1. Demand Estimation & Forecasting
Chapter 7
Demand Estimation & Forecasting

2. Empirical Demand Functions
Demand equations derived from actual market data
Useful in making pricing & production decisions
In linear form, an empirical demand function can be specified as

3. Empirical Demand Functions
In linear form
b = Q/P
c = Q/M
d = Q/PR
Expected signs of coefficients
b is expected to be negative
c is positive for normal goods; negative for inferior goods
d is positive for substitutes; negative for complements

4. Empirical Demand Functions
Estimated elasticities of demand are computed as

5. Nonlinear Empirical Demand Specification
When demand is specified in log-linear form, the demand function can be written as

6. Market-Determined vs. Manager-Determined Prices
Method of estimating parameters of an empirical demand function depends on whether price of the product is market-determined or manager-determined
Price-taking firms do not set the price of their product
Prices are endogenous, or market-determined by the intersection of demand & supply
For price-setting firms
Prices are manager-determined, or exogenous

7. Simultaneity Problem
When estimating industry demand for price-taking firms, simultaneity problem must be addressed
Arises because output & price are determined jointly by forces of demand & supply
Two econometric problems arise
Identification problem
Simultaneous equations bias problem

8. Identification Problem
Industry demand is identified when
It is possible to estimate the true demand function from a sample of observations of equilibrium output & price
Demand is identified when supply includes at least one exogenous variable that is not also in the demand equation

9. Simultaneous Equations Bias
When price is endogenous, price will be correlated with random error term in demand equation
This causes simultaneous equations bias if OLS is applied
To avoid this bias, two-stage least-squares (2SLS) can be applied if industry demand is identified

10. Industry Demand for a Price-Taker
To estimate industry demand function for a price-taking firm:
Step 1: Specify industry demand & supply equations
Step 2: Check for identification of industry demand
Step 3: Collect data for the variables in demand & supply
Step 4: Estimate industry demand using 2SLS

11. Demand for a Price-Setter
To estimate demand function for a price-setting firm:
Step 1: Specify price-setting firm’s demand function
Step 2: Collect data for the variables in demand function
Step 3: Estimate firm’s demand using OLS

12. 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)

13. Linear Trend Forecasting
If b > 0, sales are increasing over time
If b < 0, sales are decreasing over time
If b = 0, sales are constant over time

14. A Linear Trend Forecast (Figure 7.3)Q
Estimated trend line
2009 
2004    
Sales        t
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Time

15. Forecasting Sales for Terminator Pest Control (Figure 7.4)

16. 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

17. Sales with Seasonal Variation (Figure 7.5)
2001
2002
2003
2004

18. 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

19. Effect of Seasonal Variation (Figure 7.6)Qt
Qt = a’ + bt a’ a
Qt = a + bt
Sales c t
Time

20. Econometric Models
Statistical models that uses an explicit structural model to explain underlying economic relations
Technique of forecasting with simultaneous equations employs an estimated demand & supply functions to produce forecasted values for sales & price

21. Forecasting with Simultaneous Equations
Step 1: Prevailing demand & supply functions are estimated using current data
Both equations must be identified & are estimated using 2SLS
Step 2: Future values of exogenous variables are obtained by estimation or forecasting models
Forecast values are substituted into demand & supply equations

22. Forecasting with Simultaneous Equations
Step 3: Intersection of future demand & supply equations is found
Values of P & Q at the intersection are the forecast values of sales & price for that future period

23. 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