Chapter 5 Corrected

8/4/2019 Chapter 5 Corrected

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DEMAND ESTIMATION ANDFORECASTING

Chapter - 5


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DEMAND ESTIMATION AND FORECASTING

Consumer Survey:

The attempt to obtain data about demand directly byasking consumers about their purchasing habitsthrough such means as face-to-face interviews, focusgroups, telephone surveys and mailed questionnaire.


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Demand estimation

1. Regression Analysis:

2. The procedure commonly used by economiststo estimate consumer demand with availabledata is Regression Analysis.

3. Regression analysis: A statistical technique for

finding the best relationship between adependent variable and selected independent

variables.

4. If one independent variable is used, thistechnique is referred to as simple regression, ifmore than one independent variable is used, itis called multiple regression.


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Regression Analysis

It is used for demand estimation, productionestimation and cost functions.

For estimating the demand for a particular good orservice, first determine all factors that mightinfluence the demand.

The two types of data used in regression analysisare :

Cross-sectional and Time-series.


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Regression Analysis

Cross-sectional data provide information onvariables for a given period of time.

Cross-sectional data:

Data on a particular set of variables for a given

point in time for a cross-section of individualentities (e.g., persons, house-holds, cities, states,countries)


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Regression Analysis Time series data give information about the

variables over a number of periods of time.

Time Series data: Data for a particular set of variables that track their

values over a particular period of time at regularintervals (e.g., monthly, quarterly, annually )


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Regression Analysis

We then express the regression equation to beestimated in the following linear, additive fashion:

Y = a+b1X1+b2X2+b3X3+b4X4Y = Quantity of good demanded / month (Jan)

X1, X2, X3, X4 variables that affect demand.

b1, b2, b3, b4 are coefficients of X variables measuring theimpact of the variables on the demand.

Y is dependant variable, Xs are independent variablesor explanatory variables


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Regression Analysis Example: Estimation of demand for pizza by students

in a given locality: numbers consumed per month per

student (Y) Demand equation:

Y = 26.67 0.088X1 + 0.138 X2 0.076 X3 0.544 X4

Variables:X1 = Average Price in cents[inverse determinant]

X2 = Average tuition fee in $000[indicative of income]

X3 = Average price of soft drink in cents[complement]

( coefficient negative for complement and positive forsubstitute)

X4 = Location : Urban / Rural [ 1 for dense urban areaas people have choices]Urban=1; Rural=0


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Meaning of the coefficients:

The coefficient is a partial differentiation of

(Y)with respect to the variable (X); dY/dX = valueof coefficient.

Coefficient is also the value of dY when dX is equalto 1.

In other words, if price of pizza increases by onecent, the demand will reduce by 0.088 units.

If the tuition fees increase by $1000, the demandfor pizza will increase by 0.138 units.

b1,b2,b3, b4 are all coefficients of the X variablesmeasuring the impact of the variables on thedemand for pizza.


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Meaning of the Coefficients and Elasticity:

The partial derivative of Y with respect to changesin the each variable is the estimated coefficient of

each variable. YX

The point elasticity = Q X

for a given variable X Q

Understanding the elasticity, will tell the influenceof that variable on demand


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Meaning of the Coefficients and Elasticity:

Elasticity of demand for a given variable:

Ex = [dQ/Q]/ [dX/X] where Q = quantity demanded

(or) Ex = [dQ/dX]x [X/Q]

Assume X1 = 100 cents; X2 = 14 ($14,000); X3 = 110

($ 1.10); X4= 1 (Urban)Y = 26.67 0.088X1 + 0.138 X2 0.076 X3 0.544 X4

Y = 26.67 0.088x100 + 0.138x14 0.076x110 0.544x1= 10.898 (11 approx)

Price elasticity= -0.088 x [100/10.898] = -0.807

Tuition elasticity = 0.138x [14/10.898] = 0.177

Cross Price elasticity= -0.076x [110/10.898] = -0.767


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2. Problems in the use of Regression

Analysis:

The identification Problem

Multicollinearity

Auto correlation


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The Identification Problem: (Figure 5.1)

Supposing we plot demand for pizza for a 20 yearperiod, the scatter plot is showing upward trend.

Why so?

Why demand increased when the price went up?Answer: Over a 20 year period, the non pricedeterminants have over powered the priceincrease.

There could be other factors that may beoperating.


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The Identification Problem: (Figure 5.1)

Fig (a) = Scatter Plot.

Fig (b) = Curve if supply remained constant over

20 years Fig (c) = Curve if supply and demand increased

during the 20 years

Fig (d) = Supply shifted (increased) far more than

the demand during the 20 year period.

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Multicollinearity:

One of the key assumptions made in theconstruction of the multiple regression equation isthat the independent variables are not related toeach other.

If two variables are closely associated, it becomesdifficult to separate out the effect that each has onthe dependent variable.

The existence of a such condition is referred to asMulticollinearity.


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Multicollinearity:

In such cases, statisticians use two stage least

squares method or indirect least squares methodfor plotting the graph.

In the pizza example, higher tuition fee is linked tohigher income.

However, higher income is related to higher

education and hence higher levels of healthconsciousness and hence lowers the demand forfast foods such as pizza !!


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Autocorrelation: Figure 5.2

Autocorrelation problem may be encounteredwhen time series data are used.

Assuming Y is the dependent variable and X isindependent variable.

Autocorrelation occurs when the Y variable relatesto the X variable according to a certain pattern.


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Autocorrelation: Figure 5.2

For example Figure 5.2(a) reveals that as X increases(presumably over time), the Y value deviates from theregression line in a very systematic way.

In other words, the residual term, or the differencebetween the observed value of Y and the estimated

value of Y given as X(Y), alternates between a positiveand a negative value of approximately the samemagnitude throughout the range of X values.( SeeFigure 5.2(b) )

Thus autocorrelation would render regressionequation inaccurate. Durbin Watson test is used todetect autocorrelation.


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Forecasting:3.Why forecasting?

All organizations conduct their activities in an

uncertain environment and the major role offorecasting is to reduce this uncertainty.

Subjects for forecasts:

GDP

Components of GDP such as: consumption,expenditure, residential construction, agriculturaloutput, manufacturing output, services, etc.

Industry forecasts : Coco cola (soft drinks),bottled water , automobiles, housing, etc.

Forecast of sales for specific product (eg.) DietCoke.


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Forecasting

4. Demand estimation deals with finding out effect ondemand (quantity demanded) due to a change in one ormore of independent variables

Demand forecasting is more on obtaininginformation regarding future levels of sales given thelikely assumptions about changes in independent

variables

Many a time, future sales are obtained by projecting thepast into the future.


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Forecasting techniques:

Some points for consideration

Amount of historical data available

Time allowed to prepare forecast Higher the accuracy needed, more complex the

method and higher the cost

Advisable not to discard simple methods and movingtoo quickly to complex methods.


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Forecasting

Pre - requisites of a good forecast:

Must be consistent with other business parameters

Must be based on the knowledge of the relevant

past (in case of existing products) In some cases (totally a new product) it is done

based on expert opinion.

Must consider the economic and politicalenvironment as well as potential changes

Forecast must be timely.


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Forecasting Techniques:

Qualitative Techniques:

Expert Opinion.

Opinion Polls and Market Research. Survey of Spending Plans.

Quantitative Techniques:

Economic Indicators. Projections. (Nave and Causal Forecasting)

Econometric Models


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Expert opinion:Jury of Executive Opinion:

Forecasts are generated by a group of corporateexecutives assembled together it could be intraorganizational or inter organizational.

The Delphi Method: Developed by Rand Corporation in 1950s and primarily

used for predicting technological trends and changes.

Delphi also uses a panel of experts, who do not meet.The process is carried out by a sequential series ofquestions and answers. Iterations are carried out tillthe answers are narrowed and finally a consensus is

obtained.

O i i ll d k t h


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Opinion polls and market research:

Opinion Polls: A forecasting method in which sample

populations are surveyed to determine consumption

trends.

Rather than soliciting opinion of experts, opinion polls

survey a population whose activity may determinefuture trends.

Opinion polls can be very useful because they may

identify changes in trends. Choice of the sample population is very important

because unrepresentative sample will give misleadingresults.


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Market Research

Market research is closely related to opinionpolling.

Market research will indicate not only why theconsumer is or is not buying but also who theconsumer is, how he or she is using the productand what characteristics the consumer thinks are

most important in the purchasing decision.

Surveys of Spending Plans / Consumer


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Surveys of Spending Plans / ConsumerIntentions:

The use of surveys of spending plans is quite similar to

opinion polling and market research, and themethods of data collection are also quite alike.

Survey of spending plans seek information about

macro type data relating to economy (as againstproduct related data)

Consumer intentions:

Since consumer expenditure is the largest component

of the GDP, changes in consumer attitudes and itsinfluence on spending are crucial variable in theforecasts.


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Economic Indicators / Barometric techniques:

The barometric technique of economic indicators is

designed to alert the business to changes in economicconditions

In a barometric method of forecasting economic

data are formed into indexes to reflect the state of the

economy.

The success of this technique depends on the ability to

identify one or more historical economic series whose

direction not only correlates with, but also precedes thatof the series to be predicted.


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Table 5-4 Economic Indicators

Indexes of Indicators:

Leading,

Coincident, andLagging indicators

are used to forecast changes in economic activity.


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Economic Indicators:

Leading Indicators:

Average hours manufacturing.

First Claim for Unemployment insurance.

Manufacturers new orders for production ofconsumer goods and materials.

Building permits and new private housing units

Money supply.

Index of consumer expectations.


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Coincident Indicators:

Personal Income. Industrial Production.

Manufacturing and Trade sales.

Employees on Pay Rolls


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Lagging Indicators:

Average duration of unemployment (in weeks) Ratio of Inventory to Sales (for Manufactured and

Trade goods).

Average Prime rate charged by banks.

Outstanding loans ( of commercial and industrial)


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13. Projections: Trend projections:

A form of nave forecasting that projects trends frompast data.

Nave forecasting:

Quantitative forecasting that projects past datawithout explaining the reasons for future trends.

Here the past data are projected into the futurewithout taking into consideration reason for change.

It is simply assumed that past trends will continue.

Three types of projection techniques: .


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Trend Projections

Three types of projection techniques: Constant Compound growth rate

Visual time series projection

Time series projection using the least squaresmethod.

If annual data are to be forecast, any of thesemethods can be used.

If there are seasonal pattern in the data, asmoothing method must be applied.


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Trend Projections:

Constant Compound growth rate: This is an extremely simple and widely used method in

business situations.

When quick estimates of the future are needed, this methodcan be used.

This method is quite appropriate when the variable to bepredicted increases at a constant percentage.


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Constant Compound Growth rate

From the data of first year and the last year, we can

calculate the growth rate using the formula below:(1+i)n = E/B

E = Last years amount

B = First years amounti = growth rate (to be calculated)

n = number of years

Fig. 5-3 : If the growth rate is varying, this methodwill give an erroneous result.


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Visual Time Series Projections:

A series of numbers is often difficult to interpret. Plotting the observations on a graph paper can be

very helpful because the shape of a complicatedseries can be more easily discerned from a picture.

Two types of graph can be used: The data is represented on a graph sheet, such that

the variable on the vertical axis and the time on thehorizontal axis and a graph is plotted.

A semi logarithmic graph sheet (arithmetic scale

along X-axis and log-arithmetic scale on Y-axis)may be used, when the variable increasesexponentially.


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Visual Time Series Projections: Time series models that extrapolate past data into

the future were used by 60% companies surveyed;causal forecasting by 24% of companies and

judgmental methods by 8%


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Projections:

Time series projection using the least squares

method: Instead of visual estimation, a more precise

statistical method technique, called the method

of least squares can be employed.Whereas demand estimation requires the use of

one or more independent variables, in the contextof time series analysis, there is only one

independent variable Time. It merely says that series of numbers to be

projected (forecast)changes as a function of time.


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Time series Analysis:

The following are advantages of time seriesanalysis:

It is easy to calculate. Many software packages areavailable

It does not require much judgment or analyticalskills

It gives the line with the best possible fit. It

provides information regarding statistical errorsand statistical significance

It is usually reliable in the short-run.


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Characteristics of Time Series Data:

Data collected over a period of time, usually exhibits four

different characteristics.Trend: This is the direction of movement of data over a

relatively long period of time either upward or

downwardCyclical fluctuation: These are deviations from the trenddue to general economic conditions.

Seasonal f luctuation: A pattern that repeats seasonally

/annually.Irregular: Departure from norm may be caused by special

events or may just represent noise in the series. They

occur randomly and thus cannot be predicted.


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Forms of Trend Projection / Equation Mathematical expression of time series data:

Yt = f (Tt, Ct, St, Rt )Yt = Actual value of the data in the timeseries at time (t).

Tt = Trend component at t

Ct = Cyclical component at tSt = Seasonal component at t

Rt = Random component at t.

Forms of equation:Yt = Tt+ Ct+ St+ Rt

Yt = (Tt) (Ct) (St) (Rt)


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18. Forecasting with Smoothing Techniques:

The smoothing techniques, either moving average orexponential smoothing work best when there is nostrong trend in the series, when there are infrequent

changes in the direction of the series and whenfluctuations are random rather than seasonal orcyclical.


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Forecasting with Smoothing Techniques:

Moving Average: The average of actual past results is used to

forecast one period ahead.

Et+1 = (Xt+ Xt-1+ ---------+ Xt- N+1) /NWhere Et+1 = Forecast for the next period (t+1)

Xt, Xt-1 =Actual valves at their respective times

N = Number of observation included in theaverage

19. Exponential Smoothing:


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The moving average method awards equal importance to

each of the observations included in the average and gives noweight to observations preceding the oldest data included.

Exponential smoothing allows for the decreasing importanceof information in the more distance past.


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Exponential Smoothing This is achieved by the mathematical technique of

geometric progression. Older data are assigned increasingly smaller

weights.

Simply put, it can be expressed as:Et+1 = w Xt + ( 1 -w)Et

w = Weight assigned to an actualobservation at period (t).

Xt = Actual value at time t.

Et = Forecast value at time t.


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Exponential Smoothing:

This method does not need the extensive historicaldata as required for moving average method.

The most crucial decision the analyst must make isthe choice weighting factor.

Figure 5-8 Exponential smoothing with varyingweightage


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Econometric Models:All the quantitative forecasting techniques

discussed earlier can be classified as nave.

Econometric models can be termed causal orexplanatory.

Regression analysis is an explanatory technique. Unlike the case of a nave projection, which relies

on past patterns to predict the future, regressionanalysis establishes a relationship between adependent and independent variables forpredicting a future outcome.


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Econometric forecasting model Econometric forecasting model:

A quantitative causal method that uses a numberof independent variables to explain the dependent

variable to be forecast.

Econometric forecasting employs both single andmultiple equation models.

Casual Forecasting / Explanatory Forecasting:

A quantitative forecasting method that attempts touncover functional relationships betweenindependent variables and the dependent variable.

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Chapter 5 Corrected