*
* RATS Program for Fama efficient markets analysis
* pp 176-182, based upon pp 150-158
*
cal(m) 1950:2
*
* Read in data
*   column 1: year
*   column 2: month
*   column 3: 1-month inflation rate
*   column 4: 3-month inflation rate
*   column 5: 1-month T-bill rate
*   column 6: 3-month T-bill rate
*   column 7: cpi
*
open data mishkin.xls
data(org=columns,format=xls) 1950:2 1990:12 year month pai1 pai3 tb1 tb3 cpi

*
* create variables
*
set pai = ((cpi/cpi{1})**12-1)*100
set r   = tb1-pai

graph(footer="Figure 2.3 Inflation and Interest Rates",key=below,$
  klabels=||"1-month T-bill rate","Inflation rate"||) 2
# tb1
# pai
graph(footer="Figure 2.4 Real Interest Rates")
# r

*
* Part (d): test for serial correlation
* simple statistics
*
* METHOD=YULE is used to get the statistics shown in the text. The default method
* for RATS versions 5 and later is METHOD=BURG, which gives similar results when
* the autocorrelations are small, but more accurate results when they are close
* to 1.
*
table 1953:1 1971:7 tb1 pai r
correlate(qstats,number=12,span=1,method=yule) r 1953:1 1971:7

*
* Part (e): Fama regressions 1953:1 to 1971:7
* w/o conditional homoskedasticity
*
linreg(robusterrors) pai 1953:1 1971:7;# constant tb1
test;# 2;# 1
*
* Part (f): Conditional heteroskedasticity with various
* finite-sample corrections
*
linreg(noprint) pai 1953:1 1971:7 resids ;# constant tb1
compute xxols=%xx
prj(xvx=p)
*
* With degrees of freedom correction
*
mcov(lastreg) / resids
linreg(create,lastreg,form=chisq,$
   covmat=xxols*%cmom*xxols*(float(%nobs)/%ndf),$
   title="OLS with DM Adjustment to White Std Errors")
test;# 2;# 1
*
* With (1-p)**1 correction - divide resids by sqrt(1-p) so that squaring will get
* the right factor.
*
set p1resids = resids/sqrt(1-p)
mcov(lastreg) / p1resids
linreg(create,lastreg,form=chisq,$
   covmat=xxols*%cmom*xxols,$
   title="OLS with DM (p=1) Standard Errors")
test;# 2;# 1
*
* With (1-p)**2 correction
*
set p2resids = resids/(1-p)
mcov(lastreg) / p2resids
linreg(create,lastreg,form=chisq,$
   covmat=xxols*%cmom*xxols,$
   title="OLS with DM (p=2) Standard Errors")
test;# 2;# 1
*
* Part (g): Fama regressions 1953:1 to 1971:7 with conditional homoskedasticity
*
linreg pai 1953:1 1971:7 resids;# constant tb1
test;# 2;# 1


*
* Part (h): Breusch-Godfrey
* As described on page 147, the pre-sample residuals are set to zero.
*

set resids 1952:1 1952:12 = 0
linreg resids 1953:1 1971:7
# constant tb1 resids{1 to 12}
cdf(title="Breusch-Godfrey Autocorrelation Test") chisquared %trsquared 12

*
* Part (j): Add seasonal dummies to Fama regression
*

seasonal mdummies
linreg pai 1953:1 1971:7
# mdummies{0 to -11} tb1

*
* Part (k): Fama regression with better inflation measure
*

linreg(robusterrors) pai1 1953:1 1971:7
# constant tb1
test;# 2;# 1

*
* Part (l): Past October 1979.
*

linreg(robusterrors) pai1 1979:11 1990:12
# constant tb1
test;# 2;# 1