Clearing Labor Markets and Unemployment

Bob Murphy has been asking questions about sticky wages (here, here), and Stephen Williamson talks about sticky wages as the primary Keynesian "tweak" to the standard neoclassical growth model that everyone is taught. I personally have a tough time knowing exactly how invested to get in this. Of course wages are actually downwardly rigid, I don't second guess that. Certainly that's going to add to unemployment. But I personally have a hard time understanding how this is a major cause of unemployment.

The implicit assumption is that a clearing labor market is a labor market without unemployment. That just seems wrong to me. We care about how markets clear because we think markets have a tendency to clear under normal circumstances. So it makes sense that we would want to pay attention to (1.) the forces that bring about that clearance, (2.) perhaps the special cases that would disturb a clearing market, and (3.) some insight into where that market clears - where quantity and price settle or at least where they tend towards. If you want to understand market quantities and prices, knowing how markets clear is important.

But unemployment is different. A lot of people sort of implicitly assume that unemployment is the same as a labor surplus, so that if they can explain why firms that would hire labor at a given wage might coexist with workers who would take a job at a given wage, they are "explaining unemployment". But this concept of labor surplus has little to do with the empirical phenomenon of unemployment that ostensibly we're interested in explaining. When people talk about "the unemployment rate" in the United States they are refering to the Bureau of Labor Statistics (BLS) definition: the share of the labor force that wants to work, is ready to start work, and is actively looking for work. Some people also care about those who want to work but aren't actively looking out of frustration, so the BLS also produces other figures to include these workers too. That definition is more or less how we think about "unemployment" in our own lives, right?

Notice what's missing from that, though. The reservation wage. As an empirical phenomenon, we really don't care about the relationship between a person's reservation wage and the market clearing wage when we identify this phenomenon called "unemployment". So why does it play such an important role in how we theorize about the causes of unemployment?

And what is "unemployment" in a simple model of the labor market? The "unemployed" are actually the workers between the equilibrium quantity and the upper right point of the labor supply curve. I've illustrated this here:


So for me, explaining what causes fluctuations in the quantity of labor (i.e. - impact of liquidity preference on investment demand and multiplier effects on consumption) or explaining why people might be in the labor market looking for work but not working (i.e. - search theory) seems a lot more important than explaining how labor surpluses can crop up (i.e. - sticky wages). I don't really know why I should even care about labor surpluses in and of themselves. I'd personally rather have an economy with a relatively high labor surplus and relatively low unemployment than an economy with relatively low (or zero) labor surplus and relatively high unemployment.

So part of me just wants to concede the point on sticky wages. Let's say all this sticky wages stuff is a red herring. Now, with that out of the way and the market cleared, is it cleared at a level where everyone that wants work is working? If not, why not?