ESTIMATING CONFIDENCE BOUNDS FOR ADVERTISING EFFECT DURATION INTERVALS

ABSTRACT:

Duration intervals measure the dynamic impact of advertising upon sales. To be more precise, the p % duration interval measures the time lag between the advertising impulse and the twinkling that p % of its issue has decayed. In this paper, we derive an expression for the duration interval for a dynamic type linking sales to advertising, and greatest in quantity important, we put forward a process to provide confidence bounds around the estimated duration interval. The way is illustrated in two examples.

(ProQuest Information and Learning: denotes formulae omitted.)

This application of mind concerns an analysis of the dynamic consequences of current and past advertising upon current and future sales. There is general agreement in the marketing literature that advertising positively affects sales. Furthermore, this event may last for multiple periods and is pendent on the product and market characteristics. A variety of econometric time series patterns have been put forward to describe this consequence (see, for example, Assmus and Lehmann 1984; Clarke 1976; Weinberg and Weiss 1982; and for a novel summary, see Leeflang et al. 2000)1 An important and desired feature of fitly specified models for describing advertising issues on sales is that they allow for a distinction between long-run and short-run issues of advertising.

An often-applied type is the geometric distributed lag type best known as the Koyck (1954) protoplast This model is rather easy to analyze, and the so-called duration interval is easy to derive from it. A p % duration interval measures the time lag between the advertising impulse and the jiffy that p % of its issue has decayed. This duration interval is a point estimate that come [i]or[/i] go after [i]or[/i] behinds from the estimated model parameters. Many academic studies report these estimates and evaluate the values across returnss or temporal aggregation levels (see for example, Clarke 1976) Indeed, the duration interval is not independent from the sampling scheme. This is owed to the fact that temporal aggregation (that is, say, going from monthly to annual data) changes the pattern structure, and this leads to other parameters. As these parameters determine the duration interval, it changes, too (see among others, Clarke 1976; Leeflang and Reuyl 1985; and Leone 1995)

We are, however, not aware of studies where measures of uncertainty around the point estimates of the duration interval are reported. individual possible reason for this is that analytic expressions for these confidence bourns are not available, and individual therefore has to rely upon simulation techniques. We believe that statistical estimates should be accompanied through confidence bounds. First, this emphasizes that the number that is obtained is an estimate and should be interpreted as of that kind second, the confidence bounds allow managers to understand the precision of that number, which should help in advertising decision making. For example, the timing of the nearest ad may depend on the duration interval of the popular one, and confidence intervals can help managers arrive at specific decisions.

The goal of the not absent study is to fill in this gap in the literature. We present a method to compute confidence confines around p % duration intervals. In the extremity one can then make statements of the like kind as the one we make in our empirical section below, which is that "with 95% confidence, the 95% duration interval of advertising is between about 48 and 57 hours."

To achieve generality, we consider this means for the autoregressive distributed lag (ADL) design of order (p. m), which goe back to at least Griliches (1967) not long ago this model has been fortunately implemented in Tellis, Chandy, and Thaivanich (2000) This type encompasses the Koyck model and various other patterns A nice feature of this mould which stands in contrast to the Koyck mould is that it allows the long-run events to be smaller or larger than the shortrun results The Koyck model implies that the long-run consequences are always larger. We provide an alternative representation of the ADL mould which allows for direct inference upon long-run and short-run effects. In fact, if the prototype parameters are estimated for this representation, individual directly obtains estimated standard errors for the long-run consequences which is quite convenient.

The outline of the at hand study is as follows. In the "Main Results" section, we discuss the relevant features of the ADL mould including the method of computing confidence bourns around the p % duration intervals. Finally, in the "Illustrations" section, we illustrate its relevance for single of the cases concerning hourly data in Tellis, Chandy, and Thaivanich (2000) and for the familiar monthly Lydia Pinkham data.

MAIN accrues

This section begins with a discussion of the ADL protoplast Next, we propose an alternative representation of this protoplast which allows for direct estimation of the long-run and short-run events Then we deal with the computation of the point estimate of the duration interval, as well as with its confidence confines