Category Using gret l for Principles of Econometrics, 4th Edition

Serial Correlation in Residuals

The correlogram can also be used to check whether the assumption that model errors have zero covariance-an important assumption in the proof of the Gauss-Markov theorem. The example that illustrates this is based on the Phillips curve that relates inflation and unemployment. The data used are from Australia and reside in the phillips-aus. gdt dataset.

The model to be estimated is

inf = ві + в2 Аи* + et (9.6)

The data are quarterly and begin in 1987:1. A time-series plot of both series is shown below in Figure 9.10. The graphs show some evidence of serial correlation in both series.


Figure 9.10: This plot shows the relationship between inflation and the change in unemployment in Australia, 1987:1 – 2009:3.

The model is estimated by least squares and the residuals are plotted ag...

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Gretl also has a “session” concept that allows you to save models, graphs, and data files into a common “iconic” space. The session window appears below in Figure 1.12. The session window is very handy. It contains icons that give you immediate access to information about the data set, that opens the edit data window, that display any scalars you have computed, summary statistics, correlations and any notes you may want to make.

Objects are represented as icons and these objects can be saved for later use. When you save your session, the objects you have added should be available again when you re-open the session. To add a model to your session, use the File>Save to session as icon option from the model’s pull-down menu...

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Predictions in the Log-linear Model

In this example, you use the regression to make predictions about the log wage and the level of the wage for a person having 12 years of schooling. The naive prediction of wage merely takes the antilog of the predicted ln(wage). This can be improved upon by using properties of log­normal random variables. It can be shown that if ln(w) N(y.,a2) then E(w) = e^+a2/2 and

var(w) = e2^2 (ef2 — 1).

That means that the corrected prediction is yc = exp(bi + b2x + <t2/2) = e(bl+b2a:)e<j2/2. The script to generate these is given below.

1 open "@gretldirdatapoecps4_small. gdt"

2 logs wage

3 ols l_wage const educ

4 scalar l_wage_12 = $coeff(const)+$coeff(educ)*12

5 scalar nat_pred = exp(l_wage_12)

6 scalar corrected_pred = nat_pred*exp($sigma"2/2)

7 print l_wage_12 nat_pred corrected_pred

The result...

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Testing Equivalence of Two Regions

The question arises, is the wage equation different for the south than for the rest of the country? There are two ways to do this in gretl. One is very easy and the other not so easy, but makes for a useful example of how to use loops to create interactions among variables.

A Chow test is used to test for structural breaks or changes in a regression. In other words, one subsample has different intercept and slopes than another. It can be used to detect structural breaks in time-series models or to determine whether, in our case, the south’s wages are determined differently from those in the rest of the country. The easy method uses gretl’s built-in chow command to test for a change in the regression...

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Multiplier Analysis

Multiplier analysis refers to the effect, and the timing of the effect, of a change in one variable on the outcome of another variable. The simplest form of multiplier analysis is based on a finite distributed lag model

Подпись: (9.19)yt = a + во Xt + PlXt-1 + в2 Xt-2 +——– + в Xt-q + et

Подпись: dE (yt) dxt-s Подпись: es Подпись: (9.20)

The estimated coefficients from this model can be used to produce impact, delay and interim multipliers. The impact multiplier is the impact of a one unit change in xt on the mean of yt. Since X and y are in the same time period the effect is contemporaneous and therefore equal to the initial impact of the change. The s-period delay multiplier is

is the effect of a change in x s-periods in the past on the average value of the dependent variable in the current period...

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