Equilibrium Price Function Research Articles

Competitive Storage and Commodity Price in Continuous Time

The competitive storage model is analyzed in the literature in discrete time and is applied for empirical studies of the markets for agricultural commodities. In this model, there is a storable commodity supplied at every period with stochastic disturbances, and there are traders who aim at making speculative profits by using their storage. The literature has established results such as the existence of an equilibrium price function, which depends on the current availability of the commodity. The present article proposes an extension to the competitive storage model by considering continuous time. The relevance of this extension is justified by the technical convenience it brings, as well as by its suitability to the mineral markets in which the time series data is available for daily frequency. I consider serially correlated disturbances of net supply together with an upper bound on storage capacity, and characterize the equilibrium price function in this framework. The no-arbitrage and no-trade conditions define the intertemporal choice of commodity traders and imply the existence of an equilibrium price function. The equilibrium price depends on "the long-term availability of commodity" defined as the sum of storage and the expected cumulative disturbances of net supply over the infinite horizon. The various cases of the equilibrium price dynamics, such as "full storage", "empty storage" and "the trading zone", are characterized. The two types of the equilibrium price function, which are relevant to full storage, are revealed, and an explicit approximate solution for the case of a low-elastic net demand is derived. Numerical simulations of the equilibrium price function dem on­strate the effects of the model parameters on this function.

Asset pricing in a pure exchange economy with heterogeneous investors

In this paper, we provide a complete solution to the problem of equilibrium asset pricing in a pure exchange economy with two types of heterogeneous investors having higher/lower risk aversion. Using a perturbation method, we obtain analytical approximate formulas for the optimal consumption-sharing rule, which is numerically justified to be accurate for a large risk aversion and heterogeneity. We present analytical formulas for the equilibrium pricing function, Sharpe ratio, risk-free rate, stock price and optimal trading strategies. We then analyse the properties of the equilibrium and derive some testable hypotheses, which enhance our understanding on the economics of financial markets.

New Tests of Expectation Formation with Applications to Asset Pricing Models

We develop new tests for expectation formation in financial and macroeconomic models under various informational assumptions. Survey data suggests stock price forecasts are not anchored by consumption forecasts and rejects this aspect of the formation of stock price expectations in a wide range of asset pricing models. The evidence casts some doubt on the modeling of expectation formation in the asset pricing models which assume agents possess the knowledge of the equilibrium pricing function as in Rational Expectations and Bayesian Rational Expectations models. Relaxing this knowledge appears necessary for models to reconcile the survey evidence and potential resolutions are discussed.

Equilibrium in production chains with multiple upstream partners

In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production network.

A tractable approach to compare the hedonic and discrete choice frameworks

The two primary approaches to estimate marginal willingness-to-pay (MWTP) are hedonic (Rosen, 1974) and discrete choice (McFadden, 1974). While both approaches rely on revealed preference methods to estimate MWTP, the primitives underlying both models are different, making it difficult to compare them. This paper establishes the assumptions needed to develop a tractable framework to compare both approaches. I begin with a discrete choice model and show how to derive the gradient of the equilibrium price function implicitly. I then incorporate Rosen’s insight that the price gradient is equal to the MWTP of the marginal individual whose indifference curve is tangent to the price function in equilibrium. However, with discrete choices, some individuals may be inframarginal and their indifference curves will not be tangent to the price function. The analytical mapping I derive formalizes this intuition and shows that the price gradient depends on weighted averages of marginal utilities where higher weights are assigned to individuals whose choice probabilities indicate more uncertain choices (marginal individuals). As this choice becomes more certain, the weights start to decrease. This result shows how choice probabilities and other moments of choice data can be used to distinguish marginal versus inframarginal individuals.

Regression analysis of historic oil prices: A basis for future mean reversion price scenarios

We propose price forecasting algorithms based on regression analysis of historic oil prices over 150years (1861–2012). From 1986 onward daily market prices allow more detailed analyses of the principal crude oil benchmarks (West Texas Intermediate [WTI] and Brent). The mean reversion price for a given time period corresponds to the marginal cost of supply. When supply and demand are out of equilibrium, spot prices move in a bandwidth bound at the bottom by cash cost of supply and at the top by the concurrent price of demand destruction. Short-term elasticity of demand is 0.015 (highly inelastic), and long-term elasticity of supply changed from 0.99 (highly elastic) during 1965–1983 to 0.39 (less elastic) during 1984–2012. We derive functions for the long-term equilibrium price and expand them into scalable equilibrium price functions for forecasting future price scenarios if “business-as-usual” is assumed. We also consider how two hypothetical black swan events (“unknown unknowns”) may affect the mean equilibrium price.

Rationalizable Information Equilibria

Rational expectations equilibria (REE) assume that the ex post equilibrium price function is able to reveal ex ante information. This paper drops the assumption of information revealing prices and instead constructs an internal reasoning process through which highly rational price-takers can infer information from other market participants under the assumption that their utility maximization problems are common knowledge. Based on this reasoning process, we introduce the novel competitive equilibrium concept of rationalizable information equilibria (RIE). Our formal analysis establishes that (i) the RIE concept amounts to a refinement of the (generalized) REE concept whereby (ii) REE with interior net-trades are generically RIE.

Spatial Dependence, Idiosyncratic Risk, and the Valuation of Disaggregated Housing Data

We investigate whether spatial idiosyncratic risk plays an important role in explaining average housing prices in a representative U.S. market. We discuss a parsimonious hedonic model of demand for differentiated products and derive an equilibrium price function that depends on idiosyncratic risk, among other factors. Empirically, we use a nonlinear spatial regression model and identify a potential measure of idiosyncratic risk from sales data of individual residential properties in Ames, Iowa. The results show that, for our disaggregated housing data, there is a significant volatility interdependence among cross-sectional units because of geographical proximity. In our sample, a 1% increase in idiosyncratic risk, ceteris paribus, is associated with a 0.80% increase in average price of residential properties. We find that accounting for spatial autocorrelation and heteroskedasticity increases the evidence that idiosyncratic risk, which is captured by space-varying volatility, reveals important information about average housing prices. We conclude that using a spatial regression model that allows interaction between property prices and volatility yields strong predictive power.

Asset Market Dynamics in Equilibrium Models with Heterogeneous Agents: Analytical Results

We examine market dynamics in a discrete- time, Lucas-style asset-pricing model with heteroge- neous, utility-optimizing agents. Finitely many agents trade a single asset paying a stochastic dividend. All agents know the probability distribution of the dividend but not the private information such as wealth and asset holdings of other agents. The market clearing price is determined endogenously in each period such that sup- ply always equals demand. Our aim is to determine whether and how the pricing function evolves toward equilibrium. In the special case where all agents have logarithmic utility, but possibly different holdings and discount factors, we completely describe the market dynamics, including the evolution of the pricing and demand functions, and asset holdings of the agents. The market converges to a stable equilibrium state where only the most patient agents remain, and the equilibrium pricing function is the same as the one arising in the simple homogeneous setting.

A Study on Lucas’ “Expectations and the Neutrality of Money’’

This short article shows that the functional equation on the equilibrium price function is more complicated than that considered by Lucas [1], and that modification is required to complete the proof. Furthermore, we shall provide a sufficient condition that guarantees the uniqueness of the equilibrium price function.

Asset pricing in a Lucas fruit-tree economy with the best and worst in mind

This paper studies a Lucas (1978) fruit-tree economy under the assumption that the agents are Choquet expected utility (CEU) rather than standard expected utility decision makers. More specifically, the agents' non-additive beliefs about the economy's dividend payment process are modeled as neo-additive capacities so that the agents' decision behavior emphasizes the best, respectively worst, possible economic scenarios. In contrast to existing models of Lucas-type economies with ambiguity averse agents (Epstein and Wang, 1994), which ensure dynamic consistency through heavy restrictions on admissible ambiguity attitudes, my approach gives up dynamic consistency to the effect that quite general ambiguity attitudes become admissible. As the main formal result I establish the existence of a unique stationary equilibrium price function for this CEU Lucas economy. As the main economic insight I obtain that a representative agent who is rather preoccupied with the worst case scenario gives rise to a lower risk-free rate and a higher equity premium than predicted by the original expected utility Lucas economy. This difference is the greater the more surprising the economic information is that the agent receives.

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Maturity, Indebtedness, and Default Risk

We advance quantitative-theoretic models of sovereign debt by proving the existence of a downward sloping equilibrium price function for long-term debt and implementing a novel method to accurately compute it. We show that incorporating long-term debt allows the model to match Argentina's average external debt-to-output ratio, average spread on external debt, the standard deviation of spreads, and simultaneously improve upon the model's ability to account for Argentina's other cyclical facts. We also investigated the welfare properties of maturity length and showed that if the possibility of self-fulfilling rollover crises is taken into account, long-term debt is superior to short-term debt. (JEL E23, E32, F34, O11, O19)

Hedonic estimation of housing demand elasticity with a markup over marginal costs

We show that recent developments in hedonic pricing theory allow modeling of the equilibrium pricing function as the marginal cost of an additional housing unit plus a markup that varies inversely with the elasticity of demand. Useful information about demand elasticity at a given point on the envelope function can be recovered from the hedonic regression and limited information on marginal costs. In particular, the elasticity of the envelope with respect to any characteristic such as interior area provides information on the elasticity of demand. Relative price elasticities (i.e., elasticities that vary from a base value in a known way with interior area, unit type or neighborhood characteristics) can be computed from the elasticity of the hedonic envelope. Like Yinger (2010), our method is based on a single hedonic equation. We test our method using sales of new high rise condominiums in two districts within Shenzhen, China: Futian and Longgang. The results strongly confirm the main hypothesis of this paper: price elasticity with respect to size is increasing for more complex types of units. Together with estimates of marginal costs of production, these results imply that relative demand elasticity is declining for larger, more complex units.

DAMPAK PERUBAHAN TARIF IMPOR KEDELAI TERHADAP KESEJAHTERAAN MASYARAKAT INDONESIA

In 1998-2004, Indonesia liberalized soybean trade on zero percent tariff rate, then reinstated tariff rate on 10 percent in 2005-2007 and removed It again in early 2008 due to price instability in world market. Because of Indonesian high import-dependency on soybean, the change of soybean import tariff is very important for farmer, consumer, and government. The objectives of this research are : 1) to analyze the effect of soybean import tariff change on domestic price, soybean quantitiy supplied, demanded, and imported; and (2) to analyze effects of soybean import tariff change on social welfare. Analyses used are partial equilibrium analysis, price, demand, and supply function and economic surplus indicator. Partial equilibrium analysis conclude that 10% tariff-cut scenario would increase soybean demanded and decrease soybean supplied in response to the decrease of both wholesaler and producer price. Thus, it would lead the increase of net welfare gain, but would squeeze the national soybean agriculture by the decrease of producer surplus and the increase of soybean import quantity. Meanwhile, the increase of tariff rat by 10% has the opposite results. It is suggested, therefore, that Indonesian government has to retain the import tariff to protect soybean producer and improve soybean production at the same time to pursue national food independency, especially for soybean.

Maturity, Indebtedness, and Default Risk

We present a novel and tractable model of long-term sovereign debt. We make two sets of contributions. First, on the substantive side, using Argentina as a test case we show that unlike one-period debt models, our model of long-term sovereign debt is capable of accounting for the average spread, the average default frequency, and the average debt-to-output ratio of Argentina over the 1991-2001 period without any deterioration in the model's ability to account for Argentina's cyclical facts. Using our calibrated model we determine what Argentina's debt, default frequency and welfare would have been if Argentina had issued only short-term debt. Second, on the methodological side, we advance the theory of sovereign debt begun in Eaton and Gersovitz (1981) by establishing the existence of an equilibrium pricing function for long-term sovereign debt and by providing a fairly complete set of characterization results regarding equilibrium default and borrowing behavior. In addition, we identify and solve a computational problem associated with pricing long-term unsecured debt that stems from nonconvexities introduced by the possibility of default.

Maturity, Indebtedness, and Default Risk

In this paper, the authors present a new approach to incorporating long-term debt into equilibrium models of unsecured debt and default. They make three sets of contributions. First, the authors advance the theory of sovereign debt begun in Eaton and Gersovitz (1981) by proving the existence of an equilibrium price function with the property that the interest rate on debt is increasing in the amount borrowed. Second, using Argentina as a test case, they show that unlike a one-period debt model, their model of long-term debt is capable of accounting for the average external debt-to-output ratio, average spread on external debt, and the standard deviation of spreads for the 1993-2001 period, without any deterioration in the model's ability to account for Argentina's other cyclical facts. Third, the authors propose a new and very accurate method for solving the model.

The empirical relevance of the competitive storage model

The empirical relevance of models of competitive storage arbitrage in explaining commodity price behavior has been seriously challenged in a series of pathbreaking papers by Deaton and Laroque (1992, 1995, 1996). Here we address their major criticism, that the model is in general unable to explain the degree of serial correlation observed in the prices of twelve major commodities. First, we present a simple numerical version of their model which, contrary to Deaton and Laroque (1992), can generate the high levels of serial correlation observed in commodity prices, if it is parameterized to generate realistic levels of price variation. Then, after estimating the Deaton and Laroque (1995, 1996) model using their data set, model specification and econometric approach, we show that the use of a much finer grid to approximate the equilibrium price function yields quite different estimates for most commodities. Results are obtained for coffee, copper, jute, maize, palm oil, sugar and tin that support the specifications of the storage model with positive constant marginal storage cost and no deterioration as in Gustafson (1958a). Consumption demand has a low response to price and, except for sugar, stockouts are infrequent. The observed magnitudes of serial correlation of price match those implied by the estimated model.

Equilibrium Blocking in Large Quasilinear Economies

We study information transmission in large interim quasilinear economies using the theory of the core. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, as blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We consider independent, ex-post and signal-based replicas of the basic economy. For each, we offer an array of negative and positive convergence results as a function of the complexity of the mechanisms used by coalitions. We identify conditions under which asymmetric information remains as an externality and non-market outcomes stay in the core, as well as those for the core to converge to the set of incentive compatible ex-post Walrasian allocations. Further, all the results are robust to the relaxation of the incentive constraints, and hence suggest a process through which information may get incorporated into a fully revealing equilibrium price function.

The Pricing of Revenue Assurance: Reply

In their comment, Yin and Turvey (YT) suggest an approach to overcome a potential problem with Stokes, Nayda, and English’s (SNE’s) methodology for valuing revenue insurance. The problem, as discussed in SNE and YT, is that farm gross revenue is not a traded asset. Therefore, revenue insurance, which is itself a derivative security (i.e., a security that derives its value from the value of another asset—in this case, farm gross revenue), is difficult to price using standard asset pricing methods because buying and selling the underlying asset to hedge away risk is not possible. SNE assume an equilibrium pricing function exists and, and in doing so, are left with one unobservable parameter in their pricing formula. YT’s comment is essentially to propose a method for eliminating this unknown parameter. The problem is that an underlying asset, for which a derivative security is written against, is not tradable. The importance of tackling this issue cannot be over emphasized and YT are to be commended for their efforts. Indeed, virtually no other research besides SNE and YT approaches the problem of premium determination for agricultural insurance from the perspective of treating the insurance as a derivative security. 1 The importance of doing so is that one gains access to contemporary asset pricing methodology. In this reply, we focus on two important issues related to the problems created by nontradability. First, we clarify the tradable versus nontradable distinction in terms of its implications for arbitrage free pricing. The results we present provide the necessary background for motivating YT’s equation (1). Whereas YT begin their comment by assuming an economy that justifies their equation (1), we provide a mathematical characterization of the economy that insures the equation holds. Taking this approach gives us the opportunity to define the issues YT raise more clearly because the mathJ.R. Stokes is assistant professor at the Pennsylvania State University, University Park, PA; W.I. Nayda is Manager of Financial Analysis and Development at Capital One, Inc., McLean, VA. 1 Counter examples include research by Turvey and Amanor