non-neutralities, (multiple equilibria), but even here the focus is more on natural rates of output and unemployment, rather than on the natural rate of interest itself (though one would almost always imply the other).

The concept and existence of the natural rate of interest plays a central role in modern Neo-Wicksellian/New Keynesian macroeconomics...

In my own case, recently I made the more modest critique that the natural rate may exist, and be unique, but we cannot come anywhere close to observing it in real time...

And that's leaving aside the problem that different financial assets will have different natural rates, and the spreads between them may vary over time, especially in a financial crisis.

Now, funnily enough, there is one small exception *I know about* (others may know of others) to my statement that macroeconomists ignore CCCC. David Laidler recently wrote a paper for the CD Howe that explicitly used CCCC to critique the Neo-Wicksellian monetary policy of the Bank of Canada. And David is a monetarist!

...I, personally, remain unconvinced by the Cambridge critique. *As far as I can see*, if a Walrasian/Arrow-Debreu equilibrium exists, and is unique, it defines within it a natural rate of interest (subject to qualifications in my question below). *As far as I can see* a lot of the CCCC debate was really about whether the natural rate could be determined *independently of preferences*. And (outside of very special one-good Y=F(K,L) models) it cannot. So what? I say. Preferences matter too, in determining relative prices including intertemporal prices like interest rates.

BUT, the chances of getting a nicely-well-behaved downward-sloping Investment demand function (and hence IS curve) out of anything other than a one-good model? I wouldn't bet on it. But my hunch is that the complications that arise from firms being sales-constrained (ignored in the Walrasian model) are more important than anything coming out of CCCC. Hence this post.

Now, my question: I never found Sraffa easy to understand. Sraffa said (I think) that the natural rate on wheat would, in general, be different from the natural rate on barley. Right? If so, is this what he meant:

Suppose the relative price of barley against wheat is rising at (say) 1% per year. Then, under perfect competition, and free flow of capital across sectors, the barley natural rate of interest must be one percentage point lower than the wheat natural rate of interest.

Is that what Sraffa was saying? (With all due allowance for over-simplification?)" -- Nick Rowe
I doubt Rowe is aware of the existence of Colin Rogers. I don't know what it means to talk of a natural rate of interest in the Arrow-Debreu model of intertemporal equilibrium. (This is certainly not Wicksell's long period approach.) Money does not exist in the model. For every numeraire, one will get another interest rate (for a loan for one one period of the numeraire good, starting at a designated time period). Which of these many interest rates is the "natural rate"? (It would help if when Rowe asks his question about Sraffa on own rates of interest of barley and wheat, he would bring up that he referencing Sraffa's critique of Hayek, not the more mature Production of Commodities by Means of Commodities.) Rowe has not grasped that classical economics and extensions of the economics of Keynes provide different theories of distribution. One need not close Sraffa's model by assuming intertemporal utility-maximization. I don't see why I need I care about Rowe's hunches on "importance", although, I suppose, he gets points for recognizing the arbitrariness of a downward-sloping investment demand function.

"Those re-switching examples never seemed to me to pay enough attention to the term structure of interest rates. There was always a flat term structure assumed. Not to mention how the term structure of investment would interact with the desired term structure of saving and consumption at the aggregate level, to create a term structure of interest rates." -- Nick Rowe
I find this incomprehensible. Let the interest rate on a loan for n years be 100 rn percent. Typically, in a reswitching example, the following relationship holds:
1 + rn = (1 + r1)n
This is a term structure of interest rates. Suppose one wanted to allow expectations of future yearly interest rates to differ from the current yearly interest rate. That is easy to introduce, but those extra degrees of freedom make it even easier to show violations of traditional neoclassical parables. Although it's easy to construct closed reswitching examples, I don't see why mainstream economists cannot consider open models.

Bill Woolsey's comment in the same thread is too stupid to bother with. I would think it possible to discuss analytical points somewhat separately from ideology.


Nick Rowe said...

Aha! Robert! *You* were the "Sraffa(ish)" blogger I was trying to think of to who I wanted to ask my question!

And now you have answered it:

"For every numeraire, one will get another interest rate (for a loan for one one period of the numeraire good, starting at a designated time period). Which of these many interest rates is the "natural rate"?"

Thanks! That's what I thought, but I wasn't sure if I had interpreted Sraffa's wheat/barley example correctly.

If that's the problem, it's no biggie. We just have to make sure we specify the price index we are using when we subtract inflation from the nominal interest rate to give a specific numerical value for the natural rate. Which makes perfect sense.

Funnily enough, I had a good email conversation with my old Adelaide colleague Colin Rogers just a couple of months back. On the role (or lack thereof) of money in Woodford's macroeconomics.

I shall have to ask Colin if he thinks that the Capital Controversies have had much impact on modern macroeconomics, as exemplified by the dominant Woodfordian paradigm.

Robert Vienneau said...

One could argue that the Cambridge Capital Controversies had a pervasive subterranean influence on the direction of mainstream economics. Such an argument is independent of the incorrectness of much of mainstream economics.

Colin Rogers and Michael Woodford had an exchange of views in the Cambridge Journal of Economics.

Different agents consume different bundles of goods at any given time in intertemporal equilibria. They would therefore be interested in the price level in terms of different numeraires. Since money does not exist in the model and no numeraire is picked out univocally by the model, "the" natural rate of interest cannot be defined in the model. David Glasner is just mistaken.