Demand estimation and forecasting

Shivraj Singh Negi (HS07H022)

Demand Estimation and Forecasting

ContentsDemand Estimation.....................................................................................................................................4

Methods of Demand Estimation..................................................................................................................5

Qualitative Methods................................................................................................................................5

Consumer surveys:..............................................................................................................................5

Market experiments:...........................................................................................................................5

Quantitative Methods.............................................................................................................................6

Statistical methods..............................................................................................................................6

Model specification.............................................................................................................................6

Mathematical models:.........................................................................................................................6

Statistical models.................................................................................................................................8

Data collection.........................................................................................................................................8

Types of data.......................................................................................................................................8

Sources of data....................................................................................................................................9

Presentation of data..........................................................................................................................10

OLS (Ordinary Least Squares) Method for Regression...........................................................................11

Goodness of fit..................................................................................................................................11

Correlation.........................................................................................................................................11

The coefficient of determination.......................................................................................................12

Power Regression..................................................................................................................................13

Case Study: The Pizza Dillemna.............................................................................................................13

Demand Forecasting..................................................................................................................................14

Need for Forecasting.............................................................................................................................14

Type of Demand Forecasting.................................................................................................................14

Approaches to Forecasting....................................................................................................................15

The Requirements for Demand Forecasting..........................................................................................15

Factors affecting Method Selection.......................................................................................................16

Techniques of Forecasting.........................................................................................................................16

Qualitative Techniques..........................................................................................................................17

Survey Method..................................................................................................................................17

Economics Of Industrial Organizations


Expert’s Opinion Method...................................................................................................................17

Consumer’s Interview Method..........................................................................................................17

Historical Analogy Method................................................................................................................18

Test Marketing...................................................................................................................................18

Quantitative Techniques........................................................................................................................18

Trend Method....................................................................................................................................19

Controlling the Forecast........................................................................................................................24

REFERENCES/SOURCES:.............................................................................................................................25



Demand EstimationIn the present century, Globalisation has completely overhauled the way businesses are performed. At present, managers have to deal with an increasingly uncertain and varying business environment due to the fast changing economic scenario. The decision-making task has become difficult and extremely important. Needless to mention that the uncertainty in business environment is due to the complex behavior of market related variables like demand, market share, people’s perception and factors affecting demand in the present day as a result of recent policy changes and market forces. The need of the hour for a manager is to know the behavior of the market related variables, their interrelationship and future movement. One of the most important aspects for a manager in the present day is to know the process of estimation of demand and forecasting of demand. Both of these terms are different: Demand estimation attempts to quantify the links between the level of demand for a product and the variables which determines it whereas demand forecasting simply attempts to predict the level of sales at some particular future date .Demand estimation involves a number of stages. Some of these stages may be omitted in the simpler methods of estimation, like the first two steps (for simpler estimates). However, with a statistical study, or econometric analysis there are essentially seven stages:

1. Statement of a theory or hypothesis. This usually comes from a mixture of economic theory and previous empirical studies. An example of such a theory might be that the quantity people buy of a particular product might depend more on the past price than on the current price. This obviously has implications regarding perfect knowledge, information costs, habit formation and irrational behavior.

2. Model specification. This means determining what variables should be included in the demand model and what mathematical form or forms such a relationship should take. These issues are again determined on the basis of economic theory and prior empirical studies. Various alternative models may be specified at this stage, since economic theory is often not robust enough to be definitive regarding the details of the form of model.

3. 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. However, there may be some interaction between the two stages, particularly as far as the mathematical form is concerned; as stated above, economic theory alone may be unable to specify this. Therefore the presentation of data will also be considered in this stage. We have to discuss both the type of data to be collected and the sources of data.

4. Estimation of parameters. This means computing the values of the coefficients of the variables in the model, which as we have seen in the previous chapter correspond to the effects of an independent variable on the dependent variable. These effects can be measured in different ways, for example in terms of the marginal effects and elasticities.

5. Checking goodness of fit. Once a model, or maybe several alternative models, have been estimated, it is necessary to examine how well the models fit the data and to determine which model fits best. If the fit is not good it may be necessary to return to step 2 and re-specify the model before moving on to the next stage.



6. Hypothesis testing. Having determined the best model, we want to test the hypothesis stated in the first step; in the example quoted we want to test whether current price or past price has a greater effect on sales.

7. Forecasting. This is the ultimate focus of most econometric analysis. In this context we are trying to forecast sales, and maybe producing many forecasts in the light of various possible scenarios. It should be clear from the above process that, as far as managerial decision making is concerned, the last two stages are the most important. However, it is not possible to test hypotheses or make forecasts reliably without a good understanding of the prior stages.

Methods of Demand EstimationThere are a variety of ways that can be used to estimate demand, each of which has certain advantages and disadvantages. They are divided into Qualitative and Quantitative Methods.

Qualitative MethodsConsumer surveys: Firms can obtain information regarding their demand functions by using interviews and questionnaires, asking questions about buying habits, motives and intentions. These can be quick on-the-street interviews, or in-depth ones. They might ask, for example, how much more petrol respondents would buy if its price were reduced by 15 pence per litre, or which brand of several possibilities they prefer.

These methods have certain drawbacks:

a) Validity: Consumers often find it difficult to answer hypothetical questions, and sometimes they will deliberately mislead the interviewer to give the answer they think the interviewer wants.

b) Reliability: It is difficult to collect precise quantitative data by such means.c) Sample bias: Those responding to questions may not be typical consumers.

In spite of these problems, there are advantages of surveys:

a) They give up-to-date information reflecting the current business environment.b) Much useful information can be obtained that would be difficult to uncovering other ways; for

example, if consumers are ignorant of the relative prices of different brands, it may be concluded that they are not sensitive to price changes. Firms can also establish product characteristics that are important to the buyer, and priorities. Methods such as multidimensional scaling can be used to give rating scores on product characteristics.

Market experiments: As with consumer surveys these can be performed in many ways. Laboratory experiments or consumer clinics seek to test consumer reactions to changes invariables in the demand function in a controlled environment. Consumers are normally given small amounts of money and allowed to choose how to spend this on different goods at prices that are varied by the investigator. However, such experiments have to be set up very carefully to obtain valid and reliable results; the knowledge of being in an artificial environment can affect consumer behavior.



Other types of market study involve using real markets in different geographic locations and varying the controllable factors affecting demand. This kind of test marketing has the advantage that direct observation of consumers’ actual spending behavior is possible rather than just recording answers to hypothetical questions regarding such behavior. There are still number of problems with this method, however:

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

b) The number of variations in the variables is limited because of the limited number of market segments available. Thus only a small number of sample observations are possible.

c) Experiments may have to be long-lasting in order to reveal reliable indications of consumer behavior. We have seen in the previous chapter that price elasticity, for example, can be very different in the long run from in the short run because it takes time for consumers to change their habits

Quantitative Methods

Statistical methodsWhile the above methods are useful, they often do not provide management with the kind of detailed information necessary to estimate a useful demand function, and thereby test the relevant hypotheses and make forecasts. Statistical techniques, especially regression analysis, provide the most powerful means of estimating demand functions. Regression techniques do have various limitations:

1) They require a lot of data in order to be performed.

2) They necessitate a large amount of computation.

3) They suffer from a number of technical problems.

In spite of these limitations, regression techniques have become the most popular method of demand estimation, since the widespread availability of powerful desktop PCs and software packages have made at least the first two problems easy to overcome.

Model specificationThere are two major aspects of this stage. In order to understand this we must first distinguish a statistical relationship from a deterministic relationship. The latter are relationships known with certainty, for example the relationship among revenue, price and quantity:

R=P*Q; if P and Q are known R can be determined exactly.

Statistical relationships are much more common in economics and involve an element of uncertainty. The deterministic relationship is considered first.

Mathematical models: It is assumed to begin with that the relationship is deterministic. With a simple demand curve the relationship would therefore be:



Q=f (P)

If we are also interested in how sales are affected by the past price, the model might in general become:

Qt=f (Pt, Pt-1)

where Qt represents sales in one month, Pt represents price in the same month and Pt-1 represents price in the previous month. This last variable, involving graph values in a previous time period, is known as a lagged variable. Other variables could also be included on the right hand side if economic theory or previous empirical studies indicated that they might be important. The decision regarding which variables to include is a difficult one. Theory often tells us that certain variables, like price, promotion and income, should affect sales, but before we collect the data and analyze the results we do not know for certain which variables are relevant; in fact, even after analyzing the data we do not know for certain which variables are important because we are estimating a relationship from sample data, and therefore we can only make conclusions in probabilistic terms. Therefore there is always a grey area if a priori economic theory conflicts

Figure 1

with a posteriori empirical results. Subjective judgment cannot be avoided in this case. As mentioned in the introduction, economic theory is often not robust enough, meaning sufficiently specific, to be able to do this. We therefore often use scatter graphs, explained in the next section, to help us to specify the mathematical form. These are particularly useful for bi-variate, or two-variable, relationships, although several graphs can be used for multivariate relationships, which involve many variables. For example, in



the situation above we might draw graphs of both sales as a function of current price and sales as a function of previous month’s price.

From these graphs it might be possible to determine whether a linear or power relationship is the more appropriate mathematical form. As seen in the previous chapter, the linear and power forms of sales as a function of current price can be shown as follows:

Linear: Q=a+bP

Power: Q=aP^b

Frequently it is not possible to determine the mathematical form from the graphs either.

Statistical modelsIn practice we can very rarely specify an economic relationship exactly. Models by their nature involve simplifications; in the demand situation we cannot hope to include all the relevant variables on the right hand side of the equation, for a number of reasons:

1. We may not know from a theoretical viewpoint what variables are relevant in affecting the demand for a particular product.

2. The information may not be available, or impossible to obtain. An example might be the marketing expenditures of rival firms.

3. It may be too costly to obtain the relevant information. For example, it might be possible to obtain information relating to the income of customers, but it would take too much time (and may not be reliable).

If we simplify the relationship to just two variables the scatter graph given shows that the relationship is far from perfect; in a perfect relationship the points would exactly fit a straight line, or some other regular curve. We therefore have to specify the relationship in statistical terms, using a residual term to allow for the influence of omitted variables. This is shown for the linear form as follows:

Qi=a +bPi +di

where di represents a residual term. Thus, even if P is known, we cannot predict Q with complete accuracy because we do not know for any observation what the size or direction of the residual will be.

Data collectionStatistical methods place a big demand on data; therefore, the collection of data is crucial in practice. This stage is often ignored in the kinds of problems with which students are frequently faced, where they are already presented with data in a usable form; this stage of the analysis is also usually discussed in more detail in market research courses. Three aspects are discussed here: types of data, sources of data and presentation of data.

Types of dataThere are two main types of data that firms can collect.



a.Time series DataThis refers to data on a single entity at different periods of time. These data can be collected annually, quarterly, monthly or at any regular interval. Thus sales of firm A in the period 1994–99 would involve time series data. Such data may be quantitative, meaning that they are measured numerically on an ordinal or cardinal; examples are sales, prices and income. Alternatively, data may be qualitative, meaning that they are nominal, or expressed in categories; examples are male/female, married/single/widowed/divorced, east/west. The treatment of such variables, often called dummy variables, is considered, under extensions of the model.

b. Cross-section dataThis refers to data on different entities at a single period of time. In managerial economics these entities are normally firms, thus sales of firms A-F in 1999 would involve cross-section data. Sometimes the entities are individuals, industries or areas. The different types of data have certain advantages and disadvantages to the investigator .In practice the investigator may have little choice, because only one type of data may be available or feasible to use. Sometimes the two types of data can be pooled, that is combined together. For example, a study of six firms over six time periods would yield thirty-six observations; such data allow more observations, which is an advantage in analysis. However, pooling data has to be done with care to avoid problems of interpretation.

Sources of dataIn practice we should try to collect data relating to all the variables that we think might affect sales, on either a time-series or cross-section basis, according to how we have specified the model. Later, after the statistical analysis, some of these variables may be omitted. There are many sources of data available, but in general the following are the most important in demand estimation, and indeed in most of managerial economics.

1) Records of firms. Sales, marketing and accounting departments keep records of many of the key variables of interest. Such data are normally up to date.

2) Commercial and private agencies. These include consulting firms, market research firms and banks. In addition, a firm may want to commission one of these agencies to carry out a particular study, but it would have to consider the cost involved compared with using freely available data.

3) Official sources. These include government departments and agencies, and international agencies like the EU, OECD, WTO and the various UN agencies. Such data tend to be more macroeconomic in nature, although there are also many industry studies. The data may also be somewhat out of date, since it takes time to collect, collate and publish it, sometimes as long as a couple of years. Much of the above data is now available on the Internet, particularly those from the third source and some of those from the second.

It is important to appreciate that the use of any of the above sources, whether published on the Internet or not, involves abstraction. This means using data that have been collected by someone else; such data are frequently referred to as secondary data. Although it is obviously easier and cheaper to use such data, there are limitations of which the investigator has to be aware. The data have been collected for a



different purpose from that of the current investigation and the investigator does not know the conditions under which the data were collected. The definitions used may be different from those now desired. For example, the price variable measured and recorded in a firm’s records may be the quoted price, not the actual price allowing for any discounts. Clearly it is the second measure that is important in demand estimation, but the investigator may not be aware of the original definition used.

Presentation of dataa) Tables: The most basic method of presenting demand data is in the form of a table. To begin with, we will take a two-variable study, involving just quantity (sales) and current price, to simplify the analysis. In reality this is only justified if either:

1) No other variables affect sales (highly unlikely), or2) Other variables do affect sales but remain constant (still fairly unlikely).

The main advantage of limiting the study to two variables is that such relationships can easily be shown graphically. Consider the example in Table 2, relating to a cross-section study of seven firms. The reason for recording the price variable in the last column, after graph column show regular increments of one unit; although one is unlikely to find such regularity in practice; it simplifies the numerical analysis and allows easier insights as far as statistical inference is concerned.

Table 2

b) Graphs: In order to examine the relationship more closely the next step is to draw a graph. There are two main principles involved here:

Sales (Q) should be measured on the vertical axis as the dependent variable; this is contrary to most price–quantity graphs, but the rationale for this was explained in the previous chapter.

Scales should be selected so as to have the data spread over the whole graph; this involves looking at both the highest and lowest values in the data. Scales should not therefore automatically start at zero.

The result is a scatter graph, as shown in Figure 1; no attempt is made to join the points together in any way. We can see several things from this graph:

There is generally an inverse relationship between the variables. The relationship is not a perfect one; the points do not lie exactly on a straight line or

hyperbola. This is because of the omission of other variables affecting sales, meaning



that the assumption made earlier regarding these variables (that they did not affect sales or remained constant) was not completely justified.

The relationship is approximately linear, although a hyperbola may also fit well.

For simplicity we will assume, to begin with, that the relationship is linear. If we want to describe the relationship using an equation, we need to draw a line of best fit. There are three basic criteria for the method of doing this. It should be:

Objective Mathematically sound Easy to compute.

Although the second and third criteria are somewhat vague, they provide a simple justification for using the method of OLS (ordinary least squares)regression, which satisfies all the above criteria. In addition, and ultimately more important, OLS is justified on two, more technical criteria: the Gauss–Markov theorem and maximum likelihood estimation (MLE).

OLS (Ordinary Least Squares) Method for RegressionThe method of least squares means finding the line that minimizes the sum of the squares of the differences between the observed values of the dependent variable and the fitted values from the line. To put it mathematically, we need to find an equation Ŷ=aX+b which minimizes the sum of squared deviations ∑(Y-Ŷ)2, where Ŷ is the estimated value of the dependent variable as per the fitted curve. The technique for solving for the values of a and b is to use partial differentiation with respect to both a and b, set both expressions equal to zero to minimize them, and solve them simultaneously. The resulting solutions are as follows:

Goodness of fitWhereas regression analysis examines the type of relationship between variables, correlation analysis examines the strength of the relationship, or goodness of fit. This refers to how closely the points fit the line, taking into consideration the units of measurement. Some idea of this can be obtained from a visual inspection of the graph, but it is better to use a quantitative measure.

CorrelationMore specifically the correlation coefficient (r) measures the degree of linear association between variables. It should be noted that correlation says nothing about causation. The causation between the variables could be reversed in direction, or it could act in both directions in a circular manner. For example, high sales could lead to economies of scale in production, enabling firms to reduce their price.



An alternative explanation of correlation between variables is that there may be no causation at all between two variables; they may both be influenced by a third variable.

A notorious example is that empirical studies show that there is a strong relationship between the number of teachers in a country and alcohol consumption. This does not mean that teachers are heavy drinkers, or that people who are heavy drinkers become teachers! It is more likely that both the number of teachers and the level of alcohol consumption are influenced by the level of income in the country. If one substitutes purchases of TV sets or mobile phones for alcohol the same relationship would still hold good, since all these consumer goods are much influenced by income.

It should also be stressed that correlation only applies directly to linear relationships, meaning that weak correlation does not necessarily imply a weak relationship; there might be a strong non-linear relationship. Thus drawing a graph of the data is important, since this can give an insight into this possibility. The formula for calculating the correlation coefficient can be expressed in a number of ways, but probably the most common is:

The coefficient of determinationThe problem with the correlation coefficient is that it does not have a precise quantitative interpretation. A better measure of goodness of fit is the coefficient of determination, which is given by the square of the correlation coefficient, and is usually denoted as R2. This does have a precise quantitative interpretation and it measures the proportion of the total variation in the dependent variable that is explained by the relationship with the independent variable.

In order to understand this measure more fully it is necessary to examine the statistical concept of variation and the components of explained and unexplained variation. This is best done with the aid of a graph (see figure below).

In statistical terms, variation refers to the sum of squared deviations. Thus the total variation in Y is the sum of squared deviations from the mean of Y, or the total sum of squares (TSS). However, for each X, Total Deviation or TD, can be partitioned into two



components, explained deviation (ED) and unexplained deviation (UD). The first component is explained by the regression line, in other words the relationship with X. Thus:

TD = UD + ED

It can also be shown that: TD2 = ED2 + UD2, which can be rewritten as TSS = ESS + RSS,where RSS is the residual sum of squares and is unexplained by the regression line. These relationships are frequently illustrated in an analysis of variance, or ANOVA, table. The definition of the coefficient of determination indicates that it is given by: R2 = ESS/TSS.

Power RegressionIt was assumed in the above analysis that the relationship between the variables was linear. Demand relationships are usually considered to be in linear or power form. Rarely do we have a strong a priori belief regarding which mathematical form is correct from the point of view of economic theory; therefore, we tend to see which form fits the data best in practice and use that one.

The power form, Q=aPb, cannot be estimated directly using the OLS technique because it is a linear method, meaning that the estimators a and b are linear combinations of the values in the data. However, the power equation canbe transformed into a linear one by taking the logarithms of both sides to obtain: log(Q)=a+b log(P).

This ignores the error term for the sake of simplicity of expression. The relationship is now linear in logarithms and therefore OLS can be applied.

Case Study: The Pizza DillemnaDuring the presentation, we discussed the application of the OLS technique to real demand estimation using the case of Pizza sales in and around universities. The model was linear with 4 independent variables, and using supplied data, we had calculated the values of the coefficients, the error terms and the significance of the independent variables.

The aim is to estimate the demand for Pizza by college students. First we select variables for the model that you believe are relevant and for which data can be found.The variables assumed here are:

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 demand equation is : Y = a + b1X1 + b2X2 + b3X3 + b4X4

Results of linear regression based on actual data came out to be :

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

Standard Error of the Y-estimate = 1.64.The standard errors of the coefficients are listed in parenthesis.

Values of Elasticity such as Price Elasticity, Income Elasticity and Cross-price Elasticity are found to be -0.807, 0.177 and -0.767 respectively. The R2 = 0.717 value shows the how close the data is to the regression equation approximation.



Demand ForecastingWe will now shift the focus to the process of Demand forecasting. It is a very important aspect of demand analysis. Some companies may actually produce on order, but large numbers of firms produce for a future anticipated demand. Accurate demand forecasting is necessary in order to produce right quantities at the right time and arrange well in advance for the various factors of production like raw materials, equipment, machine accessories, labor and building. These forecasting based decisions will influence current level of production, which is dependent upon anticipated future demand. This is necessary to avoid an unmanageable inventory build up or a glut in market.

Demand forecasting reduces the uncertainties associated with business. A forecast is a prediction or estimation of a future event. Accuracy of a forecast is determined by its nearness to the actual value in future. A passive forecast assumes business conditions and factors influencing the demand to stay stable and same, while an active forecast assumes a change in the business conditions and demand influencing factors in future.

Need for Forecasting1. Long Range Strategic Planning for corporate objectives such as profit, market share, Return on

Capital Employed (ROCE), strategic acquisitions, international expansion, etc. 2. Annual Budgeting for operating plans such as annual sales, revenues, profits3. Annual Sales Plans for regional and product specific targets.4. Resource Needs Planning for HRM, Production, Financing, Marketing, etc

Type of Demand ForecastingBased upon the time period for which demand forecasting is being done, it can either be short term or long term. Both are associated with the kind of business decisions that are required to be taken in order to meet the short term and long term changes in demand. A third type called medium term demand forecast can be done between the two. Short term demand forecast is usually done for periods of less than one year.

A short term demand forecast is done for production schedules of less than one year. It is done to deal with annual variations in sales. This takes care of an optimum use of current production capacity to meet the demand for the current financial year. Long term demand forecast are related to the need for capacity expansion or reduction depending upon the demand. It also takes care of changes in labor force needed and financial mechanism required to fund the expansion. This capacity expansion is usually not possible in the short run. If the firm anticipates major changes in demand then it will change the production capacity accordingly. For making a forecast a firm usually takes into account facts like population, competition in the market, technology, and government policies. The longer the time horizon of the forecast lesser is the accuracy of the forecast as the number of factors which can influence the demand becomes too high and their precise measurement is not possible. A medium term forecast is usually done to bridge the gap between the short term and long term forecast. It deals with business cycles that usually last for periods from two to five years.



The choice for the kind of forecast is also influenced by nature of the business. Where the output is diversified and it is easier to shift between different production mixes, short term forecast is preferred. In businesses with complex technology, like aircraft manufacturing, steel, motors where the shift in production mix is not easy and takes long time, long term forecast are done. The results of short term and the long term demand forecast may not be necessarily in agreement. The demand may be different for short term forecast and may show entirely different behavior for the long term forecast.

Approaches to Forecasting

Judgmental Approaches: the forecast is based upon the judgment and expertise of experts.

Experimental Approaches: A demand experiment is conducted among a small group of consumers who are adequately representative of characteristics of general population. This type of approach is adopted when the product being introduced is new, and there is no pre-existing data available.

Relational Causal Approaches: Interviews and other methods are used to determine the reasons why consumers purchase a particular product. Once these reasons are clear, the forecast can be done.

Time Series Approaches: Sales and other data for different markets, for different periods of time is analyzed to get a general trend or pattern in sales.

The Requirements for Demand Forecasting For making a demand forecast of market firms have to do a market research in order to understand the probable future conditions of the markets thoroughly. Some of the elements of the market research are:

Consumer Related Elements: Total number of consumers, distribution of consumers/ products, total purchasing power and per capita household income, income elasticities, consumer tastes, social customs etc, consumer purchasing details, effect of design, color etc on consumer preferences.

Supplier Related Elements: Current level of sales, Current level of goods, Trends in sales and stocks, market share, patterns of seasonal fluctuations, Research and Development trends, company strength and weaknesses, product life cycle (age) and new product possibilities.

Market Related Elements: The effect of prices and price elasticities, product characteristics, identification of competitive and complementary products, number and nature of competitors, forms of market competition (price, advertisement, brand policy etc), general price levels, and prices of similar goods.

Other Elements: Economic environment of the country which includes levels of economic activities, employment, trends in income, national income, population, education etc, government policies, taxation and international economic climate.

The quantitative information related to these elements is collected and their effect on demand analyzed carefully. Then the firm may proceed to assess general economic and national situation in future (like population, income, price levels, technology, productivity, and international trade and government



policies). Then the future total market demand for the commodity or product is estimated, based on the previously estimated general economic and national factors. In the last step the firm will estimate its share in the total market.

Factors affecting Method Selection

1. Time Factor: The lead time required for making decisions dependent on results of the model is crucial. Based on the time required for actually changing the output, in nature and level, it can be a short, medium or long term forecast.

2. Level of Forecasting: Demand forecasting may also be classified based upon whether it is done by an individual firm for its own product (micro), by an industrial or trade organization for the products of a particular industry (Industrial level) and if it is done for total industrial output based on national income or aggregate expenditure of that country.

3. General or Specific Forecasting: It can be general or total (if a firm has done a general forecast) or a specific forecast (if a firm has done area wise, commodity wise or industry wise forecast).

4. Problems and Methods of Forecasting: The methods and problems of forecasting demand for a new product (which has never been tested and there is no market data for it) are different from techniques used in forecasting for old product or commodity (for which market data and past behavior is available).

5. Classification of Goods: Demand forecast may depend upon the nature of goods like consumer and capital goods, durable and non-durables etc.

6. Knowledge of Different Market Conditions: Based upon the market structure and conditions (monopoly market, oligopolistic or competitive market) the forecast will be different.

7. Benefit Factors: The firms also have to do a cost-benefit analysis of the forecast method used. The expense and the effort invested should be justified by the potential benefits. The level of complexity and amount of accuracy required for forecast also effects the method selection.

8. Other Factors: Other special factors that need to be taken into account are political factors, sociological factors, psychology of consumers, and patterns of income distribution.

Techniques of Forecasting

The methods used may be divided broadly into two categories, qualitative and quantitative. Demand forecasting is full of uncertainties due to changing conditions. Consumer behavior is unpredictable as it is motivated and influenced by a multiplicity of forces. Every method developed for forecasting has its advantages and disadvantages and selection of the right method is crucial to make as accurate as possible forecast. A right combination of quantitative and qualitative methods is to be used.



Qualitative TechniquesQualitative techniques are generally used when there is insufficient data available for quantitative analysis. They are also known as subjective methods as they are dependent upon intuition based on experience, intelligence, and judgment. They are also preferred for giving a quick estimate and cost savings.

Some of these techniques are as follows

Survey Method

The information about future demand of goods is obtained directly through a survey method. They are important for short term forecasts. Firms generally use them while introducing a new product into the market. It involves conducting consumer interviews, mailing questionnaires to consumers in order to judge their intentions about their demand for goods. Sometimes the employees, distributors and partners involved in the sales are interviewed. This is known as sales force composite method or collective opinion method. The salespersons are asked to report their estimates of expectations of sales in their territories. A similar exercise is done with the retailers and the wholesalers of the company. The average values thus obtained, from sales executives, marketing managers, business and managerial economists and other members of the trade, reflect the estimate of forecast.

Survey methods are dogged by numerous problems that are normally associated with surveys. There is always a risk of subjectivity, bias and over estimation or optimism about future (or a tendency to over report the expected sales), which may lead to a wrong forecast. The consumers picked for survey may not take the survey seriously or may not be a representative population sample.

Expert’s Opinion Method

This method is also known as the Delphi Method. Under this method a group of experts are repeatedly questioned for their opinion/comments on some issues and their agreements and disagreements are clearly identified. This involves a number of rounds involving their ‘interrogation, response and feedback’. In the first round they are asked for information necessary for forecast. The subsequent rounds involve questioning until a complete consensus is reached. The experts belong to a heterogeneous group with diverse background. This technique is used in technological forecasting, defense strategies, education and manpower planning, business demand forecasting etc.

This method has problems associated with selection of an appropriate expert panel, their timing schedules, time taken between different rounds and also the fact that the final result is not quantitative in nature. It is only a reasonable guess.

Consumer’s Interview Method

The consumers are contacted personally to know about their plans and preferences regarding the consumption of the product. All the potential buyers are then drawn and they are approached and



asked how much they plan to buy the listed product in future. This method gives first hand information for demand forecast. There are three main methods for the interviews.

Complete Enumeration method: All the consumers of the product are interviewed and their future plans for product is ascertained.

Sample Survey Method: A sample of consumers is interviewed.

End use Method: Information about the end use of the product is collected form the industrial users to calculate the demand in industries, exports etc.

Historical Analogy Method

This method is used for forecasting demand for a new product or an existing product when introduced in a new area. When it is an existing product, then its sales data for a previous place (which has similar socio-economic conditions as the place where the product is being introduced) is taken for studying and estimating the future demand. In such cases one has to carefully account for sociological and psychological differences. Generally, places which are as similar as possible are taken for studying. If the product has not been used anywhere, then the past consumption pattern of some other similar product is taken as basis for forecasting the demand for the product.

The process is difficult as it is tough to find very similar locations, account for all the differences or find a similar product.

Test MarketingIt involves selecting a test area which can be regarded as true sample of total market. The product is launched in that area in the same manner in which it is intended to be used when product is launched nationally. All marketing devices are selected with this in mind. The sales data of the product tin the test area is then used to forecast the demand for the product nationally.

This method is costly and time consuming. Considerable energy and effort goes as all marketing devices are used for a small area. Selection of an appropriate test area is also difficult. The test needs to be run for a long period of time, to be sure about the sales data. Also differences in sociological and psychological characteristics need to be taken into account for this data. The launch if product in a test area gives competitors to prepare for the imitation of the product or prepare their own strategies to deal with the product.

Quantitative Techniques

Quantitative techniques are used for long run forecasting. They are used to explain time series and cross-section data for estimating long term demand. As they are quantitative in nature and give precise numbers, they are considered to be superior techniques of demand forecasting. Some of these methods are



Trend Method

The time series data of sales of a product may show some variation because of systematic forces. It may show a trend which is due to the effect of certain basic demand influencing factors like population, capital, technology etc. Cyclic variation in sales may be indicator of business cycles. There could be some variation based on seasonal variation also. Some other factors like strike, riots, theft, political disturbances etc will contribute to ‘random variation’. Time series analysis in statistics provides techniques by which all these variations and their effects on sales are isolated and identified. Several Quantitative techniques are used for this.

Graphical Method

Annual Sales data is plotted on paper and line is drawn through the points. This method is simple and less expensive.

Fitting Trend Equation

To get a relationship between sales of product and time, we have to fit the trend line by Least Square Method. The graph is plotted and trend line is plotted, which on extrapolation gives the forecasts for sale. The short term fluctuations are removed to get a more accurate forecast. This is ‘ironed out’ or ‘smoothened’ line. A three year moving average is used to remove the short term fluctuations in a more efficient manner. We may get the relationship in a form of an equation, each of which will tell us something unique about the sales relationship with time. If it is a

Linear Trend Equation: Demand for the product is increasing over time at a constant rate.

Quadratic Trend Equation: The marginal time increment of demand varies linearly with time, which means that total sales increases (or decreases) first and then decreases (or increases) thus showing a turning point on the sales-time graph.

Logarithmic Trend Equation: Time Elasticity of demand is constant.

Exponential Trend Equation: Rate of growth of demand is constant over time.

The advantage of this process is that it removes the short term fluctuations. Sales curve of any commodity eventually turns out to be ‘S’ shaped. This is known as product life cycle. The first stage is Research and Development, where product is market tested. No sales occur but a lot of expenditure is incurred. In Introduction stage product is launched and commercial exploitation and marketing begins. Sales grow in the next two stages of ‘market development’ and ‘exploitation’. Intensive advertising and sales promotion is done. At this optimum level of resource utilization the firm gets maximum profit here. As similar products by competitors flood the market, growth rate of sales decline in the ‘maturity’ stage. Price elasticity is very high, and in the later ‘saturation’ stage the high cross elasticity between different brands makes rate of sales growth zero. Marketing becomes ineffective, but firms maintain quality,



services etc to maintain market share. Eventually this leads to the phase of decline the product life comes to an end. All these phases give the exponential shape to the curve.

The knowledge of product life cycle helps in planning the marketing process and budget.

The trend method assumes that the conditions which existed in past influencing the sales of the product will continue to hold in future also. Thus it cannot predict any sudden changes, and nothing can be done to correct this limitation.

Leading Indicators Method

If there are frequent turning points then trend method cannot explain the relationship fully between time and sales as there is negative relationship sometimes, while at other it is positive. Therefore some other indictor is used which shows a similar variation as the commodity. It can be GNP, personal income, bank rate, WPI, Industrial production, Employment Rate etc. There might be some time lag or lead in case of these indictors affecting the demand of the product. After identifying the product, one may use the regular least square approach to get the sales forecast. This is also known as barometric method as indicator is used as a barometer to forecast the demand.

Box Jenkins MethodBox 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. This method is used only for short term predictions since it is suitable only for demand with stationary time series sales data, i.e. the one that does not reveal the long term trend.


Product life cycle curve is S shaped.


The models are designated by the level of auto regression, 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.

There are 3 components of the ARIMA process:

AR(Autoregressive) process.

MA(Moving Average) process.

Integration process.

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

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.

Consider 4 industries,

Industry 1: X1=X11+X12+X13+X14+C1






Xij = Output of the industry i which is purchased by industry j for the production of its output.

Ci = Demand of the customers for products for final use.

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

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



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

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.

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



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.

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.

Advantages:

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.

Disadvantages:

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 time gap, less stable will be the coefficients, thus reducing the forecasting accuracy.

2. Also changes in the production technology, tastes and preferences during the period make 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).

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, and forecasting method.



REFERENCES/SOURCES:Armstrong, J. S. (2001). Standards and Practices for Forecasting. In Principles of Forecasting: A Handbook for Researchers and Practitioners (pp. 1-46). Kluwer Academic Publishers.

Barthwal, R. R. (2010). Industrial Economics An Introductory Textbook. New Age International Publishers.

J. Scott Armstrong, K. C. (2005). Demand Forecasting: Evidence-based Methods. In L. M. Southern, Strategic Marketing M.anagement: A Business Process Approach.

Savvides, D. S. (n.d.). Demand Estimation & Forecasting. EC611--Managerial Economics . Cyprus: European University Cyprus.

Webster, T. J. (2003). Managerial Economics Theory and Practice. San Diego: Academic Press.

Wilkinson, N. (2005). Managerial Economics A Problem Solving Approach. Cambridge: Cambridge University Press.

Mangerial Economics, Keat and Young


Demand estimation and forecasting

Education

Transcript of Demand estimation and forecasting