US savings behaviour, and empirical research strategies

In this post I want to look at a paper by Chris Carroll, Jiri Slacalek and Martin Sommer for two reasons. The first is for what the paper tells us about US consumption behaviour, and potentially consumption behaviour in any advanced economy. The second thing I want to use it for is as an example of different ways of doing empirical research in a microfoundations world.

The mainstay of modern macroeconomics is the consumption Euler equation, where consumption is proportional to the sum of financial wealth and human wealth, where human wealth is the discounted present value of future labour income. This model implies consumption aims to smooth out erratic movements in income through borrowing and saving. In this model periods of high saving can reflect periods of temporarily higher income, or temporarily high real interest rates. Adaptations of this model that are commonplace are to assume that some proportion of consumers are liquidity constrained, and therefore consume all their income, or that consumption is subject to ‘habits’, which generates additional inertia. This model with or without these adaptations is not very helpful in explaining why savings rose sharply in the Great Recession.

Rather more worrying is that this model is not very good at explaining US savings behaviour before the Great Recession either. As I noted here, US savings rates fell steadily for about twenty years from the early 1980. You might think that explaining such a large and important trend would be a sine qua non of any consumption function routinely used in macromodels, but you would be wrong. Consistency with the data is not the admissibility criteria for a microfounded macromodel.

The Carroll et al paper finds two explanations for the pre-recession trend and the increase in savings during the recession. The first is easier credit conditions, and the second is employment uncertainty. The mechanism through which both work is precautionary savings. If the risk increases that your income will fall sharply because you will lose your job, you need to build up some capital to act as a buffer. The easier credit is to obtain, the less precautionary savings you need.

The reason why precautionary savings represents a significant departure from the basic Euler equation model is intuitive. If you want to hold a certain amount of precautionary savings, you have a target for wealth. A wealth target pulls in the opposite direction to consumption smoothing. If you have a one-off increase in income, consumption smoothing says you should consume it very gradually, perhaps only consuming the interest. The marginal propensity to consume that extra income is tiny. But this leaves wealth higher for a very long time. If you have a wealth target, your marginal propensity to consume that additional income will be larger, perhaps a lot larger.

Now for the methodology part. These empirical results are in sections 3 and 4 of their paper. They call their empirical results in section 4  ‘reduced form’, because they come from a regression relating saving to wealth, credit constraints and expected unemployment. However the authors feel that this is not enough. In section 2 they discuss a structural theoretical model. Because modelling labour income uncertainty is very difficult, their microfounded model assumes that once someone becomes unemployed, they become unemployed forever. Section 5 then estimates this structural model.

The authors describe a number of reasons why directly estimating the structural model may be better than estimating the reduced form. But in order to get their structural model they have to make the highly unrealistic assumption noted above. The reduced form, on the other hand, does not have this assumption imposed on it. So I do not think we can say that the results in Section 5 are more or less interesting than those in Section 4, which is why both are interesting, and why both are included in the paper. There does not seem to be any compelling reason to elevate one above the other.

OK, a last  - perhaps wild - pair of questions. Is it the case that, compared to a few decades ago, there are far fewer papers in the top journals that simply try and explain historical time series for a single key macro aggregate (like consumption or saving)? If that is the case, is this due to the difficulties in getting microfounded models to fit, or something else?