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01-03-2015

Unit roots and the dynamics of market shares: an analysis using an Italian banking micro-panel

Author: Caterina Giannetti

Published in: Empirical Economics | Issue 2/2015

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Abstract

The paper proposes the use of panel data unit-root tests to assess market-share instability in order to obtain indications of industry dynamics. The idea is to consider movements in market shares as much more than mere elements of the market structure. In fact, these movements reflect conduct that arises from that market. If shares are mean-reverting, then firm actions have only a temporary effect on shares. On the other hand, if shares are evolving, as signaled by the presence of unit roots, then any gain in shares with respect to the competitors is long term. To illustrate the potential of unit-roots tests, the paper considers an application to the Italian retail banking industry.

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For a discussion on the importance of turbulence on market structure dynamics, see Sutton (1997) and Davies and Geroski (1997).

This condition roughly corresponds to the perfectly elastic demand curve for a firm in perfect competition.

The demand elasticity could be independent of prices, e.g. $q=kp^{-\eta }$.

In perfect competition, there are many competitors, each with an insignificant share of the market. See also footnote 2.

In particular, dependent on the alternative under consideration, two types of tests can be identified. The first type of test considers a homogeneous alternative (i.e. $H_{0}=\alpha _{1}=\cdots =\alpha _{n}=\alpha <1$). An example appears in Levin et al. (2002). The idea of this approach is to perform a pooled Dickey–Fuller $(DF)$ test with the residuals. The second type of test allows for heterogeneity of all parameters. Im et al. (2003) criticize the assumption of a common root under the alternative, and require $\left| \alpha _{i}\right| <1$ for a sufficiently large number of units. In this case, it is thus natural to perform $n$ tests individually and to average over individual DF statistics.

Reviews of the literature on dynamic micro panels are provided in Baltagi (2005) and Arellano (2003). For a general survey of the literature about unit-root tests, see Breitung and Pesaran (2008).

Mean stationarity (constant first moment) requires $\alpha <1$ and $\delta _{0}=0$ and $\delta _{1}=1$. The covariance stationarity (constant first and second moments) also requires homoskedasticity over time of the $v_{it}$ shocks (i.e. $\mathrm{var}(v_{it})=\sigma _{vi}^{2}$) for $(i=1,\ldots ,N)$ and that $\mathrm{var}(v_{i0})=\sigma _{vi}/(1-\alpha )^{2}$.

More precisely, Harris and Tzavalis (1999) show that the limiting distribution is

$$\begin{aligned} \sqrt{n}(\hat{\alpha }_{WG}-1-B)\rightarrow N(0,C), \end{aligned}$$

(14)

where $\hat{\alpha }_{WG}$ is the within-group estimator and $B$ and $C$ are given as

$$\begin{aligned} B=-3\left\{ (T+1)\right\} ^{-1} \end{aligned}$$

(15)

and

$$\begin{aligned} C=\left\{ 3(17T^{2}-20T+17)\right\} \left\{ 5(T-1)(T+1)\right\} ^{-1}. \end{aligned}$$

(16)

Kruiniger and Tzavalis (2002) propose unit-root tests in short panels where error terms are serially correlated and heteroskedastic.

For example, Chu et al. (2007) used the panel SURADF tests to investigate Gibrat’s law of proportionate effects for 48 electronic firms in Taiwan. Panel SURADF tests handle cross-sectional dependence across firms and, at the same time, investigate a separate unit-root null hypothesis for each and every individual panel member, identifying how many and which series in the panel are stationary process.

Beginning in the 1980s, the Italian banking system experienced a series of reforms aimed at increasing competition in the market through liberalizing the way in which banks organized their branch and an easing of the geographical restrictions on lending. In fact, the opening of new branches had been regulated by the ‘branch distribution plan’, issued every four years. The last distribution plan was issued in 1986.

http://siotec.bancaditalia.it/sportelli/main.do?function=language&language=ita.

For this test I built a STATA command csdar.ado, relying on xtcsd.ado as developed by Hoyos and Sarafidis (2006).

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Title: Unit roots and the dynamics of market shares: an analysis using an Italian banking micro-panel
Author: Caterina Giannetti
Publication date: 01-03-2015
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 2/2015
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-013-0795-1

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