*2.2. Stage 2: Vollrath Index*

Due to the above shortcomings of the Balassa method, at the second stage, the authors check RCA results by measuring relative trade advantages for the same array of 37 product groups:

$$RTA = \frac{\frac{X\_{ij}}{X\_{it}}}{\frac{X\_{nj}}{X\_{nt}}} - \frac{\frac{M\_{ij}}{M\_{it}}}{\frac{M\_{nj}}{M\_{nt}}} \tag{2}$$

where *RTA* = relative trade advantage; *X* = export; *M* = import; *i* = country; *j* = product group (domestic market); *t* = product group (international market); *n* = group of countries.

The Vollrath index of relative trade advantage is a tool to identify the competitive advantages of the products by measuring their relative portions in trade. It is a comparison of how well a country performs in exporting a particular set of products compared to the total export of all its products [80]. In contrast to RCA, RTA takes account of both exports and imports and thus demonstrates net trade advantages and disadvantages. *RTAij* > 0 means a country *i* possesses relative trade advantage in a product *j*, while *RTAij* < 0 demonstrates relative trade disadvantage. After the identification of product groups *j* for which *RTAij* > 0, the results are applied upon previously calculated RCAs, two sets are compared, and the matches between the two types of advantage are identified. The use of two indexes for the same dataset reduces the risk of random error.

The Vollrath index was used by Rusali and Gavrilescu [81] in discovering competitive advantages and disadvantages in Romania's agricultural trade, by Drabik and Bartova [82] in the study of the Slovak food trade specialization pattern, and by Carraresi and Banterle [83] in the assessment of the agricultural competitive performance in the EU countries. Similar to RCA, when measuring the competitiveness of agricultural products in an export portfolio of a country through RTA, it is crucial to examine the extent to which trade advantages are consistent with competitiveness [84]. Ballance et al. [85] discovered that results on the consistency of the RCA and RTA indexes are mixed. Khai et al. [86] examined coherence between the RCA and RTA indexes and concluded that despite the high consistency, the competitiveness of some product groups remained unclear. Ferto and Hubbard [87] tested a coherence between RTA and competitiveness in the cases of agricultural exports in Europe and found that the two indexes were not consistent in cardinal and ordinal measures.

#### *2.3. Stage 3: Lafay Index*

There have been many attempts to increase the consistency between various measures and improve the relevance of the competitiveness analysis. Since both RCA and RTA are structural, it is important to eliminate the influence of cyclical factors [88]. One of the most promising methods to do that is the Lafay index (LI):

$$LI\_{ij} = \frac{1000}{Y\_i} \times 2 \frac{X\_{ij} \times M\_i - X\_i \times M\_{ij}}{X\_i + M\_i} \tag{3}$$

where *LI* = Lafay index; *X* = export; *M* = import; *i* = country; *j* = product group.

The Lafay index allows to test both RCA and RTA indicators by considering the difference between each product's normalized trade balance and the overall normalized trade balance [89]. It also weights each product's contribution according to the particular importance in trade. *LIij* > 0 means a country *i* possesses a competitive advantage in a product *j*, otherwise, there is a disadvantage. LI captures intra-industry flows by using both the exports and imports variables and controlling the distortions due to the macroeconomic factors with the GDP variable [90]. For the purpose of this study, it is important that LI does not take into account world variables [47], which is crucial in the establishment of a reliable picture of competitive advantages for smaller economies.

So far, the three-indexes approach has not been widely applied in the literature. Ishchukova [91] and Benesova et al. [92] employed consecutive matching of RCA, RTA, and LI indexes to discover comparative advantages of agricultural exports and distinguishing competitive export products based on the parameters of the amount of foreign exchange, comparative advantage, and trade balance. Maitah et al. [89] used a similar approach for the analysis of the positions of agricultural producers both in comparison to domestic producers from other sectors and in relation to their foreign competitors. Erokhin and Gao [66] modified the approach by applying the three indexes to the same dataset and calculating Lafay index for the same array of product groups constituting a country's export portfolio, not for separate territories as compared to the earlier studies.

The application of the three-indexes approach to trade in agricultural products has definite limitations coming from the very nature of agricultural production. As it has been demonstrated by Ishchukova [91], Maitah et al. [89], Ishchukova and Smutka [93,94], and Erokhin and Gao [66], the three-indexes approach allows to check advantages and model policy responses on the potential strengthening of the advantages or evening out the disadvantages. Theoretically, the most obvious response is to reallocate the resources in such a manner as to increase the production and export of those products in which a country enjoys an advantage. In agriculture, though, simple reallocation is not possible due to the natural limitations (available arable lands and other land resources, quality of land, climate conditions), social and economic factors (rural labor, longer return on investment compared to non-agricultural sectors), time (cycles in crop and animal production, seasonality, etc.), and technical constraints (irrigation, transportation, storage, processing, other kinds of infrastructures in rural areas). Moreover, a simple abandoning of the production of non-competitive agricultural products may decrease the availability of these products on the domestic market and in such a way impose a threat to food self-sufficiency and food security of a country. In Central Asia, where agricultural production is additionally hampered by hot and dry climate, desertification [95], scarcity of arable lands, salinization

and land degradation [96], prevalence of small-scale farming, and low diversification of crops [1], among other factors, an establishment of a sustainable value chain requires the matching of competitive advantages with agricultural production capabilities, i.e., production advantages.
