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

Testing for ARCH

Testing for the presence of ARCH in the errors of your model is straightforward. In fact, there are at least two ways to proceed. The first is to estimate the regression portion of your model using least squares. Then choose the Tests>ARCH from the model’s pull-down menu. This is illustrated in Figure 14.3 below.

This brings up the box where you tell gretl what order of ARCH(q) you want as your alternative hypothesis. In the example, q = 1 which leads to the result obtained in the text. The output is shown below in Figure 14.5. Gretl produces the LM statistic discussed in your text; the relevant part is highlighted in red.

The other way to conduct this test is manually. The first step is to estimate the regression

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The Reduced Form Equations

The reduced form equations express each endogenous variable as a linear function of every exogenous variable in the entire system. So, for our example

Qi =пц + П21 psi + П31 dii + П41 pfi + Vii (11.3)

Pi =П12 + П22 pSi + П32 dii + П42Р/ + Vi2 (11.4)

Since each of the independent variables is exogenous with respect to q and p, the reduced form equations (11.3) and (11.4) can be estimated using least squares. In gretl the script is

1 open "@gretldirdatapoetruffles. gdt"

2 list z = const ps di pf

3 ols q z

4 ols p z

The gretl results appear in Table 11.1 Each of the variables are individually different from zero q = 7.89510 + 0.656402 ps + 2.16716 di – 0.506982 pf

(2.434) (4.605) (3.094) (-4.181)

T = 30 R2 = 0.6625 F(3, 26) = 19.973 <r = 2.6801
(t-statistics in parentheses)

p = -32...

Qualitative and Limited Dependent Variable Models

There are many things in economics that cannot be meaningfully quantified. How you vote in an election, whether you go to graduate school, whether you work for pay, or what college major you choose has no natural way of being quantified. Each of these expresses a quality or condition that you possess. Models of how these decisions are determined by other variables are called qualitative choice or qualitative variable models.

In a binary choice model, the decision you wish to model has only two possible outcomes. You assign artificial numbers to each outcome so that you can do further analysis. In a binary choice model it is conventional to assign ‘1’ to the variable if it possesses a particular quality or if a condition exists and ‘0’ otherwise...

Vector Error Correction and Vector Autoregressive Models: Introduction to Macroeconometrics

The vector autoregression model is a general framework used to describe the dynamic interre­lationship between stationary variables. So, the first step in your analysis should be to determine whether the levels of your data are stationary. If not, take the first differences of your data and try again. Usually, if the levels (or log-levels) of your time-series are not stationary, the first differences will be.

If the time-series are not stationary then the VAR framework needs to be modified to allow consistent estimation of the relationships among the series. The vector error correction model (VECM) is just a special case of the VAR for variables that are stationary in their differences (i. e., I(1)). The VECM can also take into account any cointegrating relationships among the variables.