5 An investigator analysing the relationship between wages and unemploy- ment starts by estimating the following static linear regression model using aggregate time series data Wt = Bot BIPt + Bout + Et, where we is the logarithm of the nominal wage, p, the logarithm of the price level, and Up the unemployment rate (measured as a percentage). (a) A colleague criticises the investigator's estimates of this regression on the grounds that, since wages and prices are trended, the result- ing relationship is 'spurious'. Explain what is meant by a spurious regression, and how you might detect it. (b) The investigator now reformulates his regression to allow for dynamic effects, so that it takes the form Wt = 00 + 01p: + 02p1-1 + 030/ + 04U-1 + 0501-1 + Et Explain how you could use estimates of the coefficients of this regres- sion to compute the long run effect of a higher price level on nominal wages. (c) A second colleague now argues that the regression should be refor- mulated so that nominal wages are allowed to respond to movements in the expected price level p;, so that it becomes W = bo + Gip; + 02p-1 + 03Ut + 0401-1+ 05we-1 + Et Suggest two strategies which you might employ to estimate such a regression