Economics 310 Lecture 27 Distributed Lag Models
Dec 20, 2015
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.
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?
Role of “Time” or “lag” in Economics
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SUMMARY OUTPUT
Regression StatisticsMultiple R 0.22076461R Square 0.04873701Adjusted R Square 0.03447825Standard Error 3.02573705Observations 475
ANOVAdf SS MS F Significance F
Regression 7 219.0471264 31.29245 3.41804 0.001418212Residual 467 4275.424556 9.155085Total 474 4494.471682
Coefficients Standard Error t Stat P-value Lower 95%Intercept 3.10859938 0.362060615 8.585853 1.35E-16 2.39713063mg 0.25615126 0.424810093 0.602978 0.546816 -0.578623619mg-1 -0.3547323 0.859144959 -0.41289 0.679877 -2.042998759mg-2 0.04661922 0.955379154 0.048797 0.961102 -1.83075265mg-3 -0.03928199 0.960509863 -0.0409 0.967395 -1.926735984mg-4 0.19367237 0.953796304 0.203054 0.839181 -1.68058911mg-5 -0.62968985 0.857586208 -0.73426 0.46316 -2.314893275mg-6 0.72688165 0.424265971 1.713269 0.087327 -0.106823999
Estimation of Distributed Lag Models
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Problems with koyck Model We converted a distributed lag
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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.
Gasoline Consumption Example of Koyck Lag
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.988322853R Square 0.976782062Adjusted R Square 0.973879819Standard Error 0.268219836Observations 19
ANOVAdf SS MS F Significance F
Regression 2 48.42568707 24.21284 336.5612 8.4448E-14Residual 16 1.151070089 0.071942Total 18 49.57675716
Coefficients Standard Error t Stat P-value Lower 95%Intercept 6.860131612 1.534694078 4.470032 0.000387 3.606726238Relative Price -2.29831002 0.384178333 -5.9824 1.91E-05 -3.11273153Lag Consumption 0.791345188 0.059796617 13.23395 4.92E-10 0.66458205
Koyck Lags Economic rational for Koyck model
Adaptive Expectations Partial Adjustment
Estimation of Autoregressive models Method of Instrumental Variables
Detecting autocorrelation Durbin h-test
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Partial Adjustment model
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model can be estimated consistently by OLS
Estimating Koyck model Model can be estimated by
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Simple method of estimation is instrumental variables.
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Shazam commands to estimate adaptive expectations model
file output c:\mydocu~1\koyck.outsample 1 30read (c:\mydocu~1\koyck.prn) invest int salessample 2 30genr saleslag=lag(sales)genr investlg=lag(invest)genr intlag=lag(int)inst invest int sales saleslag investlg (int intlag sales saleslag)stop
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