Empirical Demand Functions

1
Empirical Demand Functions

• Problems in Specification Estimation

2
Objectives of Discussion

• Provide overview of several different methods of
  estimating demand functions
• Provide more in-depth examination of statistical
  demand estimation
• Discuss what is involved in setting up a
  statistical demand estimation
• Look at the special issues that are involved in
  estimating Price Takers Demand
• Examine the techniques issues in estimating an
  Price Setters demand

3
Consumer Surveys Demand Estimation

• Advantage
• Can focus more directly on question of interest
• Many problems
• Sample selection--3 Rs--random, representative
  robust
• Bias--interviewer, respondent and analyst
• Over-commitment bias--gap between intentions
  actions
• Confusing questions
• Lack of information by respondents
• Attention decay

4
Market Simulations Experiments

• Technique
• test market environments or market experiments
  are set-up to measure responses
• Problems
• Very expensive to conduct a meaningful experiment
• Usually undertaken on a scale that is too small
  to generalize
• Always have many uncontrollable variables that
  may affect results

5
Statistical Demand Estimation

• Problems
• Frequently misused by untrained, or unscrupulous
• Finding the right database
• Advantages
• Potential to yield more accurate results than
  other methods
• Involves data based on observation, rather than
  participation--less likelihood of biased or
  incorrect data
• Can estimate the affects between two variables,
  while holding other factors constant
• Can develop probability statements about results

6
Specifying the Demand Model

• Specifying the variables to be included
• Rely on theory of consumer behavior
• Variables suggested--Price, income, price of
  related goods, size of market, price
  expectations, tastes
• Frequently ignore price expectations tastes
  because hard to get good data
• Choosing appropriate measures for variables?
• For example what price do you use in a study of
  housing?
• What measure do you use for income in study of
  housing?--per capita income? household income?
• What geographic boundaries do you choose for
  measuring a variable?

7
Specifying the Demand Model

• Choosing a functional form?
• For demand functions usually choose between
  linear form power function
• Linear function

• Parameters in linear function tell change in Qx
  for 1-unit change in associated variable

..\Case Studies\MP3 Players at Sunny's Music.xls
8
Linear Demand Function Elasticity

• Most price elasticities are dependent on point at
  which it is measured on demand curve
• Usually measure E at mean values of all
  right-hand side variables
• Coefficient must be significant for elasticity
  estimate to be valid
• Other elasticity coefficients measured in similar
  manner

9
Power Function

• Used frequently when think demand is nonlinear
• Exponents are the elasticities of associated
  variables
• Elasticities are constant
• Can be estimated with same techniques of linear
  function by taking logs of both sides
• ..\Case Studies\MP3 Players at Sunny's Music.xls

10
Estimating Market Demand

• What is main problem with estimating Mkt Demand?
• Values for price and quantity are determined
  affected by variations in both supply demand
• Leads to what is referred to as The
  Simultaneity Problem--actually two problems
• The identification problem--being able to
  identify if changes in price quantity are
  movements along a demand curve or movements
  between equilibrium points
• Simultaneous Eq. Bias--Because price is
  endogenous, it is correlated with the error terms
  cant be estimate with OLS

11
The Identification Problem

• In order to identify the demand curve, must have
  observations of price and quantity that can be
  traced to shifts in Supply curve
• To trace out a demand curve, need to have way of
  allowing for shifts in supply while holding
  demand fixed.
• This happens when supply equation includes at
  least one variable that causes supply to shift,
  but does not have any effect on demand e.g.
• Qd a b(P) and QS k d(P) f(L) where L
  is price of labor.
• C7 Simultaneous Shifts.ppt
• C7 Trace Demand.ppt

12
2SLS

• OLS technique for estimating equations doesnt
  work when have simultaneous equations such as
  exist in market demand situation
• The technique of two stage least squares is then
  used
• The second stage of 2SLS produces estimates that
  look very similar to OLS
• Main difference is that technique does not
  produce a measure of overall goodness of fit like
  OLS
• t-statistics can still be used to test individual
  coefficients

13
Estimating Individual Firms Demand

• Many times easier than estimating market demand
  because no simultaneity problem
• Can only estimate demand for price-setting
  firms because price taking firms demand is
  perfectly elastic
• Use typical demand specification in most cases

14
Time-Series Forecasts

• A time-series model shows how a time-ordered
  sequence of observations on a variable is
  generated
• Simplest form is linear trend forecasting
• Sales in each time period (Qt ) are assumed to be
  linearly related to time (t)

15
Linear Trend Forecasting

• If b gt 0, sales are increasing over time
• If b lt 0, sales are decreasing over time
• If b 0, sales are constant over time

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A Linear Trend Forecast(Figure 7.1)
Q
?
?
?
Sales
?
?
?
?
?
?
?
t
2004
2005
2006
1997
1998
1999
2000
2001
2002
2003
Time
17
Forecasting Sales for Terminator Pest Control
(Figure 7.2)
18
Seasonal (or Cyclical) Variation

• Can bias the estimation of parameters in linear
  trend forecasting
• To account for such variation, dummy variables
  are added to the trend equation
• Shift trend line up or down depending on the
  particular seasonal pattern
• Significance of seasonal behavior determined by
  using t-test or p-value for the estimated
  coefficient on the dummy variable

19
Sales with Seasonal Variation(Figure 7.3)
2004
2005
2006
2007
20
Dummy Variables

• To account for N seasonal time periods
• N 1 dummy variables are added
• Each dummy variable accounts for one seasonal
  time period
• Takes value of 1 for observations that occur
  during the season assigned to that dummy variable
• Takes value of 0 otherwise

21
Effect of Seasonal Variation(Figure 7.4)
Qt
Sales
t
Time
22
Some Final Warnings

• The further into the future a forecast is made,
  the wider is the confidence interval or region of
  uncertainty
• Model misspecification, either by excluding an
  important variable or by using an inappropriate
  functional form, reduces reliability of the
  forecast
• Forecasts are incapable of predicting sharp
  changes that occur because of structural changes
  in the market