Economics – Demand Estimation Essay Sample

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What Is Demand Estimation?
When running a small business, it is important to have an idea of what you should expect in the way of sales. To estimate how many sales a company will make, demand estimation is a process that is commonly used. With demand estimation, a company can gauge how much to produce and make other important decisions.

Demand estimation is a process that involves coming up with an estimate of the amount of demand for a product or service. The estimate of demand is typically confined to a particular period of time, such as a month, quarter or year. While this is definitely not a way to predict the future for your business, it can be used to come up with fairly accurate estimates if the assumptions made are correct. Methods of Demand Estimation:

There 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 Methods:

Qualitative methods consists of following points. Consumer 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 Rs.15 per liter, or which brand of several possibilities they prefer. These methods have certain drawbacks. Market experiments:

As with consumer surveys these can be performed in many ways. Laboratory experiments or consumer clinics seek to test consumer reactionsto 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 andreliable 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.

Quantitative methods:

Statistical methods

While 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. Statisticaltechniques, 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 specification:
There 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 andPt-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 conflict.

Statistical models:
In 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 collection

Statistical 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 data

There are two main types of data that firms can collect.
a. Time series Data
This 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 data

This 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 data

In practice we should try to collect data relating to all the variables that we thin k 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 data
a) 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.  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 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

OLS (Ordinary Least Squares) Method for Regression:

The 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

More 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 indirection, 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.

The coefficient of determination
The 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)

Demand Estimation and Fore casting. In statistical terms, variation refers to the 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.

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