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hintsps2SP06

# hintsps2SP06 - Hints to Problem Set 2 Pablo D'Erasmo 1 DATA...

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Hints to Problem Set # 2 Pablo D’Erasmo * January 26, 2006 1. DATA Download the variables from FRED (the Federal Reserve Bank of St. Louis Economic Database at http://research.stlouisfed.org/fred2/ Construct the quarterly unemployment rate as an average of the monthly rates. Timing of the variables and shocks is very important in this model. Thus, make sure to pair GNP growth rates and unemployment data correspondingly. 2. VAR to VMA The Matlab command to run a regression of y on X is “regress(y,X)”, where y (n × 1) is the dependent variable and X (n × p) is the matrix of p independent variables, in this case the number of lags p = 8. Run two OLS regressions (one for Δ y and other for u to find the 32 coefficients). If the command “regress”is not available in your version of Matlab, you can fin the coefficients by computing ( X X ) - 1 X y for each equation. As the VAR(8) process is covariance stationary (we take this as true), the lag polynomial: ( I n - B 1 L - B 2 L 2 - ... - B 8 L 8 ) (1) is invertible, where B i are the (2 × 2) matrices representing the regression coeffi- cients. In general, the inverse is given by the following form:

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