Yuanhua Feng

Constant market share (CMS) analysis is widely applied to decompose a country's export change into the demand growth, competitive and interaction effects (Jepma, 1986; Chen et al., 2000) and is a useful tool for marketing research. Its outputs can also be used for further statistical analysis (Batista, 2008). We introduce a tree-form CMS for modelling trade between a focus country (A) and a destination (B) based on a complex data set classified at three levels. That is A's aggregate exports and B's total imports from the world are first divided into *n* first-level categories, the *i*-th first-level category consists of *n*_{i} second-level sub-categories and the (*i,j*)-th second-level category is again composed of *n*_{ij} third-level sub-categories. Denote the quantities of A's exports, B's imports from the world and A's market shares at those levels in the initial and final years by q^{0}, q^{1}; q^{0}_{i}, q^{1}_{i}; q^{0}_{ij}, q^{1}_{ij} and q^{0}_{ijk}, q^{1}_{ijk}; Q^{0}, Q^{1}; Q^{0}_{i}, Q^{1}_{i}; Q^{0}_{ij}, Q^{1}_{ij} and Q^{0}_{ijk}, Q^{1}_{ijk}; s^{0}, s^{1}; s^{0}_{i}, s^{1}_{i}; s^{0}_{ij}, s^{1}_{ij} and s^{0}_{ijk}, s^{1}_{ijk}, and *i* = 1, …, *n*, *j*=1, …, *n*_{i}, and *k*=1, …, *n*_{ij}, respectively. Let Δ denotes the change between the initial and final years. The (entire) tree-form CMS model is defined by

Δq = s^{0}ΔQ + ΔsQ^{0} + ΔsΔQ

+ (∑_{i}s^{0}_{i}ΔQ_{i} − s^{0}ΔQ) + (∑_{i}Δs_{i}Q^{0}_{i} − ΔsQ^{0}) + (∑_{i}Δs_{i}ΔQ_{i} − ΔsΔQ)

+ (∑_{i,j}s^{0}_{ij}ΔQ_{ij} − ∑_{i}s^{0}_{i}ΔQ_{i}) + (∑_{i,j}Δs_{ij}Q^{0}_{ij} − ∑_{i}Δs_{i}Q^{0}_{i}) + (∑_{i,j}Δs_{ij}ΔQ_{ij} − ∑_{i}Δs_{i}ΔQ_{i})

+ (∑_{i,j,k}s^{0}_{ijk}ΔQ_{ijk} − ∑_{i,j}s^{0}_{ij}ΔQ_{ij})+(∑_{i,j,k}Δs_{ijk}Q^{0}_{ijk} − ∑_{i,j}Δs_{ij}Q^{0}_{ij})+(∑_{i,j,k}Δs_{ijk}ΔQ_{ijk} − ∑_{i,j}Δs_{ij}ΔQ_{ij}), (1)

where the three terms in the second, third and fourth rows of Model (1) are called the first-, second- as well as third-level effects. Model (1) can provide us detailed sources that cause the change of exports. Furthermore, the so-called first-level branch-, second-level branch- and leaf-models can be defined by taking out the *i*-th, (*i,j*)-th and (*i,j,k*)-th element of Model (1), respectively. The sum of the three level-effects at each level is always zero. It is found that if the market shares for all commodities are both homogenous in the initial and final years, respectively, or if the market growth in all of the categories is the same, the three level-effects will all vanish. The tree-form CMS model is applied to analyze growth causes of China's exports to Germany, particularly in agricultural products. It is found that the growth causes before China's accession to WTO (or the 2008 financial crisis) and thereafter are clearly different. Our theoretical findings are also confirmed by those data examples.

**References:**

Batista, J.C. (2008). Competition between Brail and other exporting countries in the US import market: a new extension of constant-market-shares analysis, *Applied Economics* 40, 2477-2487.

Chen, K., Xu, L. and Duan, Y.F. (2000). Ex-post competitiveness of China's export in agri-food products: 1980-96, *Agribusiness* 16, 281-294.

Jepma, C.J. (1986). *Extensions and application possibilities of the constant market shares analysis: the case of the developing countries exports*, University Press Groningen, Holland.

**Keywords:** Tree-form CMS; Decomposition of market growth; Agricultural trade; Complex data set

**Biography:** Zhichao Guo is a PhD student of China Agricultural University. She is currently working as a research assistant at the University of Paderborn on a collaboration project in the area of Economics and Quantitative Methods. Her research interests are international trade, particularly in agricultural products, time series analysis and financial econometrics. Her first paper including a part of the research results is now under revision for a well known international journal.