You collect unadjusted, quarterly data on nominal wages, unemployment, and price

Question

You collect unadjusted, quarterly data on nominal wages, unemployment, and prices in the United States from 1940 through 2011 from the United States Bureau of Labor and Statistics. Wages are the median wage in the United States in each quarter, the unemployment rate is reported for each quarter, and price is an index based on the Consumer Price Index in each quarter.    

A. Can we use the data as is to run a reliable regression of the unemployment rate on wages? Why or why not, and is there any way we could transform the data into something more reliable?

B. You next decide to further examine the relationship between wages and prices over this time period. You run a regression of ln(wage) on price and lagged price and obtain the following results (standard errors in parentheses):

ln(wage) it = 0.576 + 0.041*price it – 0.0224*price it-1 + 0.016*price it-2 – 0.029*price it-3 + µit

                            (0.013) (0.01)                 (0.008)                   (0.019)                  (0.01)

N = 284, R2 = 0.958

What is the temporary and permanent impact of an increase in prices on wages based on these results?

C. Can we say that this model has a strong goodness-of-fit using the information from part B? Why or why not?

Explanation / Answer

This being a statistics forum , we will focus on the statistical analysis fo the question and not on the economic analysis as it is out of scope of the forum,

a) yes , based on the data it is possible to fit a regression equation as all the variables under consideration are continous in nature and can be measured on a number scale . both wage and rice are continous in nature

b)

ln(wage) it = 0.576 + 0.041*price it – 0.0224*price it-1 + 0.016*price it-2 – 0.029*price it-3 + µit

                            (0.013) (0.01)                 (0.008)                   (0.019)                  (0.01)

the equatin suggests that for every unit increase in the price of the current month the wages would increase by a factor of coefficient of price it , which is 0.041 . For every unit change in the price of the current -1 month , the wage would decrease by a factor of 0.0224

c) yes the model is a good fit , as the r2 value is high and is 0.958 , which means that model is able to explain 96% of the variation of the data . R2 value ranges from 0 to 1 . Higher the r2 value better the model fitment or goodness of fit of the model

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