David Mushinski
November 28, 2021
ECON/AREC635
Problem Set 3
This problem set is worth 30 points. It is due at the beginning of class on Monday December 6
(you may hand it in earlier, if you wish).
For each subpart of this problem set, you MUST provide and identify the STATA and MATA
code relevant to your answer in that subpart. You will lose substantial (or all) credit if you do not
provide STATA and MATA code. You may work with one other student in the course on the
problem set and submit a joint set of answers.
For hypothesis tests:
i)
ii)
iii)
be sure to specify your null and alternative hypotheses clearly (with reference to the
parameters in underlying equation being tested),
establish a 5% level of significance and use prob values or critical statistics to
undertake your test, and
identify your test results and identify which hypothesis you Accept (Fail to Reject).
If you decide that you must calculate Newey-West standard errors use the T1/3 standard for lags.
Suppose that we are interested in the fish prices at a popular fish market in a large U.S. city.
You wish to estimate the following relationship
yt = β1 + β2∙x2t + β3∙x3t + β4∙x4t + β5∙x5t + β6∙x6t + β7∙x7t + β8∙t + εt
(I)
where
y is average fish price on a given day,
x2 = 1 if the day is Monday, and = 0 otherwise,
x3 = 1 if the day is Tuesday, and = 0 otherwise,
x4 = 1 if the day is Wednesday, and = 0 otherwise,
x5 = 1 if the day is Thursday, and = 0 otherwise,
x6 = average wave height over the prior two days,
x7 = average wind speed over the prior two days, and
t = a time trend (i.e., t = 1,…,97).
Assume that ε follows an AR(1) process; i.e.,
εt = ρ∙εt-1 + ut
ut ∼ N(0,σ2𝑢 ).
Suppose that we have data for 97 consecutive days the fish market was open (note that they
weren’t necessarily consecutive days - daily- because the market was open Monday through
Friday). The data is in the STATA data set "econ 635 2021 ps 3.dta". When using STATA, be
sure to pay attention to the “tsset” command and how STATA handles time series data.
1
(A) [10 points] In MATA and in STATA, test for the presence of a positive AR(1) process
(i.e., ρ > 0) using the Durbin-Watson test statistic. Be sure to identify your hypotheses
and the critical values of your statistics.
(B) [5 points] Using MATA, test for the presence of a positive AR(1) process using the
following relationship
et = ρ•et-1 + ut
where the et are residuals from estimating equation (I) using the Ordinary Least Squares
(OLS) estimator.
(C) [5 points] In STATA, obtain estimates of the parameters in equation (I) using the OLS
estimator (be sure to report the correct standard errors).
(D) [10 points] In MATA and in STATA, obtain estimates of the model’s parameters using
the Prais-Winsten (two-step) estimator and report standard errors of the parameter
estimates.
Use the estimate of rho from part (B); i.e., the ρ̂ from
et = ρ̂•et-1 + ut .
(Note: the challenge in this question involves forming the P transformation matrix.)
2