Friday, August 21, 2009

Dissecting the so-called Multiplier II: A Little Incentive Goes A Long Way

We have been told that unemployment insurance (and other means-tested benefits, to which I collectively refer as "UI") stimulates the economy because it redistributes from savers to consumers, and that consumption has a multiplier.

MULTIPLIERS TELL US MAGNITUDE, NOT DIRECTION

For the sake of this discussion, I will ACCEPT the (dubious) proposition that consumption has a multiplier: an exogenous increase in the consumption spending by one group will create jobs and ultimately increase the consumption spending of others.

This proposition does NOT imply that government spending on UI has a multipler, because UI likely LOWERS aggregate consumption. The so-called multiplier only tells us the amount of the consumption impact, not the direction. If UI lowers consumption, and the multplier is large, then UI lowers consumption by a lot.

WHAT IS THE **DIRECTION** OF UI'S EFFECT ON CONSUMPTION?

The "Keynesian" view is that essentially ALL persons unemployed are unemployed through no action of their own. All UI does is raise their consumption. Keynesians will admit that the taxpayers/government-debt-purchasers who finance UI will consume less as a result of UI, but they say that the marginal propensity to consume is greater for the unemployed than for the persons who pay for UI.

For the sake of argument, I will accept their proposition that the two groups have different marginal propensities to consume, and denote those propensities as U and E (with 1 > U > E > 0).

I also agree that many people would be unemployed even without UI, but "essentially all" is an exaggeration. UI makes it easier to be without a job, and there must be SOME people who are unemployed because of UI. Let G denote the ratio of genuinely unemployed (the ones characterized by Keynesians) to this second group. All I am saying is that G << infinity.

Let dR << 1 denote the impact of UI on the funds accessible to unemployed persons (that is, funds available under UI minus funds accessible from friends, family, etc., in the absence of UI), expressed as a ratio to the productivity of persons on the margin of employment.

If all unemployed were "genuine," then the consumption impact would be (U-E)dR when expressed as a ratio to the productivity of persons on the margin of employment.

If all unemployed were in that state because of the incentives presented to them by UI, then the output impact would be -1 when expressed as a ratio to the productivity of persons on the margin of employment, because the decision not to work means that output is destroyed. The consumption impact in this case is -A, where A the effect of aggregate output on consumption (you could think of it as an average of U and E).

When both types coexist, the sign of the consumption impact is the sign of:

(U-E)G dR - A

Notice that (a) the first term includes the GAP between two marginal propensities to consume, whereas the second term includes the LEVEL and (b) dR << 1 appears only in the first term.

Thus, if you think the net consumption impact is positive, it is not enough to say that G > 1 (genuine unemployment is more common), you need a G of something like 10.

Succinctly put, any positive consumption impact of UI comes from DIFFERENCES in spending patterns across types of persons, whereas the negative impact comes from the fact that output is destroyed when someone makes the choice not to work. The former effect is small, so it had better occur many times in order to dominate the second effect.

2 comments:

nick said...

Hong Kong has no UI or other "safety net" to speak of, a top marginal tax rate of 15%, and a regular influx of penniless migrants from the mainland. Its GDP is among the highest in the world and Its unemployment rate, now around 5.5%, is consistently below that of the U.S. Anyone who says government spending and a "safety" net are crucial to maintaining jobs and keeping an economy humming needs to explain Hong Kong.

Don said...

"Succinctly put, any positive consumption impact of UI comes from DIFFERENCES in spending patterns across types of persons, whereas the negative impact comes from the fact that output is destroyed when someone makes the choice not to work. The former effect is small, so it had better occur many times in order to dominate the second effect."

I don't think that there's a problem pointing out that UI can be a disincentive to work in some cases. Usually though, when I read this point being made, it's backed up by an anecdote. In UI, it is understood that some people will not accept Job A because they are waiting for Job B. There is a loss in output there I suppose. But, if Job B is a job that a person is better for and increases productivity, and possibly because Job B ends up going to someone less productive, there could be a trade-off. That's why you need to explain WHY you didn't accept Job A if it was offered to you in UI. But I agree with you in that we should understand that there's a trade-off, however hard to disentangle.

So, I don't have a problem with the point that you're making. In fact, I see a clear benefit in the analysis that you do. It's a model that can allow a person to see oddities in the economy. For instance, I thought that you picked up on the Productivity Number very early. The model said that people were not accepting work. I disagreed with that interpretation, but found the model very useful.

I'm sure that you don't agree with this. In my case, my belief about models being useful comes from studying the philosophy of science.

Here is a reasonable post, in my mind, about the Stimulus:

http://www.knowingandmaking.com/2009/08/what-is-return-on-fiscal-stimulus.html

I also think that your post is useful as well. Political Economy involves looking at the results of such models and making tough policy decisions in the real world. I'm beginning to believe that I'm the only person who thinks like this. Frankly, that's why I post, other than it allows me to write in between times when I'm working on my novels.

Don the libertarian Democrat