Economics 105: Statistics

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 AssumptionsAssumption Violation

“well-specified model” (1) &

(5)

zero conditional mean of errors (2)

Wrong functional formOmit Relevant Variable (Include Irrelevant Var)Errors in VariablesSample selection bias, Simultaneity bias

No serial correlation in errors (4)

constant, nonzero mean due to systematically +/- measurement error in Y

can only assess theoretically

Heteroskedastic errors

Homoskedastic errors (3)

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

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

hypothesisThe sampling distributionof 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 limitsfor 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.?•

Year

Total Wells Drilled

real price per bbl

Average Price per bbl

Producer Price Index

1930 212327.98657

7 1.19 14.9

1931 12432 5.15873 0.65 12.6

1932 150407.76785

7 0.87 11.2

1933 123125.87719

3 0.67 11.4

1934 189177.75193

8 1 12.9

1935 214207.02898

6 0.97 13.81987 3519414.9805

4 15.4 102.8

1988 32479 11.76801 12.58 106.9

1989 2782414.1354

7 15.86 112.2

1990 27941 17.2227 20.03 116.3

1991 2996014.1630

9 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.?•

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”

• Graphical evidence of serial correlation

Serial Correlation Example• Calculate DW test statistic• Compare to critical value at chosen sig level

– 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

• Since .192 < 1.55, reject H0: = 0 in favor of H1: > 0 at α=5%

ObservationPredicted Total Wells Drilled Residuals e(t-1) e(t) - e(t-1) (e(t)-e(t-1))^2 e(t)^2 Year

1 31744.01844 -10512.01844 110502532 1930

2 24780.30007 -12348.30007 -10512 -1836.28 3371930.199 152480515 1931

3 31205.40913 -16165.40913 -12348.3 -3817.11 14570321.58 261320452 1932

4 26549.55163 -14237.55163 -16165.4 1927.857 3716634.527 202707876 1933

5 31166.20738 -12249.20738 -14237.6 1988.344 3953512.848 150043081 1934

6 29385.89982 -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

SUM 1257013355 6517936259