Cyclicality of Real Wages? Counter, pro or acyclical? Is the real wage counter or pro- cyclical? I've read in some textbooks that the real wage is mildly pro-cyclical, but I've also found some papers stating that it's acyclical.

So, which is it? Also, if the real wage is pro-cyclical, does that mean that there's some sort of price rigidity, i.e., the economy is not always on the Price-Setting curve?
Are Wages Procyclical?

Here's the entry from Table 1 in King and Rebelo (2000; Resuscitating Real Business Cycles). The variable of analysis is log-wages, detrended with HP filter. It has a std, relative std, first-order autocorrelation and correlation with output of 0.68, 0.38, 0.66, 0.12. 

This leads the authors to conclude that 


  The real wage is much less volatile than output.


You can see that for their long US period, 0.12 is a positive number, but pretty close to zero. This is why different authors take this number as either acyclical or weakly procyclical. 

Price rigidity required for procyclical wages?

Assume that some sort of fluctuation in TFP "drives" the business cycle. Furthermore, if markets are competitive, the wage rate should be set by the marginal product:

$$ w = AF_L(K, L)$$

If $L$ stays constant over the business cycle (e.g. with inelastic labor supply), this setup will generate wages $w$ that vary with $A$, and hence any change in $A$ will result in a one-for-one change in $w$ and in $Y$: $Y$ and $w$ are perfectly correlated, while $L$ is fixed.

This is pretty much the prediction of the RBC model, and it is the opposite of what we observe in the data: $L$ is volatile, while $w$ is fixed. If you'd assume that $L$ responds strongly to changes in $A$, $w$ might be pretty constant over the business cycle. This is what we observe in reality. 

And most of the labor-side of RBC research is to come up with ways that force $L$ to respond so much.

King and Rebelo (2000) should be a key paper of any introductory reading list for macroeconomics and I strongly recommend reading it.

The case of less competition

If there is literally zero competition, then firms will at all times only pay the household his outside-option value, making him indifferent between working and not working. If that outside option is constant over the business cycle (for which we have to some extent theoretical and empirical arguments), wages will be acyclical.

However, to the extend that there is no perfect monopsony, firms have to compete for workers and offer higher wages whenever workers are worth more. Hence, wages will be procyclical even if, to some extent, firms are not perfectly competitive on the labor side. The more competitive they are, the more pro-cyclical wages should be.

Alternatives and extensions to the neoclassical model

The above model was just a simple one to generate a case in which pro-cyclicality of wages can be generated without price stickiness. There is much more to the subject than an answer here can provide. Here's some more references:


Barro (1977): Long-term contracting, sticky prices, and monetary policy. *Wages are long-term contracts, hence if firms are less risk-averse than workers, firms will insure workers against wage changes over the business cycle and we can observe (optimally) constant wages 
Beadry and DiNardo (1991) is a follow-up on that discussion
Haefke et al (2013, JME) is also a very recent follow-up
Bewley (1999): Why wages don't fall in a recession
Shimer and Hall (two separate papers, both in the same 2005, AER) are the standard references on whether the more modern and reasonable frictional DMP model can match labor (and wage) volatility over the business cycle.