Friday, November 27, 2009

More about the Productivity Norm

In Less Than Zero, George Selgin describes a scenario where an increase in supply in a single market is cleared by a lower price. Because demand is unit elastic, total expenditure remains unchanged in the market. If aggregate total expenditure in the entire economy is fixed, then aggregate expenditures in the rest of the economy is unchanged as well. The change in the one market with the increase in supply doesn't create a net excess demand (or supply) for other goods, and so no need for their prices to rise (or fall.)

But suppose there is a rule imposing a stable price level. What happens? The one price has fallen. The average of prices has fallen (assuming this price was included in whatever measure of the price level is to be stabilized.) To get the price level back up to target, it is necessary to increase the quantity of money, creating an excess supply of money at the current price level. In the long run, the prices of all goods, including resources, are slightly higher. Even the price of the good with the increase in supply is slightly higher than it would have been if there had been no increase in the quantity of money. Of course, it remains lower than it was before the increase in supply that initiated the entire process.

Selgin suggests that stabilizing the price level is needlessly disruptive. The context of this particular argument was "menu costs," the cost of changing particular money prices. Instead of simply lowering the one price with the increased supply, stabilizing the price level requires its price to fall, but a bit less, and all the other prices increase a bit. As Selgin emphasizes in other contexts, however, the menu costs is just one element of the problems created by an excess supply of money.

I am convinced. If there were a situation where a change in the price of a single good left the entire economy in equilibrium, creating monetary disequilibrium to get the price level back to a target would be undesirable. That a regime of price level stability could have this effect counts as a disadvantage.

Understood properly, Selgin's thought experiment suggests that targeting any growth path of nominal expenditure is superior to targeting any growth path of the price level. It does not, however, provide a strong reason to favor the particular growth path of nominal expenditure he favors--a growth rate equal to total factor supply (2%?) rather than productive capacity (3%) or a path generating low inflation (5%.) Given any particular growth path for nominal expenditures, the expectations generated by the regime will impact price setting strategies. There is no need to generate period by period monetary disequilibrium to maintain the trend growth path of prices generated by the regime. Regardless of the trend growth path, changes in productivity will result in changes in the growth path of prices.

With various growth paths of nominal expenditure, Selgin's thought experiment, understood as a ceteris paribus exercise, would imply a slightly lower growth path for prices. That is, if this were an extra improvement in productivity beyond normal, the result is a very slight shift to a lower growth path of prices. Of course, from a different perspective, if productivity increased so little, with just a single good having some improvement in productivity, then the result would be a shift to a higher growth path of prices.

Perhaps there is something to the "menu cost" argument, though I find it hard to believe that the growth process--one properly characterized as creative destruction--can be understood by thinking about an increase in supply in a single market with unit elastic demand.

Selgin uses supply and demand analysis, and with demand unit elastic, (I did my best to draw a rectangular hyperbola,) expenditures on this product and revenues received by sellers are unchanged by the lower price and higher quantity. P1*Q1 = P2*Q2. If aggregate nominal expenditure is unchanged (or left on the same growth path,) then this change leaves total expenditures in the rest of the economy unchanged as well.

However, what does this imply using indifference curve analysis?

This diagram shows income Y and the higher price Pa1 and then the lower price, Pa2. Preferences are such that the decrease in the price of the good results in an increase in consumption from Xa1 to Xa2. The demand for the composite good, Xo, remains unchanged.

Of course, indifference curves apply to an individual, and if this is a representative agent, the result would be unit elastic demand for good a. In reality, some individuals could expand expenditures on good a and reduce expenditures on other goods while other individuals might reduce expenditures on good a and spend more on other goods. Selgin's assumption just requires that on the whole, the mix in total expenditures remain unchanged. (However, adding those complications also suggest that the rest of the economy shouldn't be characterized as a single composite good.)

I suppose it is just my priors, but I think that part of the growth process should instead be characterized by the following indifference curve diagram:

One important aspect of the process of creative destruction is that improved technology allowing greater productivity for one good allows resources to be freed in order to expand the production of other goods. The market process allows improvements in the technology for producing one good to increases the production of whatever particular goods people want to purchase most with the additional real income. An unfortunate side effect of this process is technological unemployment.

How does this relate to the productivity norm? The operations of such a monetary regime would not interfere with the process. Total expenditure on other goods would expand. It does suggest, however, that the impact of a regime of price level stability--higher prices of other goods and services, partly offsetting the lower price of the particular good with improved productivity--would occur with a productivity norm, though to a smaller degree.

A second aspect of the growth process is more difficult to describe using supply and demand diagrams or indifference curves--the introduction of new and better consumer goods and services. Perhaps it is an illusion, but that is the element of "creative destruction," that seems most important to me. How does that relate to the productivity norm?

I think the most plausible scenario is that more is spent on the improved good. There is a higher price and quantity that good. (For a new good, it is clearly higher than the zero price and quantity before it existed) Less remains to be spent on other goods and services. The price of the improved good rises (or there is a new price introduced into the economy.) Other prices fall. The impact on the price level is ambiguous, but let us take that to mean more or less unchanged.

Rather than deflation, this element of the process of creative destruction has little impact on the price level. However, our price level statisticians would note that the apparently stable CPI is allowing the purchase of higher quality goods and services. Using either crude or sophisticated methods to make adjustments, they would show a decrease in the "cost of living." In other words, the statistics would report deflation. Rather than hearing complaints that the CPI understates the inflation that average people can see, the complaints would be of the imaginary deflation that is being reported by the statisticians.

In conclusion, Selgin is correct that a stable growth path of nominal expenditure is better than a stable growth path for the price level. Different growth paths for nominal expenditure imply different trends for various measures of the price level. I don't see the mild deflation favored by Selgin as especially harmful. But then, I am not persuaded that it provides any benefits relative to a growth path of nominal expenditures that results in a stable price level on average.


  1. Bill, I very much appreciate your very thoughtful posts addressing the productivity norm. I understand that, while you appreciate the advantages of stable nominal spending over stable P, you are not convinced that a deflationary income growth trend has any advantages over a trend that stabilizes P in the long-run.

    But there is at least one argument favoring a deflationary trend over a constant P trend. It is Friedman's "optimum quantity of money" argument. It seems to me that, other things equal, this ought to sway the balance in favor of a productivity norm policy. Indeed, a productivity norm doesn't quite generate optimal deflation in Friedman's senses, and so is something of a compromise between his ideal (in that article) and stable long-run P.

    And a minor point: in my "single good" case discusses above, P stabilization also requires some upward adjustment of all nominal _factor_ prices. Those prices also would not have to adjust at all under a productivity norm.

  2. George:

    Thank you for the comments.

    I think both of your points are correct, but there are complications.

    Somewhere you explained the difference between the trend of wages in aggregate and the profile of an individual's wages over a career. As a practical matter, the debate between price level stability and the productivity norm is about what happens wages over the generations and the size of the increase in nominal wages during a career. Stable wages on average doesn't mean that there are fewer wage agjustments. As for capital income, the trends just impact nominal interest rates. And residuals are residuals. I am not sure how much saving there is in factor income adjustments, but I think there has to be some advantage to the productivity norm.

    As for the optimal quantity of money, I think in a world where 90% of money (by the MZM measure) is deposits, focusing on the real yield on zero-interest currency has the tail wagging the dog. As a free banker, I am sure you can imagine I have more to say about that matter. Still, I think the productivity norm does have advantages along those lines. Just not much.

  3. Bill,

    Of course wage rates won't remain constant for any individual over time, even under a policy that stabilizes a wage index. Neveretheless I think that a stable P policy is bound to increase the overall burden of factor price adjustment--giving factor prices that much more "work" to do.

    Consider the case for P stability--and forget productivity innovations for the moment. Individual prices for many--most?--goods will change over time with or without P stability; indeed, they will vary much more than individual wage rates, though not for the same reason that wage rates very (goods don't get "raises"!). Yet no one believes this a reason for arguing that there's therefore no point in stabilizing P. The fact that individual prices are busy anyway doesn't justify putting any extra burden on them.

  4. Bill, Nice post. I hope to do a post on this within a week or two. A few quick comments. I think the pros and cons of mild deflation have less to do with pure theory than with the specific institutional setup you are dealing with. For instance:

    A. The fact that we have a suboptimal policy of taxation of nominal capital income provides a much more powerful argument for mild deflation that does Friedman's optimal quantity of money argument.

    B. The fact the central banks seem to have trouble operating in a zero interest rate environment provides an argument against mild deflation unless we can get a different monetary setup. I beleive that one reason mild deflation didn't seem to hurt in the late 1800s is because the gold standard kept long run inflation expectations near zero, and prevented liquidity trap conditions in the capital markets. It also helped that the real return on capital was then much higher than in a country like Japan circa 2009. I see this problem going away if we do NGDP level targeting rather than growth rate targeting.

    Neither of these are the sort of purely theoretical arguments you'd see in a textbook, but in the real world they may matter more than issues like optimal quantity of money and menu costs.

  5. I don't think it matters what growth path in nominal expenditure you target so long as its small to keep things linear, and d^2(nominal expendature per capita)/dt^2 is 0.

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