The Unbroken Window

Economists like to model everything. Open up any issue of the American Economic Review and you will find all kinds of fancy expositions on optimal interventions in markets with adverse selection, the effects of housing assistance on labor supply, whether union militancy can promote economic growth, models of credit constraints, models of persuasion, currency misalignments and much, much more. (Aside: there are days when I consider converting this blog into a simple synthesizer of what’s new in economic research, but my sense is that there is not a very big market for reading is, so I stash all those away for class prep – only to have students think I make up the stuff anyway).

And in modern macroeconomics we have all kinds of fancy models, in particular New Keynesian models which go a step beyond old Keynesian IS-LM models to more intimately incorporate consumption decisions over time than their old school counterparts. And while the New Keynesian model still relies on talking about the identity C+I+G = Y, it takes a much greater effort to incorporate some of the macro-realities that we’ve come to understand since the 1970s. So, these models have elaborate underlying models of consumption and investment and they recognize that prices are not sticky all the time and in all places.

That’s great.

But what’s not great, and what I simply do not see in most places is economists taking any time to model out G. Think about that for a moment. Even in some of the papers I mentioned above it is simply assumed that government is neutral and works the way we wish it to work in our head. Government spending and consumer spending are interchangeable. When the government spends a dollar it really only spends a dollar. The role of incentives and information is assumed away or relegated to a footnote that suggests that what is modeled out may not be what actually occurs. And of course, very little effort is given to modeling out the productivity of government expenditures (an old paper did do that once, and I have a student who is following up on that paper now).

So, we have a model of everything except for the one thing we really need a model of: government. I am sure you will hear things like, “well, it’s just too complex with too many moving parts” to model. Maybe. But that does not prevent us from modeling, and in some impressive detail, other extremely complex systems. Keep this in mind the next time you see an I-S curve tell you this is how the goods market works, or an L-M curve tell you this is how the money market works or a consumption function telling you how individuals decide to consume or save … where is the analogous picture in the government sector? And are all governments created equal? Would you model the federal government out the same way as the states and local governments? Why?

If you think I was given the tools to do such a thing in graduate school, think again. I spent my time in graduate school regurgitating things like this:

Sunspots’ is short-hand for ‘the extrinsic random variable’ (or ‘extrinsic randomizing device’) upon which agents coordinate their decisions. In a proper sunspot equilibrium, the allocation of resources depends in a non-trivial way on sunspots. In this case, we say that sunspots matter; otherwise, sunspots do not matter. Sunspot equilibrium was introduced by Cass and Shell; see Shell (1977) and Cass and Shell (1982, 1983). Sunspot models are complete rational-expectations, general-equilibrium models that offer an explanation of excess volatility. It was by no means a new idea that economies can and do generate excess volatility, but the sunspots model is the first general-equilibrium model to exhibit excess volatility even when agents are fully rational. The sunspots model also allows for non-rational agents, but the excess volatility from this source – while possibly empirically substantial – is less novel.

‘Sunspots’ is a spoof on Jevons (1884), who in serious empirical work attempted to explain the business cycle by relating it to the observed (through telescopes) cycle of actual sunspot activity. To the extent that actual sunspot activity does affect economic fundamentals (such as crop yields and cancer risk), this is an instance of intrinsic uncertainty, but the effects of actual sunspots on fundamentals are probably very small. If actual sunspots have only a minor effect on the fundamentals, but they do have a substantial effect on the economy, it must be that actual sunspots serve a role in the economy beyond their effects on the fundamentals. Manuelli and Peck (1992) show that a sunspot equilibrium can be interpreted as the limit of traditional rational-expectations equilibria as the uncertainty in the fundamentals vanishes. See also Spear, Srivastava, and Woodford (1990). Roughly speaking, ‘Jevons equilibrium’ becomes‘Cass-Shell equilibrium’ as the effects of actual solar activity on the fundamentals go away. Cass-Shell sunspot equilibria are easy to interpret because in the basic sunspots models the only uncertainty is extrinsic uncertainty. Hence any volatility in outcomes is excess volatility. Engineers compute ‘gain’ in noise as the volatility of the output signal divided by the volatility of the input signal. In a sunspot equilibrium, the gain is + ∞.

The first sunspots model, Shell (1977), is of an overlapping-generations exchange economy with taxes and transfers denominated in fiat money.

Sunspots’ is short-hand for ‘the extrinsic random variable’ (or ‘extrinsic randomizing device’) upon which agents coordinate their decisions. In a proper sunspot equilibrium, the allocation of resources depends in a non-trivial way on sunspots. In this case, we say that sunspots matter; otherwise, sunspots do not matter. Sunspot equilibrium was introduced by Cass and Shell; see Shell (1977) and Cass and Shell (1982, 1983). Sunspot models are complete rational-expectations, general-equilibrium models that offer an explanation of excess volatility. It was by no means a new idea that economies can and1do generate excess volatility, but the sunspots model is the first general-equilibrium model to exhibit excess volatility even when agents are fully rational. The sunspots model also allows for non-rational agents, but the excess volatility from this source – while possibly empirically substantial – is less novel.‘Sunspots’ is a spoof on Jevons (1884), who in serious empirical work attempted to explain the business cycle by relating it to the observed (through telescopes) cycle of actual sunspot activity. To the extent that actual sunspot activity does affect economic fundamentals (such as crop yields and cancer risk), this is an instance of intrinsic uncertainty, but the effects of actual sunspots on fundamentals are probably very small. If actual sunspots have only a minor effect on the fundamentals, but they do have a substantial effect on the economy, it must be that actual sunspots serve a role in the economy beyond their effects on the fundamentals. Manuelli and Peck (1992) show that a sunspot equilibrium can be interpreted as the limit of traditional rational-expectations equilibria as the uncertainty in the fundamentals vanishes. See also Spear, Srivastava, and Woodford (1990). Roughly speaking, ‘Jevons equilibrium’ becomes‘Cass-Shell equilibrium’ as the effects of actual solar activity on the fundamentals go away. Cass-Shell sunspot equilibria are easy to interpret because in the basic sunspots models the only uncertainty is extrinsic uncertainty. Hence any volatility in outcomes is excess volatility. Engineers compute ‘gain’ in noise as the volatility of the output signal divided by the volatility of the input signal. In a sunspot equilibrium, the gain is + ∞.

The first sunspots model, Shell (1977), is of an overlapping-generations exchange economy with taxes and transfers denominated in fiat money.