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.
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... Read More
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)... Read More
The structural equations are estimated using two-stage least squares. The basic gretl commands for this estimator are discussed in Chapter 10. The instruments consist of all exogenous variables, i. e., the same variables you use to estimate the reduced form equations (11.3) and (11.4).
The gretl commands to open the truffle data and estimate the structural equations using two – stage least squares are:
1 open "@gretldirdatapoetruffles. gdt"
2 list z = const ps di pf
3 tsls q const p ps di; z
4 tsls q const p pf; z
The second line of the script estimates puts all of the exogenous variables into a list called z. These variables are the ones used to compute the first-stage regression, i. e., the list of instruments. Line 3 estimates the coefficients of the demand equation by TSLS... Read More
The marginal effect of a change in xij on Pi is
= Ф(в 1 + в2Хі2 + взХіз)ві (16.2)
where ф() is the standard normal probability density. That means that the marginal effect depends on all of the parameters of the model as well as the values of the variables themselves. In the travel example, suppose we want to estimate the marginal effect of increasing public transportation time. Given that travel via public transport currently takes 20 (dtime=2) minutes longer than auto, the marginal effect would be
„ , – = ф(ві + @2dtime-) = ф(—0.0644 + 0.3000 x 2)(0.3000) = 0.1037 (16.3)
This computation is easily done in a script:
1 open "@gretldirdatapoetransport. gdt"
2 probit auto const dtime
3 scalar i_20 = $coeff(const)+$coeff(dtime)*2
4 scalar d_20 = dnorm(i_2... Read More