*
* Example 4.4 from pages 52-53
*
open data tablef2-2[1].txt
calendar 1960
data(format=prn,org=columns) 1960:1 1995:1 year g pg y pnc puc ppt pd pn ps pop
*
* Form the log variables needed. (The log function in RATS is the natural log).
*
set loggpop = log(g/pop)
set logpg   = log(pg)
set loginc  = log(y)
set logpnc  = log(pnc)
set logpuc  = log(puc)
*
linreg loggpop
# constant logpg loginc logpnc logpuc
*
* You can get the critical value for the t-test with the function %INVTTEST. Note
* that this gives the two-tailed critical value, which is what we want in this
* case. Also note that the degrees of freedom of the regression is in %NDF. The
* estimate of the income elasticity is the 3rd coefficient (thus %BETA(3)) and
* its standard error is %STDERRS(3). Thus, we can do the entire calculation
* without needing to put numbers into a calculator:
*
compute lower=%beta(3)-%invttest(.05,%ndf)*%stderrs(3)
compute upper=%beta(3)+%invttest(.05,%ndf)*%stderrs(3)
disp
disp "95% confidence interval for income elasticity" lower upper
*
* Test-statistic. The text makes a slight error here. Because the test is
* one-sided, not two, the .05 critical value should be from the .05 column in the
* table, not the .025. When done with RATS, you use .10 on %INVTTEST, as the
* function assumes a two-tailed test. An alternative way to do a test like this
* is to compute the marginal significance level or p-value. If this is less than
* the desired level (say .05), the null is rejected. This is done with the %TTEST
* function. Since that also is designed for a two-tailed test, the resulting
* p-value needs to be doubled.
*
compute tstat=(%beta(3)-1)/%stderrs(3)
disp "Test Statistic for unitary elasticity" tstat
disp "Critical value" %invttest(.10,%ndf)
disp "P-value" #.###### 2*%ttest(tstat,%ndf)