Economics 105: Statistics
•Please practice your RAP, so you can keep it to 7 minutes. We
have lots of them to do.
• please copy your Powerpoint file to your stats
P:\economics\Eco 105 (Statistics) Foley\userid\ lab space.
Tue Apr 24: Thompson, Shanor, Nielsen, Moniz-Soares, Maher, Dugan, Burke,
Adabayeri
Thur Apr 26: Ryger-Wasserman, Lockwood, Gordon, Givens, Christ, Blasey, Bernert,
Avinger
Tue May 1: Yearwood, Swany, Ream, Polak, Pettiglio, Murray, Esposito, Bajaj
Thur May 3: Yan, Tompkins, Mwangi, Mooney, Lockhart, Clune, Charles, Bourgeois
• Review #3 due Monday May 7, by 4:30 PM.
Violations of GM Assumptions
Assumption
Violation
“well-specified
model” (1) &
(5)
Wrong functional form
Omit Relevant Variable (Include Irrelevant Var)
Errors in Variables
Sample selection bias, Simultaneity bias
zero conditional
mean of errors (2)
constant, nonzero mean due to
systematically +/- measurement error in Y
can only assess theoretically
Homoskedastic errors
(3)
Heteroskedastic errors
No serial correlation in
errors (4)
There exists serial
correlation in errors
Detection: The Durbin-Watson Test
• Provides a way to test
H0:  = 0
• It is a test for the presence of
first-order serial correlation
• The alternative hypothesis
can be
– 0
–  > 0: positive serial
correlation
• Most likely alternative in
economics
–  < 0: negative serial
correlation
• DW Test statistic is d
n
d=
å (e - e
t =2
t -1
t
n
åe
t =1
2
t
)
2
Detection: The Durbin-Watson Test
• To test for positive serial correlation with the
Durbin-Watson statistic, under the null we
expect d to be near 2
– The smaller d, the more likely the alternative
hypothesis
The sampling distribution
of d depends on the values of
the explanatory variables.
Since every problem has a
different set of explanatory
variables, Durbin and Watson
derived upper and lower limits
for the critical value of the test.
Detection: The Durbin-Watson Test
• Durbin and Watson derived upper and
lower limits such that d1  d*  du
• They developed the following decision rule
Detection: The Durbin-Watson Test
• To test for negative serial correlation the decision
rule is
• Can use a two-tailed test if there is no strong prior
belief about whether there is positive or negative
serial correlation—the decision rule is
Serial Correlation
• Table of critical values for Durbin-Watson
statistic (table E11, page 833 in BLK textbook)
•http://hadm.sph.sc.edu/courses/J716/Dw.html
Serial Correlation Example
• What is the effect of the price of oil on the
number of wells drilled in the U.S.?
Wellst = b0 + b1OilPricet + e t
•
Year
Total
Wells
Drilled
real
price
per bbl
Avera
ge
Price
per bbl
Produ
cer
Price
Index
1930
21232
7.986577
1.19
14.9
1931
12432
5.15873
0.65
12.6
1932
15040
7.767857
0.87
11.2
1933
12312
5.877193
0.67
11.4
1934
18917
7.751938
1
12.9
1935
21420
7.028986
0.97
13.8
1987
35194
14.98054
15.4
102.8
1988
32479
11.76801
12.58
106.9
1989
27824
14.13547
15.86
112.2
1990
27941
17.2227
20.03
116.3
1991
29960
14.16309
16.5
116.5
Serial Correlation Example
• What is the effect of the price of oil on the
number of wells drilled in the U.S.?
• Welˆlst = 12076.6 + 2462.55 * OilPricet
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.806486157
R Square
0.650419921
Adjusted R Square
0.644593586
Standard Error
10422.6806
Observations
62
ANOVA
df
Regression
Residual
Total
Intercept
real
SS
MS
F
Significance F
1
12127108610 1.21E+10 111.6345
2.5537E-15
60
6517936259 1.09E+08
61
18645044869
Coefficients
Standard Error t Stat
P-value
Lower 95%
12076.66238
2912.941825 4.145865 0.000108 6249.913083
2462.551305
233.0698428 10.56572 2.55E-15 1996.342358
Serial Correlation Example
• Analyze residual plots … but be careful …
Serial Correlation Example
• Remember what serial correlation is …
• This plot only “works” if obs number is in same
order as the unit of time
Serial Correlation Example
• Same graph when plot versus “year”
30000
Residuals
20000
10000
0
1920
-10000
1930
1940
1950
1960
1970
1980
1990
-20000
-30000
Year
• Graphical evidence of serial correlation
2000
Serial Correlation Example
n
• Calculate DW test statistic
• Compare to critical value at chosen sig level
d=
å (e - e
t =2
t -1
t
)2
n
åe
t =1
= .192
2
t
– dlower or dupper for 1 X-var & n = 62 not in table
– dlower for 1 X-var & n = 60 is 1.55, dupper = 1.62
Predicted Total
Wells Drilled
Observation
Residuals
e(t-1)
e(t) - e(t-1)
1
31744.01844
-10512.01844
2
24780.30007
-12348.30007
-10512
-1836.28
3
31205.40913
-16165.40913
-12348.3
4
26549.55163
-14237.55163
5
31166.20738
6
29385.89982
(e(t)-e(t-1))^2
e(t)^2
Year
110502532
1930
3371930.199
152480515
1931
-3817.11
14570321.58
261320452
1932
-16165.4
1927.857
3716634.527
202707876
1933
-12249.20738
-14237.6
1988.344
3953512.848
150043081
1934
-7965.899815
-12249.2
4283.308
18346723.71
63455559.9
1935
61
54488.44454
-26547.44454
-19062
-7485.46
56032054.78
704766811
1990
62
46953.99846
-16993.99846
-26547.4
9553.446
91268331.83
288795984
1991
1257013355
6517936259
SUM
• Since .192 < 1.55, reject H0:  = 0 in favor of H1:  > 0 at α=5%