Sunday 20 February 2011

Economists and (Ugly) Models

Well, you know what they say: economists do it with models.

But, no. This is not about Cindy Crawford-like miracles of human genetics (or, if that floats your boat, hunks like ___________; help me out here: fill in the blanks) and little, ugly, nerdish, boring, old men.

No, I'm talking about economic models of the simple variety, which recently appear to have become quite popular in the economic blogosphere and media.

Greg Mankiw (Harvard) proposed one:

"You have a driveway covered in snow and would be willing to pay $40 to have it shoveled. The boy next door can do it in two hours, or he can spend that time playing on his Xbox, an activity he values at $20."

Uwe E. Reinhardt (Princeton), who, as Mankiw, also likes that model, summarizes its conclusion thus:

"So if you pay him $30 to shovel your driveway, you will both be better off by $10. (...) As far as economists are concerned, how can anyone argue with that?"

Don't look at me: I can't argue with that! The conclusion follows from the premises, however unrealistic.

Reinhardt goes one step further, adding competition to the example, presumably to make it more realistic:

"Another boy from the neighborhood comes along and offers to shovel your driveway for $10. (...) You pay him $15. Now you are very much better off [my comment: precisely $25 better off], and that other boy gains, too, because he would have done the job for $10 [my comment: so he's better off by $5]."

As Reinhardt explains, now the first boy is not happy; but the second boy is.

Again, I don't object. However, now I feel a lot less sanguine about the whole thing: following that logic one concludes that the neighborhood kids will be accepting $20.01 $0.01 to do the job. And, believe it or not, one can still say that everybody is still better off!

I am not sure what Reinhardt had in mind with his extension: however, it argues the not surprising point that competition among workers reduces their wages, which is not considered in Mankiw's version.

What seems curious to me is that one could build an obvious variation yielding entirely different outcomes.

Let's modify the example: Anthony and Benjamin need their driveways cleared. Anthony is willing to pay $40 for that; Benjamin, $50. Anthony and Benjamin are, let's say, economics professors and hate shovelling snow.

Charlie, their young neighbour, is willing to do it for $20.

As in Mankiw's scenario, after talking to Anthony, Charlie agrees to do the job for $30.

However, seeing this, Benjamin calls Charlie: "Psst, boy! Over here! I'll pay you $40 to clear my driveway".

Clearly, Charlie is ecstatic (20 bucks ahead, not bad!) and Benjamin is happy, too. Anthony, on the other hand, is not so happy: he's gotta grab the shovel.

This result, diametrically opposed to the Mankiw/Reinhardt's example, isn't surprising either: bosses' competition for labour increases wages.

What's the difference between this situation and the Mankiw/Reinhardt one? In the latter the kids were made to compete against each other to get the job; in the former, it's the economics professors who compete to get the worker.

The first point I'm trying to make is this: Mankiw's example is frankly misleading. By ignoring competition, it doesn't show the kids are really better off with trade.

With Reinhardt's more realistic modification this becomes clear: $0.01 above the monetary equivalent of doing nothing either Mankiw's equivalence worth of playing Xbox ($20), or above $0,  is not an improvement (See Update 22/02/2011).

However, in both cases the economics professors are not only measurably better off, but the worse off the kids are, the better off the professors.

Now with my second point: things don't need to be like that. In my modification, Charlie was measurably better off. In other words, the choice between the 3 set of outcomes is not determined by the example and is arbitrary.

The third and final point I will make is this: as employers (and in this case, economics professors), Anthony and Benjamin have not only the knowledge and incentives to steer the situation away from one where they compete against each other to hire Charlie; they also have the political means to do that.

Let me put it this way: they could talk to Daniel (Charlie's non-democratically elected and mean stepfather) and convince him that he could live quite comfortably by making his stepchildren (the whole 1.3 billion of them) work for a few cents each, which they'll pay Daniel, in exchange for living in Daniel's house.

And that's precisely what Anthony (or is it Benjamin?) does here:

Peter Tasker. Rising wages will burst China’s bubble. Financial Times. 10/01/2011. Requires subscription. Registration required.


21/02/2011. Oopsie, I had forgotten the last link.

22/02/2011. Actually, my logic above is flawed and I noticed the mistake today.

Mankiw established that the first boy had an alternative use for his time (playing with the Xbox); that alternative use was worth the same as $20 for that boy.

But Reinhardt did not establish anything similar for his neighborhood kids; that's why the second boy was happy to work for $10!

On that assumption, the Mankiw/Reinhardt scenario leads not to a top payment of $20.01 (as I wrongly stated above), but to $0.01.

It appears the Financial Times also has a free registration option, for limited access.

So as to leave my mistake on record, I struck through the mistaken text, and added the corrected version, with a reference to this update.

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