WORKERS,WARRIORS, AND CRIMINALS: SOCIAL CONFLICT IN GENERAL EQUILIBRIUM

We incorporate appropriation activities (social conflict) into canonical models of trade and study how economic shocks and policies affect the intensity of conflict. We show that not all shocks that could make society richer reduce conflict: positive shocks to labor‐intensive industries diminish conflict, while positive shocks to capital‐intensive industries increase it. The key requirement is that conflict activities be more labor intensive than the economy as this determines how shocks affect the returns and costs of conflict. Our theory is consistent with several observed patterns of conflict and implies that empirical work should take into account the relative factor intensities of the productive and conflict sectors in each country. Incorporating appropriation into a canonic general equilibrium model affects what policies may be deemed desirable: in order to reduce conflict and generate Pareto‐improvements policy must be distortionary, while reforms that appear efficiency‐enhancing under the unrealistic assumption of perfect property rights may backfire. This offers one explanation for why reforms based on traditional models without appropriation may be delayed and become unpopular when implemented, and why societies may sympathize with seemingly inefficient redistribution.     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics

We study a model of lumpy investment wherein establishments face persistent shocks to common and plant‐specific productivity, and nonconvex adjustment costs lead them to pursue generalized (S, s) investment rules. We allow persistent heterogeneity in both capital and total factor productivity alongside low‐level investments exempt from adjustment costs to develop the first model consistent with the cross‐sectional distribution of establishment investment rates. Examining the implications of lumpy investment for aggregate dynamics in this setting, we find that they remain substantial when factor supply considerations are ignored, but are quantitatively irrelevant in general equilibrium. The substantial implications of general equilibrium extend beyond the dynamics of aggregate series. While the presence of idiosyncratic shocks makes the time‐averaged distribution of plant‐level investment rates largely invariant to market‐clearing movements in real wages and interest rates, we show that the dynamics of plants' investments differ sharply in their presence. Thus, model‐based estimations of capital adjustment costs involving panel data may be quite sensitive to the assumption about equilibrium. Our analysis also offers new insights about how nonconvex adjustment costs influence investment at the plant. When establishments face idiosyncratic productivity shocks consistent with existing estimates, we find that nonconvex costs do not cause lumpy investments, but act to eliminate them.     

A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements

Rationalizability is a central solution concept of game theory. Economic models often have many rationalizable outcomes, motivating economists to use refinements of rationalizability, including equilibrium refinements. In this paper we try to achieve a general understanding of when this multiplicity occurs and how one should deal with it. Assuming that the set of possible payoff functions and belief structures is sufficiently rich, we establish a revealing structure of the correspondence of beliefs to sets of rationalizable outcomes. We show that, for any rationalizable action a of any type, we can perturb the beliefs of the type in such a way that a is uniquely rationalizable for the new type. This unique outcome will be robust to further small changes. When multiplicity occurs, then we are in a “knife‐edge” case, where the unique rationalizable outcome changes, sandwiched between open sets of types where each of the rationalizable actions is uniquely rationalizable. As an immediate application of this result, we characterize, for any refinement of rationalizability, the predictions that are robust to small misspecifications of interim beliefs. These are only those predictions that are true for all rationalizable strategies, that is, the predictions that could have been made without the refinement.     

Markov Perfect Industry Dynamics With Many Firms

We propose an approximation method for analyzing Ericson and Pakes (1995)‐style dynamic models of imperfect competition. We define a new equilibrium concept that we call oblivious equilibrium, in which each firm is assumed to make decisions based only on its own state and knowledge of the long‐run average industry state, but where firms ignore current information about competitors' states. The great advantage of oblivious equilibria is that they are much easier to compute than are Markov perfect equilibria. Moreover, we show that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain “light‐tail” condition, then oblivious equilibria closely approximate Markov perfect equilibria. This theorem justifies using oblivious equilibria to analyze Markov perfect industry dynamics in Ericson and Pakes (1995)‐style models with many firms.     

MANAGING CREDIT BUBBLES

We study a dynamic economy where credit is limited by insufficient collateral and, as a result, investment and output are too low. In this environment, changes in investor sentiment or market expectations can give rise to credit bubbles, that is, expansions in credit that are backed not by expectations of future profits (i.e., fundamental collateral), but instead by expectations of future credit (i.e., bubbly collateral). Credit bubbles raise the availability of credit for entrepreneurs: this is the crowding‐in effect. However, entrepreneurs must also use some of this credit to cancel past credit: this is the crowding‐out effect. There is an “optimal” bubble size that trades off these two effects and maximizes long‐run output and consumption. The equilibrium bubble size depends on investor sentiment, however, and it typically does not coincide with the “optimal” bubble size. This provides a new rationale for macroprudential policy. A credit management agency (CMA) can replicate the “optimal” bubble by taxing credit when the equilibrium bubble is too high and subsidizing credit when the equilibrium bubble is too low. This leaning‐against‐the‐wind policy maximizes output and consumption. Moreover, the same conditions that make this policy desirable guarantee that a CMA has the resources to implement it.     

Uncertainty Shocks in a Model of Effective Demand

Can increased uncertainty about the future cause a contraction in output and its components? An identified uncertainty shock in the data causes significant declines in output, consumption, investment, and hours worked. Standard general‐equilibrium models with flexible prices cannot reproduce this comovement. However, uncertainty shocks can easily generate comovement with countercyclical markups through sticky prices. Monetary policy plays a key role in offsetting the negative impact of uncertainty shocks during normal times. Higher uncertainty has even more negative effects if monetary policy can no longer perform its usual stabilizing function because of the zero lower bound. We calibrate our uncertainty shock process using fluctuations in implied stock market volatility, and show that the model with nominal price rigidity is consistent with empirical evidence from a structural vector autoregression. We argue that increased uncertainty about the future likely played a role in worsening the Great Recession. The economic mechanism we identify applies to a large set of shocks that change expectations of the future without changing current fundamentals.     

FINANCIAL CONTAGION THROUGH CAPITAL CONNECTIONS: A MODEL OF THE ORIGIN AND SPREAD OF BANK PANICS

Financial contagion is modeled as an equilibrium phenomenon in a dynamic setting with incomplete information and multiple banks. The equilibrium probability of bank failure is uniquely determined. We explore how the cross‐holding of deposits motivated by imperfectly correlated regional liquidity shocks can lead to contagious effects conditional on the failure of a financial institution. We show that contagious bank failure occurs with positive probability in the unique equilibrium of the economy and demonstrate that the presence of such contagion risk can prevent banks from perfectly insuring each other against liquidity shocks via the cross‐holding of deposits. (JEL: G2, C7)     

Consumption Commitments and Habit Formation

We analyze the implications of household‐level adjustment costs for the dynamics of aggregate consumption. We show that an economy in which agents have “consumption commitments” is approximately equivalent to a habit formation model in which the habit stock is a weighted average of past consumption if idiosyncratic risk is large relative to aggregate risk. Consumption commitments can thus explain the empirical regularity that consumption is excessively sensitive and excessively smooth, findings that are typically attributed to habit formation. Unlike habit formation and other theories, but consistent with empirical evidence, the consumption commitments model also predicts that excess sensitivity and smoothness vanish for large shocks. These results suggest that behavior previously attributed to habit formation may be better explained by adjustment costs. We develop additional testable predictions to further distinguish the commitment and habit models and show that the two models have different welfare implications.     

Robust Predictions for Bilateral Contracting with Externalities

The paper studies bilateral contracting between one principal and N agents when each agent's utility depends on the principal's unobservable contracts with other agents. We show that allowing deviations to menu contracts from which the principal chooses bounds equilibrium outcomes in a wide class of bilateral contracting games without imposing ad hoc restrictions on the agents' beliefs. This bound yields, for example, competitive convergence as N →∞ in environments in which an appropriately‐defined notion of competitive equilibrium exists. We also examine the additional restrictions arising in two common bilateral contracting games: the “offer game” in which the principal makes simultaneous offers to the agents, and the “bidding game” in which the agents make simultaneous offers to the principal.     

Impulse Balance and Multiple‐Period Feedback in the Newsvendor Game

Human subjects in the newsvendor game place suboptimal orders: orders are typically between the expected profit‐maximizing quantity and mean demand (“pull‐to‐center bias”). In previous work, we have shown that impulse balance equilibrium (IBE), which is based on a simple ex post rationality principle along with an equilibrium condition, can predict ordering decisions in the laboratory. In this study, we extend IBE to standing orders and multiple‐period feedback and show that it predicts—in line with previous findings—that constraining newsvendors to make a standing order for a sequence of periods moves the average of submitted orders toward the optimum.     

Stable and Coordinating Contracts for a Supply Chain with Multiple Risk‐Averse Suppliers

We analyze a decentralized supply chain with a single risk‐averse retailer and multiple risk‐averse suppliers under a Conditional Value at Risk objective. We define coordinating contracts and show that the supply chain is coordinated only when the least risk‐averse agent bears the entire risk and the lowest‐cost supplier handles all production. However, due to competition, not all coordinating contracts are stable. Thus, we introduce the notion of contract core, which reflects the agents' “bargaining power” and restricts the set of coordinating contracts to a subset which is “credible.” We also study the concept of contract equilibrium, which helps to characterize contracts that are immune to opportunistic renegotiation. We show that, the concept of contract core imposes conditions on the share of profit among different agents, while the concept of contract equilibrium provide conditions on how the payment changes with the order quantity.     

Informing Ex Ante Event Studies with Macro‐Econometric Evidence on the Structural and Policy Impacts of Terrorism

Economic consequence analysis is one of many inputs to terrorism contingency planning. Computable general equilibrium (CGE) models are being used more frequently in these analyses, in part because of their capacity to accommodate high levels of event‐specific detail. In modeling the potential economic effects of a hypothetical terrorist event, two broad sets of shocks are required: (1) physical impacts on observable variables (e.g., asset damage); (2) behavioral impacts on unobservable variables (e.g., investor uncertainty). Assembling shocks describing the physical impacts of a terrorist incident is relatively straightforward, since estimates are either readily available or plausibly inferred. However, assembling shocks describing behavioral impacts is more difficult. Values for behavioral variables (e.g., required rates of return) are typically inferred or estimated by indirect means. Generally, this has been achieved via reference to extraneous literature or ex ante surveys. This article explores a new method. We elucidate the magnitude of CGE‐relevant structural shifts implicit in econometric evidence on terrorist incidents, with a view to informing future ex ante event assessments. Ex post econometric studies of terrorism by Blomberg et al . yield macro econometric equations that describe the response of observable economic variables (e.g., GDP growth) to terrorist incidents. We use these equations to determine estimates for relevant (unobservable) structural and policy variables impacted by terrorist incidents, using a CGE model of the United States. This allows us to: (i) compare values for these shifts with input assumptions in earlier ex ante CGE studies; and (ii) discuss how future ex ante studies can be informed by our analysis.     

Level‐k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private‐Value Auctions?

This paper proposes a structural nonequilibrium model of initial responses to incomplete‐information games based on “level‐k” thinking, which describes behavior in many experiments with complete‐information games. We derive the model's implications in first‐ and second‐price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level‐k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common‐value auctions and overbidding in those independent‐private‐value auctions without the uniform value distributions used in most experiments.     

The Network Origins of Aggregate Fluctuations

This paper argues that, in the presence of intersectoral input–output linkages, microeconomic idiosyncratic shocks may lead to aggregate fluctuations. We show that, as the economy becomes more disaggregated, the rate at which aggregate volatility decays is determined by the structure of the network capturing such linkages. Our main results provide a characterization of this relationship in terms of the importance of different sectors as suppliers to their immediate customers, as well as their role as indirect suppliers to chains of downstream sectors. Such higher‐order interconnections capture the possibility of “cascade effects” whereby productivity shocks to a sector propagate not only to its immediate downstream customers, but also to the rest of the economy. Our results highlight that sizable aggregate volatility is obtained from sectoral idiosyncratic shocks only if there exists significant asymmetry in the roles that sectors play as suppliers to others, and that the “sparseness” of the input–output matrix is unrelated to the nature of aggregate fluctuations.     

INVESTMENT AND TIME TO PLAN AND BUILD: A COMPARISON OF STRUCTURES VS. EQUIPMENT IN A PANEL OF ITALIAN FIRMS

“Time‐to‐build” models of investment expenditures play an important role in many traditional and modern theories of the business cycle, especially for explaining the dynamic propagation of shocks. We estimate the structural parameters of a time‐to‐build model using annual firm‐level investment data on equipment and structures. For expenditures on equipment, we find no evidence of time‐to‐build effects beyond one year. For expenditures on structures, by contrast, there is clear evidence of such effects in the range of two to three years. The contrast between equipment and structures is intuitively reasonable and consistent with previous results. The estimates for structures also indicate that initial‐period expenditures are low and increase as projects near completion. These results provide empirical support for including “time‐to‐plan” effects for investment in structures. More generally, these results suggest a potential source of specification error for Q models of investment and production‐based asset pricing models that ignore the time required to plan, build, and install new capital. (JEL: D24, G31, C33, C34)     

Fractional Price Matching Policies Arising from the Ocean Freight Service Industry

We consider a situation in which shippers (customers) can purchase ocean freight services either directly from a carrier (service provider)in advance or from the spot market just before the departure of an ocean liner. The price is known in the former case, while the spot price is uncertain ex‐ante in the latter case. Consequently, some shippers are reluctant to book directly from the carrier in advance unless the carrier is willing to “partially match” the realized spot price when it is lower than the regular price. This study is an initial attempt to examine if the carrier should bear some of the “price risk” by offering a “fractional” price matching contract that can be described as follows. The shipper pays the regular freight price in advance; however, the shipper will get a refund if the realized spot price is below the regular price, where the refund is a “fraction” of the difference between the regular price and the realized spot price. By modeling the dynamics between the carrier and the shippers as a sequential game, we show that the carrier can use the fractional price matching contract to generate a higher demand from the shippers compared to no price matching contract by increasing the “fraction” in equilibrium. However, as the carrier increases the “fraction,” the carrier should increase the regular price to compensate for bearing additional risk. By selecting the fractional price matching contract optimally, we show that the carrier can afford to offer this price matching mechanism without incurring revenue loss: the optimal fractional price matching contract is “revenue neutral.”     

Bargaining and Cooperation in Strategic Form Games

In this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form. A multistage bargaining procedure for N players, the “proposer commitment” procedure, is presented. It is inspired by Nash's two‐player variable‐threat model; a key feature is the commitment to “threats.” We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies, the traditional coalitional function may not be adequate when utilities are not transferable. (JEL: C70, C71, C78, D70)     

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post‐Lasso in the first stage is root‐n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well‐approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic “beta‐min” conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso‐based IV estimator with a data‐driven penalty performs well compared to recently advocated many‐instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso‐based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post‐Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non‐Gaussian, heteroscedastic disturbances that uses a data‐weighted ℓ₁‐penalty function. By innovatively using moderate deviation theory for self‐normalized sums, we provide convergence rates for the resulting Lasso and post‐Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that logp = o(n^1/3). We also provide a data‐driven method for choosing the penalty level that must be specified in obtaining Lasso and post‐Lasso estimates and establish its asymptotic validity under non‐Gaussian, heteroscedastic disturbances.     

The Granular Origins of Aggregate Fluctuations

This paper proposes that idiosyncratic firm‐level shocks can explain an important part of aggregate movements and provide a microfoundation for aggregate shocks. Existing research has focused on using aggregate shocks to explain business cycles, arguing that individual firm shocks average out in the aggregate. I show that this argument breaks down if the distribution of firm sizes is fat‐tailed, as documented empirically. The idiosyncratic movements of the largest 100 firms in the United States appear to explain about one‐third of variations in output growth. This “granular” hypothesis suggests new directions for macroeconomic research, in particular that macroeconomic questions can be clarified by looking at the behavior of large firms. This paper's ideas and analytical results may also be useful for thinking about the fluctuations of other economic aggregates, such as exports or the trade balance.