2. The following question is inspired by the Baker and Bernstein reading. Use th

Question

2. The following question is inspired by the Baker and Bernstein reading. Use the accompanying dataset to answer it. The data come from the Federal Reserve Economic Database.

a) Calculating “Unemployment Rate – NAIRU”. What is the median of this variable? Interpret in 2-3 sentences what this means about whether we have more often been above or below full employment since 1964.

b) Calculate the correlation between the Unemployment Rate-NAIRU gap and average weekly hours of production and non-supervisory employees. Report the correlation coefficient, and report whether it is significant at the 95% confidence level. Explain how you arrived at your answer in 2-3 sentences.

Year Unemployment rate NAIRU Unemployment rate - NAIRU Average weekly hours (Production and Nonsupervisory Employees) 1964 5.2 5.6 38.5 1965 4.5 5.7 38.6 1966 3.8 5.8 38.5 1967 3.8 5.8 37.9 1968 3.6 5.8 37.7 1969 3.5 5.9 37.5 1970 5.0 5.9 37.0 1971 6.0 6.0 36.8 1972 5.6 6.1 36.9 1973 4.9 6.1 36.9 1974 5.6 6.2 36.4 1975 8.5 6.2 36.0 1976 7.7 6.2 36.1 1977 7.1 6.2 35.9 1978 6.1 6.3 35.7 1979 5.9 6.3 35.6 1980 7.2 6.2 35.2 1981 7.6 6.2 35.2 1982 9.7 6.1 34.7 1983 9.6 6.1 34.9 1984 7.5 6.1 35.1 1985 7.2 6.0 34.9 1986 7.0 6.0 34.7 1987 6.2 6.0 34.8 1988 5.5 5.9 34.6 1989 5.3 5.9 34.5 1990 5.6 5.9 34.3 1991 6.9 5.8 34.1 1992 7.5 5.7 34.2 1993 6.9 5.5 34.3 1994 6.1 5.4 34.5 1995 5.6 5.3 34.3 1996 5.4 5.2 34.3 1997 4.9 5.1 34.5 1998 4.5 5.1 34.5 1999 4.2 5.0 34.4 2000 4.0 5.0 34.3 2001 4.7 5.0 34.0 2002 5.8 5.0 33.9 2003 6.0 5.0 33.7 2004 5.5 5.0 33.7 2005 5.1 5.0 33.7 2006 4.6 5.0 33.9 2007 4.6 4.9 33.8 2008 5.8 4.9 33.6 2009 9.3 5.0 33.1 2010 9.6 5.1 33.4 2011 8.9 5.2 33.6 2012 8.1 5.1 33.7 2013 7.4 5.0 33.7 2014 6.2 4.9 33.7

Explanation / Answer

a.

Median is 0.2
The interpretation of median 0.2 is that it is the middle most value out of 51 observations. It means 25 observations fall below full employment and 25 observation fall above employment.

b. Correlation coefficient sing excel

=CORREL(Unemployment rate - NAIRU:Average weekly hours (Production and Nonsupervisory Employees)

= -0.58203

To find the singificace level we can use t-test assuming unequal variance in excel where we can compare the "t critical one-tail" with "P(T<=t) one-tail". If the p value is less than t citical value then the correlation is significant.

Year Unemployment rate NAIRU Unemployment rate - NAIRU Average weekly hours (Production and Nonsupervisory Employees) 1964 5.2 5.6 -0.4 38.5 1965 4.5 5.7 -1.2 38.6 1966 3.8 5.8 -2 38.5 1967 3.8 5.8 -2 37.9 1968 3.6 5.8 -2.2 37.7 1969 3.5 5.9 -2.4 37.5 1970 5 5.9 -0.9 37 1971 6 6 0 36.8 1972 5.6 6.1 -0.5 36.9 1973 4.9 6.1 -1.2 36.9 1974 5.6 6.2 -0.6 36.4 1975 8.5 6.2 2.3 36 1976 7.7 6.2 1.5 36.1 1977 7.1 6.2 0.9 35.9 1978 6.1 6.3 -0.2 35.7 1979 5.9 6.3 -0.4 35.6 1980 7.2 6.2 1 35.2 1981 7.6 6.2 1.4 35.2 1982 9.7 6.1 3.6 34.7 1983 9.6 6.1 3.5 34.9 1984 7.5 6.1 1.4 35.1 1985 7.2 6 1.2 34.9 1986 7 6 1 34.7 1987 6.2 6 0.2 34.8 1988 5.5 5.9 -0.4 34.6 1989 5.3 5.9 -0.6 34.5 1990 5.6 5.9 -0.3 34.3 1991 6.9 5.8 1.1 34.1 1992 7.5 5.7 1.8 34.2 1993 6.9 5.5 1.4 34.3 1994 6.1 5.4 0.7 34.5 1995 5.6 5.3 0.3 34.3 1996 5.4 5.2 0.2 34.3 1997 4.9 5.1 -0.2 34.5 1998 4.5 5.1 -0.6 34.5 1999 4.2 5 -0.8 34.4 2000 4 5 -1 34.3 2001 4.7 5 -0.3 34 2002 5.8 5 0.8 33.9 2003 6 5 1 33.7 2004 5.5 5 0.5 33.7 2005 5.1 5 0.1 33.7 2006 4.6 5 -0.4 33.9 2007 4.6 4.9 -0.3 33.8 2008 5.8 4.9 0.9 33.6 2009 9.3 5 4.3 33.1 2010 9.6 5.1 4.5 33.4 2011 8.9 5.2 3.7 33.6 2012 8.1 5.1 3 33.7 2013 7.4 5 2.4 33.7 2014 6.2 4.9 1.3 33.7 Median 5.8 0.2

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