Slotting allowances: a time series analysis of aggregate effects over three decades

Abstract

Slotting fees and related discounts are important but controversial mechanisms for obtaining shelf space in marketing channels for consumer packaged goods. The theoretical field is divided between the efficient market and the market power schools of thought. Results from empirical studies and analytical models point in different directions. This paper analyzes trends in key macro economic variables to see if the patterns are more consistent with an underlying market efficiency model vs. a market power one. The data span 30+ years and focus on retailers in the marketing channel for food and kindred products. The variables studied include new product introductions, retail selling area, consumer price indices, profitability, cost of goods sold and selling expenditures. Efficient market explanations do not fare well in the analyses in comparison with market power explanations for practically all the variables studied. The paper conlcudes with recommendations for regulators and retail management.

Appendix

Model selection

The difference between the Box Jenkins and Dickey-Fuller methods is that the former focuses on model selection based on an analysis of the decay patterns in autocorrelograms. The Dickey-Fuller approach first tests for unit roots to determine whether a series should be analyzed in levels or first differences; it provides an explicit statistical test of the unit root hypotheses, and it employs lagged values of ΔY _t to account for serial autocorrelations and nuisance variance and ensure the errors are white noise (Maddala and Kim 1998, p. 47).

Typically both approaches give similar results. However, starting with unit root tests is not always advisable. The standard tests do not necessarily resolve the question whether the “true” DGP is trend stationary (TSP) or difference stationary (DSP) and can create problems.¹⁶ Second, the appropriate unit root test distributions and significance criteria depend on the model being used, particularly when the model involves an analysis of event interruptions in the series or structural breaks (Bai and Perron 2003; Perron 1989). Maddala and Kim sum it up thus: “The problem of choosing between difference-stationary and trend-stationary models has been often approached as a hypotheses testing problem (that of testing for unit roots), but it should properly be approached as a model selection problem” (p. 406). They suggest that it is “more important to take the serial correlation structure in both the models into account…” Likewise McCallum (1993) recommends that the DGP be modeled in both levels and first differences, and the model chosen which requires the smaller amount of correction to remove autocorrelation of the residuals.

Structural breaks and unit roots

If the model selection procedure results in a model without structural break dummies (i.e., there are no significant effects related to the hypothesized event), the unit root tests applied are the standard ADF (Augmented Dickey-Fuller) t and associated critical values, and the PP (Phillips-Perron) t which uses the ADF critical values but adjusts the t statistic. A significant t means no unit root. On the other hand, if the model selected includes a structural break, then the unit root hypothesis that ρ = 1 is tested using Eq. 2A and Perron’s (1989) critical values (c.v.) for T(ρ-1) for λ. λ = (T _B-1)/T is the “break fraction,” the ratio of pre-break sample size to total sample. The null hypothesis of a unit root is rejected if T(ρ-1)< c.v.(λ). If the tests indicate a unit root the analysis strategy switches to Eq. 3 to see if the DGP is difference stationary. The test for ρ = 1 not withstanding, if β, γ, θ and δ ≠ 0, the DGP is not clearly trend or difference stationary and thus the models of Eqs. 1 and 3 are compared to see which has better statistical properties, i.e., for which the residual series is clearly white noise, and the estimated parameters and SEs are consistent and reliable. In addition, this study uses the Newey-West covariance estimator that is consistent in the presence of both heteroskedasticity and autocorrelation of unknown form (Newey and West 1987), and is superior to the standard OLS and White methods in estimating the standard errors of the parameters (point estimation and consistency of the parameters themselves are not affected by any of the above methods).

Stationarity and white noise

A series is weakly or covariance stationary if the innovation series is white noise, i.e., there are no remaining correlations among the residuals. This is evaluated by the auto and partial correlation functions (ACF and PACF) relative to the theoretical functions: the former should decay rapidly and fall according to the theoretical function, and the latter should not have any significant spikes after lag 1 (evaluated to L = 24 in this study). Further the residuals are white noise if the Ljung-Box χ² statistic (also known as the Q statistic) is not significant for all lags up to L, and the Breusch-Godfrey Lagrange Multiplier test (LM test) is insignificant to L. [The Obs*R² statistic is computed from the regression of the residuals on lagged residuals and the original regressors. Unlike the Durbin-Watson statistic, the LM test is applicable for higher order ARMA errors and for models with lagged as well as nonlagged variables.] When there are alternative models that meet the tests, the best fitting is selected via fit indices—i.e., the model with the smallest Akaike Information Criterion (AIC), Schwartz Bayesian Information Criterion (BIC) and Root Mean Square Error (RMSE).

Cointegration

A well known problem in studying the relationship between two economic time series Y_t and X_t arises if both are integrated I(d). A long term relationship, real or spurious, between two trending variables is very likely to be found. One solution is to difference the data until both are I(0). But if there is a true relationship between trending series measured in levels, differencing can cause serious difficulties (lack of a unique long run solution, and noninvertible moving average errors). On the other hand, if there is a genuine economic structure relating two I(d) variables, then there is a linear combination of Y_t and X_t that is I(0)—i.e., the variables are cointegrated. In this paper no two series are modeled in the manner Y _t = f(X_t), rather X_t is typically a control or reference series. The problems of spurious regression of the kind encountered in Y _t = f(X_t) are not an issue here. Nevertheless, where models compare variables that are I(d), the Johansen cointegration test is used and reported. If they are cointegrated there is a genuine relationship between Y_t and X_t and inferences relating or contrasting them are valid. Cointegratiom tests are irrelevant where both variables are I(0).

Sensitivity to the break point

A debate in the interrupted time series literature is about the selection of the intervention or break point. Perron used exogenous break points consistent with well known major economic disturbances. Critics argued that this amounted to “pre-testing” because the break points were the result of prior examination of the data. Zivot and Andrews (1992) provide a methodology for determining endogenous break points in a data series by sequentially testing all possible break dates in the series. Although preferable to eye balling for break points, the latter approach is data driven nevertheless.

The break point in this paper is determined exogenously, not based on an examination of the data, but from the known chronology of the phenomenon. There are three reasons that favor using an exogenously determined break point. First the orientation of this study is that of assessing the impact of ongoing structural change occurring over many years. The goal is not to find breaks in the data and model the DGP as accurately as possible (e.g., for forecasting purposes) but to see if the data patterns support the theoretical explanation of underlying phenomena. Second, an a priori specified date offers a stronger test of the hypotheses as the results must hold across the early years of the phenomenon (when its effects are likely to be weaker) as well as later years. The data patterns show that visible changes typically occur between 2 to 3 years from the hypothesized start date. Third, selecting a common date for all the data series studied is conceptually more appealing than having different dates for different series determined from the data.

Nevertheless it is useful to test the sensitivity of the results to the exogenously selected event date. Although there is reason to believe that slotting fees emerged in 1982 (Smith 1989; Sudhir and Rao 2006; Sullivan 1997; Supermarket News 1984), some accounts mention a time a couple of years later (Sullivan 1997). To study the sensitivity of the results to the chosen break point, the following analyses were conducted. First, rolling break points were analyzed starting with 1980 and through 1984. Second, the models were estimated after eliminating the data for 5 years from 1980 to 1984.¹⁷ Overall it seems that 1982 provides a stronger test of the theoretical propositions and is the appropriate break point both exogenously (deductively) and endogenously (inductively).