Managerial Economics Estimating Demand Example Aalto University School of Science Department of Industrial Engineering and Management January 12 – 28, 2016 Dr. Arto Kovanen, Ph.D. Visiting Lecturer

 Estimating parameters of demand functions can be challenging  We cannot observe the utility function/level of utility  Utility functions and incomes vary between consumers  We only observe the aggregate traded amount, which may be different than demanded by consumers  Observed prices are suppose to be equilibrium prices (not always the case)  This gives rise to simultaneous equation bias (both P and Q are determined at the same time) and identification problem (is it the demand or supply curve) General observations

 A non-linear demand equation for Q(t) = AP(t) b ε(t) which can be presented in a linear form as follows LnQ(t) = LnA + b*lnP(t) + lnε(t) where b can be interpreted as the price elasticity of demand for Q and ε is the random error term  For OLS to be valid, b and P should be uncorrelated with the error term  For instance, if Q is demand for coffee and P is the price of coffee Estimating demand

 What substitutes do consumers have for coffee?  If tea is a substitute for coffee, the demand for coffee will also depend on the price of tea  Hence the error term will depend of the price of tea  If the prices of coffee and tea are correlated, then the OLS technique will produce a biased estimate of “b”  Hence it is important to incorporate variables other than own price and income in the demand estimation Estimating demand (cont.)

 U.S. coffee demand (Huang, Siegfried and Zardoshty, 1980) for period 1961 – 1977, using quarterly data: lnQ(t) = 1.27 – 0.16*lnPC(t) *lnY(t) (- 2.14)(1.23) ln*PT(t) – 0.01*Trend(t) – 0.10*D1 (0.55) (-3.33) – 0.16*D2 – 0.01*D3 R2 = 0.80 where PC = price of coffee, Y = per capita disposal income, PT = price of tea, Q = coffee consumption per head, and Ds are dummy variables Estimating demand for coffee

 This is taken from previous course material prepared by Professor Hannele Wallenius  Data concerns the consumption of pizza among college students in America  What variables are likely to be important for explaining the demand for pizza?  What kind of data is collected?  Data covers 30 college campuses (for a given period t)  Average number of slices of pizza consumed per month Regression for pizza

 Other data:  Average price of a slice of pizza sold on the campus  Price of soft drink (complementary product consumed together with pizza; recall that Americans under the age of 21 are not legally allowed to consumer alcoholic drinks)  Tuition fee (a proxy for income; higher tuition fee implies higher income (of the parents))  Location of the campus (urban=1, non-urban=0); this is a proxy for substitutes for pizza (i.e., are the other dinner options, such as Chinese, Mexican, etc.) Regression (cont.)

The regression model to be estimated is as follows: Y = a + b1*PP + b2*PS + b3*T + b4*L where a = intercept PP = price of pizza slice (in cents) PS = price of soft drink (in cents) T = tuition (in thousands of US dollars) L = location (dummy variable) Regression (cont.)

The estimation result is: Y = – 0.088*PP *PS *T – 0.544*L (3.28)* (0.018)* (0.020)* (0.087) (0.884) R-square = R-square adjusted for degrees of freedom = 0.67 F – statistic = 15.8 (significant) Numbers in parenthesis are t-test values Regression (cont.)

Regression – Chart actual and forecast

 How to interpret these results?  Are the signs of the estimated parameters consistent with the theory?  What should be the sign of PP (law of demand)?  What should be the sign of PS (complementary good)?  What determines the sign of the income proxy (normal or inferior good)?  How about the location variable (recall that urban=0)? Regression (cont.)

 How much a one dollar (100 cents) increase in the price of pizza is going to change the demand for pizza?  Is the demand or pizza elastic or inelastic?  What is the price elasticity of pizza demand?  What is the cross-price elasticity?  Stationarity, constancy of variance, autocorrelation  Heteroscedasticity (error variance is not constant) Regression (cont.)