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Economics 310

This lecture discusses polynomial distributed lags (PDL) and their significance in economic modeling. It covers the Koyck restriction that resolves infinite lag problems and illustrates how polynomial lags handle finite lags effectively. Key advantages of PDLs include reduced parameter estimation, improved degrees of freedom, less multicollinearity, and better estimation efficiency. The lecture also explores real interest rates and their relationship with U.S. economic output growth from 1956 to 2000, as well as end-point restrictions and challenges in determining polynomial degree and lag length.

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Economics 310

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  1. Economics 310 Lecture 28 Polynomial Distributed lags

  2. Rational for Polynomial Lags • Koyck restriction solved problem of infinite lag. • Polynomial Lag does same for finite lag. • Reduces number of parameters to be estimated. • Saves degrees of freedom • Reduces multicollinearity and increases efficiency of estimation.

  3. Polynomial Lag Model

  4. Estimating Polynomial Lag

  5. Estimating Polynomial Lag

  6. Model in Matrix Form

  7. Model in Matrix Form

  8. Model in Matrix form

  9. 2nd Degree Polynomial lag

  10. 3rd Degree Polynomial lag

  11. Shazam Command

  12. Shazam example • Rate of growth of real output in U.S. economy from 1956.1 to 2000.1 as function of real interest rate. • Real interest rate = federal funds rate - rate of growth of CPI.

  13. 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

  14. End Point Restrictions • End point restrictions make the model more realistic. • Don’t believe impact starts before period 0. • This is known as a near end point restriction. • If impact ends in period “K”, we have a far end point restriction.

  15. Incorporating end point restriction

  16. Problems with Polynomial Lag • Deciding the degree of the polynomial • Deciding the length of the lag • Data mining.

  17. Tools to decide lag and degree of polynomial

  18. Comparing Alternative models

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