The anatomy of buyer–seller dynamics in decentralized markets

Abstract

In this paper I investigate the nexus between buyer–seller dynamics, financial frictions and market efficiency in decentralized markets. To do so, I introduce financial frictions in a dynamic market with heterogeneous traders. Heterogeneously constrained buyers sequentially enter the market to acquire units of a generic good from heterogeneously endowed sellers. I characterize two closely related classes of equilibria, respectively called homogeneous equilibrium with no entry (HEWNE) and homogeneous equilibrium with entry (HEWE). Both equilibria prescribe a market where only the efficiently endowed type of seller exists in the limit. However, the two equilibria diverge in the specification of agents’ behavior subsequent to trade. In HEWNE, sellers and buyers exit the market upon successful trading. In HEWE, like in supply chains, in every period certain types of buyers replace exiting sellers, thus becoming potential sellers for subsequent waves of buyers. First, I identify the critical role of frictions in steering the complex evolution of market heterogeneity for both classes of equilibria. Secondly, I operationalize the combined study of HEWNE and HEWE to obtain sharp predictions on market efficiency for a range of empirically-relevant situations in which buyer–seller dynamics are decoupled, for example when entry of new sellers is delayed or stopped. Third, I test the theoretical findings against a simulated artificial market.

Introduction

In this paper I study a dynamic decentralized market in which a (possibly growing) pool of heterogeneous sellers faces sequential waves of financially constrained buyers. Buyers bargain with available sellers to acquire units of a generic good. Buyers have a heterogeneous demand schedule that depends on the individual budget constraint. I show that the presence of a regulator controlling buyers’ financial constraints bears direct implications on the long-run efficiency of the market. Specifically, I show the existence of two classes of equilibria which may sustain the dynamic market formation along a path in which an efficiently-endowed type of seller does emerge in the limit. I use these two equilibria to inspect the market allocation efficiency for a range of realistic classes of market dynamics in which buyer–seller dynamics are decoupled.

In decentralized markets,² an investor who wishes to sell must search for a buyer, incurring opportunity or other costs until one is found. Often, traders must be approached sequentially. Hence, when two counter-parties meet, their bilateral relationship is inherently strategic. Prices are set through a bargaining process that reflects each investor’s alternatives to immediate trade (Duffie et al., 2005). These search-and-bargaining features are empirically relevant in many markets, such as those for mortgage-backed securities (Glaeser & Kallal, 1997), corporate bonds (John & Nachman, 1985), emerging market debt (Arellano, 2008), bank loans (Diamond & Rajan, 2000) and derivatives³ such as contract default swaps (Riggs et al., 2020) to name some of the most prominent examples.⁴ In real-estate markets, for example, prices are influenced by imperfect search, the relative impatience of investors for liquidity, outside options for trade, and the role and profitability of brokers (Duffie et al., 2005). Markets are dynamical, and as such, the distribution of potential opportunities that traders face may evolve as markets unfold in time, possibly as a function of traders’ own evolving expectations, heterogeneous tastes (Manea, 2017) and financial availability. In particular, financial constraints and corporate leverage critically shape the evolution of market structures around the world (see, for an empirical analysis, Lucey & Zhang, 2011). Under the lenses of allocative efficiency, the following question critically arises: how do financial frictions affect allocation efficiency via market dynamics?

To contextualize the problem, consider for example the functioning of cross-divisional capital transfers in internal capital markets within conglomerates (see, for an example of financial conglomerates, Campello, 2002). These are decentralized markets in which complex flows of capital can take place across heterogeneous and financially-autonomous production units (PUs) via pairwise transactions.⁵ In such context, capital can flow from established firms (i.e. the “sellers”) via multiple market operations to newly acquired PUs (i.e. the “buyers”). The efficiency of internal capital markets in resource allocation is a highly disputed issue (see Khanna & Yafeh, 2007 for a review) as efficiency interacts with the degree of regulatory intervention on corporate leverage,⁶ hence it is critical to understand the theoretical link between centralized intervention, market dynamics and efficiency.

I address the above question by constructing and studying a model of a dynamic decentralized market. The model allows to pin down the relationship between financial constraints, market dynamics and allocative efficiency. Formally, I embed the dynamic market with frictions in the frictionless framework of an infinite horizon bargaining game played in discrete time as introduced⁷ by Manea (2017). The economy consists of a continuum of firms drawn from a finite set of types. Firms exogenously enter the market over time and exit upon trading. In this model, the market formation is made of an initial stage $t=0$ and two intertwined processes taking place in each period $t=1,2,\dots$. In the initial stage $t=0$, every firm discovers her own endowment (potentially heterogeneous across firms), and induces an individual demand for the good as a function of technical conditions and the financial constraint. The first process takes place within each period $t=1,2,\dots$. At the beginning of period $t$, a measure of buyers enters in the economy in order to satiate the individual demand for the capital good. This process is the intra-period purchase of units of capital: buyers purchase capital from the pool of sellers available in the market in period $t$. The distribution of available sellers determines the market composition at $t$. Each buyer is randomly matched with a seller and parties bargain over a single unit of the good. Importantly, the exchange incentive structure is determined by the market composition at $t$. Once all buyers have satiated their own demand (provided that there is a surviving positive measure of sellers in the market) the market moves one step ahead to $t+1$. This bring us to the second process characterizing market formation, that is the evolution of the market composition across periods. The market composition, determined by the outcome of the realized exchanges, is the key dimension of this model, linking intra-period and inter-period dynamics.

I study the model by means of two classes of equilibria that diverge in the specification of the intertemporal dynamics. The first equilibrium, which I call Homogeneous Equilibrium with no Entry (HEWNE) expands the canonical matching scenario, in which both the seller and the buyer leave the market upon successful trade. In this work, buyers’ exit is conditional on satisfaction of an individual demand for good, therefore buyers are allowed to obtain multiple units of the good before leaving the market. The second equilibrium I characterize is the Homogeneous Equilibrium With Entry (HEWE). In this equilibrium, the subset of buyers that are endowed with at least the first-best investment level at the end of period $t$ settle in the economy as potential sellers for waves of buyers entering at $t+1,t+2,\dots$, thus replenishing the pool of sellers. In this equilibrium, the market converges to an expansionary path where in the limit a uniform type of seller exists, the first-best type seller.⁸ I use these equilibria to explore the implications on market efficiency of various types of buyer–seller dynamics. Last, I construct an artificial market to validate in simulations the main theoretical results presented along the paper.

My contribution is twofold. First, I contribute to the theoretical literature on search and bargaining⁹ by introducing financial frictions in the seminal framework of Manea (2017). My paper expands his work by introducing heterogeneity along a dimension which is crucial for the evolution of real markets: the limited purchasing power of buyers. This is a systemic variable, a leverage parameter (uniform across traders) which may be controlled by regulators. By characterizing a relationship between frictions and market dynamics, I show that frictions can generate rich dynamics in the evolution of market composition. Second, I use the model to answer the question introduced in Section 1.1. More specifically, I assess allocation efficiency for several market protocols which are consistent with empirical OTC markets characterized by heterogeneous traders.

I frame the efficiency problem in a decentralized market taking place between PUs with heterogeneous endowments and uniform first-best investment. PUs sell units of capital to other PUs against the promise of future payment.¹⁰ To study efficiency, I ask whether the market can autonomously converge to a situation in which available sellers produce on the efficient frontier, or, in other words, I look at the conditions that enable a homogeneous type of seller to exist in the limit. I answer this crucial question by operationalizing the two classes of equilibria introduced above, HEWNE and HEWE. With respect to HEWNE, I show that the relationship between the market composition (i.e. the distribution of available sellers) and financial constraint is nonunivocal. The capability for a market to reach an efficient redistribution of inputs – whereby sellers are on the efficient production frontier – is subject to a tipping point which depends on the specific level of financial frictions in place and the initial heterogeneity of sellers. When the allowed leverage is moderate, the exchange structure has a limited impact on sellers’ distribution. This implies that sellers heterogeneity does not disappear in the limit. On the other hand, when the exchange structure is characterized by a high enough financial leverage, a bifurcation takes place and two extreme cases can emerge depending on the initial distribution: either the market will converge to an efficient equilibrium, where available sellers are endowed with the first-best investment level, or it will converge to an equilibrium in which available sellers can be endowed with heterogeneous investment levels.

Relatively to HEWE, I show that entry of new sellers in every period imposes stronger conditions for the homogeneous type of seller to exist in the limit (i.e. the efficient outcome), hence there exists an ordered relationship between HEWNE and HEWE. The ordering is relevant from a normative point of view, as it allows to predict market evolution for empirically-relevant situations where exit of buyers is decoupled from entrance of sellers, possibly in non-trivial ways. I discuss allocative efficiency in the three following scenarios. In the first scenario, entrance of new sellers is asynchronous with respect to exit of buyers, as it can be the case, for example, of sellers requiring a certain number of periods to produce an exchangeable good and set-up exchange. In the second scenario, new sellers enter only for a limited number of periods, thus replicating a market undergoing a permanent negative supply shock. In the third scenario, existence of the homogeneous type of seller is discussed for a market that combines the above cases: delayed entry of sellers is interrupted altogether after a certain number of periods. For the three cases, I provided a taxonomy of bounds on financial constraint that allow the efficient outcome to survive.

Some authors have recently integrated financial constraints in models of dynamic markets. In particular, Liu and Wang, 2014, Moll, 2014 and Mino (2015) studied the evolution of market economies in which firms are heterogeneous and financially constrained. Similarly to Mino (2015), in this paper I consider an endogenous market process. However, the setting draws on the granular non-stationary dynamic bargaining framework proposed by Manea (2017), which I further characterize in order to study two complementary classes of equilibria which lend sharp predictions on the asymptotic shape of the market. Other contributions introduced frictions in frameworks similar to Manea (2017). Lauermann and Noldeke (2015) have proven existence of a steady-state equilibrium for an economy with search friction. While their main contribution is to show that a dynamic equilibrium can be achieved with non-transferable utilities, steady states analysis is constrained by the fact that the bargaining game is treated as a “black box” (Lauermann & Noldeke, 2015).

The rest of the paper is organized as follows. In Section 2 I define the primitives of the dynamic market. In Section 3 I introduce two classes of equilibria which support the market formation as the outcome of the bargaining game with financial frictions. In Section 4 I explore market formation under three market structures in which buyer–seller dynamics are decoupled. In Section 5 I simulate an artificial market to validate the implications of the equilibria developed in the previous sections. Additional results and proofs are contained in Appendix A.