This project has two parts, A and B.
A. Consider Koenig’s second regression:
∆y = β (pmi – δ) + γ ∆pmi.
∆y is real GDP/GNP growth as the dependent variable. PMI and ∆PMI are the right-hand side variables as defined by Evan Koenig, (2002), “Using the Purchasing Managers’ Index to Assess the Economy’s Strength and the Likely Direction of Monetary Policy,” Federal Reserve Bank of Dallas Economic and Financial Policy Review, Vol. 1, No. 6.
Run a simple OLS regression: ∆y = α + β. PMI + γ ∆PMI + u, using the sample period 1979:06 – 2014:02. The variable u is the usual regression error with zero expectation. Find out the implied threshold value δ and the coefficient of PMI from this linear regression. Run also the non-linear regression ∆y = β (PMI + δ) + γ ∆PMI to confirm your estimate of δ. Test the null hypothesis that δ is 0.50.
Use both real-time and revised GDP growth data that I have supplied to you and compare the results with the possible explanations for any differences. You have to collect the monthly PMI data from the ISM website or FRED database at the Federal Reserve Bank of St. Louis website. The GDP growth values (real-time and currently revised) are given as an Excel attachment.
Note: Be careful when you generate the variables. You have to follow Koenig precisely and his footnote 8.
B. Nowcasting using Mixed Data Sampling ( MIDAS ) regression:
Determine the individual contributions of three intra-quarterly (monthly) PMI’s in nowcasting quarterly real GDP growth (do this with real-time data only) using your data set. For example, in prediction GDP growth for the first quarter, use the PMI values for January (announced at the beginning of February), February (announced at the beginning of March) and March (announced at the beginning of April. You have to define three such variables. Thus, you will run a simple regression of ∆y on a constant and 3 variables pmi1, pmi2, and pmi3, where pmi1 takes only (January, April, July, Oct) values, pmi2 takes (Feb, May, Aug, Nov) values, and pmi3 takes (March, June, Sept, Dec) values. Thus, in this regression, all your variables are quarterly, and monthly PMI values have been converted into three separate variables each representing the first, the second and third month of each quarter.
Submit a typed report of 2-3 pages with regression results and your commentary. The report should not look clumsy. You can add a graph comparing real GDP growth and PMI (quarterly averages).
WARNING: Please is careful when you generate the variables. You have to follow Koenig precisely and his footnote #8. With your report, including the last 20 values of ∆y, PMI, and ∆PMI at quarterly frequencies. Your work will have no value of you can’t generate these values correctly. I suggest using Excel.
Discuss data issues with classmates and make sure all of you are using the same data before doing the regressions. There is only one truth!