# Estimating the Multiplier

As many of you know, I have expressed skepticism that the stimulus package will work. At the heart of the debate is whether the multiplier associated with government spending is greater than one. Some recent literature should allow us to do some back-of-the-envelope calculations of the multiplier.

A recent paper by Matthew Shapiro and Joel Slemrod (non-gated link) uses survey data to determine the effects of the 2008 stimulus package in which individuals received tax rebates. They find that 20% of those interviewed suggested that they would “mostly spend” the rebate. 32% would mostly save the check and the remaining 48% would mostly pay down their debt. At first glance, this would seem to suggest that the fraction of the population likely to increase their consumption is 20%. The authors, however, note that there is a difference between “save” and “mostly save”. Thus, they estimate the marginal propensity to consume (MPC) to be roughly .3.

In Mankiw-Campbell land, this roughly translates to the idea that the fraction of consumers that are rule-of-thumb consumers (those that live paycheck-to-paycheck) is about .3. We can then use this measure of the number of rule-of-thumb consumers to estimate the multiplier based on a recent study by Jordi Gali, et. al (HT: Ambrosini).

The paper by Gali, et. al provides two ways to estimate the multiplier based on the fraction of rule-of-thumb consumers. First, with competitive labor markets, the fraction of rule-of-thumb consumers would have to be roughly .65 to generate a multiplier of 1. Clearly, this is well above the estimate provided above. Second, with non-competitive labor markets, the fraction of rule-of-thumb consumers would have to be .25 to generate a multiplier of 1. Further, a rule-of-thumb fraction of .3 implies a multiplier greater than 1, but less than the administration’s estimate of 1.5.

Naturally, this raises the question as to whether the labor market in the United States is competitive. Gali et. al define a non-competitive labor market as that in which unions set the wage and employment is determined by the labor demand curve. The idea that the wage is determined by labor demand is certainly a reasonable assumption, especially given the current circumstances (Thanks Will). Thus, based on the work presented, the multiplier may be slightly above 1.

(A BRIEF NOTE: The paper by Shapiro and Slemrod examines the impact of a temporary government stimulus. The current stimulus package contains both temporary and permanent aspects. Nevertheless, I think that their estimates provide a meaningful guide. The current stimulus provides permanent tax cuts through the “making work pay” rebate. It also includes temporary spending provisions such as infrastructure spending etc. In addition, some of the spending side is likely to be permanent. Thus, the increase in consumption is likely to be greater than that estimated by Shapiro and Slemrod because the tax cut is permanent. However, this effect might be offset by the permanent increases in government spending in the package, which will crowd out private investment. Also, the package has been sold as a temporary stimulus to the American people and thus treating the entire thing as temporary when evaluating the behavior of consumers is likely a good first-approximation. Finally, these are merely back-of-the-envelope calculations and should be taken with a grain of salt.)

### 3 Responses to Estimating the Multiplier

1. Do you think the competitiveness of the labor market is counter-cyclical?

2. What if the multiplier is 1? Then what?

3. goldman sachs

Raivo Pommer
raimo1@hot.ee

Geld

Auf Druck der amerikanischen Steuerzahler, die AIG bereits mit etwa 180 Milliarden Dollar gestützt haben, musste der einst weltweit größte Versicherungskonzern offenlegen, wohin das Geld geflossen ist. Rund 100 Milliarden Dollar gingen an Kunden im In- und Ausland. Auch andere Banken, von denen es bisher hieß, sie seien gut durch die Krise gekommen, wie Goldman Sachs und Société Générale, sind wie die Deutsche Bank in den Genuss von mehr als elf Milliarden Dollar an AIG-Hilfen gekommen.

Ist das ein Skandal? Nein. Die Zahlen zeigen aber zweierlei: Erstens gibt es wohl auf der ganzen Welt keine größere Bank mehr, die nicht direkt oder indirekt von Staatshilfen profitiert. Ja, vermutlich würde es das ganze Bankensystem so nicht mehr geben, hätten die Regierungen nicht massiv eingegriffen. Dies ist aber – zweitens – gerade der Grund, weshalb Finanzkonzerne wie AIG und hierzulande die Hypo Real Estate gerettet werden.