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.    

You to 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

A. Do you believe that prices and wages in your model are covariance stationary? Why or why not, and how could you adjust your model accordingly?

B. You now decide to run another model with the goal of examining how wages have fluctuated during this period.

wage it = *wage it-1 + µit

How would you characterize this model given what we have learned about time series, and how did you arrive at this conclusion?

C. You run the model from Part B and obtain the following results:

Based on these results, what can we say about the relationship between wages this quarter and wages last quarter? Does this affect any of our time series assumptions, and is there an alternative way we could specify our model to accommodate this relationship?

Explanation / Answer

A) The signs of coefficients of Price with Wage is reversing in lags, positive with the price, negative with lag 1, positive with lag 2, and negative with lag 3. Since the covariance is oscitilating, the process/time series does not appear to be stationary.

B) In this model the wage is modeled to depend on its own previous lagged observation,also known as autoregressive model of order 1. However, this model might not be appropriate as the covariate process Price seems to have very good explanatory power of explaining the variance in wage as seen by the very high R2 value.

C) If the fitted model is Wageit = 1.004 *Wageit-1+error, we can say the process is non-stationary as a stationary process would always have the coefficient value lesser than 1.

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