Let's investigate the possibility of heteroskedasticity in time-
series data by looking at a model of the black market for U.S. dollars in Brazil that was
studied by R. Dornbusch and C. Pechma.1 In particular, the authors wanted to know if
the Demsetz-Bagehot bid-ask theory, previously tested on cross-sectional data from the
United States, could be extended to time-series data outside the United States. 2 They
estimated the following model on monthly data from Brazil for March 1979 through
December 1983:
where:
. St=the average daily spread between the bid and asking prices for the U.S. dollar
on the Brazilian black market in month t
. It=the average interest rate in month t
. Vt=the variance of the daily premium between the black market rate and the official
exchange rate for the dollar in month t
(a) Use the authors' data in Table 10.2 (datale=BID10) to estimate Equation 10.22 and test the residuals for positive first-order serial correlation.
(b) If serial correlation appears to exist, reestimate Equation 10.22 using GLS. Do the coefficient estimates change? Which equation do you prefer? Why?
(c) The authors noted that S nearly doubled in size during their sample period. Does this make you concerned about the possibility of heteroskedasticity? Why or why not?
(d) Test the residuals of Equation 10.22 for heteroskedasticity using the Breusch{Pagan test. (Hint: A possible proportionality factor is a time-trend variable that equals 1 for March 1979 and that increases by 1 for each following month.)
(e) Test the residuals of your GLS version of Equation 10.22 for heteroskedasticity. Did running GLS change the possibility of heteroskedasticity?
(f) What remedy would you suggest for any heteroskedasticity that might exist in such a time-series model? Be specific.