Excess demand and equilibration in multi-security financial markets: the empirical evidence

Abstract

Price dynamics are studied in a dataset of more than 11,000 transactions from large-scale financial markets experiments with multiple risky securities. The aim is to determine whether a few simple principles govern equilibration. We first ask whether price changes are driven by excess demand. The data strongly support this conjecture. Second, we investigate the presence of cross-security effects (the excess demands of other securities influence price changes of a security beyond its own excess demand). We find systematic cross-security effects, despite the fact that transactions in one market cannot be made conditional on events in other markets. Nevertheless, stability is not found to be compromised in our data. A curious relationship emerges between the signs of the cross-effects and the signs of the covariances of the payoffs of the corresponding securities. It suggests a link between price discovery in real markets and the Newton procedure in numerical computation of general equilibrium. Next, we investigate whether the book (the set of posted limit orders) plays a role in the process by which excess demand becomes reflected in transaction price changes. We find strong correlation between excess demands and a weighted average of the quotes in the book. The correlation is far from perfect, and we document that our weighted average of the quotes in the book explains part of the variance of transaction price changes that is unaccounted for by excess demands.

Introduction

Price discovery is taken here to refer to the process with which markets reach their general equilibrium. Since Walras, it has long been conjectured that excess demand drives markets towards their equilibrium.¹ Other models have been suggested (among others, by Hicks and Marshall), but the Walrasian model has become the dominant tool of analysis of dynamics in general equilibrium economics. Much is known about the theoretical properties of the Walrasian model—see, e.g., Negishi (1962) and Arrow and Hahn (1971). In this article, we wish to determine its value as a descriptive model of how markets reach their equilibrium.

The Walrasian model is very stylized and information is used parsimoniously. Agents submit demands; if this leads to demand imbalances, prices change in the direction of the demand imbalance; agents’ demands subsequently adjust to the price changes; etc. Note that agents need only observe price changes. There are obvious doubts as to the Walrasian model's descriptive validity as a model of price discovery. First, it is myopic: agents’ demand adjustments are assumed to be purely reactive, as if no more price changes will take place. Second, even though excess demand may influence price changes in actual market settings, it is not a priori clear through which channel. Markets are almost never organized as a tatonnement (the mechanism that inspired the Walrasian model). In the tatonnement, excess demand changes prices in a mechanical way, through the actions of the auctioneer. The markets to be studied here, instead, are organized as a continuous, electronic open book. There is no auctioneer who deliberately changes prices, and market participants are never asked to reveal their excess demand.

The purpose of this study, therefore, is to evaluate the descriptive power of the simple Walrasian model. Do transaction price changes indeed correlate with excess demand as generally conjectured? If so, through which mechanism does excess demand influence price changes, i.e., how is excess demand expressed in the microstructure of a market? In particular, does the “book” (set of posted limit orders) play a role, or is it merely a passive “liquidity provider?”

It has recently become popular to analyze market microstructure in terms of a detailed game between strategic players. We do not attempt to provide an explicit game-theoretic model of how excess demand translates into price changes. The extensive form of the (dynamic open book) game played in the markets that we are going to study is yet to be written down and one can reasonably doubt that anybody will ever be able to do so, let alone determine the resulting equilibrium, or equilibria (if there are more than one). Essentially, the complexity of the microstructure of our multi-market situation precludes formal game-theoretic analysis. Instead, we will limit our analysis to empirically identifying the mechanics through which excess demand is expressed, if at all.

To evaluate the descriptive validity of the Walrasian model of price discovery, we investigate over 11,000 transactions from several large-scale financial markets experiments. Our using experimental data can be justified quite simply by the fact that supplies and payoff distributions are known in an experimental context (because they are design features), making excess demand readily computable (up to an additive constant). In the field, neither supplies nor payoff distributions are known accurately and the exercises we perform in this article would not generate equally clear answers. The experiments involved large-scale (up to 70 subjects), internet-based experimental markets with three or four securities.

We find overwhelming support for the idea that excess demand drives transaction price changes. Significantly, we discover systematic cross-security effects, whereby a security's transaction prices are influenced by the excess demands of other securities, beyond the security's own excess demand. This has important implications for stability analysis (which studies whether markets always will move towards their general equilibrium). The existing analysis assumes absence of cross-security effects. Well-known results (e.g., global stability obtains in the case of substitutes) may be invalidated when cross effects are present.

At the same time, we find high correlation between excess demands in all markets, on the one hand, and a weighted average of quotes in the book of a market, on the other hand. The weighted average puts more weight on the thinner side of the book (bid side, ask side). It appears that excess demands are expressed in the marketplace, among others, through orders in the book. Note that this is not a priori evident: excess demand may be revealed in the marketplace solely through transactions, with the book merely providing liquidity.²

We find that the correlation between excess demands and the order book is far from perfect, which explains why it may take time for markets to equilibrate, and why markets can ostensibly veer away from equilibrium. We document that the book partly explains transaction price changes that are not correlated with excess demands.

Our findings have implications for the quality of a market, with which we understand its speed to discover general equilibrium. As the correlation between orders in the book and excess demands increases, markets can be expected to reach general equilibrium faster. This correlation can only be increased if traders are given incentives to quickly reveal their true demands. This also means that the rules of the book are crucial for continuous, open-book markets to discover general equilibrium.

Section 2 discusses the theory. Section 3 describes the data. Section 4 explains the estimation strategy. Section 5 presents the empirical tests. Section 6 concludes.