Back in this post, I mentioned that the observed distribution could produce the slight deviation from from a constant price P in the market P:NGDP→NW (aggregate demand sending signals to nominal wages). I'll put a little bit of meat on that claim here. Let's start with a population with a distribution of incomes:
Now let's select some fraction of this distribution to receive a normally distributed raise. This is accomplished by drawing from a Bernoulli distribution and a normal distribution and taking the product; the 0's of the Bernoulli draw mean zero raise and the 1's mean a normally distributed raise. Here is the resulting distribution (over the entire period from 1960-2013):
Compare this with the distribution here. And here is the model result from the sticky wage post (red) alongside this simulation (black), which shows the plausibility of this observed distribution leading to the deviation from sticky wages:
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Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.
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