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### Economics 105: Statistics

### Serial Correlation

### Serial Correlation Example

### Serial Correlation Example

### Serial Correlation Example

### Serial Correlation Example

### Serial Correlation Example

### Serial Correlation Example

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

Wrong functional form

Omit Relevant Variable (Include Irrelevant Var)

Errors in Variables

Sample selection bias, Simultaneity bias

“well-specified model” (1) & (5)

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

can only assess theoretically

zero conditional mean of errors (2)

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

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 d1d* 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

Table of critical values for Durbin-Watson statistic (table E11, page 833 in BLK textbook)

http://hadm.sph.sc.edu/courses/J716/Dw.html

What is the effect of the price of oil on the number of wells drilled in the U.S.?

What is the effect of the price of oil on the number of wells drilled in the U.S.?

Analyze residual plots … but be careful …

Remember what serial correlation is …

- This plot only “works” if obs number is in same order as the unit of time

Same graph when plot versus “year”

- Graphical evidence of serial correlation

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%

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