Saturday, September 13, 2014

Rognlie on productivity and employment

Matt Rognlie is one of those people who really knows how to reason from a model, and he can do so quantitatively by using compelling rules of thumb and back-of-the-envelope reasoning. Google around for some good examples.

In the comments to this post, Matt writes:

Let's ignore non-labor sources of income for a moment. Then, in a very simple static model of labor supply, unless substitution effects are much stronger than income effects (which would imply a counterfactual secular rise in labor hours), a fall in the level of real wages does not imply a decline in labor hours. If we adopt cancellation between substitution and income effects as a baseline, then hours should be constant regardless of the real wage. Not clear why a fall in productivity, say, should translate into a decline in hours. 
Dynamically, there is a similar invariance of labor hours to shifts in the long-run level of productivity, but there may be some intertemporal substitution of labor depending on the (1) real interest rate vs. the (2) rate of expected real wage growth. Specifically, labor supply today is increasing in (1) - (2), though the actual amount of intertemporal substitution is determined by the Frisch elasticity, which does not seem to be that high in practice. The recent recession involved declines in both (1) and (2), maybe with an overall decrease in (1) - (2), but (I don't think) quantitatively enough to get a large decline in labor supply. Intertemporal substitution is pretty problematic as a mechanism in general, since the people whose employment fell the most tended to be the ones who don't have much ability to smooth wages over time and thus can't engage in much intertemporal substitution. . . . 
Anyway, I could go on and on about the ways in which a classical labor supply model is not a good description of reality, and we'd probably agree there. My point is to emphasize that since it's hard to justify the decline in employment in a frictionless model, there are probably some substantial labor market imperfections at work here. And a lot of the most plausible imperfections suggest that we should pursue policies to boost aggregate demand, if only as an application of the theory of the second best.

To be clear, when I hint at the idea that trends in firm dynamics could be affecting the business cycle, I'm not really thinking about a productivity channel. I'm thinking in very rough partial equilibrium terms about the simple fact that high firm growth rates are increasingly rare, so I'm left wondering where we'll get the labor demand "needed" to accommodate growth in the labor force (and also, as a side issue, wondering whether we need the high rates of excess reallocation that we used to see). That's all pretty non-rigorous, basically lump-of-labor reasoning, so it's a long way from being ready for prime time. I don't know how to build a model of this yet, because we still are mostly ignorant about what's driving the trends. But my view is this: either these trends in firm dynamics matter for the cycle or they don't. If they don't, I'm very curious about why they don't. If they do, they may complicate the AD/AS story.


  1. Thanks for the post and comments!

    I agree with you that forces like these may play some role in the short term employment situation. But I view this as more of an invitation to Keynesianism than anything else. (And - just to be clear - by that I don't mean the politically inflected Keynesianism that insists on fiscal stimulus as the core tool of cyclical management, but a somewhat broader tradition involving nominal rigidities and the importance of demand, for which "Keynesian" is an inapt but hard-to-replace descriptor.)

    The reason is simple: often, the kind of rough "partial equilibrium" reasoning that you invoke here is actually the most accurate way to characterize the business cycle! The sophisticated general equilibrium feedbacks suggested by theory are inconsiderately absent in practice. For instance, general equilibrium creates a pervasive force for negative comovement - if, say, factors are being underused in one industry, their price will fall and they will be reallocated to another. Yet at cyclical frequencies, this rarely happens - notably, the basic RBC model predicts that a positive productivity shock will increase employment in the investment goods sector while decreasing employment in the consumption goods sector, but somehow the two tend to move together throughout the cycle.

    Researchers have introduced a million ad hoc kludges to deal with unpleasantness like this, and it's possible that some of those kludges are right. (Though usually, they lead to another layer of empirical puzzles unnoticed by the original researchers, taking still more years and publications to sort through.) But a much more satisfying answer, one that doesn't flagrantly disregard Occam, is that there is some far-reaching force that offsets general equilibrium responses in the short term. And it's not hard to see what that force might be: transmission in general equilibrium happens through prices, and if (for whatever reason) these prices are slow to adjust in practice, there's no reason to expect all that substitution to happen right away.

    The nice thing about this explanation, aside from its (relative) parsimony, is that it is consistent with a few otherwise baffling facts. For instance, it has been known since Mussa that real exchange rates behave very differently based on the nominal exchange rate regime - almost impossible to explain given flexible prices, but very easy given sticky ones. Or, to take a very different example, there's the puzzling fact that the relative price of cars stays roughly constant during a recession, even when production has plummeted and most plausible calculations of the marginal social cost of producing a car imply that it must decline dramatically. (Unless all that unused capital and labor is near-perfectly substitutable toward other industries or toward leisure - and that's just counterfactual.)

    The sticky price and wage viewpoint resolves a huge fraction of the empirical puzzles in general equilibrium macro in one swoop. One can argue that this isn't really a resolution, since it just pushes us to the deeper question of why prices and wages are sticky in the first place. But it's a start, and it's more credible than the alternative program of stumbling around for yet another quick fix every time we run into a new puzzle. (Again, Occam's razor: a single ad-hoc assumption with broad explanatory power is a lot more convincing than a zoo of ad-hoc assumptions tailored to each individual case. Ironically, much of the dissatisfaction with "New Keynesian macro" comes from its recent enthusiastic embrace of the latter. It's unfortunate how the association of nominal rigidities with fit-the-data-at-all-costs, let's-introduce-a-new-shock-for-everything researchers has obscured the essential fact that such rigidities actually offer the most parsimonious way to explain key macroeconomic phenomena.)

  2. So, what does this all have to do with your hypothesis about firm dynamics affecting unemployment? As I mentioned in the first comment, if we use flexible-price general equilibrium models with reasonable calibrations, it's hard to expect much of an effect. Credible labor supply elasticities are simple too low - if a change in firm growth dynamics causes, all else equal, employment to fall substantially, there should be a large downward reaction of real wages, and the resulting blowup in profits will introduce a lot of entry and expansion. I could go on at length about why quantitatively I don't think that the story would work, but my guess is that (conditional on the assumption of, say, a Frisch elasticity well below 1) we're on the same page about this.

    The reason why it could matter nevertheless in the short run is simple: wages are rigid, and people aren't always on their labor supply curves. A shortfall in job creation need not immediately be matched by a commensurate fall in real wages and rise in profits. Hence your mechanisms could be very important - but they're important for the same reasons that the "AD/AS story" matters too.