1. Chapter 7 Demand Estimation and Forecasting

2. Learning Objectives
Explain strengths and weaknesses of direct methods of demand estimation
Specify an empirical demand function
Employ linear regression methodology to estimate the demand function for a single price-setting firm
Forecast sales and prices using time-series regression analysis
Use dummy variables in time-series demand analysis to account for cyclical or seasonal variation in sales
Discuss and explain several important problems that arise when using statistical methods to forecast demand

3. Direct Methods of Demand Estimation
Consumer interviews
Range from stopping shoppers to speak with them to administering detailed questionnaires

4. Direct Methods of Demand Estimation
Potential problems with consumer interviews
Selection of a representative sample, which is a sample (usually random) having characteristics that accurately reflect the population as a whole
Response bias, which is the difference between responses given by an individual to a hypothetical question and the action the individual takes when the situation actually occurs
Inability of the respondent to answer accurately

5. Direct Methods of Demand Estimation
Market studies & experiments
Market studies attempt to hold everything constant during the study except the price of the good
Lab experiments use volunteers to simulate actual buying conditions
Field experiments observe actual behavior of consumers

6. Empirical Demand Functions
Demand equations derived from actual market data
Useful in making pricing & production decisions

7. Empirical Demand Functions
In linear form, an empirical demand function can be specified as
where Q is quantity demanded, P is the price of the good or service, M is consumer income, PR is the price of some related good R, and N is the number of buyers

8. 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

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

10. Nonlinear Empirical Demand Specification
When demand is specified in log-linear form, the demand function can be written as
To estimate a log-linear demand function, covert to logarithms
In this form, elasticities are constant

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 the firm’s demand function
Step 3: Estimate firm’s demand

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
Use regression analysis to estimate
values of a and b
If b > 0, sales are increasing over time
If b < 0, sales are decreasing over time
If b = 0, sales are constant over time
Statistical significance of a trend is
determined by testing or by examining
the p-value for

14. A Linear Trend Forecast (Figure 7.1)Q
Sales t
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012 
Estimated trend line
2018  12
2013  7

15. Forecasting Sales for Terminator Pest Control (Figure 7.2)
2013
2014

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 7.3)
2010
2011
2012
2013

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 one (1) for observations that occur during the season assigned to that dummy variable
Takes value of zero (0) otherwise

19. Effect of Seasonal Variation (Figure 7.4)Qt
Qt = a′ + bt a′ a
Qt = a + bt
Sales c t
Time

20. 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

21. Some Final Warnings
Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market

22. Summary
Consumer interviews and market studies are two direct methods of demand estimation
Problems can include: (1) selection of a representative sample; (2) response bias; and (3) inability of the respondent to answer accurately
Empirical demand functions are demand equations derived from actual market data and are extremely useful in making pricing and production decisions
The first step to estimating a single price-setting firm’s demand is to specify the demand function; the second step is to collect data; the third step is to estimate the parameters using the linear regression

23. Summary
A time-series model shows how a time-ordered sequence of observations on a variable is generated
The simplest form of time-series forecasting is linear trend forecasting
Seasonal or cyclical variation can bias results in linear trend models; to account for this, dummy variables are added to the trend equation
Dummy variables take a value of 1 for those observations that occur during the season assigned to that dummy variable, and a value of 0 otherwise
When making forecasts, analysts must recognize the limitations that are inherent in forecasting