Managerial EconomicsEstimating Demand Example

Aalto UniversitySchool of Science

Department of Industrial Engineering and Management

January 12 – 28, 2016Dr. 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)bε(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) + 0.51*lnY(t)(- 2.14) (1.23) + 0.15ln*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*Lwhere 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 = 26.67 – 0.088*PP - 0.076*PS + 0.13*T – 0.544*L (3.28)* (0.018)* (0.020)* (0.087) (0.884)

R-square = 0.717R-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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00

2.00

4.00

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16.00

Y-hat Y

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.)