Demand Estimation

Outline of the lecture ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

What questions should the manager answer? ,[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object]

Statistical Estimation of the Demand Function ,[object Object],[object Object]

The estimation of a demand function using econometric techniques involves the following steps ,[object Object],[object Object],[object Object],[object Object],[object Object]

Identification of the variables ,[object Object],[object Object],[object Object]

Collection of the data ,[object Object]

Formulation of the model ,[object Object]

1. Linear Model ,[object Object]

Linear Model ,[object Object],[object Object]

Interpretation of the value of β ,[object Object]

Interpretation of the value of β ,[object Object],[object Object],[object Object],[object Object],[object Object],The β coefficients are equivalent to the partial derivatives of the demand function:

Interpretation of the value of β and using β to determine elasticity ,[object Object],[object Object]

1.1 Simple Linear Regression Model ,[object Object]

Estimating the simple linear regression coefficients

Example 1 ,[object Object],[object Object]

Answer ,[object Object],[object Object],[object Object]

Using the regression equation to make predictions ,[object Object]

Standard Error of the estimate ,[object Object],[object Object]

Returning to our previous example 155.447 to 246.643 (that is, from 155,447 gallons to 246,643 gallons).

Testing ,[object Object],[object Object]

Testing ,[object Object],[object Object],[object Object]

Correlation Coefficient ,[object Object],[object Object]

Correlation Coefficient ,[object Object]

The Coefficient of Determination

The Coefficient of Determination ,[object Object],[object Object]

F-ratio ,[object Object],[object Object]

Association and Causation ,[object Object]

1.2 Multiple Linear Regression ,[object Object]

2. Non Linear Models ,[object Object],[object Object]

2.1 Quadratic Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

2.2 Log-linear Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Regression techniques ,[object Object],[object Object]

Estimating Coefficients ,[object Object]

The Least-Squares regression estimation

Estimating the demand for lobsters dinners using the OLS Qi Pi Qi-Q(bar) Pi-P(bar) (Pi-P(bar)) 2 (Pi-P(bar))(Qi-Q(bar)) 100 15 0 -1 1 0 90 18 -10 2 4 -20 85 19 -15 3 9 -45 110 14 10 -2 4 -20 120 13 20 -3 9 -60 90 19 -10 3 9 -30 105 16 5 0 0 0 100 14 0 -2 4 0 40 -175 b -4.375 a 170

Estimating the demand for lobster dinners ,[object Object],[object Object]

Problems in Regression Analysis 1. Multicollinearity ,[object Object],[object Object],[object Object]

Multicollinearity ,[object Object]

2. Heteroscedasticity ,[object Object],[object Object],[object Object]

Heteroscedasticity ,[object Object]

3. Autocorrelation ,[object Object],[object Object]

Autocorrelation ,[object Object]

Demand Estimation

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Demand Estimation