ECONOMETRIC METHODS IN MARKETING RESEARCH

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1 Abstract ECONOMETRIC METHODS IN MARKETING RESEARCH Nada Pleli, Šemso Tanković Faculty of Economics, Kennedyjev trg 6, Zagreb, Croatia This article deals with contemporary econometric approach to marketing issues in offer to develop useful marketing econometric models and suggest related estimation methods. In marketing phenomena exist several interactions among marketing variables. Thus both the simplest marketing system and the more complex ones have to be expressed as a set of simultaneous relationships. The estimates of those models may have value in marketing practice, too: in forecasting future sales and in improving decision rules. Keywords: marketing system, econometric model, estimating, marketing econometrics Introduction The academic marketing discipline has increased over the past three decades by quantitative methods and related software being used on firm level, on industry level or on the national economy level. In econometric approach, regardless of the level, we have to specify marketing system as an econometric model, to discuss the identification problem and to choose the estimation method [18]. The estimated marketing econometric model has to be tested and evaluated, and can also be used for marketing forecasting. The marketing researchers and the marketing practitioners, too, are very interested in application of econometric methods in marketing investigation. There is a new scientific discipline: marketing econometrics, like, for instance, macroeconometrics, biometrics, demometrics. In the very several fields, econometrics involves the application of regression analysis in order to test theories and estimate single-equation model or simultaneous relationships econometric model. We begin with the simplest marketing system where there is no competition so that the marketing organization or firm and the industry are identical. Even that simplest marketing econometric model consists of two simultaneous equations. Consequently, there is no single-equation model in marketing econometrics. Marketing systems and econometric models First, we consider the simplification of marketing system made up of two units: the marketing organization or firm and the market or consumers. Further, we assume there is no competition on the market (the case of a monopoly). The marketing organization communicates to the consumers through several marketing actions, such as advertising its products or services, setting prices, and so on. The consumers reply to the marketing s actions through sales, and the firm collects these informations. Therefore, we already have two flows of communications between the marketing organization and the market. The third flow of communication is an internal flow: the marketing organization makes plans for future actions on the basis of current and past information's. Except these three communication flows, there are two physical flows in this system: the movement of products and/or services from the marketing organization to consumers, and the simultaneous movement of sales money from the customers to the firm.

2 Formulation of the problem and description of the model If a marketing organization had only one marketing instrument or controllable variable which was influenced demand, for example, advertising, this simplificated marketing system in symbolic notation is, as follows: q t = f ( A t, Z t ), (1) A t = g ( p t-1 q t-1 ), (2) where q t = marketing organization s sales in units at time t, A t = marketing organization s advertising expenditures at time t, Z t = environmental factors (uncontrollable variable) at time t, p t-1 = price of the product at time t-1, q t-1 = marketing organization s sales in units at time t-1. Logically is to be supposed that the prior s period demand and the current s period one influence to the current s period price. Therefore, we have the third function in representing of considered marketing system: p t = h ( q t, q t-1 ). (3) Relationship (1) represents market behavior and it is named the sales response function, and the relationship (2) expresses a firm s decision rule for setting its advertising budget at time t as some percentage of the t-1 st period sales revenue. The analysts assume the relationships (1) - (3) are stochastic and linear in econometric sense [18]. Stochastic character of these equations means including random variables in the model, at least in one equation. Now, we can write marketing econometric model, as follows: q t = a o + a 1 A t + a 2 Z t + ε 1t (4) A t = b o + b 1 p t-1 q t-1 + ε 2t (5) p t = c o + c 1 q t + c 2 q t-1 + ε 3t (6) where, in econometrical terms, q t, p t and A t are endogenous variables, Z t, p t-1 and q t-1 denote predetermined variables. Z t is egzogenous variable, and the last ones are lagged endogenous ones. a o, a 1, a 2, b o, b 1, c o, c 1 and c 2 are unknown parameters. Last but not at least, ε 1t, ε 2t and ε 3t represent random disturbances. Equation (5) becomes linear one by introducing regressor variable: x t-1 = p t-1 q t-1. (7) There are developed theory of identification and choosing an estimation method, and the marketing econometricians use all of these tools. First, let us consider the simultaneous

3 equation marketing system consists of the equation (4) and (5). If we could suppose that the random disturbances, ε 1t and ε 2t, are independent, the model (4) (5) is a special kind of econometric model called recursive model. In that special case, equation (4) and (5) are identified, and ordinary least squares method (OLS) gives consistent and unbiased estimates. Now, we consider the marketing econometric model, as follows: q t = a o + a 1 A t + a 2 Z t + ε 1t (8) A t = b o + b 1 x t-1 + ε 2t (9) p t = c o + c 1 q t + c 2 q t-1 + ε 3t (10) The rank identifiability condition is met. Equations (8) (10) are overidentified. We consider the matrix G, which contains the coefficients of the current endogenous variables in each equation. For that purpose, we rearrange the model (8) (10) into this one: In that case, the matrix G is, as follows: 0 = -A t + b 0 + b 1 x t-1 + ε 2t (11) 0 = -q t + a 0 + a 1 A t + a 2 Z t + ε 1t (12) 0 = -p t + c o + c 1 q t + c 2 q t-1 + ε 3t (13) G = a (14) 0 c 1 1 The marketing econometric system (11) (13) is complete, and matrix G is square one. It is regular and triangular matrix. In the next step we examine the covariance matrix Σ. If it is diagonal, i.e., E ( ε ε τ ) = σ 2 I, the system is recursive equation system. If the covariance matrix Σ is not diagonal, use three-stage least squares method (3-SLS), because of the overidentifiliabity [18]. Let us remark that we can do estimating by OLS or 3-SLS by econometric program package SORITEC. In describing real markets we have to consider organizational complexities, for instance, equations between individuals or groups, and market complexities such as non-homogenate market for a product or service in consideration. The marketing organization s actions can become more or less complex and the market s information's, too. Further, we have to think about multiple products and/or services, because contemporary marketing organizations offer more than one brand (product or services), and we have to think about the effects of market competition on a sales response. In the marketing system, i.e., in the econometric marketing model, we must not forget the role of the middlemen such as retailers and wholesalers. That is to say, the products and/or services and communications do not flow directly from the marketing organization to the market, and vice versa. Last but not at least, we have to take into consideration dynamic nature of marketing processes, because, for instance, both the plan and the execution can be late, and, therefore, the advertising budget depends about prior s period sales, etc.

4 Regards econometric theory, we have to respect some assumptions, the first one is about linear independencies among the predetermined variables. Violation of this assumption is called multicolinearity. But, if we doubted about near multicolinearity, it is advisable to compute correlation matrix determinant and, if it was close to zero, to apply ridge regression [17]. The simultaneous linear equation marketing model in consideration has to be complete, maximum lag has to equal one period, random disturbances are normally distributed with zero mean and an unknown but finite covariance matrix. Further, we do not consider identities, and, of course, equations are identified. In general, every econometric study begins with data, and econometric study in marketing begins with data, too. The purpose of data is to give empirical basis to econometric theory. But, data quality sometimes does not satisfy. Regards of data problem, we can distinguish two kinds of variables: observable variables, and unobservable ones. Marketing projects contain both of them. Marketing econometricians are solving the problem of unobservable variables in two ways. One way suggests omitting such kind of variables from the model. The other way intends to develop instruments to measure the unobservable variables, either directly or as a function of observable variables. The measurement errors could be the problem in econometric studies, too. In a single equation model, measurement errors in the dependent variable can be solved with absorbing them into the disturbance errors. This procedure can be followed in simultaneous linear equation model as well, but the analysts have to take care about correlation of the measuring errors across equations. Econometric models in marketing can be used at any level of aggregation, such as marketing systems can be developed on several levels of aggregation. The marketing practitioner can describe the marketing system on the various economic levels (marketing organization demand, industry demand, national economy demand or world demand), or on the behavioral levels for a firm s demand (individual sales response, market segment sales response or company sales response). Instead of conclusions Above line of thinking has resulted in the following conclusions. Simultaneous linear equation systems, the most sophisticated part of econometrics, represent the powerful means in the quantitative approach to analyzing marketing systems. Both marketing as a science and marketing as a profession are included with the set of relationships among marketing variables. The authors hope of extending econometric way of thinking to the various fields of the human activities, especially to marketing investigation, and would be very pleased if this paper inspired and encouraged marketing analysts, especially in Croatia, to help in preparing the decision-making [15]. References [1] ALLEN, R.G.D. : Macroeconomic Theory, A Mathematical Treatment, Macmillan, London, 1968 [2] ANDERSEN, E.B. : Introduction to the Statistical Analysis of Categorical Data, Springer Verlag, Berlin, 1997 [3] AYERS, D.; DAHLSTROM, R.; R.; SKINNER, S. J. : An Exploratory Investigation of Organizational Antecedents to New Product Success, Journal of Marketing Research,

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