### Balance Sheet Recessions

**Matthew Martin**7/25/2012 07:37:00 PM

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In monetary macroeconomic models, it is commonplace to shove real money balances into the utility function, which allows us to examine how money effects the economy while avoiding some of the pitfalls of some other models, such as the cash-in-advance models of Lucas and Friedman, which contradict reality by assuming that the velocity of money is fixed. I'm surprised, though, that I haven't come across models in which households have preferences over savings, though. I haven't worked through the math yet, but it seems to me that such a model would explain a lot to of the peculiar features of the real world data that we observe.

Here's the intuition: Households value consumption and real savings in each period (these preferences are convex, monotone increasing, etc). Households can save by either lending money or investing in capital. Since they cannot lend without a borrower, this means that in the aggregate, real savings in each period must equal real investment in capital.

This has a number of effects. First, I think it can be used to explain the equity premium puzzle both by lowering the risk-free rate since households get utility from savings, and by allowing additional risk aversion without raising the level of aversion to risk on consumption (I use the term "explain" loosely--we would be able to reliably model equity premia this way, but not necessarily explain them in a "microfoundations" way).

Second, it would help explain the excess volatility in household consumption. Since households have convex preferences over savings, and in the aggregate savings equals investment, this modeling assumption means that households will want to "smooth" investment over time. Normally when there is an aggregate negative productivity shock, RBC models predict that consumption will change very little, and investment will absorb most of the variation in output. But convex preferences over savings (investment) means that households will not adjust investment by as much as the RBC model predicts, and will absorb more of the shock by changing consumption.

Third, I think this would help explain why labor moves more than macro models usually predict over the business cycle, because investment absorbs less of the fluctuations in output than these models would predict, meaning labor will absorb more of it.

Finally, this would (I think) help improve on most macro model's ability to match the persistence of shocks that we observe in the data. The standard RBC model achieves the right amount of persistence by simply assuming that productivity shocks themselves are persistent, which is deeply unsatisfying since it is hard to see why this would be the case. This model says that investment will adjust more slowly to shocks, giving us more persistence.

Now for the interesting part: This model suggests that government deficit spending during negative productivity shocks would be welfare improving. The reason is that if the government increases debt in recessions, then the private sector can increase real savings without increasing investment, meaning that they can stabilize consumption and labor and let investment absorb the shock to productivity, leading to an increase in overall utility across the business cycle. This could, in turn, help reduce the persistence of recessions, letting them to more closely match the short-lived blips that the RBC model suggests they optimally would be.

That said, I'm not saying that this modeling assumption--including real savings in the utility function--would by itself turn the RBC framework into a completely realistic model. But it could, I think, improve upon both RBC and New Keynesian models' abilities to reliably match the features of the data and the policy implications that empirics seem to suggest. The assumption would also be guaranteed to get rejected by some journal referees because it lacks sufficient "microfoundations," meaning that there is no discernible reason for households to desire to smooth savings across periods.