Transcript Chapter 4: Demand Estimation The estimation of a demand function using

Chapter 4: Demand Estimation
The estimation of a demand function using
econometric techniques involves the
following steps
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Identification of the variables
Collection of the data
Specification of the demand model
Estimation of the parameters using OLS
Development of forecasts (estimates)
based on the model
Regression Analysis
• Line of Best Fit
• Ordinary Least Square (OLS) Method:
Minimize the sum of the squared deviations
of each point from the regression line
• The actual dependent variable (Y) is plus
and minus 2se of the estimated dependent
variable at an approximate 95% confidence
Significance Test to Estimated
Coefficients (t-statistics)
• H0: β=0 ( No relationship between X and
Y)
• Ha: β≠0 ( linear relationship between X
and Y)
• There are two ways of doing the testing:
– Calculate the t statistic and compare it to the
critical value
– Use the p-value technique
Coefficient of Determination (R2)
• It measures the proportion of the variation
in the dependent variable that is explained
by the regression line (the independent
variable).
• The coefficient of determination ranges
from 0 (when none of the variation in Y is
explained by the regression) to 1( when all
the variation in Y is explained by the
regression.
Statistical Validity of the Model
(F-ratio)
• It is used to test whether the estimated
regression equation explains a significant
proportion of the variation in the dependent
variable.
• The decision is to reject the null hypothesis of no
relationship between X and Y ( that is, no
explanatory power) at the k level of significance
if the calculated F-ratio is greater than the Fk,1,n-2
value obtained from the F-distribution.
Association and Causation
• The presence of association (correlation)
does not necessarily imply causation.
Example 1
• A 1984 study of cigarette demand in the following
logarithmic regression equation:
ln Q  2.55  0.29 ln P  0.09 ln Y  0.8 ln A  0.1w
where Q=annual cigarette consumption; P=average price of cigarette; Y=per capita
income; A=total spending on cigarette advertising; w=dummy variable (w=1 to 1
after 1953 when American Cancer Assoc warned that smoking is linked to lung
cancer, and w=0 otherwise.
R2=0.94, t-statisitcs are tp=-2.07; , tY=-1.05; , tA=4.48; , tw=-5.2.
a. Which variables have effect?
b. What does the coefficient of ln P represent?
c. Are cigarette purchase sensitive to income?
Example 2
• The following rregresion was estimated for 23 quarters
between 2000 and 2005 to test the hypothesis that tire sales
(T) depend o new auto sales (A) and total miles driven (M):
%T  0.45  1.41%M  1.12%A
where n=23 observation; R2=0.83; F=408; se=1.2; sintercept=0.32; sM=0.19; sA=0.41.
a. Does the regression and estimated coefficients make economic sense?
b. Discuss the statistical validity of the equation?
c. Are the coefficients on “miles driven” and “new auto sales” significantly different
for 1.0? Explain.
d. Suppose “miles driven” is expected to fall by 2% and “new auto sales” by 13%
due to expected recession? What is the predicted changes in sales quantity of
tires? If actual tire sales dropped by 18%, would this be suprising?
Example 3 : Excel Exercise
• Using the data for 6 US regions (Atlanta, Baltimore,
Chicago, Denver, Erie and Fort Lauderdale) during 8
quarters, we estimate the following model using
excel package:
Q   0  1P   2 A  3 P o   4 M   5 Pop   6t
where Q=quarterly sales; P=retail price (in cents); A=$1000 advertising
expenditure; Po=rivals’ price (in cents); M=disposable income; t=trend.
Regression in Excel
• Enter data to each column
• Under “Tools” menu select “Data Analysis”
• Select “Regression” and click OK
• Enter “Input Y Range” and “Input X
Range” and click OK to run regression.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.962902081
R Square
0.927180417
Adjusted R Square
0.916523892
Standard Error
1441.727186
Observations
48
ANOVA
df
Regression
Residual
Total
Intercept
Price
Advertising
Rival's Price
Income
Population
Time Trend
6
41
47
SS
1.09E+09
85221668
1.17E+09
Coefficients
-4516.291428
-35.98500601
203.713184
37.95978087
777.0511727
0.255519212
356.0470971
Standard
Error
4988.242
7.018681
77.29213
7.065183
66.42341
0.1253
92.28777
MS
1.81E+08
2078577
t Stat
-0.90539
-5.12703
2.635627
5.372795
11.69845
2.039255
3.85801
Significance
F
F
87.00589
9.94E-22
P-value
Lower 95% Upper 95%
0.37055
-14590.3 5557.668
7.45E-06
-50.1595
-21.8105
0.011802 47.61857 359.8078
3.36E-06 23.69136 52.22821
1.21E-14 642.9064
911.196
0.047905
0.00247 0.508568
0.000397 169.6682
542.426
Potential Problems in Regression
• Equation Specification
– Linear versus Nonlinear Models
• Omitted Variables
• Multicollinearity
– Two or more explanatory variables are highly
correlated
• Autocorrelation
– Error terms are highly correlated
• Simultaneity and Identification