You have two difference stationary series that are cointegrated. Consequently, an error correction model of the short-run dynamics can be estimated using least squares. A simple error
and the estimates
AaUst = 0.491706+—0.0987029et_ 1
Ausat = 0.509884 ++0.0302501et_ 1
(t-statistics in parentheses)
which are produced using
1 ols diff(aus) const uhat(-1)
2 ols diff(usa) const uhat(-1)
The significant negative coefficient on et-1 indicates that Australian GDP responds to a temporary disequilibrium between the U. S. and Australia.
The U. S. does not appear to respond to a disequilibrium between the two economies; the t-ratio on et-1 is insignificant. These results support the idea that economic conditions in Australia depend on those in the U. S... Read More
Another feature of gretl that makes it extremely powerful is its ability to work with another free program called R. R is actually a programming language for which many statistical procedures have been written. Although gretl is powerful, there are still many things that it won’t do, at least without some additional programming. The ability to export gretl data into R makes it possible to do some sophisticated analysis with relative ease.
Quoting from the R web site
R is a system for statistical computation and graphics. It consists of a language plus a run-time environment with graphics, a debugger, access to certain system functions, and the ability to run programs stored in script files.
The design of R has been heavily influenced by two existing languages: Becker, Chambers & Wilks’ ... Read More
To test for weak instruments, regress each independent variable suspected of being contemporaneously correlated with the error (xk) onto all of the instruments (internal and external). Suppose xK is the endogenous regressor. The first stage regression is:
xk = Yi + Y2X2 +—– + Y к-1XK-1 + вігі +——- + Olzl + vk (10.5)
In this notation, the z1, …, zl are the external instruments. The others, x2, …, zk-1 are exogenous and are used as instruments for themselves (i. e., internal to the model). If the F – statistic associated with the hypothesis that the coefficients on the external instruments, в1, …, eL are jointly zero is less than 10, then you conclude that the instruments are weak. If it is greater than 10, you conclude that the instruments are strong enough... Read More
The model (15.2) is reestimated using fixed effects. Race and education do not change for individuals in the sample, and their influences cannot be estimated using fixed effects.
1 open "c:Program Filesgretldatapoenels_panel. gdt"
2 list xvars = const educ exper exper2 tenure tenure2 south union black
3 panel lwage xvars —fixed-effects
4 xvars -= educ black
5 panel lwage xvars —fixed-effects
Even though the parameters for black and educ are not identified in this model, we included them anyway in line 3 just to see how gretl handles this. The results are:
Fixed-effects, using 3580 observations
Included 716 cross-sectional units
Time-series length = 5
Dependent variable: lwage
The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www. gnu. org/copyleft/.
Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License “or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation... Read More
It is possible to estimate a regression and find a statistically significant relationship even if none exists. In time-series analysis this is actually a common occurrence when data are not stationary. This example uses two data series, rwl and rw2, that were generated as independent random walks.
rw 1 : yt = yt-1 + vu (12 1)
The errors are independent standard normal random deviates generated using a pseudo-random number generator. As you can see, Xt and yt are not related in any way. To explore the empirical relationship between these unrelated series, load the spurious. gdt data and declare the data to be time-series.
1 open "@gretldirdatapoespurious. gdt"
2 setobs 1 1 —special-time-series
The sample information at the bottom of the main gretl window indicates that the data have alrea... Read More