# Pocketful of Multipliers (II): Options for Stimulus Packages

As the debate over the nature and size of a stimulus package wends its way through the Congress [0], [1], [2], I thought it would be useful to bring numbers into the debate, especially as we are considering fiscal stimulus in a time when the Bush Administration has constrained, by dint of previous profligacy, our options. In particular, I want to return to the issue of multipliers, discussed in nearly a year ago. Here, I want to provide a little more specificity, regarding the impact depending upon the type of outlays.

From the testimony of Economy.com’s Mark Zandi back in July (thanks to Chad Stone for the pointer):

What is a multiplier? It’s:

ΔY/ΔZ

where Y and Z are measured in real dollars. Note that in principle, one can re-write the multiplier in terms of percentage point change of income relative to baseline income for a given percentage point change of the Z-to-Y baseline ratio.

What is apparent is that some tax cuts, or really rebates, can have a substantial effect. But in most cases, tax policies will have a relatively minor impact on aggregate demand, relative to increases in spending on goods and services. That’s because the first round of injection of the dollar into the economy via tax reductions or transfer increases initially augments disposable income, and then, by indirectly increasing consumption, increases GDP over time. In other words, for an increase in transfers, the impact of one dollar increase in outlays by the government is:

(c(1-t)) + (c(1-t)) 2 + (c(1-t)) 3 + …. = c(1-t)/(1-c(1-t))

Whereas for spending on goods and services:

1 + (c(1-t)) + (c(1-t)) 2 + (c(1-t)) 3 + …. = 1/(1-c(1-t))

Where c is the marginal propensity to consume (MPC) out of disposable income, and t is the marginal tax rate.

Why is the increase in extending unemployment insurance so large (and similarly for increaseing food stamps), when these are increases in transfers, and not increases in spending for goods and services? Look back to first series, and notice that if on the first round, the marginal tax rate is zero (which is definitely true for food stamps, and might be for unemployment benefits depending on the tax bracket), and the marginal propensity to consume is nearly unity, then the first term becomes close to 1. Hence, transfers to the lowest income households that have the highest MPC will have the biggest impact (of course on the 2nd and 3rd rounds, the standard fractions apply).

Increases for infrastructure spending will have a relatively large multiplier as well, exactly because these are expenditures for goods and services. To the extent that most of the input (concrete, labor) is domestically sourced, then on the first round impact, the increase in GDP is almost dollar for dollar (I’ve suppressed the marginal propensity to import in the above calculations to simplify the algebra and to provide the clearest intuition).

The above discussion explains why in my previous post on fiscal policy, I stressed that if we were to undertake any fiscal stimulus aimed at stabilizing the economy at the short to medium run, we should aim for aid to the states and localities, increases in unemployment insurance, and buttressing infrastructure spending.

One big caveat to the argument for infrastructure spending is that it usually takes a long time to plan such projects. Hence, it is not clear when the spending for such projects would actually occur, and hence the stimulus to the economy (this is called an outside policy lag, in the jargon). The “one-year horizon” shown in the table is for the horizon of one year from beginning of spending, not the beginning of planning and appropriation.

I have two observations here. First, if the spending could be directed to the states which had construction about to start, but hindered by financing or state revenue issues, then the problem of timing could be partly mitigated. I admit that it is unlikely that there are a tremendous number of such projects (although I am happy to be corrected). That leads me to my second observation.

The CBO study Options for Responding to Short-Term Economic Weakness (January 2008) laid out three principles for effective stimulus, loosely characterized as “timely, targetted, and temporary”. Spending on infrastructure is problematic on this first count if one believes the recession will be short. If one believes that it will be prolonged (in the now outdated lingo, “L-shaped” instead of “V-shaped”), then this drawback is not so significant. So, what’s the outlook? I reprise this graph from an October 18th post:

Figure 1: Log GDP, from 26 Sep release (blue line), and implied GDP gaps from WSJ survey (3-7 October survey, green x) Deutsche Bank (3-7 October forecast, teal +), and Deutsche Bank (17 October forecast, red square). Source: BEA, CBO [xls], WSJ [xls], Mayer, Hooper, Slok and Wall, “WO Update: From Financial Crisis to Global Recession,” Global Economic Perspectives (Deutsche Bank, 17 October 2008), and author’s calculations.

Several last observations.

• It’s not clear that these policies would do much good if the financial system is not restored to some semblance of working order (so, I’m in agreement with Jim). Hence, fiscal stimulus is not a substitute for financial triage. By the same token, even with an effective rescue of the financial system, deleveraging is going to be a long, drawn out process which will tend to depress aggregate demand; it seems that some fiscal stimulus should be emplaced to mitigate those contractionary effects.
• Those who are familiar with multipliers will recognize that implicit in my discussion is accomodative monetary policy (i.e., there is no transactions- and portfolio-crowding out). I think this assumption is, in usual times, not a defensible assumption. However, the times hardly seem usual; and as we get closer to the zero bound on nominal interest rates, the assumption seems ever less problematic.
• I know the preceding has been a pretty old fashioned Keynesian discussion. If I thought that the economy were near full employment and/or prices were fully flexible [3], I wouldn’t be propounding these ideas. But it seems to me we’re more in a world with some underutilized resources, requiring some sort of coordination mechanism, than an monetarist world.

Greater discussion of these options, and how to allocate the monies across states, is contained in this brief by CBPP (September 26, 2008). See also Economix and National Journal blog.

Originally published at Econbrowser on Oct 27 and reproduced here with the author’s permission.

### 2 Responses to "Pocketful of Multipliers (II): Options for Stimulus Packages"

1. Guest   October 30, 2008 at 6:20 am

I’m a civil engineer. Governments often have many feasability studies and impact studies sitting on their shelves for infrastructure projects that have been postponed indefinitely for lack of funding. With funding, detailed engineering typically takes a few months for a small project to a year or more for larger projects. Environmental approval may take longer depending on grassroots opposition or the arbitrariness of environmental bureaucrats.

2. 655321   January 20, 2009 at 12:43 pm

Great article, but in quoting or displaying the Zandi multipliers, you say nothing about their predictive ability or accuracy, a year after he published the article you reference. You really should say something about them, if you are going to put them up, other than “well here are some multipliers, do with them what you will.” The larger discussion about spending, etc is good, but without commenting on the accuracy of the multipliers you presented, I am left wondering what the point of the article is, or at least the point of bringing in specific multipliers, if you are not going to critically examine them.