Notes on Krussell & Smith, 1998 and macroeconomic theory

I’m orienting towards a new field through my work on HARK. A key paper in this field is Krusell and Smith, 1998 “Income and wealth heterogeneity in the macroeconomy.” The learning curve here is quite steep. These are, as usual, my notes as I work with this new material.

Krusell and Smith are approaching the problem of macroeconomic modeling on a broad foundation. Within this paradigm, the economy is imagined as a large collection of people/households/consumers/laborers. These exist at a high level of abstraction and are imagined to be intergenerationally linked. A household might be an immortal dynasty.

There is only one good: capital. Capital works in an interesting way in the model. It is produced every time period by a combination of labor and other capital. It is distributed to the households, apportioned as both a return on household capital and as a wage for labor. It is also consumed each period, for the utility of the households. So all the capital that exists does so because it was created by labor in a prior period, but then saved from immediate consumption, then reinvested.

In other words, capital in this case is essentially money. All other “goods” are abstracted way into this single form of capital. The key thing about money is that it can be saved and reinvested, or consumed for immediate utility.

Households also can labor, when they have a job. There is an unemployment rate and in the model households are uniformly likely to be employed or not, no matter how much money they have. The wage return on labor is determined by an aggregate economic productivity function. There are good and bad economic periods. These are determine exogenously and randomly. There are good times and bad times; employment rates are determined accordingly. One major impetus for saving is insurance for bad times.

The problem raised by Krusell and Smith in this, what they call their ‘baseline model’, is that because all households are the same, the equilibrium distribution of wealth is far too even compared with realistic data. It’s more normally distributed than log-normally distributed. This is implicitly a critique at all prior macroeconomics, which had used the “representative agent” assumption. All agents were represented by one agent. So all agents are approximately as wealthy as all others.

Obviously, this is not the case. This work was done in the late 90’s, when the topic of wealth inequality was not nearly as front-and-center as it is in, say, today’s election cycle. It’s interesting that one reason why it might have not been front and center was because prior to 1998, mainstream macroeconomic theory didn’t have an account of how there could be such inequality.

The Krusell-Smith model’s explanation for inequality is, it must be said, a politically conservative one. They introduce minute differences in utility discount factor. The discount factor is how much you discount future utility compared to today’s utility. If you have a big discount factor, you’re going to want to consume more today. If you have a small discount factor, you’re more willing to save for tomorrow.

Krussell and Smith show that teeny tiny differences in discount factor, even if they are subject to a random walk around a mean with some persistence within households, leads to huge wealth disparities. Their conclusion is that “Poor households are poor because they’ve chosen to be poor”, by not saving more for the future.

I’ve heard, like one does, all kinds of critiques of Economics as an ideological discipline. It’s striking to read a landmark paper in the field with this conclusion. It strikes directly against other mainstream political narratives. For example, there is no accounting of “privilege” or inter-generational transfer of social capital in this model. And while they acknowledge that in other papers there is the discussion of whether having larger amounts of household capital leads to larger rates of return, Kruselll and Smith sidestep this and make it about household saving.

The tools and methods in the paper are quite fascinating. I’m looking forward to more work in this domain.

References

Krusell, P., & Smith, Jr, A. A. (1998). Income and wealth heterogeneity in the macroeconomy. Journal of political Economy106(5), 867-896.