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Economics 310

Economics 310. Lecture 27 Distributed Lag Models. Type of Models. If the regression model includes not only the current but also the the lagged (past) values of the explanatory variables (the X’s) it is called a distributed-lag model .

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Economics 310

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  1. Economics 310 Lecture 27 Distributed Lag Models

  2. Type of Models • If the regression model includes not only the current but also the the lagged (past) values of the explanatory variables (the X’s) it is called a distributed-lag model. • If the model includes one or more lagged values of the dependent variable among its explanatory variables, it is called an autoregressive model. This model is know as a dynamic model.

  3. Key Questions • What is the role of lags in economics? • What are the reasons for the lags? • Is there any theoretical justification for the commonly used lagged models in empirical econometrics? • What is the relationship between autoregressive and distributed lag models? • What are the statistical estimation problems?

  4. Role of “Time” or “lag” in Economics

  5. Demonstration of distributed Lag Effect of 1 unit sustained increase in X Y time 0 1 2

  6. Example Distributed Lag Model

  7. Reasons for Lags • Psychological Reasons • Technological Reasons • Institutional Reasons

  8. Estimation of Distributed Lag Models

  9. Problems of Ad-hoc Estimation • No a priori guide to length of lag. • Longer lags => less degrees of freedom • Multicollinearity • Data mining

  10. Koyck Lag

  11. Properties of Koyck Lag

  12. Table of Mean & Median Lags

  13. Problems with koyck Model • We converted a distributed lag model to autoregressive model. • Lag dependent variable on RHS may not be independent of new error • Error term is MA(1). • Model does not satisfy conditions for Durbin-Watson d-test. Must use Durbin h-test.

  14. Gasoline Consumption Example of Koyck Lag

  15. Koyck Lags • Economic rational for Koyck model • Adaptive Expectations • Partial Adjustment • Estimation of Autoregressive models • Method of Instrumental Variables • Detecting autocorrelation • Durbin h-test

  16. Adaptive Expectation Model

  17. Facts about Adaptive Expectation model • Expected value of the independent variable is weighted average of the present and all past values of X. • The estimating equation has a MA(1) process error term.

  18. Partial Adjustment model

  19. Properties of partial adjustment model • Estimating equation looks like Koyck but is different as far as estimation is concerned • Error term is well behaved • In the limit the lagged dependent variable is uncorrelated with the error term • model can be estimated consistently by OLS

  20. Estimating Koyck model • Model can be estimated by maximum likelihood. This is difficult. • Simple method of estimation is instrumental variables.

  21. Instrumental Variable Estimation

  22. Instrumental Variable Estimation Continued

  23. Properties of IV estimators • Estimators are consistent • Estimators are asymptotically unbiased. • Parameter estimates will not be as efficient as the maximum likelihood estimates, but are easier to do.

  24. Testing autoregressive model for autocorrelation

  25. Adaptive expectations example

  26. Shazam commands to estimate adaptive expectations model file output c:\mydocu~1\koyck.out sample 1 30 read (c:\mydocu~1\koyck.prn) invest int sales sample 2 30 genr saleslag=lag(sales) genr investlg=lag(invest) genr intlag=lag(int) inst invest int sales saleslag investlg (int intlag sales saleslag) stop

  27. Results of IV estimation ofmodel |_inst invest int sales saleslag investlg (int intlag sales saleslag) INSTRUMENTAL VARIABLES REGRESSION - DEPENDENT VARIABLE = INVEST 4 INSTRUMENTAL VARIABLES 2 POSSIBLE ENDOGENOUS VARIABLES 29 OBSERVATIONS R-SQUARE = 0.9810 R-SQUARE ADJUSTED = 0.9779 VARIANCE OF THE ESTIMATE-SIGMA**2 = 10.229 STANDARD ERROR OF THE ESTIMATE-SIGMA = 3.1984 SUM OF SQUARED ERRORS-SSE= 245.51 MEAN OF DEPENDENT VARIABLE = 85.817 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 24 DF P-VALUE CORR. COEFFICIENT AT MEANS INT -2.3341 0.2323 -10.05 0.000-0.899 -0.3363 -0.1357 SALES 0.44316 0.2833E-01 15.64 0.000 0.954 0.6131 0.2655 SALESLAG -0.14122 0.3504E-01 -4.030 0.000-0.635 -0.1917 -0.0795 INVESTLG -0.41223 0.7292E-01 -5.653 0.000-0.756 -0.4883 -0.4199 CONSTANT 117.54 4.148 28.34 0.000 0.985 0.0000 1.3696 |_stop

  28. True model

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