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
75
80
85
90
95
100
105
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
2004
2005
2006
2007
2008
2009
2010
2011
400
450
500
550
600
650
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
(Slideshare) http://www.egyankosh.ac.in/bitstream/123456789/35386/1/Unit-6.pdf