Demand Estimation and Forecasting

Demand Forecasting

• Accurate demand forecasting is essential for a firm to enable it to produce the required quantities at the right time and arrange well in advance for the various factors of production, viz., raw materials, equipment, machine accessories, labour, buildings, etc.

• In a developing economy like India, supple forecasting seems more important. However, the situation is changing rapidly.

• Factors involved in Demand Forecasting– How far ahead?a. Long term – eg., petroleum, paper, shipping. Tactical

decisions. Within the limits of resources already available.

b. Short-term – eg., clothes. Strategic decisions. Extending or reducing the limits of resources.

Factors involved in Demand Forecasting

2. Undertaken at three levels:a. Macro-levelb. Industry level eg., trade associationsc. Firm level3. Should the forecast be general or specific (product-

wise)?4. Problems or methods of forecasting for “new” vis-à-vis

“well established” products.5. Classification of products – producer goods, consumer

durables, consumer goods, services.6. Special factors peculiar to the product and the market –

risk and uncertainty. (eg., ladies’ dresses)

Purposes of forecasting• Purposes of short-term forecasting

a. Appropriate production scheduling.

b. Reducing costs of purchasing raw materials.

c. Determining appropriate price policy

d. Setting sales targets and establishing controls and incentives.

e. Evolving a suitable advertising and promotional campaign.

f. Forecasting short term financial requirements.• Purposes of long-term forecasting

a. Planning of a new unit or expansion of an existing unit.

b. Planning long term financial requirements.

c. Planning man-power requirements.

Length of forecasts

• Short-term forecasts – upto 12 months, eg., sales quotas, inventory control, production schedules, planning cash flows, budgeting.

• Medium-term – 1-2 years, eg., rate of maintenance, schedule of operations, budgetary control over expenses.

• Long-term – 3-10 years, eg., capital expenditures, personnel requirements, financial requirements, raw material requirements.

(Most uncertain in nature)

Forecasting demand for new products

Forecasting demand for new products – Joel Dean1. Project the demand for a new product as an outgrowth

of an existing old product.2. Analyse the new product as a substitute for some

existing product or service.3. Estimate the rate of growth and the ultimate level of

demand for the new product on the basis of the pattern of growth of established products.

4. Estimate the demand by making direct enquiries from the ultimate purchasers, either by the use of samples or on a full scale.

5. Offer the new product for sale in a sample market, eg., by direct mail or through one multiple shop organisation.

6. Survey consumers’ reactions to a new product indirectly through the eyes of specialised dealers who are supposed to be informed about consumers’ need and alternative opportunities.

Criteria of a good forecasting method1. Accuracy – measured by (a) degree of

deviations between forecasts and actuals, and (b) the extent of success in forecasting directional changes.

2. Simplicity and ease of comprehension.

3. Economy.

4. Availability.

5. Maintenance of timeliness.

Role of Macro-level forecasting in demand forecasts

• Various macro parameters found useful for demand forecasting:

1. National income and per capita income.

2. Savings.

3. Investment.

4. Population growth.

5. Government expenditure.

6. Taxation.

7. Credit policy.

Methods of demand forecasting

1. Survey of buyers’ intentions2. Delphi method3. Expert opinion4. Collective opinion5. Naïve models6. Smoothing techniquesa. Moving averageb. Exponential smoothing7. Analysis of time series and trend projections8. Use of economic indicators9. Controlled experiments10. Judgemental approach

Methods of demand forecastingThough statistical techniques are essential in clarifying relationships

and providing techniques of analysis, they are not substitutes for judgement. What is needed is some common sense mean between pure guessing and too much mathematics.

1. Survey of buyers’ intentions: also known as Opinion surveys. Useful when customers are industrial producers. (However, a number of biases may creep up). Not very useful for household consumers.

Limitation: passive and “does not expose and measure the variables under management’s control”

2. Delphi method: it consists of an effort to arrive at a consensus in an uncertain area by questioning a group of experts repeatedly until the results appear to converge along a single line of the issues causing disagreement are clearly defined.

Developed by Rand Corporation of the U.S.A in 1940s by Olaf Helmer, Dalkey and Gordon. Useful in technological forecasting (non-economic variables).

Delphi methodAdvantages

1. Facilitates the maintenance of anonymity of the respondent’s identity throughout the course.

2. Saves time and other resources in approaching a large number of experts for their views.

Limitations/presumptions:

1. Panelists must be rich in their expertise, possess wide knowledge and experience of the subject and have an aptitude and earnest disposition towards the participants.

2. Presupposes that its conductors are objective in their job, possess ample abilities to conceptualize the problems for discussion, generate considerable thinking, stimulate dialogue among panelists and make inferential analysis of the multitudinal views of the participants.

3. Expert opinion / “hunch” method

To ask “experts in the field” to provide estimates, eg., dealers, industry analysts, specialist marketing consultants, etc.

Advantages:1. Very simple and quick method.2. No danger of a “group-think” mentality.

4. Collective opinion method Also called “sales force polling”, salesmen are required to estimate

expected sales in their respective territories and sections.Advantages:1. Simple – no statistical techniques.2. Based on first hand knowledge.3. Quite useful in forecasting sales of new products.Disadvantages:1. Almost completely subjective.2. Usefulness restricted to short-term forecasting.3. Salesmen may be unaware of broader economic changes.

5. Naïve models/ Historical methodNaïve forecasting models are based exclusively on historical

observation of sales (or other variables such as earnings, cash flows, etc). They do not explain the underlying casual relationships which produces the variable being forecast.

Advantage: Inexpensive to develop, store data and operate.

Disadvantage: does not consider any possible causal relationships that underlie the forecasted variable.

3-naïve models

1. To use actual sales of the current period as the forecast for the next

period; then, Yt+1 = Yt

2. If we consider trends, then, Yt+1 = Yt + (Yt – Yt-1)

3. If we want to incorporate the rate of change, rather than the absolute amount; then,

Yt+1 = Yt (Yt / Yt-1)

6. Smoothing techniquesHigher form of naïve models:A. Moving average: are averages that are updated as new information is

received. With the moving average a manager simply employs, the most recent observations, drops the oldest observation, in the earlier calculation and calculates an average which is used as the forecast for the next period.

Limitations:• One has to retain a great deal of data.• All data in the sample are weighed equally.B. Exponential smoothing: uses weighted average of past data as the

basis for a forecast. It uses the weights allotted to the each trend.

Yt+1 = aYt + (1-a) Yt or Y new = a Y old + (1-a) Y’ old, where,Y new = exponentially smoothed average to be used as the forecastY old = most recent actual dataY’old = most recent smoothed forecasta = smoothing constantSmoothing constant (or weight) has a value between 0 and 1 inclusive.

Exponential smoothing

• The following rules of thumb may be given :

1. When the magnitude of the random variations is large, give a lower value to “a” so as to average out the effects of the random variation quickly.

2. When the magnitude of the random variation is moderate, a large value can be assigned to the smoothing constant “a”.

3. It has been found appropriate to have “a” between 0.1 and 0.2 in many systems.

Advantages:

Exponential smoothing is a forecasting method easy to use and efficiently handled by computers. Although a type of moving average technique, it requires very little record keeping of past data. This method has been successfully applied by banks, manufacturing companies, wholesalers and other organizations.

7. Analysis of time series and trend projections

• The time series relating to sales represent the past pattern of effective demand for a particular product. Such data can be presented either in a tabular form or graphically for further analysis. The most popular method of analysis of the time series is to project the trend of the time series.a trend line can be fitted through a series either visually or by means of statistical techniques. The analyst chooses a plausible algebraic relation (linear, quadratic, logarithmic, etc.) between sales and the independent variable, time. The trend line is then projected into the future by extrapolation.

• Popular because: simple, inexpensive, time series data often exhibit a persistent growth trend.

• Disadvantage: this technique yields acceptable results so long as the time series shows a persistent tendency to move in the same direction. Whenever a turning point occurs, however, the trend projection breaks down.

The real challenge of forecasting is in the prediction of turning points rather than in the projection of trends.

Analysis of time series and trend projections

• Four sets of factors: secular trend (T), seasonal variation (S), cyclical fluctuations (C ), irregular or random forces (I).

O (observations) = TSCI

Assumptions:

1. The analysis of movements would be in the order of trend, seasonal variations and cyclical changes.

2. Effects of each component are independent of each other.

8. Use of economic indicatorsThe use of this approach bases demand forecasting on certain

economic indicators, eg.,1. Construction contracts sanctioned for the demand of

building materials, say, cement;2. Personal income for the demand of consumer goods;3. Agricultural income for the demand of agricultural inputs,

implements, fertilizers, etc,; and4. Automobile registration for the demand of car accessories,

petrol, etc.Steps for economic indicators:1. See whether a relationship exists between the demand for

the product and certain economic indicators.2. Establish the relationship through the method of least

squares and derive the regression equation. (Y= a + bx)3. Once regression equation is derived, the value of Y (demand)

can be estimated for any given value of x.4. Past relationships may not recur. Hence, need for value

judgement.

Use of economic indicators• Limitations:

1. Finding an appropriate economic indicator may be difficult.

2. For new products – no past data exists.

3. Works best when the relationship of demand with a particular indicator is characterized by a time lag. Eg., construction contracts will result in a demand for building materials but with a certain amount of time lag.

9. Controlled experiments

• Under this method, an effort is made to vary separately certain determinants of demand which can be manipulated, e.g., price, advertising, etc., and conduct the experiments assuming that the other factors remain constant.

• Example – Parker Pen Co.• Still relatively new and untried:1. Experiments are expensive as well as time

consuming.2. Risky – may lead to unfavourable reaction on

dealers, consumers, competitors, etc.3. Great difficulty in planning the study.difficult to

satisfy the condition of homogeneity of markets.

10. Judgemental approach• Required when:1. Analysis of time series and trend projections is not

feasible because of wide fluctuations in sales or because of anticipated changes in trends; and

2. Use of regression method is not possible because of lack of historical data or because of management’s inability to predict or even identify causal factors.

Even statistical methods require supplementation of judgement:

1. Even the most sophisticated statistical methods cannot incorporate all the potential factors, e.g., a major technological breakthrough in product or process design.

2. For industrial products – if the management anticipates loss or addition of few large buyers, it could be taken into account only through judgement approach.

3. Statistical forecasts are more reliable for larger levels of aggregations.

Approach to forecasting1. Identify and clearly state the objectives of forecasting.2. Select appropriate method of forecasting.3. Identify the variables.4. Gather relevant data.5. Determine the most probable relationship.6. For forecasting the company’s share in the demand, two

different assumptions may be made:(a) Ratio of company sales to the total industry sales will

continue as in the past.(b) On the basis of an analysis of likely competition and industry

trends, the company may assume a market share different from that of the past. (alternative / rolling forecasts)

7. Forecasts may be made either in terms of units or sales in rupees.

8. May be made in terms of product groups and then broken for individual products.

9. May be made on annual basis and then divided month-wise, etc.

Demand Estimation

• These are various quantitative methods to find the exact relationship between the dependent variable and the independent variable(s).

• The most common method is regression analysis

• Simple (bivariate) Regression: Y = a + bX

• Multiple Regression: Y = a +bX1 + c X2 +dX3 +...

Most common methods used are:

a) consumer interviews or surveys to estimate the demand for new products to test customers reactions to changes in the

price or advertising to test commitment for established products

b) market studies and experiments to test new or improved products in controlled

settings

c) regression analysis uses historical data to estimate demand functions

Consumer Interviews (Surveys)

• Ask potential buyers how much of the commodity they would buy at different prices (or with alternative values for the non-price determinants of demand)

face to face approachtelephone interviews

Consumer Interviews cont’d

• Problems:– Selection of a representative sample

• what is a good sample?

– Response bias• how truthful can they be?

– Inability or unwillingness of the respondent to answer accurately

Market Studies and Experiments

• More expensive and difficult technique for estimating demand and demand elasticity is the controlled market study or experiment– Displaying the products in several different

stores, generally in areas with different characteristics, over a period of time

• for instance, changing the price, holding everything else constant

Market Studies and Experiments cont’d

• Experiments in laboratory or field– a compromise between market studies and

surveys– volunteers are paid to stimulate buying

conditions

Market Studies and Experiments cont’d

• Problems in conducting market studies and experiments:a) expensive

b) availability of subjects

c) do subjects relate to the problem, do they take them seriously?

BUT: today information on market behavior also collected by membership and award cards

Regression Analysis and Demand Estimation

• A frequently used statistical technique in demand estimation

• Estimates the quantitative relationship between the dependent variable and independent variable(s)

quantity demanded being the dependent variable

if only one independent variable (predictor) used: simple regression

if several independent variables used: multiple regression

A Linear Regression Model

• In practice the dependence of one variable on another might take any number of forms, but an assumption of linear dependency will often provide an adequate approximation to the true relationship

Think of a demand function of general form:

Qi = + 1Y - 2 pi + 3ps - 4pc + 5Z + ε

whereQi = quantity demanded of good iY = incomepi = price of good ips = price of substitute(s)pc = price of complement(s)Z = other relevant determinant(s) of demandε = error term

Values of and i ?

and i have to be estimated from historical data

• Data used in regression analysiscross-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

• New technologies are currently dramatically changing the possibilities of data collection

Simple Linear Regression Model

In the simplest case, the dependent variable Y is assumed to have the following relationship with the independent variable X:

Y = + X + εwhere

Y = dependent variableX = independent variable = intercept = slopeε = random factor

Estimating the Regression Equation

• Finding a line that “best fits” the data– The line that best fits a collection of X,Y data

points, is the line minimizing the sum of the squared distances from the points to the line as measured in the vertical direction

– This line is known as a regression line, and the equation is called a regression equation

Estimated Regression Line:

XY ˆ

Observed Combinations of Output and Labor input

Skatter Plot

0

100

200

300

400

500

600

0 100 200 300 400 500 600 700 800

L

Q

L

Q

YY ˆ

Regression with ExcelSUMMARY OUTPUT

Regression StatisticsMultiple R 0,959701R Square 0,921026Adjusted R Square0,917265Standard Error47,64577Observations 23

ANOVAdf SS MS F Significance F

Regression 1 555973,1 555973,1 244,9092 4,74E-13Residual 21 47672,52 2270,12Total 22 603645,7

CoefficientsStandard Errort Stat P-value Lower 95%Upper 95%Lower 95,0%Upper 95,0%Intercept -75,6948 31,64911 -2,39169 0,026208 -141,513 -9,87686 -141,513 -9,87686X Variable 11,377832 0,088043 15,64957 4,74E-13 1,194737 1,560927 1,194737 1,560927

Evaluate statistical significance of regression coefficients using t-test and statistical significance of R2 using F-test

Statistical analysis is testing hypotheses

• Statistics is based on testing hypotheses

• ”null” hypothesis = ”no effect”

• Assume a distribution for the data, calculate the test statistic, and check the probability of getting a larger test statistic value

X

Z

Z For the normal distribution:

p

t-test: test of statistical significance of each estimated regression coefficient

i = estimated coefficient

• H0: i = 0

• SEβ: 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 (= p-value < 0.05)

• If coefficient passes t-test, the variable has an impact on demand

iSE

t i

Sum of Squares

Sum of Squares cont’d

TSS = (Yi - Y)2

(total variability of the dependent variable about its mean Y)

RSS = (Ŷi - Y)2

(variability in Y explained by the sample regression)

ESS = (Yi - Ŷi)2

(variability in Yi unexplained by the dependent variable x)

This regression line gives the minimum ESS among all possible straight lines.

The Coefficient of Determination

• Coefficient of determination R2 measures how well the line fits the scatter plot (Goodness of Fit)

R2 is always between 0 and 1 If it’s near 1 it means that the regression line is a

good fit to the dataAnother interpretation: the percentage of

variance ”accounted for”

TSSESS

1TSSRSS

R2

F-test

• The null hyphotesis in the F-test is

H0: 1= 0, 2= 0, 3= 0, …• F-test tells you whether the model as a whole

explains variation in the dependent variable• No rule of thumb, because the values of the

F-distribution vary a lot depending on the degrees of freedom (# of variables vs. # of observations)– Look at p-value (”significance F”)

Special Cases:

• Proxy variables– to present some other “real” variable, such as taste or

preference, which is difficult to measure

• Dummy variables (X1= 0; X2= 1)– for qualitative variable, such as gender or location

• Linear vs. non-linear relationship– quadratic terms or logarithms can be used

Y = a + bX1 + cX12

QD=aIb logQD= loga + blogI

Example: Specifying the Regression Equation for Pizza Demand

We want to estimate the demand for pizza among college students in USA

What variables would most likely affect their demand for pizza?

What kind of data to collect?

Data: Suppose we have obtained cross-sectional data on randomly selected 30 college campuses

(through a survey)

The following information is available:average number of slices consumed per

month by studentsaverage price of a slice of pizza sold around

the campusprice of its complementary product (soft

drink)tuition fee (as proxy for income)location of the campus (dummy variable is

included to find out whether the demand for pizza is affected by the number of available substitutes); 1 urban, 0 for non-urban area

Linear additive regression line:

Y = a + b1pp + b2 ps + b3T + b4L

where Y = quantity of pizza demandeda = the intercept

Pp= price of pizza

Ps= price of soft drinkT = tuition feeL = location

bi = coefficients of the X variables measuring the impact of the variables on the demand for pizza

Estimating and Interpreting the Regression Coefficients

Y = 26.27- 0.088pp - 0.076ps + 0.138T- 0.544 L (0.018) (0.018)* (0.020)* (0.087) (0.884)

R2 = 0.717adjusted R2 = 0.67F = 15.8

Numbers in parentheses are standard errors of coefficients.

*significant at the 0.01 level

Problems in the Use of Regression Analysis:

• identification problem

• multicollinearity (correlation of coefficients)

• autocorrelation (Durbin-Watson test)

• normality assumption fails

(outside the scope of this course)

Identification Problem

• Can arise when all effects on Y are not accounted for by the predictors

Q

P

Q

P S

D3

D2

D1

Can demand be upward sloping?!

OR…?

D?!

Multicollinearity

• A significant problem in multiple regression which occurs when there is a very high correlation between some of the predictor variables.

Resulting problem:

Regression coefficients may be very misleading or meaningless because…

– their values are sensitive to small changes in the data or to adding additional observations

– they may even be opposite in sign from what ”makes sense”

– their t-value (and the standard error) may change a lot depending upon which other predictors are in the model

Multicollinearity cont’d

Solution:

Don’t use two predictors which are very highly correlated (however, x and x2 are O.K.)

Not a major problem if we are only trying to fit the data and make predictions and we are not interested in interpreting the numerical values of the individual regression coefficients.

Multicollinearity cont’d

• One way to detect the presence of multicollinearity is to examine the correlation matrix of the predictor variables. If a pair of these have a high correlation they both should not be in the regression equation – delete one.

Y X1 X2 X3

Y 1.00 -.45 .81 .86

X1 -.45 1.00 -.82 -.59

X2 .81 -.82 1.00 .91

X3 .86 -.59 .91 1.00

Correlation Matrix

Autocorrelation

• Correlation between consecutive observations

• Usually encountered with time series data– E.g. seasonal variation in demand

time

D Creates a problem with t-tests: insignificant variables may appear significant

A test for Autocorrelated Errors:DURBIN-WATSON TEST

• A statistical test for the presence of autocorrelation

• Fit the time series with a regression model and then determine the residuals:

ttt yy ˆ

n

tt

n

ttt

d

1

2

2

21)(

The Interpretation of d:

The Durbin-Watson value d will always be 0 d 4

40 2

No correlation

Strong negative correlation

Strong positive correlation

Multiple Regression Procedure

1. Determine the appropriate predictors and the form of the regression model

– Linear relationship– No multicollinearity– Variables ”make sense”

2. Estimate the unknown and coefficients3. Check the “goodness” of the model (R2, global F-

test, individual t-test for each coefficient)4. Use the fitted model for predictions (and

determine their accuracy)