Demand estimation and forecasting

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Demand Estimationand Forecasting.

Ajai Kurian Mathew Harshavardhan RPrem RanjanShivraj Singh Negi

DEFINITION

•Estimation of various demand function of a firm(industry) or market through various processes.

•For practical purposes ,demand function for a firm or market has to be estimated from the empirical data.

•Broadly there are two types methods of Estimation:•Simple Method of Estimation(5 steps)•Statistical method of Estimation(Econometric

analysis,7 Steps).

STEPS FOR DEMAND ESTIMATION

•Statement of a theory or hypothesis.•Model specification.•Data collection.•Estimation of parameters.•Checking goodness of fit.•Hypothesis testing.•Forecasting.

MODEL SPECIFICATION

• What variables to be included and what mathematical form to

followed.

• Need to formulate many alternative models.

• Deterministic(certainity) and Statistical relationship

• It is assumed to begin with that the relationship is deterministic.

With a simple demand curve the relationship would therefore

• Q = f (P)

DATA COLLECTION• This stage can only be performed after the

demand model has been specified, otherwise it is not known for which variables we have to collect data.

Types of data:

Time series data

Cross sectional data

Pooled data

Estimation of parameters

•Coefficient of the variables.•Relates the effects of Independent

variable upon the dependent variable.•Regression analysis is used to calculate

these values.

Methods of Estimating Demand

•Consumer survey

•Market Experiment

•Statistical methods

Consumer Survey

•Seeking information through questionnaire , interviews etc.

•Asking information about their consumption behavior ie, buying habits , motives etc.

Consumer survey Advantages

• They give uptodate information about the current market scenario .

• Much useful information can be obtained that would be difficult to uncover in other ways; for example, if onsumers are ignorant of the relative prices of different brands, it may be concluded that they are not sensitive to price changes.This can be exploited by the firms for their best possible interest.

Disadvantages

• Validity

• Reliability

• Sample Bias

Market Experiment

•Here consumers are studied in an artificial environment .

•Laboratory experiments or consumer clinics are used to test consumer reactions to changes in variables in the demand function in a controlled environment.

•Need to be careful in such experiments as the knowledge of being in the artificial environment can affect the consumer behavior.

Market experiment Advantages

• Direct observation of the consumers takes place rather than something of a hypothetical theoretical model .

Disadvantages

• There is less control in this case, and greater cost; furthermore, some customers who are lost at this stage may be difficult to recover.

• Experiments need to be long lasting in order to reveal proper result.

Statistical methods•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 +..

Limitations of Statistical methods

•They require a lot of data in order to be performed.•They necessitate a large amount of computation.

Linear Regression – OLS Method• Applicable when our model employs a

linear relationship between X and Y.

•Find a line Ŷ = a + bX which minimizes sum of square errors Σ(Yi–Ŷi)2.

•Find a and b by partial differntiation.

Goodness of Fit

•Regression – type of relationshipCorrelation – strength of relationship

•An alternative to visual inspection

•Measures:▫Correlation coefficient (r)▫Coefficient of Determination (R2)

Correlation Coefficient

•Measures the degree of linear correlation▫Small correlation may imply weak linear,

but strong non-linear relationship.▫Hence, visual inspection is also important.

•Does not talk about causation▫Causation may be reversed, circular,

endogenic or third-party▫Hence, correlation cannot tell you how

good a model is.

Correlation Coefficient

• It can be calculated as follows:

•r varies from 0 to 1.•A high value of r implies that the points are

very closely scattered around the regression line.

Coefficient of Determination (R2)

•The proportion of the total variation in the dependent variable that is explained by the relationship with the independent variable.

•TD: Total DeviationED: Explained DeviationUD: Unexplained Deviation

•TD = ED + UD•ΣTD2 = ΣED2 + ΣUD2

•R2 also varies from 0 to 1.

•Low R2 values imply that:▫The model is not a good fit. Perhaps a

power regression model is needed?▫We are missing important variables. Look

at Multivariate regression?

•R2 is preferred to Correlation Coefficient (r)

Power Regression

•Mathematical form: Y=aXb

•Cannot directly use the OLS method. However by ignoring error terms and taking logarithm we get a linear model.

• log(Y) = log(a) + b*log(X)

Significance Testing• t-test: Test of significance of a particular

variable.▫t-stat = estimated coefficient/standard error▫Rule of thumb for a 95% confidence interval:

>2▫Implies that the independent variable truly

impacts the dependent variable▫Specially useful in Multivariate regression

•F-test: Checks if variation in X explains a significant amount of the variation in Y.

The Pizza Dillemna

•Estimate the demand for Pizza by college students.

•Select variables for the model that you believe are:▫Relevant, and for which▫Data can be found

The Pizza Dillemna

• Average number of pizza slices consumed per month by students (Y)

• Average Selling Price of a Pizza slice (X1)

• Annual Course Fee – proxy for student income (X2)

• Average price of a soft drink – complementary product (X3)

• Location of the campus – proxy for availability of substitutes (X4) (1 for city campus, 0 for outskirts)

The Pizza Dillemna

• Y = a + b1X1 + b2X2 + b3X3 + b4X4

• Results of linear regression based on actual data

Y = 26.67 – 0.088 X1 + 0.138 X2 - 0.076 X3 - 0.0544 X4

(0.018) (0.087) (0.020) (0.884)

R2 = 0.717 Adjusted R2 = 0.67 F= 15.8

Std Error of the Y-estimate = 1.64

(The standard errors of the coefficients are listed in parenthesis)

The Pizza Dillemna

•Values of Elasticity:▫Price Elasticity -0.807▫Income Elasticity 0.177▫Cross-price Elasticity -0.767

•T-test: b2 and b4 are not significant.•R2 = 0.717

Demand Forecasting• Estimation or prediction of

future demand for goods and services.

• Nearer it is to its true value, higher is the accuracy.

• Active and Passive forecasts. • Short term, long term and

medium term. • Capacity utilization, Capacity

expansion and Trade Cycles. • Different forecasts needed

for different conditions, markets, industries.

• Approaches to Forecasting: Judgmental, Experimental, Relational/Causal, Time Series Approaches.

Demand Forecasting• Requirements for Demand Forecasting.

▫ Elements related to Consumers.▫ Elements concerning the Suppliers.▫ Elements concerning the Markets or

Industry. ▫ Other Exogenous Elements like taxation,

government policies, international economic climate, population, income etc.

• Estimating general conditions, estimating the total market demand and then calculating the firm’s market share.

• Multiple methods of forecasting, used depending upon suitability, accuracy and other factors.

• Subjective methods used when appropriate data is not available.

Demand Forecasting

• Subjective methods depend on intuition based on experience, intelligence, and judgment.

• Expert’s opinion survey, consumer’s interview method and historical analogy method.

• Survey Methods

▫ Using questionnaires with either complete enumeration or sample survey method.

▫ Using consumers, suppliers, employees or experts (Delphi method).

▫ Problems of survey methods. ▫ Less reliable and accurate due to

subjectivity, but give quick estimates and are cost saving.

Demand Forecasting• Historical Analogy Method.

▫ Forecasting for new product or new market/area.

▫ Difficulties in finding similar conditions.

▫ Test Marketing involves launching in a test area which can be regarded as true sample of total market.

▫ Difficulties of cost, time, variation of markets and imitation by competitors.

Demand Forecasting• Systematic forces may show some

variation in time series of sales data of a product.

• Basic parameters like population, technology. Business cycles, seasonal variations and then random events.

• Main focus is to find out the type of variation and then use it for long term forecasting.

• Use judgment to extrapolate the trend line obtained from sales data.

• OLS method to prepare a smooth curve is a better option.

• We may obtain a linear trend, quadratic trend, logarithmic trend or exponential trend each of which gives us a different information about the behavior of demand.

Demand Forecasting• Linear: Y = a0 + a1(t)

• Quadratic: Y = a0 + a1(t) + a2(t)2

• Logarithmic :▫ Log Y = b0 + b1 log (t)

• Exponential :▫ Log Y = c0 + c1 (t)

• Choice of the equation is based on multiple correlation coefficient (R) of OLS.

• Averaging is used to remove any large scale fluctuations.

Demand Forecasting• The sales curve eventually

is an S shaped ‘product life cycle curve’.

• Price elasticities vary in different stages. Highest in later stages as substitutes are available.

• All these stages give exponential shape to the curve.

• Trend method assumes little variations in business conditions.

• Knowledge of curve helps in planning marketing and planning for the product.

Demand Forecasting• Leading Indicators or Barometric

method. • Time as a explanatory variable

may not always show a liner relation, so we use another commodity as an indicator for sales.

• Regression method : Identify the demand factors for commodity and expected shape of the demand function. Use regression to fit the time series data. Higher the R2 the better is explanation.

• Inadequacy of data, multi-collinearity, auto-correlation, heteroscedasticity and lack of direct estimates of future values of explanatory variables.

Need for ForecastingLong Range Strategic Planning

Corporate Objectives: Profit, market share, ROCE,strategic acquisitions, international expansion, etc.

Annual BudgetingOperating Plans: Annual sales, revenues, profits

Annual Sales PlansRegional and product specific targets

Resource Needs PlanningHRM, Production, Financing, Marketing, etc

Factors affecting Method Selection

Cost-benefit for developing forecasting model

Complexity of behavioral relationships to be forecasted

The accuracy of forecasts requiredThe lead time required for making

decisions dependent on results of the model

Box Jenkins MethodAlso known as ARIMA(‘Auto-Regressive Integrated

Moving Average’) models, this is an empirically driven method of systematically identifying, estimating, analyzing and forecasting time series.

Used only for short term predictions . Suitable only for demand with stationary time series sales data,i.e the one that does not reveal the long term trend.

The models are designated by the level of autoregression,integration and moving averages(P,d,q) where P is the order of regression,d is the order of integration and q is the order of moving average.

Box Jenkins Method

•There are 3 components of the ARIMA process:

1. AR(Autoregressive) process.2. MA(Moving Average) process.3. Integration process.

Box Jenkins Method AR process: Of order ‘p’, generates

current observations as a weighted average of the past observations over p periods, together with a random disturbance in the current period.Yt=μ+a1Yt-1+a2Yt-2+….+apYt-p+et

Box Jenkins Method MA process: Order q, each observation of Yt

is generated by the weighted average of random disturbances over the past q periods.

Yt= μ +et-c1et-1-c2et-2+….-cqet-q

Integrated Process: Ensures that the time series used in the analysis is stationary. The previous 2 equations are combined to form:

Yt=a1Yt-1+a2Yt-2+...+apYt-p+μ+et-c1et-1-c2et-2+…-cqet-q

Input-output modelAn input-output model uses a matrix

representation of a nation's (or a region's) economy to predict the effect of changes in one industry on others and by consumers, government, and foreign suppliers on the economy.

One who wishes to do work with input-output systems must deal skillfully with industry classification, data estimation, and inverting very large, ill-conditioned matrices.

Wassily Leontief, won the Nobel Memorial Prize in Economic Sciences for his development of this model in 1973.

Input-output modelConsider 4 industries,Industry 1: X1=X11+X12+X13+X14+C1

Industry 2: X2=X21+X22+X23+X24+C2

Xij= Output of the industry i which is purchased by industry j for the producion of its output.Ci = Demand of the customers for products for final use .

Input-output model

Let Xij=aijXj,i=1 to 4,j=1 to 4

or Xij/Xj=aij

where aij is the output of ith industry required to produce unit output of jth industry. Thus

X1=a11X1+a12X2+a13X3+a14X4+C1

X2=a21X1+a22X2+a23X3+a24X4+C2

X3=a31X1+a32X2+a33X3+a34X4+C3

X4=a41X1+a42X2+a43X3+a44X4+C4

Input-output model

I=Unit Matrix A=Technology Coefficient MatrixX=Output VectorC=Final Demand Vector

Input-output model

X=AX+C[I-A]X=CX=[I-A]-1C

Input-output modelIf we know/get a forecast for X, total

output, we can easily find labor, capital & other requirements. This makes Input-Output method a powerful tool for planning.

To find the component D(represented as C before),Demand, one may use the previously discussed methods or a simple projection method.

Input-output modelDit=Di0(1+ ρi)t

Dit-Level of Final Demand

ρi = Growth rate of final Demand Pt=P0(1+s)t

Pt-Population at time t

s = Rate of growth of Populationdit=di0(1+x)t

dit = Per-capita consumption in time t

x = rate of growth of per-capita consumption in time t.

Input-output model

eyi=(∆ dit/dit)/(∆ y/y)∆ eyi =Income elasticity of Demandr= ∆ y/y= Rate of growth of per capita income.Thus eyi=x/r;

x= eyi *rThus dit=di0(1+eyi*r)t

dit=Dit/Pt, di0=Di0/P0

Input-output model

We get,Dit/Pt=Di0/P0*(1+eyi*r)t

Dit=Di0/P0*(1+eyi*r)t * P0*(1+s)t

i.eDit=Di0*(1+eyi*r)t*(1+s)t

Comparing with the original eqn. for Demand,

ρi=[(1+eyi*r)(1+s)]-1

Input-output modelThis eqn. gives the growth rate of final

demand for the ith commodity in terms of its income elasticity of demand, target rate of growth of per capita income and population growth.

If these parameters are known exogenously then ρi can be computed and final demand Dit can be predicted.

Input-output modelAdvantages:1. It gives sector wise breakdown of

demand forecasts for commodities.2. Helps the firm to formulate its marketing

policies in a better way by taking into account various market segment strengths for its products.

Input-output modelDisadvantages:

1. Input-output tables are not available every year. Sometimes there may be large gap between the years for which input-output coefficients are available and the years for which the forecasts are needed. Larger the timegap,less stable will be the coefficients, thus reducing the forecasting accuracy.

2. Also changes in the production technology,tastes,preferences etc during the period makes the forecast less valid.

Controlling the ForecastControl of forecasting is the process of

comparison,evaluation,interpretation and auditing the performances of the firm against objectives and standards forecasted.

We measure the inaccuracy in forecasting in terms of Percentage Forecasting Inaccuracy(PFI).

Controlling the Forecast

PFI1=(|Yt-Yt’|*100)/Yt

PFI2=( *100)/PFI1 stands for one period forecast and

PFI2 stands for multi-period forecasts, t for time, k for length of time.

Based on these ratios we fix some acceptable limits for them which depends on the commodity type, market nature, forecasting method.

Demand estimation and forecasting

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