Demand Estimation & Forecasting Chapter 7 Demand Estimation & Forecasting

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

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

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

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

Empirical Demand Functions Estimated elasticities of demand are computed as

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

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 using ordinary least-squares regression (OLS)

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)

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

A Linear Trend Forecast (Figure 7.1) Q Estimated trend line 2012  12 2007  7    Sales        t 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Time

Forecasting Sales for Terminator Pest Control (Figure 7.2)

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

Sales with Seasonal Variation (Figure 7.3)  2004 2005 2006 2007

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

Effect of Seasonal Variation (Figure 7.4) Qt Qt = a’ + bt a’ a Qt = a + bt Sales c t Time

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