Presentation on theme: "Managerial Economics Estimation of Demand"— Presentation transcript:
1Managerial Economics Estimation of Demand How to estimate a demand equation?How to calculate demand elasticities?
2Is this how it’s done? Last This % Year Year Change Change Price $4 $ $ %Q %Ep = +25% / +25% = + 1Questions:1) Is Ep = + 1?2) What’s the right way to do it?
3Estimation of Demand I. The Direct Methods II. The indirect Methods Interviews and SurveysMarket Experimentations and SimulationsII. The indirect MethodsRegression Estimation of Consumer Demand
4Interviews and Surveys Ask buyers or potential buyers about their likely reactions to a change in each of the demand determinants.Practical Issues:Randomness of the sampleInterviewer biasThe best-of-intentions problemConfusing questions and confusing answers
5Simulation and Market Experimentations Simulation of consumer responses in constructed market situationsTest-market experiments in selected markets
6Regression Analysis of Consumer Demand A statistical technique that attempts to "explain" or "predict" movements in one economic variable, the dependent variable, as a function of the movements of a set of independent (explanatory) variables.
7Desirable Characteristics It shows explicitly the association between the dependent variable and the independent variables.It also provides statistical reliability allowing the researchers to measure the reliability of the prediction.In Econometrics, the economists call it:‘BLUE’ property.
8Procedure of Regression Analysis Specifying the variablesObtaining data on the variablesSpecifying the form of the estimation equationEstimate the regression parameters using the method of least squares.
9Demand and Elasticity Estimation Step 1 - The model:Q = f(A, Px, and Pq), whereQ = Number of 2-year contracts soldA = Advertising expenditures (in dollars)Px = Price of 1-year contract (in dollars)Pq = Price of 2-year contract (in dollars)
10The Data Time-series data for 1986-97 and the effect of inflation Time-series data and the effect of serial correlationN=12, K=4, 8 degrees of freedom
11Estimation of 2 Equations The 1st Equation - Linear Q = a + b1 A + b2 Px + b3 Pq The 2nd Equation - multiplicative Q = aAb1Pxb2 Pqb3
12The Estimated 1st Equation Q = 4, A Px Pq s.e. ( ) ( ) ( ) t stat p-value Adj R2 = , F= (p= ) SEE=52.98, N=12, K=4
13Evaluation of Regression Estimation 1. The coefficient of determination (R2) - How well does the regression line fit the data? 2. The F-Test - Does the estimated equation have sufficient explanatory power? 3. The t-Test - Is each of the independent variables statistically significant? 4. The Standard Error of the Estimate (SEE) - Can the confidence interval of the predicted value for the dependent variable be estimated?
14The Standard Error of the Estimate (SEE) How accurate is the predicted sales?The SEE can be used to construct prediction intervalsIf SEE = 53, then and approximate 95% prediction interval for the sales of 2-year contracts is equal toQ’ + 2(53)
15Uses of the 1st EquationThe demand curve for explaining demand relationships and for predicting demandEstimation of the arc elasticities of demand usingQ1-Q Pq1 - Pq2Ep =Q1+Q Pq1+ Pq2Estimation of the point elasticities of demand using ep = (dQ/dPq)(Pq/Q)
16The Multiplicative Equation Q = aAb1Pxb2Pqb3 Two key questions:What are the advantages of the multiplicative form over the linear formHow to go about estimating this non-linear equation?See pp of McGuigan/Moyer/Harris, 10th ed. for details
17The Advantages of the Multiplicative Form Q = a Ab1Pxb2 Pqb3dQ/dPq = (b3) (aAb1Pxb2 Pqb3 -1)Since epq = (dQ/dPq)(Pq/Q),epq = (b3)(aAb1Pxb2 Pqb3 -1)(Pq/Q)= (b3)[(aAb1Pxb2 Pqb3)/Q]= b3
18How to estimate the parameters of the multiplicative equation? Converting the multiplicative equationQ = a Ab1Pxb2 Pqb3into the natural-log form, we have:Ln Q = Ln a + b1 Ln A + b2 Ln Px + b3 Ln Pq