Like this presentation? Why not share!

# Demand estimation and forecasting

## by shivraj negi, student at IIT MADRAS on Oct 12, 2010

• 23,255 views

Demand estimation and forecasting presentation made by Harshawardhan Ravichandran, Ajai Kurian Mathew, Prem Ranjan and me

Demand estimation and forecasting presentation made by Harshawardhan Ravichandran, Ajai Kurian Mathew, Prem Ranjan and me

### Views

Total Views
23,255
Views on SlideShare
23,173
Embed Views
82

Likes
3
564
2

### 7 Embeds82

 http://arbitspeak.blogspot.com 42 http://arbitspeak.blogspot.in 17 http://www.arbitspeak.blogspot.com 9 http://www.arbitspeak.blogspot.in 6 http://www.docseek.net 4 http://arbitspeak.blogspot.co.uk 3 http://arbitspeak.blogspot.com.au 1
More...

### Categories

Uploaded via SlideShare as Microsoft PowerPoint

### Report content

12 of 2 previous next

## Demand estimation and forecastingPresentation Transcript

• Demand Estimationand Forecasting
.
AjaiKurian Mathew
Harshavardhan R
PremRanjan
Shivraj 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 be:
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.
• Consumer survey
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 onsumersare 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.
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
Direct observation of the consumers takes place rather than something of a hypothetical theoretical model .
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.
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.
• Coefficient of Determination (R2)
TD: Total DeviationED: Explained DeviationUD: Unexplained Deviation
TD = ED + UD
ΣTD2 = ΣED2 + ΣUD2
• Coefficient of Determination (R2)
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?
R2is 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
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 Forecasting
• Long Range Strategic Planning
• Corporate Objectives: Profit, market share, ROCE,strategic acquisitions, international expansion, etc.
• Annual Budgeting
• Operating Plans: Annual sales, revenues, profits
• Annual Sales Plans
• Regional and product specific targets
• Resource Needs Planning
• HRM, 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 required
• The lead time required for making decisions dependent on results of the model
• Box Jenkins Method
• Also 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:
AR(Autoregressive) process.
MA(Moving Average) process.
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 model
• An 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 model
Consider 4 industries,
Industry 1: X1=X11+X12+X13+X14+C1
Industry 2: X2=X21+X22+X23+X24+C2
Industry 3: X3=X31+X32+X33+X34+C3
Industry 4: X4=X41+X42+X43+X44+C4
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 Matrix
X=Output Vector
C=Final Demand Vector
• Input-output model
X=AX+C
[I-A]X=C
X=[I-A]-1C
• Input-output model
• If 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 model
• Dit=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 Population
• dit=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 Demand
r=∆ y/y= Rate of growth of per capita income.
Thus eyi=x/r;
• x= eyi *r
• Thus 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.e
Dit=Di0*(1+eyi*r)t*(1+s)t
Comparing with the original eqn. for Demand,
ρi=[(1+eyi*r)(1+s)]-1
• Input-output model
• This 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 model
It gives sector wise breakdown of demand forecasts for commodities.
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 model