Lecture 2

Ch 3 DEMAND ESTIMATION : 

Ch 3 DEMAND ESTIMATION In planning and in making policy decisions, managers must have some idea about the characteristics of the demand for their product(s) in order to attain the objectives of the firm or even to enable the firm to survive.

Demand information about customer sensitivity to: 

Demand information about customer sensitivity to modifications in price advertising packaging product innovations economic conditions etc. are needed for product-development strategy For competitive strategy details about customer reactions to changes in competitor prices and the quality of competing products play a significant role

WHAT DO CUSTOMERS WANT?: 

WHAT DO CUSTOMERS WANT? How would you try to find out customer behavior? How can actual demand curves be estimated?

From Theory to Practice: 

From Theory to Practice D: Qx = f(px ,Y, pr , pe, , N) What is the true quantitative relationship between demand and the factors that affect it? How can demand functions be estimated? How can managers interpret and use these estimations?

Most common methods used are:: 

Most common methods used are: consumer interviews or surveys to estimate the demand for new products to test customers reactions to changes in the price or advertising to test commitment for established products b) market studies and experiments to test new or improved products in controlled settings c) regression analysis uses historical data to estimate demand functions

Consumer Interviews(Surveys): 

Consumer Interviews (Surveys) Ask potential buyers how much of the commodity they would buy at different prices (or with alternative values for the non-price determinants of demand) face to face approach telephone interviews

Consumer Interviews continued: 

Consumer Interviews continued Problems: 1. Selection of a representative sample what is a good sample! 2. Response bias how truthful can they be? 3. Inability or unwillingness of the respondent to answer accurately

Market Studies and Experiments: 

Market Studies and Experiments More expensive and difficult technique for estimating demand and demand elasticity is the controlled market study or experiment Displaying the products in several different stores, generally in areas with different characteristics, over a period of time for instance, changing the price, holding everything else constant

Market Studies and Experiments continued: 

Market Studies and Experiments continued Experiments in laboratory or field a compromise between market studies and surveys volunteers are paid to stimulate buying conditions

Market Studies and Experiments continued: 

Market Studies and Experiments continued Problems in conducting market studies and experiments: a) expensive b) availability of subjects c) do subjects relate to the problem, do they take them seriously BUT: today information on market behavior also collected by membership and award cards of stores

Regression Analysis and Demand Estimation: 

Regression Analysis and Demand Estimation A frequently used statistical technique in demand estimation Estimates the quantitative relationship between the dependent variable and independent variable(s) quantity demanded being the dependent variable if only one independent variable (predictor) used: simple regression if several independent variables used: multiple regression

A Linear Regression Model: 

A Linear Regression Model In practice the dependence of one variable on another might take any number of forms, but an assumption of linear dependency will often provide an adequate approximation to the true relationship

Think of a demand function of general form:: 

Think of a demand function of general form: Qi =  + 1Y - 2 pi + 3ps - 4pc + 5Z + e where Qi = quantity demanded of good i Y = income pi = price of good i ps = price of the substitute(s) pc = price of the complement(s) Z = other relevant determinant(s) of demand e = error term Values of  and i ?

 and i has to be estimated from historical data: 

 and i has to be estimated from historical data Data used in regression analysis cross-sectional data provide information on variables for a given period of time time series data give information about variables over a number of periods of time New technologies are currently dramatically changing the possibilities of data collection!!!

Simple Linear Regression Model: 

Simple Linear Regression Model In the simplest case, the dependent variable Y is assumed to have the following relationship with the independent variable X: Y = a + bX + u where Y = dependent variable X = independent variable a = intercept b = slope u = random factor

Estimating the Regression Equation: 

Estimating the Regression Equation Finding a line that 'best fits' the data The line that best fits a collection of X,Y data points, is the line minimizing the sum of the squared distances from the points to the line as measured in the vertical direction This line is known as a regression line, and the equation is called a regression equation Estimated Regression Line: Y= â + bX ˆ ˆ

Slide17: 

Observed Combinations of Output and Labor input

Slide18: 

Slide19: 

Regression with Excel Evaluate statistical significance of regression coefficients using t-test and statistical significance of R2 using F-test

t-test: test of statistical significance of each estimated regression coefficient: 

t-test: test of statistical significance of each estimated regression coefficient b: estimated coefficient SEb: standard error of the estimated coefficient Rule of 2: if absolute value of t is greater than 2, estimated coefficient is significant at the 5% level If coefficient passes t-test, the variable has a true impact on demand

Sum of Squares: 

Sum of Squares

Sum of Squares continued: 

Sum of Squares continued TSS = (Yi - Y)2 (total variability of the dependent variable about its mean) RSS = (Ŷi - Y)2 (variability in Y explained by the sample regression) ESS = (Yi - Ŷi)2 (variability in Y unexplained by the dependent variable x) This regression line gives the minimum ESS among all possible straight lines. where Y = mean of Y

The Coefficient of Determination: 

The Coefficient of Determination Coefficient of determination R2 measures how well the line fits the scatter plot (Goodness of Fit) R2 is always between 0 and 1 If it’s near 1 it means that the regression line is a good fit to the data Another interpretation: the percentage of variance 'accounted for'

Multiple Regression Procedure: 

Multiple Regression Procedure 1. Determine the appropriate predictors and the form of the regression model 2. Estimate the unknown a and b coefficients 3. Estimate the variance associated with the regression model 4. Check the utility of the model (R2, global F-test, individual t-test for each b coefficient) 5. Use the fitted model for predictions (and determine their accuracy)

Specification of the Regression Model:: 

Specification of the Regression Model: Proxy variables to present some other 'real' variable, such as taste or preference, which is difficult to measure Dummy variables (X1= 0; X2= 1) for qualitative variable, such as gender or location Linear vs. non-linear relationship quadratic terms or logarithms can be used Y = a + bX1 + cX12 QD=aIb  logQD= loga + blogI

Example: Specifying the Regression Equation for Pizza Demand: 

Example: Specifying the Regression Equation for Pizza Demand We want to estimate the demand for pizza by college students in USA What variables would most likely affect their demand for pizza? What kind of data to collect?

Data: Suppose we have obtained cross-sectional data on college students of randomly selected 30 college campus (by a survey): 

Data: Suppose we have obtained cross-sectional data on college students of randomly selected 30 college campus (by a survey) The following information is available: average number of slices consumed per month by students average price of a slice of pizza sold around the campus price of its complementary product (soft drink) tuition fee (as proxy for income) location of the campus (dummy variable is included to find out whether the demand for pizza is affected by the number of available substitutes); 1 urban, 0 for non-urban area

Linear additive regression line:: 

Linear additive regression line: Y = a + b1pp + b2 ps + b3T + b4L where Y = quantity of pizza demanded a = the intercept Pp = price of pizza Ps = price of soft drink T = tuition fee L = location bi = coefficients of the X variables measuring the impact of the variables on the demand for pizza

Estimating and Interpreting the Regression Coefficients: 

Estimating and Interpreting the Regression Coefficients Y = 26.27- 0.088pp - 0.076ps + 0.138T- 0.544 L (0.018) (0.018) (0.020) (0.087) (0.884) R2 = 0.717 Standard error of Y = 1.64 R2 = 0.67 F = 15.8 Numbers in parentheses are standard errors of coefficients.

Problems in the Use of Regression Analysis:: 

Problems in the Use of Regression Analysis: identification problem multicollinearity (correlation of coefficients) autocorrelation (Durbin-Watson test)

Multicollinearity: 

Multicollinearity A significant problem in multiple regression which occurs when there is a very high correlation between some of the predictor variables.

Resulting problem:: 

Resulting problem: Regression coefficients may be very misleading or meaningless because… their values are sensitive to small changes in the data or to adding additional observations they may even be opposite in sign from what 'makes sense' their t-value (and the standard error) may change a lot depending upon which other predictors are in the model

Multicollinearity continued: 

Multicollinearity continued Solution: Don’t use two predictors which are very highly correlated (however, x and x2 are O.K.) Not a major problem if we are only trying to fit the data and make predictions and we are not interested in interpreting the numerical values of the individual regression coefficients.

Multicollinearity continued: 

Multicollinearity continued One way to detect the presence of multicollinearity is to examine the correlation matrix of the predictor variables. If a pair of these have a high correlation they both should not be in the regression equation – delete one. Correlation Matrix

A test for Autocorrelated Errors:DURBIN-WATSON TEST: 

A test for Autocorrelated Errors: DURBIN-WATSON TEST A statistical test for the presence of autocorrelation Fit the time series with a regression model and then determine the residuals:

Slide36: 

The Durbin-Watson value d, will always be: 0  d  4. The interpretation of d: Possible values of d: 0 2 4 Strong +Correlation Uncorrelated Strong -Correlation

Comments:: 

Comments: As more variables are added to a multiple regression equation, R2 must increase (or stay the same); F may or may not increase The F test is a test of all the i= 0. We should expect a high F value (and low p value). If so, we can investigate further t-test for coefficients can determine which ones to delete from the model

Slide38: 

OCCAM’S RAZOR. We want a model that does a good job of fitting the data using a minimum number of predictors. A high R2 is not the only goal; variables used should be 'meaningful' Don’t use more predictors in a regression model than 5% to 10% of n Would like a model with low MSE Results of t-tests for individual coefficients depend on which other predictors happen to be in the model