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

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...

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Qualitative and Limited Dependent Variable Models

16.1 Probit

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...

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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.

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Using R for Qualitative Choice Models

R is a programming language that can be very useful for estimating sophisticated econometric models. In fact, many statistical procedures have been written for R. Although gretl is very powerful, there are still many things that it won’t do out of the box. The ability to export gretl data into R makes it possible to do some very fancy econometrics with relative ease. The proliferation of new procedures in R comes as some cost though. Although the packages that are published at CRAN (http://cran. r-project. org/) have met certain standards, there is no assurance that any of them do what they intend correctly. Gretl, though open source, is more controlled in its approach...

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Threshold ARCH

Threshold ARCH (TARCH) can also be estimated in gretl, though it requires a little pro­gramming; there aren’t any pull-down menus for this estimator. Instead, we’ll introduce gretl’s powerful mle command that allows user defined (log) likelihood functions to be maximized.

The threshold ARCH model replaces the variance equation (14.3) with

ht = 5 + aief-! + Ydi-ief-! + Aht-i

The model’s parameters are estimated by finding the values that maximize its likelihood. Maximum likelihood estimators are discussed in appendix C of Hill et al. (2011).

Gretl provides a fairly easy way to estimate via maximum likelihood that can be used for a wide range of estimation problems (see chapter 16 for other examples)...

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