More Thoughts on the Welfare Consequences of Stimulus Spending

Noah Smith has a short post questioning the reasoning of an earlier post of mine about stimulus spending. He includes a short numerical example which I reproduce below.  Here’s Noah:

Suppose [the] fiscal “multiplier” is substantial. Specifically, suppose … $100 of tax rebates will increase GDP by $110. In this case, stimulus spending is a “free lunch.”

Now suppose that instead of doing tax rebates, the government can build a bridge. The social benefit of the bridge is $90, and the bridge would cost $100. In the absence of stimulus effects, therefore, the bridge would not pass a cost-benefit analysis. For simplicity’s sake, suppose that spending money on the bridge would create exactly the same stimulus effect as doing a tax rebate – spend $100 on the bridge, and GDP goes up by $110 from the stimulus effect.

In this case, the net social benefit of spending $100 building the bridge is $90 + $110 – $100 = $100.
And the net social benefit of spending $100 on a tax rebate is $110 – $100 = $10.

Bridge wins!

Noah has a couple of subtle mistakes in his calculation. First, the increase in GDP from the stimulus isn’t completely a social benefit. Typically, every good produced is produced at some cost. If I go out to eat for lunch and buy $10 of Szechuan chicken, GDP goes up by $10. However, the net social benefit doesn’t go up by this amount. The gains to me (G) must be at least worth $10 otherwise I wouldn’t have willingly spent the money. The cost to the restaurant (C) can’t be more than $10 otherwise they wouldn’t have willingly provided that dish.  The social benefit (SB) is the difference between the gains and the cost.

SB = G – C

If markets are fairly competitive then at the margin both G and C will be “close” to $10 and so the social benefit will in all likelihood be less than $10. What this means for Noah’s calculation is that the $110 stimulus might not really be worth $110.  That’s ok however since this error is symmetric. It is worth pointing out however, that stimulus which is guided by the private sector typically passed cost/benefit tests of the kind I emphasize. In my example, G > 10 and C < 10 so SB = G – C must be positive. 

The second error is more important. In his calculation, Noah is counting the out-of-pocket revenue outlay for the tax cut as a cost. This isn’t correct. The tax cut is a transfer. There are no direct social costs associated with the tax cut.

Let me try to rephrase Noah’s example to make it clear. He is considering two options:

OPTION 1: tax cut (or transfer) of $100

OPTION 2: government spending of $100

(i) In both cases the Treasury is deprived of $100. 

(ii) In both cases the private sector gains $100 in after-tax income.

(iii) In both cases the private sector uses the additional income to spend or save (this is the source of the multiplier). 

(iv) In OPTION 1 a bridge is built. The social costs (C) of the bridge include the value of time, energy, materials, effort, etc. The social benefit (B) of the bridge is the value of having the bridge.

In comparing these two options, we can ignore (i) – (iii) since they are the same in both policies. The only difference is (iv). Whether government spending is preferable depends only on whether B is bigger than C.  Note that the magnitude of the multiplier doesn’t enter the comparison. It is symmetric in both cases. My argument is not “diametrically opposed to Econ 102 textbook Keynesianism” —  GDP will go up by more under OPTION 2.  The subtlety is that in Econ 102 we typically act as if maximizing GDP is the correct objective of public policy. This isn’t true though. GDP maximization can rationalize building pyramids, the Maginot Line, the bridge to nowhere, ethanol subsidies, … A social welfare criteria would skip these projects.

In the comments section to Noah’s post a number of readers make some points which are worth mentioning. One comment points out that many people don’t pay taxes and so wouldn’t benefit from a tax cut. Certainly, unemployed people won’t benefit from a tax cut. However, we could construct transfers that would reach these people. Rachel Maddow’s suggestion of sending people envelopes with money in them would work just fine. Also, many people and firms do pay taxes. Payroll tax cuts like those passed by the Obama administration are a particularly effective way of introducing stimulus.  These simultaneously put money in people’s pockets not to mention the beneficial incentive effects of the policy. 

Another commenter points out that calculating the social costs and benefits of a given project are quite difficult.  This is absolutely true but it is a calculation that should be carefully considered none the less.  In Noah’s example, the cost of bridge is probably closely approximated by $100.  The benefit of the bridge is more difficult to assess.  Such difficulties probably come up often.  What is the benefit of protecting or cleaning up a wetland?  What is the benefit of political stabilization in the Middle East? Tricky questions but questions that should be considered nonetheless. 

Are Agent-Based Models the Future of Macroeconomics?

A couple months back, Mark Buchannan wrote an article in which he argued that ABMs might be a productive way of trying to understand the economy.  In fact, he went a bit further – he said that ABMs would likely be the future of economics and he warned young economists not to get caught watching the paint dry and to get on board with this new approach to the study.  In contrast, he pointed to the failings of the DSGE models that mainstream economists use to understand most economic issues.

An AMB is a model environment computer model that is comprised of many individual participants. These actors interact with one another and these interactions produces outcomes – in our case, economic outcomes.  These economic outcomes can then be added up to compute GDP and aggregate, investment – any of the economic statistics that we macroeconomists are accustomed to looking at – you could calculate in an ABM.

Now, if you are an economist, a macroeconomist in particular, you are probably thinking that so far this sounds very familiar – it sounds like a DSGE model.  A DSGE model is populated by many agents and they interact and the results of those interactions produce economic outcomes and we add up those outcomes and we get GDP and so forth so it sounds like ABMs are DSGE models so how are they at all different?

Well, there are actually a few important differences.  More accurately, it seems to be a combination of three key differences that distinguishes the ABMs.

Probably the most important distinguishing feature is that, in an ABM, the interactions are governed by rules of behavior that the modeler simply encodes directly into the system individuals who populate the environment.[1] For example, we could have an ABM with a purely Keynesian consumption rule. We could assume that every time a consumer earns a dollar of income, they spend 20 cents and save the remaining 80 cents. We would make similar behavioral assumptions to govern every possible interaction.  We would make these assumptions for consumers, workers, firms, investors, etc. In an ABM, behavior is the point at which a modeler starts making assumptions.

People who write down DSGE models don’t do that. Instead, they make assumptions on what people want. They also place assumptions on the constraints people face. Based on the combination of goals and constraints, the behavior is derived.  The reason that economists set up their theories this way – by making assumptions about goals and then drawing conclusions about behavior – is that they are following in the central tradition of all of economics, namely that allocations and decisions and choices are guided by self-interest. This goes all the way back to Adam Smith and it’s the organizing philosophy of all economics. Decisions and actions in such an environment are all made with an eye towards achieving some goal or some objective. For consumers this is typically utility maximization – a purely subjective assessment of well-being.  For firms, the objective is typically profit maximization. This is exactly where rationality enters into economics. Rationality means that the “agents” that inhabit an economic system make choices based on their own preferences.

A second key difference is that the interactions are often restricted to individual (or at least limited) interactions. It could be a limited number of connections between a given consumer and potential sellers. It could be a single connection between a worker and a firm and so on.

Lastly, the individuals are “heavy.”  That is, the models keep track of each and every individual in the system and the behavior of each and every one matters (to some extent) to determine the outcome. This is again unlike many standard economic systems.  In most macroeconomic systems the behavior of a single individual can be altered without having a perceptible impact on the aggregate outcome. This isn’t typically the case in ABMs. In an ABM, one individual can influence the outcome at least to a degree.

Now, all of these features have been analyzed in economics. Macroeconomists have models that explore the consequences of matching (or search) in which the individuals make deals on a bilateral basis. In game theory, we often have environments in which each player has a substantial influence on the outcome. And there are well-known models that consider ad hoc rule-of-thumb behavior. However, these modifications are rarely considered in combination.

Of the three features, the absence of rationality is the most significant.  Ironically, eliminating rational behavior also eliminates an important source of feedback – namely the feedback from the environment to behavior.  This type of two-way feedback is prevalent in economics and it’s why equilibria of economic models are often the solutions to fixed-point mappings. Agents make choices based on the features of the economy.  The features of the economy in turn depend on the choices of the agents. This gives us a circularity which needs to be resolved in standard models. This circularity is cut in the ABMs however since the choice functions do not depend on the environment. This is somewhat ironic since many of the critics of economics stress such feedback loops as important mechanisms.

The absence of rational behavior also means that the ABMs are much easier to solve than traditional models. Once you have settled on your preferred choice functions, you just assemble many such individuals together in a computer environment and simply simulate.

In fact, the predecessors of ABMs have been around for quite a while. The earlier versions were called “cellular automata.”  The most famous of these was John Conway’s famous “Game of Life.” This “game” took place on a grid (often a torus).  Each square on the grid was either on or off (alive or dead). If a cell was alive at time t, it remained alive if 2 or 3 of its eight neighboring squares were also alive.  If 1 or 0 of its neighbors was alive then the cell “died” due to isolation.  If 4 or more were alive, the cell died due to congestion. Cells could also come to life. An inactive (dead) cell would come to life if it had exactly 3 live neighbors. The environment was very intricate. Starting from a random patter of active/inactive cells, a huge array of outcomes could be supported. There could be bursts of activity followed by a dramatic collapse.

In fact, you can get simple versions of cellular automata as apps on your iPhone. Two good ones are SPEED sim, and CA2D.  CA2D has many cellular automata rules built in but it doesn’t have the Game of Life.  Below are three pictures of Conway’s game of life taken from SPEED sim.  The first panel shows an initial purely random starting point. The second panel shows the system after 25 iterations. You can see that patterns have emerged “naturally” from the initial random state. The last frame shows the steady state.

Initial Random State

After 25 Iterations

Steady State (Periodic)

Clearly even in this simple ABM we can get very complicated patterns and behavior.

Whether ABMs have any future in economics is not clear. I suspect that the rule-based approach at the heart of the ABMs will ultimately limit their usefulness – particularly if outcomes depend importantly on subtle differences in specifications of the rules or if individuals have to adhere to simple rules even when the system starts acting wild.

Another problem facing the ABMs is that they appear to be suggested as a solution to a problem that might not exist.  In their 2009 Nature article, J. Doyne Farmer and Duncan Foley write that DSGE models “assume a perfect world, and by their very nature rule out crises of the type” we experienced in 2007-2008.  DSGE models do not “assume a perfect world.” Economists are enthusiastically adding frictions and modifications to DSGE models which incorporate many real-world types of market failures.  I will concede that I would be reluctant to offer a particular version of a DSGE model that I felt accurately captured what was going on during the crisis but I don’t think this is because of a limitation of the DSGE approach.  It’s a limitation of economists fundamental understanding of financial crises.  And that’s not something that ABMs are going to fix ….

[1] An attentive reader pointed out that my original description incorrectly described the rules as applying at the system level. This is incorrect. The rules of behavior are attached to the individuals and each can have a different rule.