Download PPA 207

PPA 207: Quantitative Methods
Meeting 10, Spring 2004
1. Homework
a. Studenmund, Chapter 8, Number 9
a. I expect that competitor's price (PC), gross domestic product (Y), consumption
(C), and number of stores (N) will have a positive influence on sales of durable
goods (SQ). I expect that own price (PQ) will have a negative influence on SQ.
There are 26 observations, so dof equals 26-5-1=20. These are all one-tailed
tests so critical t at 5 percent level is 1.725. The calculated t for PC is 0.80. for
PQ it is 1.20, for Y it is 0.51, for C it is 1.49, for N it is 1.94; therefore, can only
"accept" that N has a positive influence on SQ.
b. Omitted variables could be measure of differences in advertising activity or
product mix across the years. Y and C are really measuring the same thing (the
effect of national income on purchases at these stores) and hence they are likely
to be highly collinear and one of them is irrelevant.
c. The high R squared and the high colinearity between Y and C indicates that
multicolinearity is likely to be a problem. The partial correlation coefficient
between of 0.813 between PC and PQ is not that large and these two variables
measure two separate influences on SQ (the own price effect and the substitute
price effect). Therefore I would not consider dropping one of these variables.
d. I would recommend removing Y and keeping C as a more direct measure of
what influences SQ. Also look to add some explanatory variables to account for
marketing and product differences over the years.
b. Pollock, Chapter 7, Question 2
Review answers in class
c. Go over one student’s regression run and multicolinearity check and correction
2. Studenmund, Chapter 9, Serial Correlation

Consider that you have been asked to build a simple model of property tax
revenue in Sacramento County in year “t”
Property tax revenuet = f (populationt, timet)
Either for understanding impact of these causal variables or
forecasting
Data retrieved from California Institute for County Government Web Site
COUNTY
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
SACRAMENTO
YEAR
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
PROPTXRV
86910539
99877113
113703377
127981910
137191499
154891300
173025724
186340243
181929930
129401948
98928752
104472678
104628365
106072967
POP
891113
916044
948523
979279
1.01E+06
1.05E+06
1.08E+06
1.09E+06
1.09E+06
1.09E+06
1.10E+06
1.12E+06
1.13E+06
1.18E+06
Time
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Run a time series regression
Likely problem to arise: serial correlation
Violation of classical assumption IV
Observations on the error term are likely to be correlated
First-order serial correlation (most common)
et = ρet-1 + ut
ρ = first-order autocorrelation coefficient
-1 < ρ < +1

Positive serial correlation (ρ > 0)
Most likely to observe
Unaccounted for shock in the economy raises residual value in period “t”
Causes residual value to be higher in periods “t+1”, “t+2”, etc.
See Figure 9.1
Shocks at peaks and troughs of residual graphs

Impure serial correlation
Caused by specification error
Omitted variable or an incorrect functional form
Problems created by this are picked up in error terms
So first correction is to deal with this

Consequences of serial correlation
(1) Does not bias the regression coefficient estimates
See Figure 9.6
Distribution of regression coefficient estimates are still centered
around true value
(2) Increases the variance of the regression coefficient estimates
See Figure 9.6
(3) Causes OLS to underestimate the standard errors attached to
regression coefficients
Usually allows a better fit than non-serially correlated observations would
allow
Everything is moving together
Values calculated for t statistics, F statistic, and R-squared are too
high

Consequence of serial correlation
Regression to predict real interest rate in year t

Detection of serial correlation: Durbin-Watson d statistic
Examine the residuals of a suspect regression
Run property tax revenue in SPSS
Click on Durbin-Watson statistic and retrieve unstandardized
residuals
Graph residuals against time to look for pattern
Model Summary(b)
Model
1
R
R Square
.911(a)
.829
Adjusted R
Square
.798
Std. Error of the
Estimate
Durbin-Watson
14879529.7534
1.487
a Predictors: (Constant), time, pop
b Dependent Variable: proptaxrv
Coefficients(a)
Unstandardized Coefficients
Model
1
(Constant)
pop
time
a Dependent Variable: proptaxrv
B
Std. Error
1062219011.
360
163188628.8
04
1322.577
26004688.61
3
Standardized
Coefficients
Beta
t
Sig.
-6.509
.000
181.127
3.429
7.302
.000
3715879.302
-3.286
-6.998
.000

Unstandardized Residual
30000000.00000
20000000.00000


10000000.00000



0.00000





-10000000.00000


-20000000.00000

2.50
5.00
7.50
10.00
12.50
time

DW statistic equals 1.487
Sample size = 14, one constant, and two explanatory variables estimated
(k = 3)
Two-sided 90% test of the null hypothesis of no serial correlation
See Table B-4
dL = 0.81 and du = 1.75
See Figure 9.7
DW statistic falls in inconclusive range

First try correcting functional form
Try a non-linear form
Log of property tax revenue and population
Result better because DW statistic larger and closer to acceptance of no
serial correlation
Model Summary(b)
Model
1
R
R Square
.932(a)
.868
Adjusted R
Square
Std. Error of the
Estimate
.844
Durbin-Watson
.09786
1.567
a Predictors: (Constant), time, lpop
b Dependent Variable: lproptaxrv
Coefficients(a)
Unstandardized Coefficients
Model
1
B
(Constant)
Std. Error
-112.232
15.382
lpop
9.542
1.122
time
-.182
.023
a Dependent Variable: lproptaxrv
Standardized
Coefficients
Beta
t
Sig.
-7.296
.000
3.233
8.507
.000
-3.066
-8.069
.000

Try adding omitted variable(s)
Look at data for clear break points (here 1994 – ERAF)
Create an ERAF dummy for years 1994 and beyond
Remove time dummy
Results
Better, but still not in acceptance range
Model Summary(b)
Model
1
R
Adjusted R
Square
R Square
.930(a)
.864
Std. Error of the
Estimate
.840
Durbin-Watson
.09928
1.582
a Predictors: (Constant), Eraf, lpop
b Dependent Variable: lproptaxrv
Coefficients(a)
Unstandardized Coefficients
Model
1
B
(Constant)
Standardized
Coefficients
Std. Error
-25.760
6.097
lpop
3.219
.441
Eraf
-.591
.075
Beta
t
Sig.
-4.225
.001
1.091
7.296
.000
-1.186
-7.934
.000
a Dependent Variable: lproptaxrv

Try adding omitted variable(s)
Look at data for clear break points (here 1994 – ERAF)
Create an ERAF dummy for years 1994 and beyond
Remove time dummy
Results
Better, but still not in acceptance range

Could correct with Cochrane-Orcutt method
Done directly in SPSS
Analyze=>time series=>autoregression
First produces an estimate of ρ (here = 0.65)
Second runs new regression 9.18 on p. 330
Results are so poor, I would not use
FINAL PARAMETERS:
Estimate of Autocorrelation Coefficient
Rho
Standard Error of Rho
.65453521
.23907816
Cochrane-Orcutt Estimates
Multiple R
R-Squared
.81154849
.65861096
Adjusted R-Squared
Standard Error
Durbin-Watson
.54481461
.09406975
1.2995309
Variables in the Equation:
B
SEB
BETA
T
.8230470
1.235202
.13754041
.6663260
-.4008094
.097717
-.84666687
-4.1017485
7.4652984
17.167155
SIG
T
lpop
.52191470
eraf
.00266972
CONSTANT
.67390521
.
.4348594
3. Check Learning PowerPoint Web Link

Review over Spring Break if weak in this area
Presentation required at last meeting in regard to your Paper
4. Homework Due the Start of Meeting 11 (April 13)
(1) Would anyone like to prepare a 10 minute presentation on Kahn article for
April 13 that would highlight his theoretical model, his specification (linear or log),
his corrections of multicolinearity/heteroscedasticity, and an interpretation of his
regression results? You will have access to a projection of article in classroom.
Just prepare some overheads or notes to lead a discussion on this topic. Grade
granted will substitute for one HW grade. More than one person can do.
(2) Read all of the material under meeting eleven in the syllabus; come prepared
to discuss.
(3) A typed and well developed question from reading assignment for week
eleven.
(4) Answer question 11 in Studemund, Chapter 9.
(5) By Friday (April 2) I will have updated the Checklist for Final Paper at
http://www.csus.edu/indiv/w/wassmerr/ppa207pa.htm and a very good example
of a student paper at http://www.csus.edu/indiv/w/wassmerr/paperdire.pdf .
Download both of these after then and spend some time over break looking over,
we will discuss upon return.
(6) The final paper that you will write must contain a description of at least three
other pieces of academic research in the area. You can find this research by
searching at the CSUS Library’s web page of literature bases that must be
accessed on campus or using a SacLink account
(http://library.csus.edu/databases/. I would suggest using ECONLIT and
EBSCOhost as two literature sources that will have regression studies in them.
Search using keywords that include "regression" and your topic. Be sure that 2/3
of the articles you choose use some form of regression analysis. Find your three
articles over the break and turn in next time a Xeroxed copy of the front page
(including abstract) of each article. (You will need complete copies of articles for
yourself.)