In Estimating the Original Relationship Between Money Wage Growth and the Unemployment

Essay

In estimating the original relationship between money wage growth and the unemployment rate, Phillips used United Kingdom data from 1861 to 1913 to fit a curve of the following functional form
$\left( \frac { \dot { W } } { W } + \beta _ { 0 } \right) = \beta _ { 1 } \times u r ^ { \beta _ { 2 } } \times e ^ { u } ,$
where $\frac { \dot { W } } { W }$ is the percentage change in money wages and u r is the unemployment rate.
Sketch the function. What role does $\beta _ { 0 }$ play? Can you find a linear transformation that allows you to estimate the above function using OLS? If, after taking logarithms on both sides of the equation, you tried to estimate $\beta _ { 1 } \text { and } \beta _ { 2 }$ using OLS by choosing different values for $\beta _ { 0 }$ by "trial and error procedure" (Phillips's words), what sort of problem might you run into with the left-hand side variable for some of the observations?