1. Demand Estimation and Forecasting
Regression Analysis
Problems in Use of Regression Analysis
Subjects of Forecasts
Prerequisites of a Good Forecast
Forecasting Techniques

2. Learning Objectives
Specify components of a regression model that can be used to estimate a demand equation
Interpret regression results
Explain meaning of R2
Evaluate statistical significance of regression coefficients using t-test and statistical significance of R2 using F-test

3. Learning Objectives
Recognize challenges of obtaining reliable cross-sectional and time series data on consumer behavior that can be used in regression models of demand
Understand importance of forecasting in business
Describe six different forecasting techniques

4. Learning Objectives
Show how to carry out least squares projections and decompose them into trends, seasonal, cyclical, and irregular movements
Explain basic smoothing methods of forecasting, such as moving average and exponential smoothing

5. Data Collection
Data for studies pertaining to countries, regions, or industries are readily available and reliable.
Data for analysis of specific product categories may be more difficult to obtain.
Buy from data providers (e.g. ACNielsen, IRI)
Perform a consumer survey
Focus groups
Technology: Point-of-sale, bar codes, RFID

6. Regression Analysis One use is for estimating demand functions.
Important terminology and concepts:
Least Squares Regression: Y = a + bX + e.
Confidence Intervals.
t-statistic.
R-square or Coefficient of Determination.
F-statistic.

7. Regression Analysis
Regression Analysis: A procedure commonly used by economists to estimate consumer demand with available data.
Cross-Sectional Data: provide information on variables for a given period of time.
Time Series Data: give information about variables over a number of periods of time.

8. Regression Analysis Regression equation: linear, additive
Y = a + b1X1 + b2X2 + b3X3 + b4X4
Y: dependent variable, amount to be determined
a: constant value, y-intercept
Xn: independent, explanatory variables, used to explain the variation in the dependent variable
bn: regression coefficients (measure impact of independent variables)

9. Regression Analysis Regression Results
Negative coefficient shows that as the independent variable (Xn) changes, the quantity demanded changes in the opposite direction.
Positive coefficient shows that as the independent variable (Xn) changes, the quantity demanded changes in the same direction.
Magnitude of regression coefficients is measured by elasticity of each variable.

10. Regression Analysis Statistical evaluation of regression results
t-test: test of statistical significance of each estimated regression coefficient
b: estimated coefficient
SEb: standard error of the estimated coefficient
Rule of 2: if absolute value of t is greater than 2, estimated coefficient is significant at the 5% level
If coefficient passes t-test, the variable has a true impact on demand

11. Regression Analysis Statistical evaluation of regression results
Coefficient of determination (R2): percentage of variation in the dependent variable (Y) accounted for by variation in all explanatory variables (Xn)
Value ranges from 0.0 to 1.0
Closer to 1.0, the greater the explanatory power of the regression equation
F-test: measures statistical significance of the entire regression as a whole (not each coefficient)

12. Regression Results Steps for analyzing regression results
Check signs and magnitudes
Compute elasticity coefficients
Determine statistical significance

13. Regression Problems
Identification Problem: The estimation of demand may produce biased results due to simultaneous shifting of supply and demand curves.
Advanced estimation techniques, such as two-stage least squares and indirect least squares, are used to correct this problem.

14. Regression Problems
Multicollinearity: two or more independent variables are highly correlated, thus it is difficult to separate the effect each has on the dependent variable.
Passing the F-test as a whole, but failing the t-test for each coefficient is a sign that multicollinearity exists.
A standard remedy is to drop one of the closely related independent variables from the regression.

15. Problems
Autocorrelation: also known as serial correlation, occurs when the dependent variable relates to the independent variable according to a certain pattern.
Possible causes:
Effects on dependent variable exist that are not accounted for by the independent variables.
The relationship may be non-linear
The Durbin-Watson statistic is used to identify the presence of autocorrelation.
To correct autocorrelation consider:
Transforming the data into a different order of magnitude
Introducing leading or lagging data

16. An Example
Use a spreadsheet to estimate the following log-linear demand function.

17. Summary Output

18. Interpreting the Regression Output
The estimated log-linear demand function is:
ln(Qx) = ln(Px).
Own price elasticity: (inelastic).
How good is our estimate?
t-statistics of 5.29 and indicate that the estimated coefficients are statistically different from zero.
R-square of .17 indicates we explained only 17 percent of the variation in ln(Qx).
F-statistic significant at the 1 percent level.

19. Subjects of Forecasts Gross Domestic Product (GDP) Components of GDP
E.g. consumption expenditure, producer durable equipment expenditure, residential construction
Industry Forecasts
Sales of products across an industry
Sales of a specific product

20. Prerequisites of a Good Forecast
A good forecast should:
be consistent with other parts of the business
be based on knowledge of the relevant past
consider the economic and political environment as well as changes
be timely

21. Forecasting Techniques
Factors in choosing the right forecasting technique:
Item to be forecast
Interaction of the situation with the characteristics of available forecasting methods
Amount of historical data available
Time allowed to prepare forecast

22. Forecasting Techniques
Expert opinion
Opinion polls and market research
Surveys of spending plans
Economic indicators
Projections
Econometric models

23. Forecasting Techniques
Qualitative forecasting is based on judgments of individuals or groups.
Quantitative forecasting utilizes significant amounts of prior data as a basis for prediction.
Naïve forecasting projects past data without explaining future trends.
Causal (or explanatory) forecasting attempts to explain the functional relationships between the dependent variable and the independent variables.

24. Forecasting Techniques
Expert opinion techniques
Jury of executive opinion: Forecasts generated by a group of corporate executives assembled together. The major drawback is that persons with strong personalities may exercise disproportionate influence.
The Delphi Method: A form of expert opinion forecasting that uses a series of questions and answers to obtain a consensus forecast, where experts do not meet.

25. Forecasting Techniques
Opinion polls: Sample populations are surveyed to determine consumption trends.
may identify changes in trends
choice of sample is important
questions must be simple and clear
Market research is closely related to opinion polling.
Market research will indicate “not only why the consumer is or is not buying, but also who the consumer is, how he or she is using the product, and what characteristics the consumer thinks are most important in the purchasing decision.”

26. Forecasting Techniques
Surveys of spending plans: seek information about “macro-type” data relating to the economy.
Consumer intentions
Survey of Consumers, Survey Research Center, University of Michigan
Consumer Confidence Survey, The Conference Board
Inventories and sales expectations

27. Forecasting Techniques
Economic Indicators: A barometric method of forecasting designed to alert business to changes in economic conditions.
Leading, coincident, and lagging indicators
One indicator may not be very reliable, but a composite of leading indicators may be used for prediction.

28. Forecasting Techniques
Leading Indicators predict changes in future economic activity
Average hours, manufacturing
Initial claims for unemployment insurance
Manufacturers’ new orders for consumer goods and materials
Vendor performance, slower deliveries diffusion index
Manufacturers’ new orders, nondefense capital goods
Building permits, new private housing units
Stock prices, 500 common stocks
Money supply, M2
Interest rate spread, 10-year Treasury bonds minus federal funds
Index of consumer expectations

29. Forecasting Techniques
Coincident Indicators identify peaks and troughs in economic activity
Employees on nonagricultural payrolls
Personal income less transfer payments
Industrial production
Manufacturing and trade sales
Lagging Indicators confirm upturns and downturns in economic activity
Average duration of unemployment, weeks
Ratio, manufacturing and trade inventories to sales
Change in labor cost per unit of output, manufacturing (%)
Average prime rate charged by banks
Commercial and industrial loans outstanding
Ratio, consumer installment credit outstanding to personal income
Change in consumer price index for services

30. Forecasting Techniques
General rule of thumb: if, after a period of increases, the leading indicator index sustains three consecutive declines, a recession (or a slowing) will follow.
Economic indicators have predicted each recession since 1948.

31. Forecasting Techniques
Economic Indicators Drawbacks
Leading indicator index has forecast a recession when none ensued.
A change in the index does not indicate the precise size of the decline or increase.
The data are subject to revision in the ensuing months.

32. Forecasting Techniques
Trend projections: A form of naïve forecasting that projects trends from past data without taking into consideration reasons for the change.
Compound growth rate
Visual time series projections
Least squares time series projection

33. Forecasting Techniques
Compound growth rate: Forecasting by projecting the average growth rate of the past into the future.
Calculate the constant growth rate using available data, then project this constant growth rate into the future.
Provides a relatively simple and timely forecast
Appropriate when the variable to be predicted increases at a constant percentage

34. Forecasting Techniques
General compound growth rate formula:
E = B(1+i)n
E = final value
n = years in the series
B = beginning value
i = constant growth rate

35. Forecasting Techniques
Visual Time Series Projections: plotting observations on a graph and viewing the shape of the data and any trends.

36. Forecasting Techniques
Time series analysis: A naïve method of forecasting from past data by using least squares statistical methods.
Data collected of a number of periods usually exhibit certain characteristics:
Trends
Cyclical fluctuations
Seasonal fluctuations
Irregular movements

37. Forecasting Techniques
Time Series Analysis Advantages
easy to calculate
does not require much judgment or analytical skill
describes the best possible fit for past data
usually reasonably reliable in the short run

38. Forecasting Techniques
Yt = f(Tt, Ct, St, Rt)
Yt = Actual value of the data at time t
Tt = Trend component at t
Ct = Cyclical component at t
St = Seasonal component at t
Rt = Random component at t
Additive form: Yt = Tt + Ct + St + Rt
Multiplicative form: Yt = (Tt)(Ct)(St)(Rt)

39. Forecasting Techniques
Must decompose the time series into its four components
Remove seasonality
Compute trend
Isolate cycle
Cannot do anything with random component

40. Forecasting Techniques
Seasonality: need to identify and remove seasonal factors, using moving averages to isolate those factors.
Remove seasonality by dividing data by seasonal factor

41. Forecasting Techniques
Trend Line: use least squares method
Possible best-fit line styles:
Straight Line: Y = a + b(t)
Exponential Line: Y = abt
Quadratic Line: Y = a + b(t) + c(t)2
Choose style with a balance of high R2 and high t-statistics

42. Forecasting Techniques
Cycle and Random Elements
Random factors cannot be predicted and should be ignored
Isolate cycle by smoothing with a moving average

43. Forecasting Techniques
Smoothing Techniques
Moving Average
Exponential Smoothing
Work best when:
No strong trend in series
Infrequent changes in direction of series
Fluctuations are random rather than seasonal or cyclical

44. Forecasting Techniques
Moving Average: average of actual past results used to forecast one period ahead
Et+1 = (Xt + Xt-1 + … + Xt-N+1)/N
Et+1 : forecast for next period
Xt, Xt-1 : actual values at their respective times
N: number of observations included in average

45. Forecasting Techniques
Exponential Smoothing: allows for decreasing importance of information in the more distant past, through geometric progression
Et+1 = w·Xt + (1-w) · Et
w: weight assigned to an actual observation at period t

46. Forecasting Techniques
Econometric Models: causal or explanatory models of forecasting
Regression analysis
Multiple equation systems
Endogenous variables: comparable to dependent variables of single-equation model, but may influence other endogenous variables
Exogenous variables: from outside the system, truly independent variables