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Abstract:
We explore the interaction between the allocation of decision rights over investment opportunities and the design of incentive contracts to induce unobservable effort in a multiagent, multitasking agency framework. These are linked in our model because the only available performance measures confound the two: the returns to investments are not directly observed by the principal, but instead affect the means of the signals on effort. In our model, the optimal effort-inducing incentives give very bad incentives for selecting investments, while providing incentives to make the right investment decisions is costly in terms of inducing effort. In this set-up, hierarchy can emerge endogenously, with one agent being given authority to decide about implementing projects developed by another. The agents then get very different incentive contracts. Other solutions may involve each agent being empowered to adopt projects he has developed or both having to agree before a project is accepted. Bringing in a third agent to make investment decisions may also be optimal.

Abstract:
We explore the interaction between the allocation of decision rights over investment opportunities and the design of incentive contracts to induce unobservable effort in a multiagent, multitasking agency framework. These are linked in our model because the only available performance measures confound the two: the returns to investments are not directly observed by the principal, but instead affect the means of the signals on effort. In our model, the optimal effort-inducing incentives give very bad incentives for selecting investments, while providing incentives to make the right investment decisions is costly in terms of inducing effort. In this set-up, hierarchy can emerge endogenously, with one agent being given authority to decide about implementing projects developed by another. The agents then get very different incentive contracts. Other solutions may involve each agent being empowered to adopt projects he has developed or both having to agree before a project is accepted. Bringing in a third agent to make investment decisions may also be optimal.

Abstract:
We present new identification results for models of first-price, second-price, ascending (English), and descending (Dutch) auctions. We analyze a general specification of bidders' preferences and the underlying information structure, nesting as special cases the pure private values and pure common values models, and allowing both ex ante symmetric and asymmetric bidders. We address identification of a series of such models and propose strategies for discriminating between them on the basis of observed data. In the simplest case, the symmetric independent private values model is nonparametrically identified even if only the transaction price from each auction is observed. For more complex models, we provide conditions for identification and testing when additional information of one of the following types is available: (i) one or more bids in addition to the transaction price; (ii) exogenous variation in the number of bidders; (iii) bidder-specific covariates that shift the distribution of valuations; (iv) the ex post realization of the value of the object sold. Our results include new tests that distinguish between private and common values models.

Auctions, nonparametric identification and testing, private values, common values, asymmetric bidders, unobserved bids, order statistics

Abstract:
This paper analyzes a model of oligopolistic competition with ongoing investment. It incorporates the following models as special cases: incremental investment, patent races, learning-by-doing, and network externalities. We investigate circumstances under which a firm with low costs or high quality will extend its initial lead through further cost-reducing or quality-improving investments. In many commonly-studied oligopoly games, such investments are strategic substitutes. We derive a new comparative statics result that applies to games with strategic substitutes, and we use the result to derive conditions under which leading firms invest more than lagging firms. We show that the conditions are satisfied in a variety of commonly-studied oligopoly models. We also highlight plausible countervailing effects from two distinct sources. First, leading firms may find it more costly than others to achieve the same increment to their state. This force is particularly salient in many models of patent races, where firms make research investments in an attempt to find a new technology that delivers a given level of cost or quality. Second, countervailing effects may arise in dynamic games with more than two firms, when firms are sufficiently patient.

Key words: oligopoly games, strategic substitutes, innovation, investment, increasing dominance, market concentration

Abstract:
We consider an infinitely repeated Bertrand game, in which prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria, wherein any "punishments" are borne equally by all firms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each firm is strictly increasing in its cost level: such "fully sorting" schemes offer efficiency benefits, as they ensure that the lowest-cost firm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost firm must be deterred from mimicking a lower-cost firm by charging a lower price. A rigid-pricing scheme, where a firm's collusive price is independent of its current cost position, sacrifices efficiency benefits but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i) the absence of equilibrium-path price wars and (ii) a rigid price. If firms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost firms may be distorted downward in order to diminish the incentive to cheat. When the model is modified to include i.i.d. public demand shocks, the downward pricing distortion that accompanies a firm's lower-cost realization may occur only when current demand is high.

Abstract:
We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria (SPPE), wherein any "punishments" are borne equally by all firms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each firm is strictly increasing in its cost level: Such "fully-sorting" schemes offer efficiency benefits, as they ensure that the lowest-cost firm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost firm must be deterred from mimicking a lower-cost firm by charging a lower price. A rigid-pricing scheme, where a firm's collusive price is independent of its current cost position, sacrifices efficiency benefits but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i) the absence of equilibrium-path price wars, and (ii) a rigid price. If firms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost firms may be distorted downward, in order to diminish the incentive to cheat.

Abstract:
We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria (SPPE), wherein any "punishments" are borne equally by all firms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each firm is strictly increasing in its cost level: such "fully-sorting" schemes offer efficiency benefits, as they ensure that the lowest-cost firm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost firm must be deterred from mimicking a lower-cost firm by charging a lower price. A rigid-pricing scheme, where a firm's collusive price is independent of its current cost position, sacrifices efficiency benefits but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i) the absence of equilibrium-path price wars, and (ii) a rigid price. If firms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost firms may be distorted downward, in order to diminish the incentive to cheat.

Abstract:
A seminal theorem due to Blackwell (1951) shows that every Bayesian decision-maker prefers an informative signal Y to another signal X if and only if Y is statistically sufficient for X. Sufficiency is an unduly strong requirement in most economic problems because it does not incorporate any structure the model might impose. In this paper, we develop a general theory of information that allows us to characterize the information preferences of decision-makers based on how their marginal returns to acting vary with the underlying (unknown) state of the world. Our analysis imposes one central restriction: we consider "monotone decision problems," whereby all decision-makers in the relevant class choose higher actions when higher values of the signal are realized. We show how this restriction can be exploited to characterize information preferences using stochastic dominance orders over the distributions of posterior beliefs generated by different signals. Of particular interest for applied modeling, we identify conditions under which one decision-maker has a higher marginal value of information than another decision-maker, and thus will acquire more information. The results are applied to oligopoly models, labor markets with adverse selection, hiring problems, and a coordination game.

Abstract:
This paper studies the forces which determine how diversity at a firm evolves over time. We consider a dynamic model o a single firm with two levels of employees, the entry level and the upper level. In each period, the firm selects a subset of the entry-level workers for promotion to the upper level. The members of the entry-level worker pool vary in their initial ability as well as in their type,' where type could refer to gender or cultural background. Employees augment their initial ability by acquiring specific human capital in mentoring interactions with upper level employees. We assume that an entry-level worker receives more mentoring when a greater proportion of upper-level workers match the entry-level worker's type. In this model, it is optimal for the firm to consider type in addition to ability in making promotion decisions, so as to maximize the effectiveness of future mentoring. We derived conditions under which firms attain full diversity, as well as conditions under which there are multiple steady states, so that the level of diversity depends on the firm's initial conditions. With multiple steady states, temporary affirmative action policies can have a long-run impact on diversity levels.

Abstract:
This paper studies the forces which determine how diversity at a firm evolves over time. We consider a dynamic model of a single firm with two levels of employees, the entry level and the upper level. In each period, the firm selects a subset of the entry-level workers for promotion to the upper level. The members of the entry-level worker pool vary in their initial ability as well as in their "type," where type could refer to gender or cultural background. Employees augment their initial ability by acquiring specific human capital in mentoring interactions with upper level employees. We assume that an entry-level worker receives more mentoring when a greater proportion of upper-level workers match the entry-level worker's type. In this model, it is optimal for the firm to consider type in addition to ability in making promotion decisions, so as to maximize the effectiveness of future mentoring. We derive conditions under which firms attain full diversity, as well as conditions under which there are multiple steady states, so that the level of diversity depends on the firm's initial conditions. With multiple steady states, temporary affirmative action policies can have a long-run impact on diversity levels.

Abstract:
We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. Productive efficiency is possible only if high-cost firms are willing to relinquish market share. In the most profitable collusive schemes, firms implement productive efficiency, and high-cost firms are favored with higher expected market share in future periods. If types are discrete, there exists a discount factor strictly less than one above which first-best profits can be attained purely through history-dependent reallocation of market share between equally-efficient firms. We provide further characterizations and several computational examples.

We next examine different institutional features. We find that firms may find explicit communication (smoke-filled rooms) about costs beneficial after some histories but not others. We show that if firm-level behavior is not publicly observable, the best collusive scheme sacrifices all productive efficiency. Finally, if firms can make explicit side-payments and these entail any inefficiency (e.g., if they are illegal and bear some risk of detection), then optimal collusive equilibria are non-stationary and thus involve the use of future market-share favors.

Abstract:
This paper develops an alternative approach to the widely used Difference-In-Difference (DID) method for evaluating the effects of policy changes. In contrast to the standard approach, we introduce a nonlinear model that permits changes over time in the effect of unobservables (e.g., there may be a time trend in the level of wages as well as the returns to skill in the labor market). Further, our assumptions are independent of the scaling of the outcome. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment, and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean-variance tradeoff. We provide conditions under which the model is nonparametrically identified and propose an estimator. We consider extensions to allow for covariates and discrete dependent variables. We also analyze inference, showing that our estimator is root-N consistent and asymptotically normal. Finally, we consider an application.

Abstract:
This paper develops an alternative approach to the widely used Difference-In-Difference (DID) method for evaluating the effects of policy changes. In contrast to the standard approach, we introduce a nonlinear model that permits changes over time in the effect of unobservables (e.g., there may be a time trend in the level of wages as well as the returns to skill in the labor market). Further, our assumptions are independent of the scaling of the outcome. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment, and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean-variance tradeoff. We provide conditions under which the model is nonparametrically identified and propose an estimator. We consider extensions to allow for covariates and discrete dependent variables. We also analyze inference, showing that our estimator is root-N consistent and asymptotically normal. Finally, we consider an application.

Difference-In-Differences, Identification, Nonlinear models, Nonparametric Estimation

Abstract:
We study entry and bidding patterns in sealed bid and open auctions with heterogeneous bidders. Using data from U.S. Forest Service timber auctions, we document a set of systematic effects of auction format: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. We propose a model, which extends the theory of private value auctions with heterogeneous bidders to capture participation decisions, that can account for these qualitative effects of auction format. We then calibrate the model using parameters estimated from the data and show that the model can explain the quantitative effects as well. Finally, we use the model to provide an assessment of bidder competitiveness, which has important consequences for auction choice.

Auctions, Timber

Abstract:
Many important economic questions arising in auctions can be answered only with knowledge of the underlying primitive distributions governing bidder demand and information. An active literature has developed aiming to estimate these primitives by exploiting restrictions from economic theory as part of the econometric model used to interpret auction data. We review some highlights of this recent literature, focusing on identification and empirical applications. We describe three insights that underlie much of the recent methodological progress in this area and discuss some of the ways these insights have been extended to richer models allowing more convincing empirical applications. We discuss several recent empirical studies using these methods to address a range of important economic questions.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Many important economic questions arising in auctions can be answered only with knowledge of the underlying primitive distributions governing bidder demand and information. An active literature has developed aiming to estimate these primitives by exploiting restrictions from economic theory as part of the econometric model used to interpret auction data. We review some highlights of this recent literature, focusing on identification and empirical applications. We describe three insights that underlie much of the recent methodological progress in this area and discuss some of the ways these insights have been extended to richer models allowing more convincing empirical applications. We discuss several recent empirical studies using these methods to address a range of important economic questions.

Auctions, identification, estimation, testing

Abstract:
This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have pure strategy Nash equilibria (PSNE). The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a bidder's value for an object of a firm's marginal cost of production), and the types are drawn from an atomless joint probability distribution which potentially allows for correlation between types. Agents' utility may depend directly on the realizations of other agents' types, as in Milgrom and Weber's (1982) formulation of the "mineral rights" auction. The restriction we consider is that each player's expected payoffs satisfy the following single crossing condition: whenever each opponent uses a nondecreasing strategy (that is, an opponent who has a higher type chooses a higher action), then a player's best response strategy is also nondecreasing in her type.

The paper has two main results. The first result shows that, when players are restricted to choose among a finite set of actions (for example, bidding or pricing where the smallest unit is a penny), games where players' objective functions satisfy this single crossing condition will have PSNE. The second result demonstrates that when players' utility functions are continuous, as well as in mineral rights auction games and other games where "winning" creates a discontinuity in payoffs, the existence result can be extended to the case where players choose from a continuum of actions.

The paper then applies the theory to several classes of games, providing conditions on utility functions and joint distributions over types under which each class of games satisfies the single crossing condition. In particular, the single crossing condition is shown to hold in all first-price, private value auctions with potentially heterogeneous, risk-averse bidders, with either independent or affiliated values, and with reserve prices which may differ across bidders; mineral rights auctions with two heterogeneous bidders and affiliated values; a class of pricing games with incomplete information about costs; a class of all-pay auction games; and a class of noisy signaling games. Finally, the formulation of the problem introduced in this paper suggests a straightforward algorithm for numerically computing equilibrium bidding strategies in games such as first price auctions, and we present numerical analyses of several auctions under alternative assumptions about the joint distribution of types.

Abstract:
This paper studies the bidding behavior of firms in U.S. Forest Service timber auctions in 1976--1990. When conducting timber auctions, the Forest Service publicly announces its estimates of the tract characteristics before the auction, and each bidder additionally has an opportunity to inspect the tract and form its own private estimates. We build a model that incorporates both differential information and the fact that bids placed in timber auctions are multidimensional. The theory predicts that bidders will strategically distort their bids based on their private information, a practice known as 'skewed bidding.' Using a dataset that includes both the public ex ante Forest Service estimates and the ex post realizations of the tract characteristics, we test our model and provide evidence that bidders do possess private information. Our results suggest that private information affects Forest Service revenue and creates allocational inefficiency. Finally, we establish that risk aversion plays an important role in bidding behavior.

Abstract:
This paper studies the bidding behavior of firms in U.S. Forest Service timber auctions in 1976--1990. When conducting timber auctions, the Forest Service publicly announces its estimates of the tract characteristics before the auction, and each bidder additionally has an opportunity to inspect the tract and form its own private estimates. We build a model that incorporates both differential information and the fact that bids placed in timber auctions are multidimensional. The theory predicts that bidders will strategically distort their bids based on their private information, a practice known as 'skewed bidding.' Using a dataset that includes both the public ex ante Forest Service estimates and the ex post realizations of the tract characteristics, we test our model and provide evidence that bidders do possess private information. Our results suggest that private information affects Forest Service revenue and creates allocational inefficiency. Finally, we establish that risk aversion plays an important role in bidding behavior.

Abstract:
How much discretion should the monetary authority have in setting its policy? This question is analyzed in an economy with an agreed-upon social welfare function that depends on the randomly fluctuating state of the economy. The monetary authority has private information about that state. In the model, well-designed rules trade off society's desire to give the monetary authority discretion to react to its private information against society's need to guard against the time inconsistency problem arising from the temptation to stimulate the economy with unexpected inflation. Although this dynamic mechanism design problem seems complex, society can implement the optimal policy simply by legislating an inflation cap that specifies the highest allowable inflation rate. The more severe the time inconsistency problem, the more tightly the cap constrains policy and the smaller is the degree of discretion. As this problem becomes sufficiently severe, the optimal degree of discretion is none.

rules vs. discretion, time inconsistency, optimal monetary policy, inflation targets, inflation caps

Abstract:
How much discretion should the monetary authority have in setting its policy? This question is analyzed in an economy with an agreed-upon social welfare function that depends on the randomly fluctuating state of the economy. The monetary authority has private information about that state. In the model, well-designed rules trade off society's desire to give the monetary authority discretion to react to its private information against society's need to guard against the time inconsistency problem arising from the temptation to stimulate the economy with unexpected inflation. Although this dynamic mechanism design problem seems complex, society can implement the optimal policy simply by legislating an inflation cap that specifies the highest allowable inflation rate. The more severe the time inconsistency problem, the more tightly the cap constrains policy and the smaller is the degree of discretion. As this problem becomes sufficiently severe, the optimal degree of discretion is none.

Rules vs. discretion, time inconsistency, optimal monetary policy, inflation targets, inflation caps

Abstract:
How much discretion should the monetary authority have in setting its policy? This question is analyzed in an economy with an agreed-upon social welfare function that depends on the randomly fluctuating state of the economy. The monetary authority has private information about that state. In the model, well-designed rules trade off society's desire to give the monetary authority discretion to react to its private information against society's need to guard against the time inconsistency problem arising from the temptation to stimulate the economy with unexpected inflation. Although this dynamic mechanism design problem seems complex, society can implement the optimal policy simply by legislating an inflation cap that specifies the highest allowable inflation rate. The more severe the time inconsistency problem, the more tightly the cap constrains policy and the smaller is the degree of discretion. As this problem becomes sufficiently severe, the optimal degree of discretion is none.

Abstract:
We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents with hidden values, and how the answer depends on the institutional environment. Myerson and Satterthwaite (1983) showed that efficiency and ex ante budget balance cannot be supported by a static mechanism that is interim incentive compatible and interim individually rational. We show that not only can the individual rationality constraint be relaxed in repeated trade settings, but also that stronger notions of incentive compatibility (IC) and budget balance (BB) can be compatible with efficiency. We construct efficient dynamic mechanisms for low discount factors that satisfy either (1) ex post IC and ex ante BB; or (2) interim IC and ex post BB. We analyze second-best, inefficient mechanisms that satisfy (3) ex post IC and ex post BB. We then expand the model to allow agents to store money in a bounded joint savings account, and construct non-stationary mechanisms utilizing such accounts that achieve (4) ex post IC and approximate efficiency. The alternative constraints we study correspond to different institutional environments and assumptions on the agents' knowledge about each other.

Abstract:
We analyze the productivity of information technology in emergency response systems. "Enhanced 911" (E911) is information technology that links caller identification to a location database and so speeds up emergency response. We assess the impact of E911 on health outcomes using Pennsylvania ambulance and hospital records between 1994 and 1996, a period of substantial adoption. We find that as a result of E911 adoption, patient health measured at the time of ambulance arrival improves, suggesting that E911 speeds up emergency response. Further analysis using hospital discharge data shows that E911 reduces mortality and hospital costs.

Abstract:
This paper analyzes the productivity of technology and job design in emergency response systems, or 911 systems.' During the 1990s, many 911 systems adopted Enhanced 911' (E911), where information technology is used to link automatic caller identification to a database of address and location information. A potential benefit to E911 is improved timeliness of the emergency response. We evaluate the returns to E911 in the context of a panel dataset of Pennsylvania counties during 1994-1996, when almost half of the 67 counties experienced a change in technology. We measure productivity using an index of health status of cardiac patients at the time of ambulance arrival, where the index should be improved by timely response. We also consider the direct effect of E911 on several patient outcomes, including mortality within the first hours following the incident and the total hospital charges incurred by the patient. Our main finding is that E911 increases the short-term survival rates for patients with cardiac diagnoses by about 1%, from a level of 96.2%. We also provide evidence that E911 reduces hospital charges. Finally, we analyze the effect of job design, in particular the use of Emergency Medical Dispatching' (EMD), where call-takers gather medical information, provide medical instructions over the telephone, and prioritize the allocation of ambulance and paramedic services. Controlling for EMD adoption does not affect our results about E911, and we find that EMD and E911 do not have significant interactions in determining outcomes (that is, they are neither substitutes nor complements).

Abstract:
This paper analyzes the productivity of technology and job design in emergency response systems, or 911 systems.' During the 1990s, many 911 systems adopted Enhanced 911' (E911), where information technology is used to link automatic caller identification to a database of address and location information. A potential benefit to E911 is improved timeliness of the emergency response. We evaluate the returns to E911 in the context of a panel dataset of Pennsylvania counties during 1994-1996, when almost half of the 67 counties experienced a change in technology. We measure productivity using an index of health status of cardiac patients at the time of ambulance arrival, where the index should be improved by timely response. We also consider the direct effect of E911 on several patient outcomes, including mortality within the first hours following the incident and the total hospital charges incurred by the patient. Our main finding is that E911 increases the short-term survival rates for patients with cardiac diagnoses by about 1%, from a level of 96.2%. We also provide evidence that E911 reduces hospital charges. Finally, we analyze the effect of job design, in particular the use of Emergency Medical Dispatching' (EMD), where call-takers gather medical information, provide medical instructions over the telephone, and prioritize the allocation of ambulance and paramedic services. Controlling for EMD adoption does not affect our results about E911, and we find that EMD and E911 do not have significant interactions in determining outcomes (that is, they are neither substitutes nor complements).

Abstract:
This paper studies alternative empirical strategies for estimating the effects of organization design practices on performance, as well as the factors which determine organizational design, in a cross-section of firms. Our economic model is based on a firm where multiple organizational design practices are en endogenously determined, and these organizational design practices affect output through an 'organizational design production function.' The econometric model includes unobserved exogenous variation in the costs and returns to each of the individual practices. The model is used to evaluate how different econometric strategies for testing theories about complementarity can be interpreted under alternative assumptions about the economic and statistical environment. We identify plausible hypotheses about the joint distribution of the unobservables under which several different approaches from the existing literature will yield biased and inconsistent estimates. We show that the sign of the bias depends on two factors: whether the organzational design practices are complements, and the correlation between the unobserved returns to each practice. We find several sets of conditions under which the sign of the bias can be determined, and we provide economic interpretations. Our analysis shows that for a particular set of hypotheses, a variety of different procedures may all yield qualitatively similar biases, presenting a challenge for the identification of complementarity. We then propose a structural approach, which is based on a system of simultaneous equations describing productivity and the demand for organizational design practices. As long as exogenous variables are observed which are uncorrelated with the unobserved returns to practices, the structural parameters are identified, yielding consistent tests for complementarity as well as the cross-equation restrictions implied by static optimization of the organizatin's profit function.

Abstract:
This paper studies the causes and consequences of the adoption of technology by hospitals and public emergency response systems, focusing on Basic and Enhanced 911 services. Basic 911 allows people within a given locality to access specialized call-takers and ambulance dispatchers using the single telephone number 911. Enhanced 911 is characterized by telecommunications equipment and information technology which identifies the location of emergency callers. We begin by exploring the distribution of 911 systems among counties in the U.S., showing that this locally provided service responds to income and political factors as well as population and density of a county. Then, using a database of cardiac patients in Pennsylvania in 1995, we are able to characterize some of the productivity efforts of 911 services. We show that Enhanced 911 reduces response times, which in turn reduce mortality. Further, we find that the pre-hospital system interacts with the allocation of patients to hospitals in several ways. First, patient severity affect the allocation of patients to high-technology hospitals. Second, conditional on the availability of advanced cardiac care facilities, counties with 911 systems allocate cardiac patients to hospitals with better technology. Finally, hospitals with more advanced emergency and cardiac technology treat a higher share of cardiac patients who make use of the pre- hospital system.

Abstract:
We analyze collusion in an infinitely repeated Bertrand game, where prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. Productive efficiency is possible only if high-cost firms relinquish market share. In the most profitable collusive schemes, firms implement productive efficiency, and high-cost firms are favored with higher expected market share in future periods. If types are discrete, there exists a discount factor strictly less than one above which first-best profits can be attained using history-dependent reallocation of market share between equally efficient firms. We also analyze the role of communication and side-payments.

Abstract:
We analyze a model of oligopolistic competition with ongoing investment. Special cases include incremental investment, patent races, learning by doing, and network externalities. We investigate circumstances under which a firm with low costs or high quality will extend its initial lead through investments. To this end, we derive a new comparative statics result for general games with strategic substitutes, which yields the desired conditions for our investment game. Finally, we highlight plausible countervailing effects that arise when investments of leaders are less effective than those of laggards, or in dynamic games when firms are sufficiently patient.

Abstract:
This paper analyzes the problem faced by a risk-averse firm considering how much to invest in a risky project. The firm receives a signal about the value of the project. We derive necessary and sufficient conditions on the signal distribution such that (i) the agent's investment is nondecreasing in the realization of the signal and (ii) different signals can be ranked according to their ex ante information value. Finally, we provide conditions under which it is possible to compare the incentive to acquire information across agents with different risk preferences, and we identify a class of utility functions for which agents who are less risk averse purchase more information.

Portfolio problem, value of information, stochastic orderings, comparative statics, under uncertainty, monotone likelihood ratio order, monotone probability ratio order

Abstract:
This paper develops tools for analyzing properties of stochastic objective functions which take the form (formula). The paper analyzes the relationship between properties of the primitive functions, such as utility functions u and probability distributions F, and properties of the stochastic objective. The methods are designed to address problems where the utility functions is restricted to lie in a set of functions which is a "closed convex cone" (examples of such sets include increasing functions, concave functions, or supermodular functions). It is shown that approaches previously applied to characterize monotonicity of V (that is, stochastic dominance theorems) can be used to establish other properties of V as well. The first part of the paper establishes necessary an sufficient conditions for V to satisfy "closed convex cone properties" such as monotonicity, supermodularity, and concavity, in the parameter (formula). Then, we consider necessary and sufficient conditions for monotone comparative statics predictions, building on the results of Milgrom and Shannon (1994). A new property of payoff functions is introduced, called l-supermodularity, which is shown to be necessary and sufficient for (formula) to be quasisupermodular in X (a property which is, in turn, necessary for comparative statics predictions). The results are illustrated with applications.

Abstract:
This paper develops necessary and sufficient conditions for monotone comparative statics predictions in several classes of stochastic optimization problems. The results are formulated so as to highlight the tradeoffs between assumptions about payoff functions and assumptions about probability distributions: they characterize "minimal sufficient conditions" on a pair of functions (for exaple, a utility function and a probability distribution) so that the expected utility satisfies necessary and sufficient conditions for comparative statics predictions. The paper considers two main classes of assumptions on primitives: single crossing properties and log-supermodularity. Single crossing properties arise naturally in portfolio investment problems and auction games. Log-supermodularity is closely related to several commonly studied economic properties, including decreasing absolute risk aversion, affiliation of random variables, and the monotone likelihood ratio property. The results are used to extend the existing literature on investment problems and games of incomplete information, including auction games and pricing games.

Abstract:
This paper analyzes alternative empirical strategies for studying the effect of organizational design on performance, as well as the factors which determine organizational design. We begin by developing a general economic model of a firm where multiple organizational design practices are endogenously determined. The model includes exogenous variation in the costs and returns to each of the individual practices, which is the source of the heterogeneity among firms. We then argue that in many empirical applications, some of the exogenous costs and benefits of each organizational design practice will be unobserved by the econometrician. We use this model to evaluate how different econometric strategies perform under alternative assumptions, focusing on how the presence of unobserved heterogeneity impacts the interpretation of different empirical procedures.For example, we show that some of the main testing strategies which have been used in the empirical literature on organizational design cannot distinguish between two hypotheses: (H1) a set of choice variables are mutually complementary, and (H2) the choice variables do not interact in determining profits, but the unobserved returns to individual practices are positively correlated. We propose a structural approach to the problem which involves the estimation of a system of equations, including both a productivity equation as well as equations which describe the firm's optimal choices. These equations explicitly incorporate the presence of unobserved heterogeneity between firms. We analyze this approach theoretically and using simulated data, comparing it to other approaches which make different assumptions. The analysis highlights the tradeoffs between approaches in terms of computational burden, data requirements, precision, and sensitivity of the results to the assumptions required.