That Measure is Garbage

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If you ever take a course on macroeconomics, you will no doubt be introduced to the permanent income hypothesis. The basic idea is as follows. A person’s income is made up of a permanent component and a transitory component. A person’s consumption is based on the permanent component of income. Transitory fluctuations in income simply lead to changes in saving or borrowing.

This idea is actually just a straightforward application of price theory applied to a life-cycle model of consumption. For example, think of a world in which there are two goods, apples and bananas. The value I get from one additional banana will depend on how many apples and how many bananas I already have. If I have a lot of bananas and very few apples, then I will tend to put much higher value on one more apple than I would on one more banana. The same is true if we think about the two goods as being consumption now and consumption later. The more I’m consuming today relative to tomorrow, the more valuable an additional unit of consumption will be tomorrow. This leads to a tendency to “smooth out” consumption over time. Thus, transitory fluctuations in income tend to cause changes in saving and borrowing while consumption remains relatively smooth over time.

Taken literally, the permanent income hypothesis seems hard to test. Sure, in theory, it might be help to classify some income as permanent and some as transitory. But how can one do that in reality? And how can one test the theory? After all, a test of whether consumption is explained by one’s permanent income requires testing a joint hypothesis. It is testing whether the measure of permanent income is correct and whether consumption is based on permanent income. Furthermore, tests using aggregate data are notoriously limited.

Fortunately, Milton Friedman provided us with useful tests of the permanent income hypothesis using household-level data. (For relatively recent tests of these hypotheses, see this paper.)

But despite these alternative tests, people still make mistakes with regards to measurement. I previously discussed a classic example. Some researchers found that expenditures decline pretty significantly following retirement and concluded that this was a violation of the theory. The permanent income hypothesis suggests that people draw down on their savings in retirement to maintain their smooth pattern of consumption. The fact that expenditures were declining immediately after retirement seemed inconsistent with this idea.

In reality, this was simply an issue of measurement. Expenditures are not the same as consumption. A person could buy a steak (mmm, steak) and prepare it or a person could go to a restaurant for a steak. The expenditure on a steak dinner at the restaurant will be higher than the expenditure for the steak dinner at home. While one might argue that the bundle of goods is different between the steak at home and the steak at the restaurant, the issue is home production. Specifically, the implicit wage of the person preparing the steak at home will never be included in the expenditure whereas the wage of the restaurant cook will. Expenditures therefore tend to given more weight to consumption in the market than consumption produced through home production.

This is exactly what Mark Aguiar and Erik Hurst found. Retirees tended to spend less on food, but they tended to consume the same amount of calories. Thus, although expenditures declined, there is no sense in which consumption declined. Instead, given the lower cost of their time, retirees tend to shop for bargains and prepare their own meals.

Nonetheless, it is not always possible to get away from aggregate data. For example, one application of the life-cycle model of consumption is something called the Consumption Capital Asset Pricing Model. The basic idea behind this model is that the risk premium on an asset should be determined by the relationship between the returns on the asset and consumption. If the return is high when the marginal value of consumption is low and the return is low when the marginal value of consumption is high, that asset deserves a higher risk premium.

This makes sense if you think about consumption smoothing. Buying assets is a form of saving. Ideally, the value of your assets would be high when you want to consume more (the marginal value of consumption is high). That way, when times are bad, you can sell some of your assets at high prices to consume. If, one the other hand, asset prices are low when you want to consume more, this imposes a cost in the form of foregone consumption and you should only be willing to buy such an asset if you are rewarded with higher returns.

When people have tested this model, they find the results puzzling. In particular, a test of the model suggests that either consumption isn’t volatile enough or that households have an implausible level of risk aversion.

The puzzle has spawned a large number of papers (approximately 8,000+, according to Google Scholar). Many of these papers have focused on the limitations of the model. Perhaps the model is wrong or perhaps the model is missing something (or lots of things).

Yet, it is also possible that there is a measurement issue. After all, testing the model requires using a measure of consumption. What people tend to use is personal consumption expenditures on nondurable goods and services from the National Income and Product Accounts produced by the U.S. Bureau of Economic Analysis. Like most measures of consumption, this is a measure of expenditures. Since all measures of consumption expenditures put less weight on consumption that was generated through home production, it is possible that the puzzling results are due to mismeasurement of consumption.

Not content with these measures of expenditures, Alexi Savov decided to use his own garbage measurement of consumption. No, I’m afraid you misinterpreted. I’m not saying he used a terrible measure of consumption. I mean he literally used garbage as his measure of consumption. As it turns out the U.S. Environmental Protection Agency produces an aggregate measure of municipal solid waste. In the paper, Savov argued that this would be a preferable measure of consumption since “the timing of garbage is tightly linked to consumption because there is no benefit to keeping a good past its consumption usefulness.” In addition, a measure of garbage doesn’t distinguish between market production and home production. As a result, they get equal weight.

Clever, right? But the relevant question is whether (and to what degree) this matters.

Recall that the main problem when testing the model is that it implies that people are implausibly risk averse. The degree to which they are risk averse is measured by something called the coefficient of relative risk aversion. It isn’t really important for the purposes of this discussion to go into what this means. All that you need to know is that this coefficient of relative risk aversion is ridiculously high in standard estimates. But, when one uses garbage as the measure of consumption, the coefficient of relative risk aversion declines by approximately 80%.

That seems pretty significant. The problem with the model is that this parameter had to be really big (so big that it is not believable) to fit the data. Just by using another data source, the parameter declines quite dramatically. This tells us that a significant part of the problem is not necessarily found in the model itself, but rather in the data used to test it.

There is a broader point here. In both the permanent income hypothesis example and the asset pricing example, measurement matters. And, in each case, it is price theory that tells us why the existing measures are wrong and what we actually need to try to measure if we want to test our theory.