Facts show that real Real wages (RW) are acyclical or very little procyclical. In Keynes (1936) RW are procyclical, but he correct this issue in Keynes (1937). Instead, Kalecky allways thought (and he wrote on this topic) that RW are acyclical.
All references to Keynes are, sorry, ineffectual in an environment that defies recognition by past parameters, save, perhaps by those of the 19th century, when last was witnessed the kine of capital coagulation we have today - on a much smaller scale.
I won't present the argument here that this coagulation is creating economic devastation, on a scale that the so-called modern world has yet seen. (there are advantages of course - the oligarchies, at most times dwarfing political entities - are less likely to engage to wasteful conflicts (but then, there'll always be Bush families.)
As an empirical matter in the U.S. real wages fell in recession from the 1960s until the turn of the century. The recession of 2001 was a deflationary recession and prices slowed ahead of wages. The 2007-09 recession was a little different as real wages fell in 2008 and then oil prices collapsed.
I accidently posted when I tried (unsuccessfully) to include a chart in this post. It seems that this is not something that can be done. I was going to add that there are really two real wages. From the perspective of the worker, the real wage that matters is the consumption basket real wage (say wages/CPI). From the employers perspective, the real wage that matters is the production basket real wage (say wages/PPI). All kinds of factors can affect the relationship between PPI and CPI including taxes, currency movements, and commodity prices. My observation about real wages in recession was framed in terms of CPI and I view it as a function of monetary policy. Before 2000, recessions occurred when the Fed jammed on the monetary brakes to arrest an inflation that was getting out of hand. The resulting recession hit employment and the pricing power of labor resulting in a fall in real wages. The recession of 2001 was different because the Fed was tightening because the economy was growing strongly as a result of the disinflationary impetus from the internet and tech boom. As for Keynes, he argued that the movements in real wages were not a cause of employment shifts but a consequence of them (Joan Robinson described the as his Marshallian Baggage).
Dr. Ryding's answer is complete and comprehensive.
There are two real wages: product wage and consumption wage.
Product wages are a consequence of shifts in employment demand and may be acyclical, meaning that there may be no definite correlation between them and the business cycle.
He cites empirical evidence to show pro-cyclical movement of consumption wages for most part since the sixties, excepting a recent recession. This may be because of downward stickiness in prices was stronger than the downward stickiness of money wages in the US.
Whether this was happenstance, or whether there is some regularity in this is a matter of empirical studies across countries.