(The Durbin-Watson statistic goes to 2.9, still far from where it should be.) So I added an MA(1) term and an AR(2) term, and this finally seems to be enough to handle the serial correlation problem. So again I fit with an AR(1) term, and again I find that this gets but this time it is not sufficient to get rid of the Durbin-Watson problem. Also as in 2012, I find that the residuals are autocorrelated (a Durbin-Watson statistic of 0.5, far from the ideal 2.0), presumably because the relationship has shifted over time. So I fit the equation with c=0, and I get a=4.52 and b=0.48, which would imply that hires are approximately proportional to the square root of vacancies, the same result I got in 2012.
That shift in the “matching function” suggested a change in the underlying relationship between unemployment and job openings, not just a temporary dynamic effect associated with the time it takes to fill new openings. A closer look at the data, including the additional two years that had passed, showed that, for a given number of job openings, the amount of hiring had declined. At the time, I argued that it was not so: job openings arise, and it takes time for them to reduce the unemployment rate necessarily, there is a period when the unemployment rate remains higher than what would earlier have been associated with that number of job openings. Some saw this pattern as an indication of increased structural unemployment, with job openings becoming harder to fill from a given pool of unemployed. Back in 2010, there was a jump in US job openings (from an extremely low level) that was not accompanied by a commensurate decline in the unemployment rate.