Our data constitutes a collection of m = 1. . . M markets, observed over time, each with primitives Bm, Sm, Gm and πm (estimated). Besides the formal assumptions introduced in Chapter 3, namely, Assumption AS and Assumption CI in Rust (1994) and the parametric construction for , there are a number of additional operational assumptions that help match our problem better, restrict the size of the game and circumvent data restrictions.
Assumption 1: One Main Order. For narrowly defined markets (see below for a definition), at each point in time, the decision of the buyer can be simplified to that of how to allocate her main or largest order. In a market-quarter realization, each large buyer has a median of 1 supplier, a mean of 1.5 and the 95th percentile is 4. Table
C.43shows that for the bulk of the data the largest order accounts for more than 90% of the buyer’s demand. Therefore, the network decision of the buyer in each quarter will involve to choose one supplier to produce the main order in that market and I will consider this a choice independent of that of simultaneous allocations of smaller orders, which I will not include in the analysis.
Assumption 2: No Across-markets Interactions. As shown in the descriptives presented in Chapter2 each large buyer participates in a high number of product cate- gories simultaneously. The formulation here assumes that the linking decision the buyer makes in a given category is not related to those made in other product categories. This is supported by the evidence I presented in the binary regressions in Table??of Chapter
2. Although this restriction needs further empirical scrutiny, it is clear that allowing for sophisticated inter-market considerations can very easily expand the size of the state space and choice sets making the problem untractable.
Assumption 3: Constant revenues in the retail market for each buyer. Our data does not contain information on the retail markets. The formulation of the profit function of the buyers and that of the Nash bargaining problem assumed that in their retail markets, the price and quantities that the buyer sells are the same, irrespective of the seller producing the garment. This is compatible with a setting in which (i) there are no demand-relevant differences in the garment produced by different manufacturers and (ii) retailers decide end prices ex-ante. While the first assumption doesn’t seem too far-fetched, the second one seems to involve a higher compromise. However, anecdotal evidence collected in interviews with large buyers support this idea and we were explained that when the same product is sourced from different suppliers over time, the price remains unchanged, especially for lines of products that are highly commoditized (basic and seasonal products in Appendix F).
Assumption 4: Constant demand from each buyer. The game I proposed also relies on the idea that players do not anticipate growth in the size of the order. This means that when computing the future value of each relation and then, the values over states, players assume that future orders of a buyer have the same size as her current orders. This could be modified introducing expectations over potentially buyer-specific growth paths. This is an extension that has been evaluated.
Assumption 5: Buyers ‘search’ in a restricted neighbourhood within the product category. Alternative definitions of amarket are possible and so far I have used markets and products as synonyms. However, when markets are defined as product categories (HS code at six digits of disaggregation), choice sets can be prohibitively large for the structural procedure. Even imposing additional restrictions, like those in the reduced form regressions of Section ??, the state space can grow too large if
we allow the buyer to contemplate a high number of potential suppliers7. The exercises performed in Chapter2and presented in table??showed that the predicted probabilities of a seller being allocated an order (of a given product -HS6- at a certain point in time) was, other things equal, ‘small’ when the standard of the seller, measured in deciles in the distribution of prices, was far from that in which the order finally fell. The intuition behind this is that a product category (for example, Men’s shirts made of cotton) is still a very broad category. Assuming that any manufacturer can supply garment to buyers as dissimilar as Tommy Hilfigher and Primark seems unsuitable. The operational assumption I propose, then, is to divide each product category in deciles of its distribution of prices. Then, a market in a given point in time is a combination of a product and a decile8. Using this definition, implies assuming that a buyer’s “search” for a supplier happens in a small neighbourhood within the product category, where the neighbourhood is determined by the price of the order. Because prices are an outcome in the model, this assumption will need to undergo further testing in the structural estimation stage.
Assumption 6: One Equilibrium in all Markets. One of the highest requirements of this econometric approach, like in similar two-step estimators, is that of the ‘unique- ness’ assumption it implicitly imposes on the data. Estimates of the policy functions and transition probabilities require the availability of rich enough data on actions and states, generated from the same equilibria. This can prove quite demanding on many empirical settings, leading to the implementation of different generalising assumptions in the equilibrium selection protocol in applied work. A vast number of papers tends to pool data across markets under the assumption that the same equilibrium is being played in all the markets (Aguirregabiria and Mira,2007; Collard-Wexler, 2013; Ryan,
2012;Suzuki,2013). If the underlying data generating process violates this assumption, then the estimated policies will be a combination of those under the true equilibria and inference is not possible. Recent research has explored ways of testing for the unique- equilibrium-across-markets hypothesis (notably, Otsu et al.(2014)) and future research could implement these.