This post is about the impact of nominal and real wage flexibility on unemployment and the output gap. It starts in an academic, abstract sort of way, but the policy implications do follow. I try and make the analysis as accessible as I can to non-economists.
Start with an economy with a zero output gap (defined below) and no involuntary unemployment. Everything in the economy is just fine, which is a non-technical way of saying it is efficient. Then a ‘crisis’ happens that leads consumers to consume less and save more, so aggregate demand falls. Normally in these situations the central bank cuts nominal and real interest rates sufficiently to restore aggregate demand. Once this has happened, call everything in this economy ‘natural’, so the real interest rate that restores demand is the natural rate of interest. The natural level of output may not be the same as the pre-crisis level, because for example the new natural rate of interest can have knock on effects on how much people want to work.  However the natural level is the level of output that policymakers should aim for. 
In the Great Recession this mechanism did not work because nominal interest rates hit zero, and maybe also because monetary policy put a cap on inflation expectations. As a result, actual real interest rates are above the natural level. In addition, fiscal policy is in the hands of people who know nothing about macroeconomics, so there is no help from there. However monetary policymakers still think they could do something ‘unconventional’, so they want to know what to aim for. The answer is that, as long as what they do does not seriously distort the economy, they should try to get to the natural level of output, because that produces an efficient economy.
The difference between the actual level of output and the hypothetical natural level is called the output gap. The traditional way of defining the output gap was the difference between actual output and ‘productive potential’, which was the amount that could be produced if all factors of production were fully utilised. That is still how the gap is often measured in practice, although the measurement problems can still be huge, as Paul Krugman notes here. The problem at a conceptual level is that this approach downplays considerations of optimality, so nowadays theoretical macroeconomics uses the natural level of output to define the output gap. This has the advantage that we know what policy should be aiming to do: achieving the natural level of output.
Now imagine three almost identical economies where an output gap exists because nominal interest rates have hit zero. The level of real interest rates that would eliminate the output gap is the same in all three economies (i.e. they have the same natural levels of output). In the first economy, workers resist nominal wage cuts, so this puts a floor on how much unemployment reduces real wages. (Equally firms may be reluctant to impose wage cuts, as this research suggests - HT Kevin O’Rourke.) If nominal wages stop falling, at some point firms will stop cutting prices to protect their profits. We settle down to a new lower level of demand deficient output, high unemployment, but stable wages and prices. There is plenty for unconventional monetary policy to do, even though inflation is not falling.
In the two other economies nominal wages carry on falling. In the second economy prices get cut pari passu, so real wages remain unchanged, while in the third they do not, so real wages fall. So in the second economy inflation is lower than in the first, but real wages are the same. Does this lower rate of inflation increase or decrease the output gap? That depends only on whether actual output falls or increases because of lower inflation: the natural level of output involves a hypothetical economy which is unaffected by whether nominal wages fall or not in the actual economy . Actual output may fall if negative inflation makes debtors spend a lot less but creditors not much more - this and other mechanisms are discussed in Mark Thoma’s post here. However, if monetary policymakers have been inhibited from doing much because inflation was not falling (which would be one interpretation of UK policy, for example), then as David Beckworth says, lower inflation may raise actual output by encouraging expansionary unconventional monetary policy.
How about the third economy, where real wages have fallen? Suppose firms respond to lower real wages by substituting labour for capital, and this process continues until all those who want to work can find a job. So in the third economy involuntary unemployment goes away. But is the output gap any lower? Once again, the natural level of output has not changed. (It was set in our hypothetical economy where real interest rates fell to their natural level.) So the key question becomes whether lower real wages and lower unemployment reduces or increases aggregate demand, and therefore actual output. It could go either way. So it is perfectly possible that both actual output and therefore the output gap is exactly the same in all three economies, even though unemployment has returned to its natural rate in one, and the other two have very different inflation rates.
This comparison suggests that those who say unemployment in the first two economies is caused by wage inflexibility kind of miss the point. The basic problem is lack of aggregate demand. You could argue (I would) that the third economy is better off than the other two, because the pain of deficient demand is evenly spread (everyone has lower real wages), rather than being concentrated among the unemployed. But the first best solution is to raise aggregate demand, because that gets rid of the pain.
I started writing this post because of a recent study by Pessoa and van Reenan, who argue that the mysterious decline in UK labour productivity that I have talked about before can in large part be explained by unusually slow growth in UK real wages. The mechanism they have in mind is entirely traditional: if real wages are low firms substitute labour for capital. This in turn may explain (see Neil Irwin here for example) why UK unemployment originally rose by less than in the US (see first chart), even though the UK’s output performance was worse. On this issue looking at consumer price based measures of real wages will be misleading, so below is a very simple measure of real product wage growth in the two countries: compensation per employee less the GDP deflator. Real wage growth in the UK has noticeably fallen since the recession, whereas the fall has at least been less abrupt in the US (2013 is a forecast).
|Unemployment in the US and UK: Source ONS and BLS|
|Growth in compensation per employee less GDP deflator: OECD Economic Outlook|
In terms of just the UK economy, whether Pessoa and van Reenan are right is debatable. When I discussed this in an earlier post I referenced a Bank of England paper by MPC member Ben Broadbent, which argued that for the factor substitution story to explain most of what we have seen in the UK, investment should have completely collapsed, which it has not. This difference in view reflects a number of nitty gritty issues, like how you measure the capital stock, and whether the substitution elasticity is one (as implied by the Cobb Douglas production function), or nearer one half.
However most seem to agree that some of this factor substitution is going on in the UK. So my hypothetical discussion above suggests that, by spreading the pain of deficient aggregate demand further, this ‘real wage flexibility’ in the UK has been a good thing, but it does not mean the aggregate demand problem has decreased. If anything, it suggests that looking at unemployment underestimates the size of the output gap. Monetary policy makers please note.
 New Keynesian economists sometimes call the natural economy the outcome when all prices are completely flexible. That is OK, as long as we note that flexible prices here has to include the possibility that nominal interest rate can go negative, which in the real world it cannot.
 Opinions may differ on whether the crisis itself is a necessary correction for past errors, or whether it is itself a distortion. For example, was risk undervalued before the crisis, or is it overvalued now. In other words, was the pre-crisis economy efficient, or would there be a distortion in the post-crisis economy even without an aggregate demand problem? These are important complications compared to the story I tell here, but they will have to wait for another post.
 The idea is that the economies are identical except for the extent of nominal inertia in goods and labour markets. In economy 1 wages are sticky, in economy 3 prices are sticky but wages are flexible, and in economy 2 the degree of wage and price stickiness is such that real wages do not change.