Modelling the dynamics of market shares in a pooled data setting: econometric and empirical issues

Abstract

The objective of this article is twofold. First, it is to study the applicability of the widely used Autoregressive Distributed Lag Model (ARDL) in a pooled data setting. Second, it is to analyse Chile's market shares in the EU during the period 1988 to 2002, pointing to application problems that might jeopardize the model and searching for estimation methods that deal with the problem of inter-temporal and cross-sectional correlation of the disturbances. To estimate the coefficients of the ARDL model, Feasible Generalized Least Squares (FGLS) is utilized within the Three-Stage Least Squares (3SLS) and the nonstandard Generalized Method of Moments (GMM) frameworks. A computation of errors is added to highlight the susceptibility of the model to problems related to the underlying model assumptions.

Acknowledgement

We are grateful to Stephan Klasen and an anonymous referee for excellent suggestions that considerably improved this article.

Notes

¹ This is identical with the geometric lag model. The more complicated type of autoregressive distributed lag models corresponds to the transfer function model, also known as ARMAX model (for a good description, see Greene, 2000)

² For efficient estimation of models for panel data, see Ahn and Schmidt (1995) and Anderson and Hsiao (1982).

³ Standard GMM utilizes lagged variables as instruments. This leads to biased estimates in the presence of autocorrelation of the disturbances.

⁴ In a bivariate regression model, this assumption may not be so restrictive, but the assumption will also not always be fulfilled.

⁵ This problem was discussed extensively by Granger and Newbold (1974) and led to the development of stationarity tests (unit-root tests) such as the Augmented Dickey–Fuller test (1979), the Phillips–Perron test (1998), the Kwiatkowski, Phillips, Schmidt and Shin test (KPSS, 1992), the Generalized Least Squares (GLS)-detrended Dickey–Fuller test (Elliott et al., 1996), the Elliott, Rothenberg and Stock Point Optimal test (ERS, 1996) and the Ng and Perron test (NP, 2001).

⁶ In the last 10 years, enormous progress has been made in the field of panel/pool unit root tests. There are two types of panel/pool unit root tests. One type assumes panel homogeneity (common unit root processes for all cross-sections). These tests were developed by Levin et al. (2002), Breitung (2000) and Hadri (1999). The second type of tests allows for panel heterogeneity. The Im–Pesaran–Shin test (IPS test, 2003), the Fisher-type tests using ADF and the Phillips–Perron test (Maddala and Wu, 1999; Hadri, 2000; Choi, 2001; Hadri and Larsson, 2005) are based on individual unit roots or coefficients ρ_i for each cross-section.

⁷ For simplicity, neither constants nor trends are included in the equations.

⁸ In FGLS, the unknown serial correlation coefficient is estimated as described in Section II.

⁹ In samples with sufficiently large T and errors that follow an AR process, Electro Chemical Machining (ECM) or Dynamic Ordinary Least Squares (DOLS) techniques can be applied, but in samples with shorter T, FGLS techniques are preferable.

¹⁰ Building a system is only possible if the number of cross-sections is small.

¹¹ Advertising is important when selling a differentiated product, but not when selling rather homogeneous products (as in our case study).

¹² We fully agree with the importance of nonprice factors in the industry sectors.

¹³ The bilateral real exchange rate captures the depreciation of the euro vis-á-vis the US dollar in the 1995–2001 period and the appreciation of the Chilean peso with respect to the US dollar in the period from 1993 to 1997. In the period from 1988 to 2002, Chile's price competitiveness was by and large impeded by the appreciation of its currency vis-á-vis the euro.

¹⁴ Appreciation of the peso was less pronounced with respect to the British pound (GBP).

¹⁵ These cross-correlations show the reaction pattern between the dependent and the independent variables very clearly and should precede the building of any dynamic models. The 84 cross-correlations are available from the authors upon request.

¹⁶ The economic policy of the Pinochet government was continued under the governments of Aylwin, Frei and Lagos. Consequently, the time series display no sign of a significant structural shift.

¹⁷ Macroeconomic data usually show unit roots in the series and are therefore plausibly characterized by an autoregressive error process.

¹⁸ We have estimated the market share dynamics with an ECM based on an ARDL. However, using this procedure, we could explain much less of the variation of market shares, i.e. our R ² (adjusted) were much smaller.

¹⁹ Rao (2007) reviews three alternative approaches, namely, general to specific, vector autoregressions and vector-error correction models, to estimate short- and long-run relationships.

²⁰ ρ is usually well below 1; first differencing thus is a very imprecise (ineffective) method to remove stationarity.

²¹ In our data first-order autocorrelation of the type = turns out to be present and dominant. expresses first-order autocorrelation, henceforth to be called .

²² The system/SUR approach is recommended when the number of N is small (six in our case) and T is large (15 in our case).

²³ The number of restrictions is T(T − 1) K/2.

²⁴ Illegal logging is estimated to comprise up to 50% of all logging activity in the key countries of Eastern Europe and Russia, up to 94% in the key Asian countries, up to 80% in the key African countries, and up to 80% in the key Latin American countries (FERN, 2004).

²⁵ Even though the DW statistic must be adjusted in the presence of a lagged endogenous variable, the DW statistic is still able to roughly indicate problems of autocorrelation and misspecification. A better measure of autocorrelation is probably Bhargava's et al. (1981) DW statistic.

²⁶ All our prices contain sector-specific protection whenever relevant.