A bit more on the effects of "job protection" on unemployment rates

I screwed up in the initial algebra. The correction is below. You guys are supposed to check this for me!

In the comments to the last post Jane points out that whether higher unemployment benefits increase or decrease labor force participation and hence unemployment rate depends on whether the getting of benefits is tied to job search or not. In US at least, in order to qualify for the benefits a person must essentially list themselves as "unemployed" rather than "not in labor force" which WOULD actually increase the unemployment rate. On the other hand, even in US there are many benefits which are a function solely of income and not labor force status which would likely operate in the manner described in the last post. In addition some countries guarantee a "minimum subsistence income" which is also independent of whether one is job seeking or not. The overall point I guess is still that the crazy applied labor economists shouldn't just slap "unemployment rate" on the y-axis and "unemployment benefits" on the x-axis and try to draw some regression line through the scatter plot (and Greg Mankiw shouldn't do it in the new edition of his book) and pretend that it means something without considering carefully the actual institutional structure and how these benefits really affect incentives to 1) enter the labor force, 2) time spent looking for a job as opposed to just stating that one is looking for a job (this seems to be one of these instances where economists are forgetting one of their favorite adages that one should look at what people actually do rather than what they say they do). This is also one of the points of the HBGS paper linked to in the last post and it's a step in the right direction even though I still feel like they're playing along too much with "how's it been done so far".

Anyway, all that actually leads us to an empirically testable hypothesis. In economies where unemployment benefits are not tied to labor force participation and there is generous outside government assistance (say, housing subsidies for low income families etc.) unemployment rate would be LOWER than in economies which tie income subsidies to looking for a job (the effect may be small however since if income subsidies which are tied to looking for a job induce greater LFPR that would enter in both the denominator and numerator of the unemployment rate). This would actually be somewhat of a test as to whether people lie about looking for jobs just to qualify for unemployment benefits in the latter type of economies.

But I know that what you really want out of my posts is maths. So I'm gonna address a different aspect of the whole "job protection" issue - the prohibition, or more generally the increase in the costs, of firing workers. I'm gonna do it at a pretty low level of analysis - a reduced form model if you'd like, because if I could do it better I'd write a full paper about it, not a blog post.

If you think about it, and as derrida derider says over in CT comments, the effect of increasing costs of firing workers on the unemployment rate may actually go either way. On the one hand, the fact that it will be costly to fire some deadbeat workers once hired may make an employer less willing to hire workers in the first place and so cut back on the number of hires increasing the unemployment rate. On the other hand, all them deadbeats that do somehow end up being hired cannot be fired and hence stay out of the pool of unemployed workers decreasing the unemployment rate.

So suppose that at any point in time there's just two types of workers, those employed E(t) and those looking for a job, or searchers, S(t). We normalize the total population for simplicity to 1 so that dE/dt=-dS/dt or the inflow of workers into unemployment equals, obviously, the outflow of workers from the search pool. Here's a graph (I know you guys like these too);



So the change in the number of searchers is



where f is the rate at which employed workers are fired, q is the rate at which existing workers voluntarily quit their jobs, h is the rate at which job searchers are hired and E(t) and S(t) are the stocks of the employed and searchers at any given point in time. I'm assuming that f, q and h are exogenous because like I said, this is a reduced form model. What you'd wanna do ideally is to endogenize these fine members of the Arabic alphabet by deriving them from some profit/utility maximization set up.

But anyway, assuming a steady state where the number of job searchers (unemployed) and employed is constant (again, you'd wanna specify how this happens, that it's stable and all that) we have



or



where we dropped the time argument since these are steady state values. Using the fact that total labor force is constant at 1 and so S=1-E we have the employment rate:



and the unemployment rate:



Now, the proposition that implementation of "job protection" in terms of prohibition on firing results in employers being more reluctant to hire workers but also unable to fire some of the workers they've already hired means that:



or in other words that both the firing and hiring of workers has fallen.

Taking a total derivative of the unemployment rate we get:



or



(the reason both dh and df have minus signs in their paranthases is that both of'em are negative). So whether a prohibition on firing increases or decreases the unemployment rate depends on whether



is greater or less than

CORRECTION, LOST A FREAKIN' 1:


Interestingly, if there are no voluntary quits in this economy then the effect on the unemployment rate is always positive - more "job protection" means more unemployment. But for a high enough rate of voluntary separations (which again, here is exogenous) job protection could actually protect jobs in the sense of lowering the unemployment rate (at the cost of keeping a lot of unproductive workers employed, but that's another story). This also suggests that "job protection" of this sort would only decrease the unemployment rate in economies with already low rates of unemployment (high q/U) but not in economies with high rates of unemployment.

If there are no voluntary quits in this economy then the effect on the unemployment rate depends just on the relative magnitude of % changes in h and f. For a given levels of dh and df however, a higher quit rate makes it more likely that the change in the unemployment rate due to this policy is negative. That is the "job protection" policy is likely to lower the unemployment rate when the quit rate is high. Also if you start out in an economy with an already high unemployment rate, the effect of the policy would be to increase the unemployment rate. I hope I didn't flip a sign now that I found my 1.

Finally, and obviously, the unemployment rate would increase if the negative effect on hiring is large relative to the negative effect on firing.

Anyway. The larger point I think is that in a world where there's all kinds of institutional incentives to be or not to be in the labor force, to misreport oneself as looking for a job (hence as "unemployed") simply to acquire benefits, where employers are essentially forced to subsidize workers that they would not otherwise keep on their payroll (think of it as government outsourcing the job of providing a minimum standard of living out to the private sector), where the institutional details of how unemployment assistance and other benefits are provided play havoc with incentives in all kinds of different directions, and of course, all them other things, the unemployment rate is not really a meaningful statistics by which to compare economies by.

What are these crazy applied labor economists talking about?

or, how HIGHER unemployment benefits LOWER the unemployment rate.

Disclaimer: Am I missing something?

Dani Rodrik links to a paper by Baker, Howell, Glyn and Schmitt and Henry of Crooked Timber picks up on it, about how more "protective" labor market institutions do not necessarily, contra conventional wisdom, cause higher unemployment in Europe. The paper (which I haven't gotten all the way through) makes some good points about measurement and definitional issues and claims that when one corrects for these the supposed association between "rigid labor markets" and unemployment disappears. Which doesn't necessarily mean that there is no relationship but just that the presently available data are not of sufficient quality to allow us to discern what exactly, if anything is going on.

Ok. Fine. But. Speaking of definitional issues.

Why would anyone ever think that higher unemployment benefits lead to higher unemployment rates?!?!???

(actually there are some, like two, reasons why, which I'll hopefully get to at the end of this post).

Now, certainly one would expect that higher unemployment benefits would lead to FEWER PEOPLE WORKING (or hours or whatever) and result in lower LABOR FORCE PARTICIPATION RATE but why it would lead to higher unemployment rates is beyond me (uh... again, except for them two reasons I'll get to. So maybe more like "next to me").

So let's get this straight.
You're UNEMPLOYED if - you ain't got a job but you want one or are at least actively looking for one.
You're NOT IN THE LABOR FORCE if - you ain't got a job and you don't want nor are looking for one.

Among all the talk of definitional issues (the fact that unemployment might be defined differently in Europe or in US, that unemployment benefits are not measured comprehensively, that coverage and enforcement differs, etc.) the above distinction is never made. Now, this isn't necessarily the authors' (HBGS) fault. From what I understand, and from some of the studies they refer to in their paper, it seems like these two get conflated in the literature all the time. At the very least the OECD and couple of other organizations seem to be guilty of this confusion. So HBGS are just following (a faulty) convention.

What you typically get in these studies is a graph like one below:





where some kind of measure of unemployment benefits is on the x axis and the unemployment rate is on the y axis. The difference between HBGS and older studies is that the older studies tend to find a positive relationship while HBGS argue that with new and improved data there is no or even a negative relationship and that hopefully when better data emerges we'll get a clearer picture.

Well, I hope that the better data emerges soon and that it confirms "standard theory" which is to say SHOW A STRONG NEGATIVE RELATIONSHIP BETWEEN UNEMPLOYMENT RATE AND UNEMPLOYMENT BENEFITS. That is after all what "standard theory" (most of it, except for those two famous exceptions) says.

So what does the standard theory say? Well, the most standard of the standard theories - that of a competitive market with wages which adjust to equilibrium - doesn't, cannot, have unemployment in it. The wage clears the market and everyone who wants a job at the market wage gets one. So the level of unemployment benefits doesn't matter for the unemployment rate (though it does for the labor force participation rate). So we need a less standard theory which has unemployment in it.

Easy. Slap in some "labor market rigidity" which puts wages above equilibrium level. This could be a high enough level of minimum wages, unions, efficiency wages or whatever. Whatever your favorite culprit, with above market wages, the demand for jobs will exceed the demand for workers and there will be unemployment. This is Econ 101 Principles stuff.

Now what happens when you increase the level of unemployment benefits? Welp, that would affect the labor supply curve. For a given wage, the opportunity cost of not-working is lower so less labor will be supplied. Some folks will drop out of the labor force. Labor supply curve will shift up and back. However, keeping that higher than equilibrium wage in place, the demand for jobs will not change. Ergo, the number of unemployed - the difference between labor supply and labor demand at the higher wage - has to go down. Of course labor force participation will also decline. So which way does the unemployment RATE move? Down. But before we get there consider this graph which illustrates how a sufficiently generous level of unemployment benefits can get rid of ALL unemployment in your economy:



Ok, but how do we know that, in the context of this model, the unemployment RATE will always fall?
Well, the unemployment rate is defined as


where w* is the above equilibrium wage and b is the level of unemployment benefits. Of course we expect that labor supply, LS, decreases with the level of unemployment benefits (labor supply shifts up) so



Differentiating the UNRate we then get



So explain to me again why are people expecting to find a positive relationship between unemployment rate and unemployment benefits?

Ok, now to those two reasons why higher unemployment might raise the unemployment rate.
First is JOB SEARCH. If you're getting higher benefits while unemployed (and unemployed means you're busy searching for a new job) you might take your time with your search and cherry pick your job offers. Hence you will be unemployed for a longer period of time which means that at any given point in time there will likely be more people unemployed and searching for jobs which means higher unemployment rates. You could probably get at examining whether increased job search length is behind higher European unemployment rates by looking at vacancy and turn over data (if it were available) but I'm guessing this is probably not the case. Anyway, strictly speaking this isn't "structural unemployment" which is what Europe gets blamed for, but "frictional unemployment" (if a meaningful distinction can be made).

Second we've got the HYSTERESIS idea which is usually associated with Oliver Blanchard and some others. The argument here would roughly say, ok, increased unemp benefits initially increase labor force particiaption rate not unemployment. But this means some folks drop out of the labor market. And a lot of skill are of the "learning by doing" type so by not having a job (because they're not looking for one) these folks' skill atrophy, become obsolete or just generally don't improve. Consequently, when and if these folks reenter the labor market they're likely to be lower skilled, and have a harder time finding a job. This, BTW, is what leads folks to look at the long term unemployment rate and unemployment benefits.

Both of these are plausible stories (though I don't think the first one is that important in this context). However, even if they are true empirically, the initial "standard theory" story about decreased unemployment rate which I told above is also true. So the two (three) effects could offset each other and you'd just end up getting weak results from the data. Huh. That seems to be exactly what we're getting from the data in fact.

So to sum up. No, I don't think higher unemployment benefits are the cause of higher unemployment rates in Europe. "Standard theory" doesn't think so either. If anything, these higher unemployment benefits hide the extent of the problem by lowering labor force participation rates. The "standard theory" suggests that if unemployment benefits in Europe (btw, Europe here mostly refers to Ger, Fra, Bel, Ita and uh ... Spa I think, where the UnRate really is high. Of course it refers to Western Europe, why would you think otherwise? Just like no one ever dummies for "former Ottoman colony", only "former British colony" and "former French colony" when studying the effect of colonialism on economic growth)... so ... uh ... yeah, if benefits in Europe resembled US levels their unemployment rates would be even higher.

Now, the story with other "labor market rigidities" is of course different.

As a final comment, I just wanted to note that the otherwise good Principles of Macroeconomics textbook by John Taylor, after really really carefully defining what is meant by "unemployment rate" and "labor force participation rate" makes this same mistake - mixing up labor force participation and unemployment - in its "Case Study" section which purports to explain the higher unemployment rates in Europe. So again, I don't blame HBGS for following a sketchy precedent.