Okun's Law: A Non-Linear Threshold Modeling Approach

The relationship between the Gross National Product of the United States and the Unemployment Rate was first estimated by Arthur Okun using a linear specification in 1962. This relationship became known as Okun’s Law. Since the Great Recession of 2008, policy makers and advisors such as Janet Yellen, Chair of the Federal Reserve Board of Governors, and Christina Romer, former chief economic advisor to the President, among others have questioned the continued validity of Okun’s Law. This paper uses the General Additive Models (GAM) approach from Hastie and Tibshirani to formally test Okun’s Law for nonlinearity. This paper also uses the Multivariate Adaptive Regression Splines (MARS) estimation technique to identify whether threshold levels on the change in GDP exist that would better describe Okun’s Law. A framework for testing a MARS estimation for a structural break in the estimated coefficients is suggested. The model is tested for evidence of a structural break between the pre oil shock period from 1948 until 1973 against the post oil shock driven inflationary period beginning in 1982 and ending in 2012. The model is tested a second time for evidence of a structural break, but now the partitioning of the data follows the theory of the Great Moderation with a before and after period divided at first quarter of 1984. Throughout this paper I investigate both threshold effects and structural breaks. Threshold effects are defined as changes in the value of an estimated coefficient due to a change in the level of the independent variable. A structural break is defined as a change in an estimated coefficient over time; in other words, a change in the estimated coefficient due to a change in the estimation period. The findings support nonlinearity and threshold response. The results regarding the existence of a structural break are mixed. In addition, the MARS estimation suggests that for GDP growth within a threshold around zero there is a zone of no effect of GDP growth on the change in the unemployment rate. Within this zone of no effect, Okun’s law does not statistically exist.