# Multiple multipliers

Gali’s paper is really good. Its the best case for fiscal policy I’ve seen using the modern macro framework. I think the introduction and conclusion are accessible to a general audience and the empirical and modeling sections are good reviews of new Keynesian models and methods for you macro geeks.

Anyway, the model’s innovation is this chart (particularly the increase in consumption due to government expenditure):

 From research

The greek symbol lambda represents the percentage of the population that live hand-to-mouth. These are folks that eat everything they earn; they don’t save. The model is agnostic as to why these folks make decisions like this, i.e. limited access to credit markets, myopia, etc. On the vertical access, you see the multipliers implied by each level of hand-to-mouthers. To get multipliers above one — to make government spending worth it — less than 75% of the population needs to be savers. Christie Romer’s multiplier of 1.5 corresponds to having about 40% of the population living paycheck to paycheck.

I’ll leave it to the reader to decide what lambda is reasonable.

Rule-of-thumb consumers [wa: i.e. non-savers] partly insulate aggregate demand from the negative wealth effects generated by the higher levels of (current and future) taxes needed to finance the fiscal expansion, while making it more sensitive to current disposable income. Sticky prices make it possible for real wages to increase (or, at least, to decline by a smaller amount) even in the face 29 of a drop in the marginal product of labor, as the price markup may adjust sufficiently downward to absorb the resulting gap. The combined effect of a higher real wage and higher employment raises current labor income and hence stimulates the consumption of rule-of-thumb households. The possible presence of countercyclical wage markups (as in the version of the model with non-competitive labor markets developed above [wa: and represented by the graph above]) provides additional room for a simultaneous increase in consumption and hours and, hence, in the marginal rate of substitution, without requiring a proportional increase in the real wage.

Non-savers don’t save even though they know their taxes will be higher in the future. So when government expenditures increase employment and price stickiness keeps real wages high, the non-savers consume more.

Good stuff.

## 13 thoughts on “Multiple multipliers”

1. Gabriel says:

The thing is, I wouldn’t translate “announced and debated-for-ages fiscal stimulus” as an exogenous shock to government spending.

I always thought it was fun to think of \lambda as a measure of how “keynesian” an economy is, although… well,… misspecification and all that.

2. Clearly an anticipated fiscal bump wouldn’t change the behavior of the non-savers but my guess is everyone else would start saving more in anticipation (which our case would look like more evidence for the fiscal stimulus… it would look like precautionary savings). Also, prices would start to adjust earlier dampening the multiplier. Someone should modify this model to have pre-announced fiscal policy to see if it is quantitatively significant.

Keynes had no consumption/savings trade-off, so yeah lambda is the degree to which agents are Keynesian.

3. Claudio says:

A important political consequence of this, I think (I didn’t have time to read the paper), is that tax cuts are better than bigger public expenditures and these tax cuts must happen at the botton (for the poorer people) not at the top. Poor people (not rich ones) are credit constrain and more able to expend their tax cuts.

4. swong says:

Does that imply cuts on sales taxes? Poor people don’t have much capital or income to tax in the first place.

5. Claudio, that assumes poor people are equated with hand-to-mouth people. I don’t know if that’s true. This is important because its relatively easy to target stimulus to poor people but maybe not so to non-savers (how would you identify them?). Plus, any targeting stimulus would gives perverse incentives to not save.

swong, someone on the internets had a great idea. Take the stimulus money and compensate States for temporarily removing State sales taxes. Being temporary, it would have people move their consumption decisions forward in time and it would be revenue neutral for cash-strapped States. Also given sales tax is regressive, a tax cut would help poor people most.

6. Josh says:

I have a few questions:

(1) Do these models show that the multiplier or expected economic benefit is dependent on the size of government spending? The models seem to indicate that the multiplier is completely independent of the size of new government spending which leads to my next question.

(2) If the multiplier is not dependent on the size of the stimulus, how is the net benefit dependent on the size of the stimulus? In other words, wouldn’t this indicate that increased spending is always beneficial? Where does the dependence on the amount of government spending coming in?

(3) Where does repayment of this debt come into consideration in computing cost? Is the assumption that with a lambda greater than .25 future payment won’t influence current behavior and thus we’ll grow the economy in the short term and accept the reduction in GDP later when our economy is larger and can better handle the decline?

Here’s my basic (very basic) understanding. GDP is a function of several factor, chief among them Consumer Spending, Investment, and Government Spending, with consumer spending being the dominant factor. However, the concern (argument) is that an increase in G would come with a decrease in C and to some degree I – but the big discussion is around C.

The model as described above argues that not only would an increase in G not reduce C but under certain conditions (those described by Romer, etc.) it would actually increase C resulting in a net gain in GDP of 1.5 (or more) x G.

So, I get the debate over the size of stimulus is related to how much increase in GDP we need to get out of the recession, what I don’t get is what are the conditions now, as related to the existing arguments that wouldn’t dictate that increased G will always be beneficial?

Is it purely related to the assumption that with current unemployment G would take only idle resources?

Thanks in advance for the reply. It’s tough for non-economists to understand this stuff.

7. swong says:

That’s exactly what I was thinking. I’d still be worried about people loading up on credit to take advantage of tax holidays, though. That’s probably the subject of some different papers.

8. Josh, great questions: One thing to keep in mind with this model and the way it is analyzed is that Gali linearizes around the steady-state. This means his analysis is limited to “small” changes in government spending. The problem with generalization, then, is understanding how small is “small”. Gali analyzes spending shocks that are 1% of output. Obama’s stimulus is looking to be about 3-5% of output.

The other problem with generalizing the results from this paper is what Gabriel mentioned above, namely Obama’s plan isn’t going to be surprise “shock” of fiscal stimulus. We’ve been talking about it for months and so people have been able to adjust their consumption behavior taking an expected fiscal stimulus into account. The paper, on the other hand, analyzes unanticipated fiscal shocks. Its likely the multipliers would change (and I’m guessing they’d decrease) if you modified the model to have anticipated shocks. However, its not clear how important this criticism is in terms of magnitudes…

To directly address your questions: 1. he doesn’t analyze other sized shocks so its possible the multiplier changes with larger shocks and 3. the model assumes the government is budget constrained and that public debt doesn’t explode. If you’re able to look at the paper, take a gander at figure 4B (page 50). The top left graph is government deficits over time with the origin being the time the government spending shock came. They’re positive for the first 4 quarters or so and then go negative (i.e. debt is paid off) after that.

Your question about consumption is interesting. I think consumption is positive because under the assumptions of the model, wealth is being transferred from savers to non-savers.

The general discussion of the recession focuses too much on GDP. For a social welfare point of view (i.e. what people care about), I think the better aggregate measure to follow is consumption. The innovation of Gali’s model is to show that increased government expenditure can actually increase consumption (which is counter your and my intuition that those two things should substitute each other).

I think lambda — the proportion of the population who are non-savers — would change if the government tried to have a policy of continuously increasing consumption via government spending. There would be decreased incentive to save (don’t save and let the sucker savers pay for your current consumption) which would increase the cost of borrowing making it harder to finance government spending and so forth. This would be a very interesting extension of the Gali model (along with adding anticipated shocks).

Thanks for the questions Josh. Excellent.

9. Pushmedia1 wrote: “Obama’s stimulus is looking to be about 3-5% of output.”

GDP for one year is $15 trillion,$45 trillion over three years. Let’s pretend state government aren’t really cutting back. (They are!) 789bill/45trill = 1.7% of output… Most of it will be spent in two years, so that makes it up to 2.6% of output… Contrast that with GDP currently contracting at about 5%. Much of the federal spending will just replace state cuts, however, so we’re probably looking at more like around 500 billion in really “new” spending and tax cuts. That would mean the Obama stimulus, as big as it looks, comes in at around 1.1% of GDP…

The thing is a paper tiger…