Economics 310 Lecture 28 Polynomial Distributed lags

Rational for Polynomial Lags zKoyck restriction solved problem of infinite lag. zPolynomial Lag does same for finite lag. yReduces number of parameters to be estimated. ySaves degrees of freedom yReduces multicollinearity and increases efficiency of estimation.

Polynomial Lag Model

Estimating Polynomial Lag

Model in Matrix Form

Model in Matrix form

2nd Degree Polynomial lag

3rd Degree Polynomial lag

Shazam Command

Shazam example zRate of growth of real output in U.S. economy from to as function of real interest rate. zReal interest rate = federal funds rate - rate of growth of CPI.

Shazam Output |_ols output realint(0.12,2) R-SQUARE = R-SQUARE ADJUSTED = VARIABLE SUM OF LAG COEFS STD ERROR T-RATIO MEAN LAG REALINT E VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 513 DF P-VALUE CORR. COEFFICIENT AT MEANS REALINT E REALINT E REALINT E REALINT E REALINT E REALINT E E REALINT E E REALINT E E REALINT E REALINT E REALINT E REALINT E REALINT E CONSTANT

End Point Restrictions zEnd point restrictions make the model more realistic. zDon’t believe impact starts before period 0. yThis is known as a near end point restriction. zIf impact ends in period “K”, we have a far end point restriction.

Incorporating end point restriction

Problems with Polynomial Lag zDeciding the degree of the polynomial zDeciding the length of the lag zData mining.

Tools to decide lag and degree of polynomial

Comparing Alternative models