Using gret l for Principles of Econometrics, 4th Edition

Finite Distributed Lags

Finite distributed lag models contain independent variables and their lags as regressors.

Vi = a + воXt + ві%і-1 + в2Xt-2 + ... PqXt-q + Є (9.1)

for t = q + 1,... ,T. The particular example considered here is an examination of Okun’s Law. In this model the change in the unemployment rate from one period to the next depends on the rate of growth of output in the economy.

ut - ut-i = - y(gt - gw) (9.2)

where ut is the unemployment rate, gt is GDP growth, and gw is the normal rate of GDP growth. The regression model is

Aut = a + во gt + et (9.3)

where A is the difference operator, a = yGn, and во = — Y. An error term has been added to the model. The difference operator, Au = ut — ut-1 for all = 2,3,..., T. Notice that when you take the difference of a series, you will lose an observation.

Recognizing that changes in output are likely to have a distributed-lag effect on unemployment - not all of the effect will take place instantaneously-lags are added to the model to produce:

Aut = a + во gt + Plgt-1 + P2gt-2 +--------- + Pq gt-q + et (9.4)

Подпись: Unemployment Rate Rea' GDP

U. S. 1985:3 - 2009:3




Figure 9.3: Time-Series graphs of Okun data


Figure 9.4: Multiple time-series graphs of Okun data produced using View>Multiple

graphs>Time-series. This uses the scatters command.


D. Unemployment Rate


Real GDP growth


0.4 -


0 -




1998 2004 2010








2004 2010




Figure 9.5: Change in unemployment and real GDP growth. This uses the scatters command.

The differences of the unemployment rate are taken and the series plotted in Figure 9.5 below. and this will produce a single graph that looks like those in Figure 9.4 of POE4. To estimate a finite distributed lag model in gretl is quite simple using the lag operators. Letting q = 3 and

1 diff u

2 ols d_u const g(0 to -3)

This syntax is particularly pleasing. First, the diff varname function is used to add the first difference of any series that follow; the new series is called d_varname. Next, the contemporaneous and lagged values of g can be succinctly written g(0 to -3). That tells gretl to use the variable named g and to include g, gt-1, gt-2, and gt-3. When the lagged values of g are used in the regression, they are actually being created and added to the dataset. The names are g_number. The number after the underline tells you the lag position. For instance, g_2 is g lagged two time periods. The new variables are given ID numbers and added to the variable list in the main gretl window as shown in Figure 9.6.

The regression output that uses the new variables is:

OLS, using observations 1986:1-2009:3 (T = 95)
Dependent variable: d_u


Std. Error




























Mean dependent var Sum squared resid R[67]

F(4, 90) Log-likelihood Schwarz criterion p

Подпись:0.027368 S. D. dependent var 2.735164 S. E. of regression 0.652406 Adjusted R2 42.23065 P-value(F) 33.71590 Akaike criterion -44.66241 Hannan-Quinn 0.358631 Durbin-Watson

Notice that the t-ratio on g_3 is not significantly different from zero at 10%. We drop it and
reestimate the model with only 2 lagged values of g. For comparison, the sample is held constant.


Figure 9.6: Notice that the lagged variables used in the model are added to the list of available series. They also receive ID numbers.

The AIC reported by gretl has fallen to -59.42303, indicating a marginal improvement in the model.

If you are using the GUI rather than a gretl script to estimate the model, you have the opportunity to create the lagged variables through a dialog box. The specify model dialog and the lag order dialog are shown in Figure 9.7 below.

Добавить комментарий

Using gret l for Principles of Econometrics, 4th Edition


In appendix 10F of POE4, the authors conduct a Monte Carlo experiment comparing the performance of OLS and TSLS. The basic simulation is based on the model y = x …

Hausman Test

The Hausman test probes the consistency of the random effects estimator. The null hypothesis is that these estimates are consistent-that is, that the requirement of orthogonality of the model’s errors …

Time-Varying Volatility and ARCH Models: Introduction to Financial Econometrics

In this chapter we’ll estimate several models in which the variance of the dependent variable changes over time. These are broadly referred to as ARCH (autoregressive conditional heteroskedas - ticity) …

Как с нами связаться:

тел./факс +38 05235  77193 Бухгалтерия
+38 050 512 11 94 — гл. инженер-менеджер (продажи всего оборудования)

+38 050 457 13 30 — Рашид - продажи новинок
Схема проезда к производственному офису:
Схема проезда к МСД

Партнеры МСД

Контакты для заказов шлакоблочного оборудования:

+38 096 992 9559 Инна (вайбер, вацап, телеграм)
Эл. почта:

За услуги или товары возможен прием платежей Онпай: Платежи ОнПай