2. Economics 310 Lecture 28 Polynomial Distributed lags

3. 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.

4. Polynomial Lag Model

5. Estimating Polynomial Lag

7. Model in Matrix Form

9. Model in Matrix form

10. 2nd Degree Polynomial lag

11. 3rd Degree Polynomial lag

12. Shazam Command

13. Shazam example zRate of growth of real output in U.S. economy from 1956.1 to 2000.1 as function of real interest rate. zReal interest rate = federal funds rate - rate of growth of CPI.

14. Shazam Output |_ols output realint(0.12,2) R-SQUARE = 0.2117 R-SQUARE ADJUSTED = 0.2071 VARIABLE SUM OF LAG COEFS STD ERROR T-RATIO MEAN LAG REALINT 0.50302E-01 0.10232 0.49163 -249.06 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 513 DF P-VALUE CORR. COEFFICIENT AT MEANS REALINT 0.40681 0.7454E-01 5.458 0.000 0.234 0.1759 0.2320 REALINT 0.34633 0.4538E-01 7.632 0.000 0.319 0.1498 0.1970 REALINT 0.28403 0.2628E-01 10.81 0.000 0.431 0.1229 0.1613 REALINT 0.21991 0.2355E-01 9.338 0.000 0.381 0.0952 0.1246 REALINT 0.15397 0.3091E-01 4.981 0.000 0.215 0.0666 0.0871 REALINT 0.86203E-01 0.3736E-01 2.307 0.021 0.101 0.0373 0.0487 REALINT 0.16618E-01 0.3972E-01 0.4184 0.676 0.018 0.0072 0.0094 REALINT -0.54789E-01 0.3741E-01 -1.465 0.144-0.065 -0.0237 -0.0308 REALINT -0.12802 0.3099E-01 -4.130 0.000-0.179 -0.0554 -0.0719 REALINT -0.20306 0.2363E-01 -8.595 0.000-0.355 -0.0879 -0.1140 REALINT -0.27993 0.2623E-01 -10.67 0.000-0.426 -0.1212 -0.1571 REALINT -0.35863 0.4521E-01 -7.932 0.000-0.331 -0.1552 -0.2011 REALINT -0.43914 0.7430E-01 -5.910 0.000-0.252 -0.1900 -0.2461 CONSTANT 3.3298 0.2859 11.65 0.000 0.457 0.0000 0.9611

15. 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.

16. Incorporating end point restriction

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

18. Tools to decide lag and degree of polynomial

19. Comparing Alternative models