Chapter 4: Demand Estimation The estimation of a demand function using econometric techniques involves the following steps

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Chapter 4 Demand Estimation The estimation of a
demand function using econometric techniques
involves the following steps

• 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

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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

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Significance Test to Estimated Coefficients
(t-statistics)

• H0 ß0 ( No relationship between X and Y)
• Ha ß?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

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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.

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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.

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Association and Causation

• The presence of association (correlation) does
  not necessarily imply causation.

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Example 1

• A 1984 study of cigarette demand in the following
  logarithmic regression equation
• where Qannual cigarette consumption Paverage
  price of cigarette Yper capita income Atotal
  spending on cigarette advertising wdummy
  variable (w1 to 1 after 1953 when American
  Cancer Assoc warned that smoking is linked to
  lung cancer, and w0 otherwise.
• R20.94, t-statisitcs are tp-2.07 , tY-1.05 ,
  tA4.48 , tw-5.2.
• Which variables have effect?
• What does the coefficient of ln P represent?
• Are cigarette purchase sensitive to income?

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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)
• where n23 observation R20.83 F408 se1.2
  sintercept0.32 sM0.19 sA0.41.
• Does the regression and estimated coefficients
  make economic sense?
• Discuss the statistical validity of the equation?
• Are the coefficients on miles driven and new
  auto sales significantly different for 1.0?
  Explain.
• 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?

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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
• where Qquarterly sales Pretail price (in
  cents) A1000 advertising expenditure
  Porivals price (in cents) Mdisposable income
  ttrend.

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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.

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SUMMARY OUTPUT SUMMARY OUTPUT

Regression Statistics Regression Statistics
Multiple R 0.962902081
R Square 0.927180417
Adjusted R Square 0.916523892
Standard Error 1441.727186
Observations 48

ANOVA
  df SS MS F Significance F
Regression 6 1.09E09 1.81E08 87.00589 9.94E-22
Residual 41 85221668 2078577
Total 47 1.17E09      

  Coefficients Standard Error t Stat P-value Lower 95 Upper 95
Intercept -4516.291428 4988.242 -0.90539 0.37055 -14590.3 5557.668
Price -35.98500601 7.018681 -5.12703 7.45E-06 -50.1595 -21.8105
Advertising 203.713184 77.29213 2.635627 0.011802 47.61857 359.8078
Rival's Price 37.95978087 7.065183 5.372795 3.36E-06 23.69136 52.22821
Income 777.0511727 66.42341 11.69845 1.21E-14 642.9064 911.196
Population 0.255519212 0.1253 2.039255 0.047905 0.00247 0.508568
Time Trend 356.0470971 92.28777 3.85801 0.000397 169.6682 542.426
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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