Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

The Buyer's Option in Multi-Unit Ascending Auctions: The Case of Wine Auctions at Drouot

This paper studies multi-unit ascending (English) auctions with a buyer's option. The buyer's option gives the winner of an auction the right to purchase any number of units at the winning price. We develop a theoretical model and derive the optimal strategies for the bidders. The model predicts various behavioral implications (e.g., the winner never exercises the option, the price declines…) that are tested using a unique data set on wine auctions held at the Paris-based auction house Drouot. We also analyze why the buyer's option is used. Estimating the model in a structural econometric way, and using counterfactual comparisons, we find that the buyer's option does not affect the seller's revenue (relative to a system where the units are auctioned sequentially without the option). Drouot, however, saves a lot of time with the option and this effect represents a considerable amount of money. The time-saving effect seems thus to be the primary purpose of the buyer's option.     

ECONOMETRIC MODELS OF ASYMMETRIC PRICE TRANSMISSION

Abstract In this paper, we review the existing empirical literature on price asymmetries in commodities, providing a way to classify and compare different studies that are highly heterogeneous in terms of econometric models, type of asymmetries and empirical findings. Relative to the previous literature, this paper is novel in several respects. First, it presents a detailed and updated survey of the existing empirical contributions on price asymmetries in the transmission mechanism linking input prices to output prices. Second, this paper presents an extension of the traditional distinction between long‐run and short‐run asymmetries to new categories of asymmetries, such as: contemporaneous impact, distributed lag effect, cumulated impact, reaction time, equilibrium and momentum equilibrium adjustment path, regime effect, regime equilibrium adjustment path. Each empirical study is then critically discussed in the light of this new classification of asymmetries. Third, this paper evaluates the relative merits of the most popular econometric models for price asymmetries, namely autoregressive distributed lags, partial adjustments, error correction models, regime switching and vector autoregressive models. Finally, we use the meta‐regression analysis to investigate whether the results of asymmetry tests are not model‐invariant and find which additional factors systematically influence the rejection of the null hypothesis of symmetric price adjustment. The main results of our survey can be summarized as follows: (i) each econometric model is specialized to capture a subset of asymmetries; (ii) each asymmetry is better investigated by a subset of econometric models; (iii) the general significance of the F test for asymmetric price transmission depends mainly on characteristics of the data, dynamic specification of the econometric model, and market characteristics. Overall, our empirical findings confirm that asymmetry, in all its forms, is very likely to occur in a wide range of markets and econometric models.     

Empirical Analysis of a Dynamic Duopoly Model of Competition

Empirically validating and testing the specification of game theoretic models has received limited attention in the marketing literature. The authors provide an econometric framework for estimating the parameters of response functions when the observed data in the market place are the Nash equilibrium outcomes of an underlying dynamic duopoly game specification. Specifically, the estimation procedure accounts for the joint endogeneity of market shares and marketing efforts of market rivals using a system of simultaneous equations that included the market response function and the Nash equilibrium conditions. A formal statistical test is used to detect model misspecification. The empirical analysis is carried out using data from four product markets: pharmaceutical, soft drink, beer, and detergent. Comparisons are provided with conventional estimation of the response function parameters in which the equilibrium conditions are ignored in the estimation. Managerial implications of the empirical results are discussed.     

The Auction Price of Apartments in Moscow: Hedonic Estimation in Disequilibrium1

The purpose of this paper is to see how economic factors determine prices in the previously communist countries undergoing privatization. This does not concern the auctions of big state enterprises where the prices are found to be rigged. In this paper we estimate hedonic price functions based on a unique data set on auction prices of apartments in Moscow. We collected the data ourselves by attending the auctions and gathered data on the characteristics. We estimated the hedonic equations using a disequilibrium approach because no equilibrium prices were observed for large number of apartments that were withdrawn from the auction. We found that, as the privatization of residential housing was carried out, the hedonic price equations fit the data remarkably well.     

First price package auction with many traders

This paper studies a first price package auction in which multiple sellers participate in addition to multiple buyers. We generalize the notion of the profit-target strategy which is first introduced as a truthful strategy in a first price package auction with a single seller by Bernheim and Whinston (1986b). We then show that the set of equilibrium payoffs in profit-target strategies is equal to the bidder-optimal core, and is also equal to the set of coalition-proof Nash equilibria. Using this result, we find that any equilibrium payoff vector is weakly Pareto-dominated by the VCG payoff vector for buyers, and that the Walrasian competitive equilibrium payoff vector is weakly Pareto-dominated by some equilibrium payoff vector for buyers, even if goods are substitutes. This contrasts with the first price package auction with a single seller, in which it is shown that if goods are substitutes, then those three outcomes are payoff-equivalent.     

On the strictly descending multi-unit auction

We analyze the bidding behavior in a strictly descending multi-unit auction where the price decreases continuously without going back to the initial start price once an object is sold. We prove that any equilibrium in the multi-unit descending auction is inefficient. We derive a symmetric equilibrium for general distribution functions as well as an arbitrary number of bidders and objects. Moreover, equilibrium bidding is characterized by a set of initial value problems. Our analysis thus generalizes previous results in the literature.     

Wars of attrition and all-pay auctions with stochastic competition

We extend the war of attrition and all-pay auction analysis of Krishna and Morgan (1997) to a stochastic competition setting. We determine the existence of equilibrium bidding strategies and discuss the potential shape of these strategies. Results for the war of attrition contrast with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Furthermore we investigate the expected revenue comparisons among the war of attrition, the all-pay auction and the winner-pay auctions and discuss the linkage principle as well. Our findings are applicable to future works on contests and charity auctions.     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

Ex post tests for short-and long-run optimization

The purpose of this paper is to develop tests of long-run equilibrium models where the long-run is defined as the state where the observed levels of output and capital are consistent with optimizing behavior. We use the implied relationship between a restricted translog cost function and derived demand equations to provide a series of nested tests which can be interpreted as ex post tests for short- and long-run optimization behavior. A set of parameter restrictions on the translog system are specified for testing whether observable levels of capital and/or output of a firm correspond to the long-run optimal level. Our tests of the validity of long-run equilibrium specifications are based on data for 28 German industries for the period 1960-1981. For most of the industries the set of restrictions implied by long-run equilibrium had to be rejected.     

Sealed bid auctions versus ascending bid auctions: an experimental study

This paper considers two multi-item auction formats (ascending and sealed bid) which both identify the minimum Walrasian equilibrium prices and where truthful preference revelation constitutes an equilibrium. Even though these auction formats share many theoretical properties, there are behavioral aspects that are not easily captured. To explore this issue in more detail, this paper experimentally investigates what role the design of the auction format has for its outcome. The results suggest that the sealed bid mechanism performs weakly better in all of the investigated measures (consistent reporting, efficiency etc.). In addition, we find that the performance of the ascending auction is increasing over time, whereas the sealed bid auction shows no such tendency.     

New methods for analyzing structural models of labor force dynamics

The economic theory of decision-making under uncertainty is used to produce three econometric models of dynamic discrete choice: (1) for a single spell of unemployment; (2) for an equilibrium two-state model of employment and non-employment; (3) for a general three-state model with a non-market sector. The paper provides a structural economic motivation for the continuous time Markov (or more generally ‘competing risks’) model widely used in longitudinal analysis in biostatistics and sociology, and it extends previous work on dynamic discrete choice to a continuous time setting. An important feature of identification analysis is separation of economic parameters that can only be identified by assuming arbitrary functional forms from economic parameters that can be identified by non-parametric procedures. The paper demonstrates that most econometric models for the analysis of truncated data are non-parametrically under-identified. It also demonstrates that structural estimators frequently violate standard regularity conditions. The standard asymptotic theory is modified to account for this essential feature of many structural models of labor force dynamics. Empirical estimates of an equilibrium two-state model of employment and non-employment are presented.     

Auctions with asymmetric common-values: The first-price format

We study the performance of the first-price format in auctions with asymmetric common-values. We show that, contrary to the result for second-price auctions, a small advantage for one player translates only to small changes in bidders’ strategies, and the equilibrium remains close to the first-price equilibrium of the original game. We characterize the equilibrium bidding strategies and their behavior as the degree of asymmetry increases. Finally, we compare the revenues at the optimal auction, the first-price auction and the second-price auction.     

The specification of multi-market disequilibrium econometric models

The specifications of multi-market disequilibrium econometric models are clouded with different notions of effective demand. This paper points out that the specification of such models for econometric analysis can be achieved from the basic concept of fixed-price equilibrium and without the use of the concepts of effective demand. The specifications of Ito and Gourieroux, Laffont and Monfort are justified within this framework. With proper stochastic elements introduced in the system, the derived likelihood function from our approach does not involve multiple integrals and is computationally tractable for models with many disequilibrium markets.     

Market competition and pricing strategies in retail supply chains

This study provides a better explanation for the continued prevalence of high–low (Hi–Lo) pricing strategy. We investigate the impact of market competition on adopting two different pricing strategies in the retail industry: everyday low price (EDLP) strategy and Hi–Lo strategy. We developed two analytic models using a game-theoretic modeling approach: the profit maximization model and the sales revenue maximization model. We then conducted an econometric analysis based on retail store-level dataset. The result shows that an EDLP player's equilibrium price depends highly on the cost level rather than competitor's price whereas the Hi–Lo player's equilibrium price depends mainly on the range of promotional basket as well as the cost level.     

Forecasting residential burglary

Following the work of Dhiri et al. [Modelling and predicting property crime trends. Home Office Research Study 198 (1999). London: HMSO] at the Home Office predicting recorded burglary and theft for England and Wales to the year 2001, econometric and time series models were constructed for predicting recorded residential burglary to the same date. A comparison between the Home Office econometric predictions and the less alarming econometric predictions made in this paper identified the differences as stemming from the particular set of variables used in the models. However, the Home Office and one of our econometric models adopted an error correction form which appeared to be the main reason why these models predicted increases in burglary. To identify the role of error correction in these models, time series models were built for the purpose of comparison, all of which predicted substantially lower numbers of residential burglaries. The years 1998–2001 appeared to offer an opportunity to test the utility of error correction models in the analysis of criminal behaviour. Subsequent to the forecasting exercise carried out in 1999, recorded outcomes have materialised, which point to the superiority of time series models compared to error correction models for the short-run forecasting of property crime. This result calls into question the concept of a long-run equilibrium relationship for crime.     

First-price auctions where one of the bidders’ valuations is common knowledge

We analyze a private and independent valuation first-price auction under the assumption that one of the bidders’ valuations is common knowledge. We show that no pure strategy equilibrium exists and we characterize a mixed strategy equilibrium in which the bidder whose valuation is common knowledge randomizes her bid while the other bidders play pure strategies. In an example with the uniform distribution, we compare the expected profits of seller and buyers in this auction with those in a standard symmetric private valuation model.     

Misspecification and Expectations Correction in New Keynesian DSGE Models

This paper focuses on the dynamic misspecification that characterizes the class of small‐scale New Keynesian models currently used in monetary and business cycle analysis, and provides a remedy for the typical difficulties these models have in accounting for the rich contemporaneous and dynamic correlation structure of the data. We suggest using a statistical model for the data as a device through which it is possible to adapt the econometric specification of the New Keynesian model such that the risk of omitting important propagation mechanisms is kept under control. A pseudo‐structural form is built from the baseline system of Euler equations by forcing the state vector of the system to have the same dimension as the state vector characterizing the statistical model. The pseudo‐structural form gives rise to a set of cross‐equation restrictions that do not penalize the autocorrelation structure and persistence of the data. Standard estimation and evaluation methods can be used. We provide an empirical illustration based on USA quarterly data and a small‐scale monetary New Keynesian model.     

Regionalizing National Commodity-by-Industry Accounts

Exended input–output (IO) models are increasingly prominent in regional economic analysis. Social accounting matrices and associated multiplier decompositions, IO econometric model hybrids and computable general equilibrium models are finding greater acceptance in contexts in which simple IO models once dominated. Although the extended regional models build primarily on the foundation of regional, interindustry accounting frameworks, the data from which these regional accounts are drawn are most commonly in the form of a national commodity-by-industry account. Despite this longstanding fact, the IO table adaptation literature has focused almost solely on methods of adapting national interindustry accounts to regional economies. This paper presents a method designed specifically to regionalize commodity-by-industry accounts, in the context of the US reporting system. The focus on commodity-by-industry data demands a confrontation with several important issues that otherwise might go unattended. Using a particular system and its accompanying classification scheme ensures a comprehensive and consistent regionalization method.