Demand Estimationand Forecasting

• Regression Analysis• Problems in Use of Regression

Analysis• Subjects of Forecasts• Prerequisites of a Good Forecast• Forecasting Techniques

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

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

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

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

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.

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.

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)

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.

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

b̂SE

b̂ t

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)

Regression Results• Steps for analyzing regression

results– Check signs and magnitudes– Compute elasticity coefficients– Determine statistical significance

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.

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.

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

An Example

• Use a spreadsheet to estimate the following log-linear demand function.

0ln lnx x xQ P e

Summary OutputRegression Statistics

Multiple R 0.41R Square 0.17Adjusted R Square 0.15Standard Error 0.68Observations 41.00

ANOVAdf SS M S F Significance F

Regression 1.00 3.65 3.65 7.85 0.01Residual 39.00 18.13 0.46Total 40.00 21.78

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 7.58 1.43 5.29 0.000005 4.68 10.48ln(P) -0.84 0.30 -2.80 0.007868 -1.44 -0.23

Interpreting the Regression Output

• The estimated log-linear demand function is:– ln(Qx) = 7.58 - 0.84 ln(Px).

– Own price elasticity: -0.84 (inelastic).

• How good is our estimate?– t-statistics of 5.29 and -2.80 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.

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

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

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

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

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.

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.

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.”

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

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.

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

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

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.

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.

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

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

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

Forecasting Techniques• Visual Time Series Projections:

plotting observations on a graph and viewing the shape of the data and any trends.

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

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

Forecasting TechniquesYt = 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)

Forecasting Techniques• Must decompose the time series

into its four components– Remove seasonality– Compute trend– Isolate cycle– Cannot do anything with random

component

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

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

Forecasting Techniques• Cycle and Random Elements

– Random factors cannot be predicted and should be ignored

– Isolate cycle by smoothing with a moving average

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

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

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

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