ECO 3104

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ECO 3104

• Lecture 9

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Empirical Estimation of Demand

• General market demand function
• Q f(P,M,Pr,N T)
• since cant measure tastes, T, simply assume
  constant
• may include some demographic measures if believe
  they are related to tastes
• Can use Ordinary Least Squares (OLS) regression
  to estimate the parameters of the demand
  function.
• Must assume a particular functional form
• Most common are linear and log-linear

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Empirical Demand Functions
linear model Q b0 b1P b2M b3Pr b4N e

• price elasticity
• EP (?Q / ?P) (P/Q) b1(P/Q)
• remember, elasticity varies with position on
  demand curve
• income elasticity
• EM (?Q / ?M) (M/Q) b2(M/Q)
• cross-price elasticity
• EX,Py (?Q / ?Pr) (Pr/Q) b3(Pr/Q)

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Empirical Demand Functions

• log-linear (multiplicative) model
• Q (b0Pb1)(Mb2)(Prb3)(Nb4)
• can convert to linear form by taking logs
• ln(Q) ln(b0)(Pb1)(Mb2)(Prb3)(Nb4)
• ln(Q) ln(b0) ln(Pb1) ln(Mb2) ln(Prb3)
  ln(Nb4)
• ln(Q) ln(b0) b1ln(P) b2ln(M)
• b3ln(Pr) b4ln(N)

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Empirical Demand Functions
log-linear (multiplicative) model ln(Q) ln(b0)
b1ln(P) b2ln(M) b3ln(Pr) b4ln(N) e

• price elasticity
• b1 ?(ln(Q))/?(ln(P))
• b1 (?Q/Q)/(?P/P)
• EP b1
• price elasticity is just coefficient on price
  variable
• income elasticity
• EM b2
• cross-price elasticity
• EX,Py b3

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Empirical Estimation of Demand

• Example
• estimating individual demand for health care

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Empirical Estimation of Demand

• Choosing a specification
• should consider what other researchers have used
• a-priori reasons
• model fit
• statistical tests exist for comparing fits of
  different models
• cant use R2 if dependent variable is different
  (eg. Q in linear model vs. ln(Q) in
  multiplicative model)
• so-called Box-Cox tests can be used, but beyond
  scope of this course
• constant elasticity (log-linear) model most common

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Empirical Estimation of Demand

• Accounting for other stuff
• what factors (besides price, income, prices of
  related goods and population) should be in a
  model?
• what related-goods prices should be included?
• robustness tests
• do results vary with which additional variables
  are put into the model?
• a good model should include all of the important
  determinants of demand and have estimates that
  are invariant to the addition of other
  (unimportant) variables

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Empirical Estimation of Demand

• Simultaneity problem

• equilibrium price and quantity are simultaneously
  determined by supply and demand
• OLS will produce biased coefficient estimates

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Empirical Estimation of Demand
Price
Quantity
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Empirical Estimation of Demand

• Simultaneity problem
• one of the basic assumptions underlying OLS is
  that explanatory variables and error term are
  independent

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Empirical Estimation of Demand
If error is correlated with explanatory variable
(Price), then OLS coefficient estimates are
biased.
Price
?
?
?
?
?
e
?
?
e
D
Quantity
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Empirical Estimation of Demand

• Simultaneity problem
• since P and Q are simultaneously determined, ed
  (which is correlated with Qd) is correlated with
  P
• assumption of independence of explanatory
  variables and error is violated, producing biased
  estimates
• similar argument for es and P

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Empirical Estimation of Demand

• Simultaneity problem
• if price is exogenous to the decision-maker (ie.
  is not affected by the decision-makers actions),
  then do not have a simultaneity problem
• individual consumer
• price-taking firm

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Empirical Estimation of Demand

• Solving the simultaneity problem
• reduced-form quantity equation
• express equilibrium quantity a a function of both
  supply-side and demand-side exogenous variables

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Empirical Estimation of Demand

• reduced-form quantity equation
• since Qequil. is a function of only exogenous
  variables, get unbiased estimates
• cannot obtain price elasticity, but can estimate
  effect on equilibrium consumption of other
  variables

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Empirical Estimation of Demand

• Example
• estimating a reduced-form quantity equation for
  Coke

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End of Lecture 9