DEFINITION<br />Estimation of various demand function of a firm(industry) or market through various processes.<br />For practical purposes ,demand function for a firm or market has to be estimated from the empirical data.<br />
.<br />Broadly there are two types methods of Estimation:<br />Simple Method of Estimation(5 steps)<br />Statistical method of Estimation(Econometric analysis,7 Steps).<br />
STEPS FOR DEMAND ESTIMATION<br />Statement of a theory or hypothesis.<br />Model specification.<br />Data collection.<br />Estimation of parameters.<br />Checking goodness of fit.<br />Hypothesis testing.<br />Forecasting.<br />
MODEL SPECIFICATION<br />What variables to be included and what mathematical form to followed.<br />Need to formulate many alternative models.<br />Deterministic(certainity) and Statistical relationship<br />It is assumed to begin with that the relationship is deterministic. With a simple demand curve the relationship would therefore be:<br />Q =f (P)<br />
DATA COLLECTION<br />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.<br /><ul><li>Types of data:
Pooled data </li></li></ul><li>Estimation of parameters<br />Coefficient of the variables.<br />Relates the effects of Independent variable upon the dependent variable.<br />Regression analysis is used to calculate these values.<br />
Consumer Survey <br />Seeking information through questionnaire , interviews etc.<br />Asking information about their consumption behavior ie, buying habits , motives etc.<br />
Consumer survey <br />Advantages<br />They give uptodate information about the current market scenario .<br />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.<br />Disadvantages<br />Validity <br />Reliability<br />Sample Bias <br />
Market Experiment <br />Here consumers are studied in an artificial environment .<br />Laboratory experiments or consumer clinics are used to test consumer reactions to changes in variables in the demand function in a controlled environment.<br />Need to be careful in such experiments as the knowledge of being in the artificial environment can affect the consumer behavior.<br />
Market experiment <br />Advantages <br />Direct observation of the consumers takes place rather than something of a hypothetical theoretical model .<br />Disadvantages<br />There is less control in this case, and greater cost; furthermore, some customers who are lost at this stage may be difficult to recover.<br />Experiments need to be long lasting in order to reveal proper result.<br />
Statistical methods<br />These are various quantitative methods to find the exact relationship between the dependent variable and the independent variable(s).<br />The most common method is regression<br /> Analysis :<br />Simple (bivariate) Regression: Y = a + bX<br />Multiple Regression: Y = a +bX1 + c X2 +dX3 +..<br />
Limitations of Statistical methods<br />They require a lot of data in order to be performed.<br />They necessitate a large amount of computation.<br />
Linear Regression – OLS Method<br /> Applicable when our model employs a linear relationship between X and Y.<br />Find a line Ŷ = a + bX which minimizes sum of square errors Σ(Yi–Ŷi)2.<br />Find a and b by partial differntiation.<br />
Goodness of Fit<br />Regression – type of relationshipCorrelation – strength of relationship<br />An alternative to visual inspection<br />Measures:<br />Correlation coefficient (r)<br />Coefficient of Determination (R2)<br />
Correlation Coefficient<br />Measures the degree of linear correlation<br />Small correlation may imply weak linear, but strong non-linear relationship.<br />Hence, visual inspection is also important.<br />Does not talk about causation<br />Causation may be reversed, circular, endogenic or third-party<br />Hence, correlation cannot tell you how good a model is.<br />
Correlation Coefficient<br />It can be calculated as follows:<br />r varies from 0 to 1.<br />A high value of r implies that the points are very closely scattered around the regression line.<br />
Coefficient of Determination (R2)<br />The proportion of the total variation in the dependent variable that is explained by the relationship with the independent variable.<br />
Coefficient of Determination (R2)<br />TD: Total DeviationED: Explained DeviationUD: Unexplained Deviation<br />TD = ED + UD<br />ΣTD2 = ΣED2 + ΣUD2<br />
Coefficient of Determination (R2)<br />R2 also varies from 0 to 1.<br />Low R2 values imply that:<br />The model is not a good fit. Perhaps a power regression model is needed?<br />We are missing important variables. Look at Multivariate regression?<br />R2is preferred to Correlation Coefficient (r)<br />
Power Regression<br />Mathematical form: Y=aXb<br />Cannot directly use the OLS method. However by ignoring error terms and taking logarithm we get a linear model.<br />log(Y) = log(a) + b*log(X)<br />
Significance Testing<br />t-test: Test of significance of a particular variable.<br />t-stat = estimated coefficient/standard error<br />Rule of thumb for a 95% confidence interval: >2<br />Implies that the independent variable truly impacts the dependent variable<br />Specially useful in Multivariate regression<br />F-test: Checks if variation in X explains a significant amount of the variation in Y.<br />
The Pizza Dillemna<br />Estimate the demand for Pizza by college students.<br />Select variables for the model that you believe are:<br />Relevant, and for which<br />Data can be found<br />
The Pizza Dillemna<br />Average number of pizza slices consumed per month by students (Y)<br />Average Selling Price of a Pizza slice (X1)<br />Annual Course Fee – proxy for student income (X2)<br />Average price of a soft drink – complementary product (X3)<br />Location of the campus – proxy for availability of substitutes (X4) (1 for city campus, 0 for outskirts)<br />
The Pizza Dillemna<br />Y = a + b1X1 + b2X2 + b3X3 + b4X4<br />Results of linear regression based on actual data<br />Y = 26.67 – 0.088 X1 + 0.138 X2 - 0.076 X3 - 0.0544 X4<br /> (0.018) (0.087) (0.020) (0.884)<br />R2 = 0.717 Adjusted R2 = 0.67 F= 15.8<br />Std Error of the Y-estimate = 1.64<br />(The standard errors of the coefficients are listed in parenthesis)<br />
The Pizza Dillemna<br />Values of Elasticity:<br />Price Elasticity -0.807<br />Income Elasticity 0.177<br />Cross-price Elasticity -0.767<br />T-test: b2 and b4 are not significant.<br />R2 = 0.717<br />
Demand Forecasting<br />Estimation or prediction of future demand for goods and services. <br />Nearer it is to its true value, higher is the accuracy. <br />Active and Passive forecasts. <br />Short term, long term and medium term. <br />Capacity utilization, Capacity expansion and Trade Cycles. <br />Different forecasts needed for different conditions, markets, industries. <br />Approaches to Forecasting: Judgmental, Experimental, Relational/Causal, Time Series Approaches.<br />
Demand Forecasting<br />Requirements for Demand Forecasting. <br />Elements related to Consumers.<br />Elements concerning the Suppliers.<br />Elements concerning the Markets or Industry. <br />Other Exogenous Elements like taxation, government policies, international economic climate, population, income etc. <br />Estimating general conditions, estimating the total market demand and then calculating the firm’s market share. <br />Multiple methods of forecasting, used depending upon suitability, accuracy and other factors. <br />Subjective methods used when appropriate data is not available. <br />
Demand Forecasting<br />Subjective methods depend on intuition based on experience, intelligence, and judgment. <br />Expert’s opinion survey, consumer’s interview method and historical analogy method. <br />Survey Methods<br />Using questionnaires with either complete enumeration or sample survey method. <br />Using consumers, suppliers, employees or experts (Delphi method). <br />Problems of survey methods. <br />Less reliable and accurate due to subjectivity, but give quick estimates and are cost saving. <br />
Demand Forecasting<br />Historical Analogy Method.<br />Forecasting for new product or new market/area. <br />Difficulties in finding similar conditions. <br />Test Marketing involves launching in a test area which can be regarded as true sample of total market. <br />Difficulties of cost, time, variation of markets and imitation by competitors. <br />
Demand Forecasting<br />Systematic forces may show some variation in time series of sales data of a product. <br />Basic parameters like population, technology. Business cycles, seasonal variations and then random events. <br />Main focus is to find out the type of variation and then use it for long term forecasting. <br />Use judgment to extrapolate the trend line obtained from sales data. <br />OLS method to prepare a smooth curve is a better option. <br />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. <br />
Demand Forecasting<br />Linear: Y = a0 + a1(t)<br />Quadratic: Y = a0 + a1(t) + a2(t)2<br />Logarithmic :<br />Log Y = b0 + b1 log (t)<br />Exponential :<br />Log Y = c0 + c1 (t)<br />Choice of the equation is based on multiple correlation coefficient (R) of OLS. <br />Averaging is used to remove any large scale fluctuations. <br />
Demand Forecasting<br />The sales curve eventually is an S shaped ‘product life cycle curve’. <br />Price elasticities vary in different stages. Highest in later stages as substitutes are available. <br />All these stages give exponential shape to the curve. <br />Trend method assumes little variations in business conditions. <br />Knowledge of curve helps in planning marketing and planning for the product. <br />
Demand Forecasting<br />Leading Indicators or Barometric method. <br />Time as a explanatory variable may not always show a liner relation, so we use another commodity as an indicator for sales. <br />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. <br />Inadequacy of data, multi-collinearity, auto-correlation, heteroscedasticity and lack of direct estimates of future values of explanatory variables. <br />
Need for Forecasting<br /><ul><li>Long Range Strategic Planning
Corporate Objectives: Profit, market share, ROCE,strategic acquisitions, international expansion, etc.
The lead time required for making decisions dependent on results of the model</li></li></ul><li>Box Jenkins Method<br /><ul><li>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.</li></li></ul><li>Box Jenkins Method<br />There are 3 components of the ARIMA process:<br />AR(Autoregressive) process.<br />MA(Moving Average) process.<br />Integration process.<br />
Box Jenkins Method<br /><ul><li>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.</li></ul> Yt=μ+a1Yt-1+a2Yt-2+….+apYt-p+et<br />
Box Jenkins Method<br /><ul><li>MA process: Order q, each observation of Yt is generated by the weighted average of random disturbances over the past q periods.</li></ul> Yt= μ +et-c1et-1-c2et-2+….-cqet-q<br /><ul><li>Integrated Process: Ensures that the time series used in the analysis is stationary. The previous 2 equations are combined to form:</li></ul>Yt=a1Yt-1+a2Yt-2+...+apYt-p+μ+et-c1et-1-c2et-2+…-cqet-q<br />
Input-output model<br /><ul><li>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. </li></li></ul><li>Input-output model<br /> Consider 4 industries,<br /> Industry 1: X1=X11+X12+X13+X14+C1<br /> Industry 2: X2=X21+X22+X23+X24+C2<br /> Industry 3: X3=X31+X32+X33+X34+C3<br /> Industry 4: X4=X41+X42+X43+X44+C4<br />Xij= Output of the industry i which is purchased by industry j for the producion of its output.<br />Ci = Demand of the customers for products for final use .<br />
Input-output model<br />Let Xij=aijXj,i=1 to 4,j=1 to 4<br /> or Xij/Xj=aij <br />where aij is the output of ith industry required to produce unit output of jth industry. Thus<br /> X1=a11X1+a12X2+a13X3+a14X4+C1<br /> X2=a21X1+a22X2+a23X3+a24X4+C2<br /> X3=a31X1+a32X2+a33X3+a34X4+C3<br /> X4=a41X1+a42X2+a43X3+a44X4+C4<br />
Input-output model<br /><ul><li>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.</li></li></ul><li>Input-output model<br /><ul><li>Dit=Di0(1+ ρi)t </li></ul>Dit-Level of Final Demand<br />ρi= Growth rate of final Demand <br /><ul><li>Pt=P0(1+s)t </li></ul>Pt-Population at time t<br /> s = Rate of growth of Population<br /><ul><li>dit=di0(1+x)t </li></ul>dit = Per-capita consumption in time t<br /> x = rate of growth of per-capita consumption in time t.<br />
Input-output model<br /><ul><li>eyi=(∆dit/dit)/(∆ y/y)∆ </li></ul>eyi=Income elasticity of Demand<br /> r=∆ y/y= Rate of growth of per capita income.<br /> Thus eyi=x/r;<br /><ul><li>x= eyi *r
dit=Dit/Pt, di0=Di0/P0</li></li></ul><li>Input-output model<br />We get,<br />Dit/Pt=Di0/P0*(1+eyi*r)t<br />Dit=Di0/P0*(1+eyi*r)t * P0*(1+s)t<br />i.e<br />Dit=Di0*(1+eyi*r)t*(1+s)t<br />Comparing with the original eqn. for Demand,<br />ρi=[(1+eyi*r)(1+s)]-1<br />
Input-output model<br /><ul><li>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.</li></li></ul><li>Input-output model<br /><ul><li>Advantages:</li></ul>It gives sector wise breakdown of demand forecasts for commodities.<br />Helps the firm to formulate its marketing policies in a better way by taking into account various market segment strengths for its products.<br />
Input-output model<br /><ul><li>Disadvantages:</li></ul>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.<br />Also changes in the production technology,tastes,preferences etc during the period makes the forecast less valid.<br />
Controlling the Forecast<br /><ul><li>Control 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).</li></li></ul><li>Controlling the Forecast<br /><ul><li>PFI1=(|Yt-Yt’|*100)/Yt