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Saturday, September 7, 2013

Inherent Problems With Single Good Economic Models (Wonkish)

A typical technique used in economic models is to base the analysis on the assumption that there is a single consumer good in the economy*. I argue that this causes some analytical blind spots for mainstream analysis of the economy. Since not everyone interested in mathematical modeling, I’ll state my conclusions up front, and then explain in more detail later.This post was triggered by this article on Mike Norman Economics by Tom Hickey which discusses the problems with prices indices.

Modeling the economy with one consumer good leads to the following problems:

  1. It  is impossible by definition for the private sector to misallocate investment, as all productive capacity will be always useful. It is not too surprising that investment bubbles are hard to diagnose in advance when using mainstream economic analytical frameworks.
  2. Consumer price indices may give a misleading view of inflationary pressures as a result of the change of mix of goods purchased.
  3. Productivity is viewed as a key determinant of growth. However, the definition of productivity in a multi-good economy may not correspond to intuitive notions of productivity, making it not very useful in analysis.

The most important issue is the impossibility for the private sector to misallocate investment within these models. If there is only a single good being produced and consumed, a business is always guaranteed a market for its output. Within the model economy, any increase in capital investment will raise future labour productivity, so that future production is always enhanced (raising utility).

However, in a multi-good economy, like the real world, there is no guaranteed market for any particular output. It is possible to create productive capacity for products that will never get sold. The last two U.S. recessions were caused by overinvestment in technology and housing respectively. Both the private sector and policymakers failed to comprehend the magnitude of the problems until it was too late.

Monetary policy tightening is often blamed for recessions; but economic growth was going to be curtailed as overproduction within the bubble sectors has to be reallocated to other sectors. Such reallocation does not occur within single-good models, which instead have to attribute the drop in production due to “random shocks” or monetary policy errors. Since reallocation of resources is not on the radar, there is a tendency to hope for “soft landings”.

Within a single consumer good economic model, the price of that good has obvious importance. The significance of the single good price is then transferred to what appears to be the real world equivalent: the consumer price index (or its national equivalent). It is no surprise that this leads to a fixation on CPI targeting by policymakers. However, it is unclear that the price aggregate has the useful analytical properties as the price of a single good. This problem has been noted before, in various contexts. For example, the Austrian economic school has long complained about “the aggregation problem” and how it is allegedly impossible.

One issue is that mix changes can replace inflation. Instead of buying a standard cup of coffee, consumers have been induced to buy expensive substitutes like frothed ice frappuccinos (or whatever). Luxury cars replace standard models. This sort of substitution greatly increases revenue in exchange for a small increment to the cost of production. This has the same effect as raising prices from the point of view of the businesses, even if the price points for each class of good remains constant. An increased tendency for consumers to upscale and downscale over the cycle may have been a major contributor to measured inflation stability in recent years.

Another widely noted problem is the inclusion or exclusion of goods or services from the aggregates can cause problems for inflation targeting. The most important of which is housing. Housing currently represents a huge component of developed economies’ consumer spending, but house prices are generally not included within CPI indices (which is proper, in my view). Thus housing bubbles can inflate without policymakers treating them as symptoms of excessive demand.

Finally, productivity in an economy with multiple goods and services is less intuitive than is the case where there is only a single tangible good. For the single good economy, rising production per hour of labour can be straightforwardly understood as the result of more capital or better production technology. However, real world output is measured in terms of the value of what is sold, and services pose particular measurement problems.

For example, one could hire the best television production team in the world to create a new television channel covering the world of tiddlywinks.  Since it is safe to assume that no one would watch the channel (other than the hopelessly drunk), the value of the output would be zero. This implies that the productivity of all the labourers for the television channel is zero. Since we have assumed that this was the best production team in the world, their lack of productivity is not the result of technology problems. Rather, they are not productive because they have applied their efforts to the wrong market.

In other words, economic productivity does not match intuitive understanding of the term, rather it is a measure of how well effort is aligned towards final demand. This makes productivity an essentially useless variable for understanding the business cycle, despite its alleged importance.

* An even more wonkish footnote. The highly popular New Keynesian models use Calvo pricing, in which there are an uncountably infinite number of consumer goods. (Yes, uncountably infinite. Seriously.) However, that uncountably infinite number of goods is integrated out into a single composite good almost immediately, and so the models return to a single good with price inertia.

(c) Brian Romanchuk 2013


  1. Brian -- Excellent analysis.

    What kind of data does the BLS use to measure the cost of housing? IIRC Cullen Roche at Pragmatic Capitalism has argued that the housing cost that is included is given a weight that substantially understates its impact on the average consumer's budget. If true, that further impairs any usefulness for the CPI. Also, what do you think would be an appropriate measure of housing costs? Thanks.

    1. I would have to verify the details (I looked at this some time ago in detail), but there are two main categories under "shelter" for the CPI: owner's equivalent rent, and rent.

      The rent category is a straightforward measure of market rents, but there is some weirdness associated with energy costs. (Since many rents include energy costs (heating), but heating is another component of the CPI, rising natural gas prices depress housing costs. The aggregate CPI is unaffected, but subsets like the core CPI get hit.)

      Owner's equivalent rent is used to account for the non-renters, and it is a big category (23.8% of the total CPI, and a massive slice of the core CPI - 40%?). In the 1980's and earlier, this component used to be house prices. They have converted this to being a rent-based figure as houses are an asset, and are sensitive to interest rates (etc).

      I think the rent-based measures are probably the best you can do for the CPI. Many national statistical authorities loudly point out on their web sites that the CPI is not a "cost of living index" (not sure if the BLS has that disclaimer). The indices provide a measure of a broad basket of goods and services, but cannot be complete measures of the cost of living. Since the CPI is used in legal contracts (indexation of pensions, TIPS,...), you need to put some limits on the behaviour of the index.

      As for what I think is the best measure for non-rented housing costs, I am ambivalent. The affordability metrics (size of payments needed) make the most sense to me, but I think you need to control for the size and quality of housing. North American houses are getting bigger and fancier, but that should not drive up the measured "cost of living".

      The problem with using the monthly payment is the decision of what is the minimum down payment to use? If you assume that you have 100% mortgage finance, low interest rates would make current Canadian houses look cheap (unlike the U.S., our bubble has not popped). But raise the down payment to 50%, which sort of reflects average home equity in the economy, the big initial payment will make houses look a lot less affordable when compared to past history. People can argue both cases convincingly. For myself, I accept that it effectively another asset class, and has to be treated somewhat specially.

    2. Thanks, Brian. Good information.


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