Demand Estimation and Forecasting_lecturenotes (1)

Demand Estimation and ForecastingSharmistha Sikdar

Managerial Economics, 1st Semester, Sep 2012

Ramaiah Institute of Management Studies

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Agenda Estimation vs. Forecasting Types of Data

◦ Cross Sectional Data

◦ Time Series Data

Demand Estimation◦ Objective and Need

◦ Methods of Demand Estimation: Qualitative vs. Quantitative

◦ Qualitative Research Techniques and their Drawbacks

◦ Statistical/Quantitative Approach

◦ Types of Demand Function

◦ OLS Method of Demand Estimation

◦ Advantages and Disadvantages of Statistical Approach

Forecasting Techniques◦ Types of Forecasting – Objective & Need

◦ Methods of Forecasting: Qualitative vs. Quantitative

◦ Qualitative Research Techniques and their drawbacks

◦ Quantitative Methods

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Estimation Vs. ForecastingEstimation Forecasting

It is a process of establishing a mathematical relationship between the level of demand for a product and the estimator variables which determine itExample: If D = F(P, I, A) is a demand functionDemand estimation will help predict its functional form.

It is a technique to predict the level of demand/sales for a product at some future date.Example : If D1, D2, D3, D4, D5, D6 are the actual sales of a product from Jan-June 2012, forecasting techniques will help predict the sales for the time period July-Dec 2012

Dependent or Estimated Variable : DemandEstimator variables include: Price of the product (P) Price of complements/substitutes (Pc/Ps) Income of the consumer (I) Advertising outlays (A) Competitor Advertising (Ac)Other Macroeconomic factors such as: Interest rates (i) Consumer Price Index (CPI)

Predicted Variable : Demand/Sales at time point “t”Predictor Variables include: Time itself as in case of Trend Analysis The past values of the demand/sales: as

in Moving Averages method

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Estimation Vs. ForecastingEstimation Forecasting

• Estimation Techniques can be used to forecast the future value of demand/sales

• Forecasting techniques cannot be used to derive estimates of the parameters of demand/sales function

Demand estimation answers questions such as:• What is the monthly demand expected

for Kellogg’s Oats 500 gm. packet launched at a price, say Rs 100 from a given income segment Rs 25000-Rs 50000 ?

• How will the demand change if a tax is imposed on a certain product?

Forecasting answers questions such as :

• What will be the volume of sales in Diwali 2012 for LG washing machines?

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Data Types – Cross Sectional Data

o A type of One Dimensional Data

o Data is collected on attributes such as income, prices, etc. across

individuals, firms , regions at the same point of time.

o Example*:

August 2012 Consumer Survey Data on Demand for XYZ's Oats in Region ABCConsumer_I

DMonthly Income

# 500 gm Units Bought/month

# Family Members

Breakfast Preferences

1 Rs 30000 2 3 Western

2 Rs 35000 2 3 Western

3 Rs 40000 1 4 Indian

4 Rs 25000 1 4 Indian

5 Rs 40000 4 5 Western

* Fictitious Data created for illustration purposes only

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Data Types – Time Series Datao A sequence of data points measured typically at successive time

instants spaced at uniform time intervals

o The observations are ordered by time and a time series trend is

defined for a specific variable measured across time points.

o Examples*: Income trend of an individual Or Sales trend of a firm

* Fictitious Data created for illustration purposes only

Monthly Income Trend for an Individual

Month Income (in Rs)

Jan-12 30000

Feb-12 32000

Mar-12 32000

Apr-12 33000

May-12 33500

Jun-12 34000

Jul-12 32000

Aug-12 32000

Sales & Advertising Trend for a Firm

Month Sales (in Rs '000)Advertising Exp (in Rs

'000)

Jan-12 5000 10

Feb-12 2000 6

Mar-12 2500 6

Apr-12 3000 8

May-12 3200 8

Jun-12 2700 6

Jul-12 2600 6

Aug-12 3800 9

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DEMAND ESTIMATION

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Objective and Need

Objectiveo Identify the factors that determine the demand curve for a product o Quantify the impact of changes in these factors on the demand for the

product

Firms need to know o How sensitive the demand for their products are to changes in own price

or price of related goodso How consumers respond to changes in their own income levelso How demand for the product gets impacted with changes in promotional

strategieso How macroeconomic factors such as changes in interest rate, growth in

GDP etc impact the demand for their products

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Methods of Demand Estimation

Demand Estimation Techniques

Qualitative Research

Techniques

Quantitative/ Statistical Techniques

• Consumer Surveys

• Market Experiments

• Consumer Clinics

• Regression Analysis• Linear• Logistic

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Qualitative Research TechniquesA) Consumer Surveyso Questionnaire based information is gathered from a sample of consumerso The questions are designed to get responses on sensitivity of consumer to

price changes, quantities demanded at various price levels, awareness levels about the product and its substitutes, effectiveness of advertising and other related aspects

o Information thus collected is analyzed and the results are projected onto the population

Drawback of this approacho The questions are designed around hypothetical situations and hence

consumer responses may not be honest or realistico Reliability of the responses could be a challengeo The sample interviewed may not be representative of the population

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Qualitative Research TechniquesB) Market Experimentso Real experiments conducted by the seller of the product wherein the

product is tested out in a representative marketo Seller introduces variations in the product features such as pricing,

packaging and gathers information on the consumer reactiono The results of these experiments are then analyzed and projected onto the

population

Drawback of this approacho It is a high cost technique as the seller has to actually launch a sample of

the varied producto It is also risky for the seller as the situation cannot be fully controlledo The seller is also at a risk of damaging its brand image if the product

variant is not accepted by the consumers

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Qualitative Research TechniquesC) Consumer Clinicso An experimental set up similar to Market Experiments wherein the

consumers are asked to act in a simulated situationo The sample consumers are given some amount of money and indulged to

buyo Their buying behavior is studied and results thus analyzed is projected

onto the population

Drawback of this approacho It is a high cost technique as actual money is given to consumers to study

their buying patterno The method suffers the same drawback of the possibility of unrealistic

responses, however this is more effective than consumer surveys

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Quantitative Techniqueso A hypothesis is formulated on the basis of consumer behavior theory

and a list of possible variables that can impact demand is identifiedExample of a Hypothesis: Demand for a product is negatively related to its price

o The data on demand and other identified variables are collected from actual historical data. Data for this method is made available through various publications* and bureaus

o A mathematical relationship of the demand with other variables is specified:

D = F( P, Pc, Ps, I, A)Example: D = β0 + β1P + β2Pc + β3Ps + β4I + β5A + error

o Econometric methods are applied to estimate the parameters of the demand function, i.e., β0 , β1 , β2 , β3 , β4 , β5 as given in the example

o Using this mathematical equation demand is then estimated for the population

*In India some of these publications are provided by the Centre for Monitoring Indian Economy, the Confederation of Indian industries etc.

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Types of Demand Functiono General Form of the Demand Function

D = F( P, Pc, Ps, I, A)◦ A specific functional form needs to be chosen in order to estimate the

parameters

o The Simple Linear FormD = β0 + β1P + β2Pc + β3Ps + β4I + β5A + error

o The Exponential FormD = Pa Pc

b Psc Id AeEf , where E = error

o Taking logarithmic transformation of the exponential form this changes to the Log-Linear Form

log D= a log P + b log Pc + c log Ps + d log I + e log A + f log E

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OLS* Method of Estimationo Scope - Two Variable Linear Regression Analysis

Dependent Variable : DemandIndependent Variable : Price or income or Advertising outlays etc.

o Form of the 2 variable Linear Model D = β0 + β1X + ε

where D = quantity demanded of the product (dependent)X = Independent variable (price, income etc.)β0 and β1 are the parameters of the modelε is the error in estimation

o Interpretation of the parameters and the error termo β0 is the intercept of the demand function, i.e., the quantity demanded of the product

when the independent variable is set to 0o β1 is the coefficient that estimates the change in quantity demanded associated with a 1-

unit change in the independent variableo The error term is included to account for the fact that the predicted (theoretical) value of

demand may not be the same as the actual (observed) value

*NOTE: OLS implies Ordinary Least Squares, it is also called Least Squares

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OLS Method of Estimationo Assume a sample data taken on price and quantity demandedo Independent variable is the price o Dependent Variable is the quantity demanded of a product o The scatter plot of the data is shown in the graph belowo The estimated linear model is given by the line graph

0 1 2 3 4 5 670

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80

85

90

95

100

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Price-Quantity Demanded Scatter Plot

Quantity (Qi) (# units per week)

Pri

ce (

Pi)

(R

s p

er

unit

)

Error in Estimation for a given price pointe1

e2OLS Estimates are such that this error is minimized

NOTE: The graphical convention in many textbooks is to plot the independent variable , e.g. price , on X-axis and dependent variable, i.e., demand on Y-axis. Here we have used standard Economics convention of plotting price on Y-axis and demand on quantity on X-axis (Marshall’s graphical convention)

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OLS Method of EstimationObjective:Estimate values of β0 and β1 such that error in estimation is minimizedLet b0 and b1 be the estimated values of β0 and β1

Then, Estimated Demand for ith data point (di) = b0 + b1.Xi

Error in Estimation for ith data point (εi) = Actual Demand – Estimated Demand

= Di – (b0 + b1.Xi)

Therefore, Parameters should be estimated so as to Minimize ∑ εi

2 = ∑ {Di – (b0 + b1.Xi)}2 , where i = 1 to n (Sample size = n)

OLS estimates* are computed as :

where Dav and Xav are the arithmetic means of D and X, and summation is over i = 1 to n

n ∑ Xi2 – (∑ Xi)2

b1 = n ∑ XiDi - ∑ Xi ∑ Di , b0 = Dav - b1 Xav

• Estimates are computed using differential calculus with first order derivative set to 0 for a minimization problem• Tests for Model accuracy in the Appendix

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Pros & Cons of Statistical ApproachAdvantageso Eliminates subjectivity of the qualitative research techniqueso Bases the calculation of parameters on actual historical dataDisadvantageso Multicollinearity Problem

• If too many independent variables that are related to each other are introduced in the model the OLS method may assign coefficients arbitrarily.

• This makes it difficult to segregate the effect of two closely-related variables.• The t-test of significance of the independent variables helps identify this problem and

the correlated variables can be eliminated and model parameters re-estimated.o Identification Problem

• In case of Time Series or Pooled data all variables are allowed to vary causing shifts in demand and supply curve (Ceteris Paribus assumption violated)

• Impact of an independent variable on demand maybe overestimated or underestimated

o Autocorrelation Problem• This problem also occurs in case of TS data where the errors are not independent over

time, i.e., high error in estimation in a given period leads to a high error in the following period.

• Existence of this problem signifies that a crucial variable has been missed out in the estimation and the error term gets amplified in magnitude in each successive time-period

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DEMAND FORECASTING

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Types of Forecasting Short Term Forecasting

o Forecasting done for short periods typically 1 yearo It is done by firms to formulate policies on sales, purchase, price and financeso Sales forecasting helps firms determine productiono Price forecasting for raw materials helps reduce costs of operation by enabling businesses

to buy these in advance if a price rise is expectedo Sales and demand forecasting enables the firms to procure funds on reasonable terms

Long Term Forecastingo Forecasting typically done for longer time periods , greater than 1 yearo Enables firms to predict the long term demand for their product which can impact

decisions such as need to buy a new plant or expansion of existing unitso For multiproduct firms, long term forecasting helps decide which products to expand into

and which ones to reduce productiono The risk of error is higher in case of long run forecasting

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Methods of ForecastingForecasting Methods

Qualitative Research

Techniques

Quantitative/ Statistical Techniques

• Opinion Survey• Expert Opinion• Delphi Method• Consumers Interview

Method• Complete

Enumeration• Sample Survey• End-use Method

• Time Series• Trend Analysis• Moving Averages• Exponential

Smoothing• Barometric Technique• Regression Analysis

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Qualitative Research TechniquesA) Opinion Survey Methodo This method is also called the Sales-Force-Composite Method or Collective Opinion

Methodo The salesmen of the company are asked to submit estimates of future sales in their

respective territories.o The top executives of the company then consolidate, review and adjust the estimates to

eliminate biases of the sales-force.

Advantages of this approacho Simple and straightforward method and requires minimum technical skillo This is less expensive than consumer interview method o Based on the salesmen’s first hand and personal knowledge and thus more realistico Useful in forecasting sales of new products

Drawback of this approacho Vulnerable to subjective biases of the salesmeno Only useful for short term forecasting such as that for 1 year

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Qualitative Research Techniques

B) Expert Opiniono In many industries, sales estimates are given by experts who have a thorough

industry knowledge and are aware of the fluctuations in the macroeconomic environment

o Various public and private agencies sell periodic forecasts of businesses

Advantages of this approacho Forecasting through this method is relatively quick and inexpensiveo In case of data unavailability for elaborate statistical methods, this is a good

alternative

Drawback of this approacho Vulnerable to subjective biases of the expertso Good and bad estimates are given equal weights

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Qualitative Research TechniquesC) Delphi Methodo A variant of the survey method wherein a panel of experts is selected for a given business

problemo Both internal and external experts of the firm can be part of the panelo This method involves multiple rounds of question-answer sessionso In each round, the panel members are given a questionnaire and asked to express their opinion in

an anonymous mannero A coordinator mediates and presides over this survey. He collects the results and prepares a

summary report at the end of each roundo In the next iteration, the panelists recalibrate their forecasts basis review from previous roundo At the end of the final round the panel members reach a consensus on the forecasts

Advantages of this approacho Forecasts through this approach are more reliable than expert opinion survey method as the

consensus is reached over multiple roundso In case of data unavailability for elaborate statistical methods, this is a good alternative

Drawback of this approacho Has proved to be more successful in forecasting of non-economic rather than economic variables

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Qualitative Research TechniquesD) Consumers Interview Methodo Consumers are contacted personally and interviewed on their preferences and plans to purchase the

product in questiono The potential buyers of the product are then asked to reveal the quantity of the product that they plan to

purchase. The demand forecast for the product is then madeo This survey can be done in 3 ways-

o Complete Enumeration Method: All the consumers of the product are interviewed based on which forecast is made. The forecast is free of any bias as it contains first hand information of actual buyers of the product.

o Sample Survey Method: In this method a sample of consumers is selected for interview. Random or stratified sampling methods can be used to generate the sample.

o End-use Method: The demand for the product is found out from different sectors such as industries, consumers, export-import. Basis this data, forecasts are made on future demand.

Advantages of this approacho The forecasts are generated from first hand information and hence tend to be unbiased

Drawback of this approacho The consumers may be hesitant to reveal their purchase plans for privacyo As the consumers are numerous, this may turn out to be costly. However, the cost implications may vary

across sample survey , complete enumeration and end-use methods.o The consumers often may be unable to predict the exact amounts they plan to purchase due to multiple

alternatives available, anticipation of shortages, general irregularity in buying plans. This may reduce the accuracy of the data collected and hence affect forecasts

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Quantitative TechniquesA) Trend Analysiso The historical data for demand/sales for a given product is collectedo A trend line is fitted onto the data by developing an equation given as:

Dt = a + bT, where a = intercept and b = impact of time on demand, T = Time

Using OLS Method of parameter estimation,

Where t = 1, 2, ….n refer to n time periods, Dav = average demand across n time points, Tav = average time point

n ∑ Tt2 – (∑ Tt)2

b = n ∑ TtDt - ∑ Tt ∑ Dt , a = Dav - b1 Tav

2000

2001

2002

2003

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2005

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2008

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2011

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Actual Sales Vs Forecasted Trend

2000 2001 2002 20032004 2005 2006 20072008 2009 2010 2011Trend line

in R

s '000

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Quantitative TechniquesB) Moving Averages Methodo The historical data for demand/sales for a given product is collectedo The future values are forecasted as the simple averages of the past datao When the demand is stable, this is a good method of forecastingo E.g.: In the 3- point moving average method, the average of values collected for time-

points t-2, t-1 and t is used as the forecast for the time point t + 1o In general, this technique can be written as

Dt+1 = xt + xt-1 + xt-2 + xt-3 +………. + xt-n+1

n

Where n = number of time-points taken to compute the moving average

Dt+1 = The demand forecast for time point t+1

xt , xt-1, xt-2…….. , xt-n+1 are the actual demand values in the previous n time points

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Quantitative TechniquesC) Exponential Smoothing Methodo This is an improvement over the Moving Averages Methodo In the Moving Averages method, the values across different time points are given

equal weights in determining the forecasted value. The underlying logic of Exponential Smoothing is to give higher weightage to more recent values

o This is achieved as follows, Let Dt be the forecast for time period t,

where Dt = xt-1 + xt-2 + xt-3 +………. + xt-n+1

n

n = number of time points for which the average is computed The forecast for time period t+1 is then computed as

Dt+1 = ( xt/n ) + ( 1 – 1/n) Dt

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Quantitative TechniquesD) Regression and Correlation Techniqueo This technique uses the demand estimation OLS method to arrive at a

functional relationship between demand/sales and other independent variables such as price, income, advertising outlay.

o The data is collected across time points for all the independent and dependent variables

o The demand function is estimated asD = β0 + β1P + β2Pc + β3Ps + β4I + β5A + error

o Given this demand function future values of demand can be forecasted basis the forecasts of the independent variables P, Pc, Ps, I, A

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APPENDIX

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Tests to Measure Accuracy of OLS Estimateso Testing Overall Explanatory Power of the Model

o This test uses the coefficient of determination (R2) which is given as:R2 = Total Explained Variation Total Variation = ∑(di – Dav)2

∑(Di - Dav)2

o Higher the explained component of the variation implies the estimated demand is close to the actual demand and lower is the error in estimation. That is, higher the value of R2 better is the model fit

o The value of R2 ranges from 0 to 1o If R2 = 0, there is no relationship between Demand and the

independent variable, hence b1 = 0, b0 = Dav and di = Dav

Where, Di is the actual demanddi is the estimated demandDav is the sample mean demand

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Tests to Measure Accuracy of OLS Estimateso Evaluating Explanatory Power of Individual Independent Variable

o This is achieved through the t-test that enables determine whether there is a significant relationship between the dependent and the independent variable

o The t-test statistic is computed as t = where SE(b1) is the standard deviation or standard error of the estimated b1

o The estimated value of the parameter β1 varies with samples. If demand is indeed explained by the independent variable X, then the variation in the parameter estimate (b1) across different samples should be small. That is, SE(b1) should be small. In that case, the t-statistic should have a high value.

o This implies higher the value of the t-statistic better is the explanatory power of the independent variable and the coefficient b1 is said to be statistically significant

b1/ SE(b1)

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References Managerial Economics – Cauvery, Sudhanayak, Girija, Meenakshi Managerial Economics – Suma Damodaran Consumer Behavior and Estimating and Forecasting Demand – Howard Davies

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