Estimating Dynamic Models of Imperfect Competition

We describe a two‐step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including industry competition models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).     

KNOWING THE RIGHT PERSON IN THE RIGHT PLACE: POLITICAL CONNECTIONS AND RESISTANCE TO CHANGE

We use a political economy model of Schumpeterian growth with entry to investigate how an incumbent politician can strategically use the level of red tape to acquire incumbency advantage. By setting sufficiently high red tape, the politician induces the incumbent firm in the intermediate sector to invest in political connections, which are valued also by voters, who recognize that bureaucratic costs can be reduced by connected firms. Within this framework, we study the Markov perfect equilibria of an infinitely repeated game among politicians, firms, and voters, and show that all equilibria are characterized by investments in political connections and the re‐election of the incumbent politician. Political connections may prevent entry of advanced competitors and cause the economy to lag behind the technological frontier. Our model provides a possible explanation for the persistence of inefficient democracies and political barriers to technology development, where these reflect shared rather than conflicting interests.     

The Costs of Environmental Regulation in a Concentrated Industry

The typical cost analysis of an environmental regulation consists of an engineering estimate of the compliance costs. In industries where fixed costs are an important determinant of market structure, this static analysis ignores the dynamic effects of the regulation on entry, investment, and market power. I evaluate the welfare costs of the 1990 Amendments to the Clean Air Act on the U.S. Portland cement industry, accounting for these effects through a dynamic model of oligopoly in the tradition of Ericson and Pakes (1995). Using the two‐step estimator of Bajari, Benkard, and Levin (2007), I recover the entire cost structure of the industry, including the distributions of sunk entry costs and capacity adjustment costs. My primary finding is that the Amendments have significantly increased the sunk cost of entry, leading to a loss of between $810M and $3.2B in product market surplus. A static analysis misses the welfare penalty on consumers, and obtains the wrong sign of the welfare effects on incumbent firms.     

Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long‐run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.     

Collusion With Persistent Cost Shocks

We consider a dynamic Bertrand game in which prices are publicly observed and each firm receives a privately observed cost shock in each period. Although cost shocks are independent across firms, within a firm costs follow a first‐order Markov process. We analyze the set of collusive equilibria available to firms, emphasizing the best collusive scheme for the firms at the start of the game. In general, there is a trade‐off between productive efficiency, whereby the low‐cost firm serves the market in a given period, and high prices. We show that when costs are perfectly correlated over time within a firm, if the distribution of costs is log‐concave and firms are sufficiently patient, then the optimal collusive scheme entails price rigidity: firms set the same price and share the market equally, regardless of their respective costs. When serial correlation of costs is imperfect, partial productive efficiency is optimal. For the case of two cost types, first‐best collusion is possible if the firms are patient relative to the persistence of cost shocks, but not otherwise. We present numerical examples of first‐best collusive schemes.     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Noisy Stochastic Games

This paper establishes existence of a stationary Markov perfect equilibrium in general stochastic games with noise—a component of the state that is nonatomically distributed and not directly affected by the previous period's state and actions. Noise may be simply a payoff‐irrelevant public randomization device, delivering known results on the existence of correlated equilibrium as a special case. More generally, noise can take the form of shocks that enter into players' stage payoffs and the transition probability on states. The existence result is applied to a model of industry dynamics and to a model of dynamic electoral competition.     

Market Impact on IT Security Spending

Traditionally, IT security investment decisions are made in isolation. However, as firms that compete for customers in an industry are closely interlinked, a macro perspective is needed in analyzing these decisions. We utilize the notions of direct‐ and cross‐risk elasticity to describe the customer response to adverse IT security events in the firm and competitor, respectively, thus allowing us to analyze optimal security investment decisions. Examining both symmetric and asymmetric duopoly cases using a continuous‐time Markov chain (CTMC) model, we demonstrate that optimal IT security spending, expected firm profits and willingness of firms to cooperate on security improvements are highly dependent on the nature of customer response to adverse events. We also examine the investment problem when security attacks on different firms are correlated.     

Reputation for Quality

We propose a model of firm reputation in which a firm can invest or disinvest in product quality and the firm's reputation is defined as the market's belief about this quality. We analyze the relationship between a firm's reputation and its investment incentives, and derive implications for reputational dynamics. Reputational incentives depend on the specification of market learning. When consumers learn about quality through perfect good news signals, incentives decrease in reputation and there is a unique work–shirk equilibrium with ergodic dynamics. When learning is through perfect bad news signals, incentives increase in reputation and there is a continuum of shirk–work equilibria with path‐dependent dynamics. For a class of imperfect Poisson learning processes and low investment costs, we show that there exists a work–shirk equilibrium with ergodic dynamics. For a subclass of these learning processes, any equilibrium must feature working at all low and intermediate levels of reputation and shirking at the top.     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

Investment in Shared Suppliers: Effect of Learning,Spillover, and Competition

We investigate the optimal strategies for firms to invest in their suppliers when the benefits of such investments can spillover to other firms who also source from the same suppliers. We consider two Bayesian firms that can invest in improving the quality of their shared supplier; the firms do not have complete information on the true quality of the supplier, but they update their beliefs based on the supplier's performance. We formulate the problem as an investment game and obtain Markov perfect equilibria characterized by the investment thresholds of both firms. The equilibrium investment strategies of the two firms are characterized by a region of preemption and a region of war of attrition. We also examine how the interplay between spillover, competition, and returns from the investment at shared suppliers affect the investment threshold and the time to the leader's investment, and identify the conditions under which competition delays or hastens the first investment in a shared supplier.     

ON‐THE‐JOB SEARCH AND MORAL HAZARD

We analyze the interaction between intertemporal incentive contracts and search frictions associated with on‐the‐job search. In our model, agency problems call for wage contracts with deferred compensation. At the same time workers do on‐the‐job search. Deferred compensation improves workers' incentives to exert effort but distorts their on‐the‐job search decisions. We show that deferred compensation is less attractive when the value to the worker–firm pair of on‐the‐job search is high. Moreover, the interplay between search frictions and wage contracts creates feedback effects. If firms in equilibrium use contracts with deferred compensation, fewer firms with vacancies enter the on‐the‐job search market, and this in turn reduces the distortions created by deferred compensation. These feedback effects between the incentive contracts used and the activity level in the search markets can lead to multiple equilibria: a low‐turnover equilibrium where firms use deferred compensation, and a high‐turnover equilibrium where they do not. Furthermore, the model predicts that firms are more likely to use deferred compensation when search frictions are high and when the gains from on‐the‐job search are small.     

External Knowledge Sourcing and Firm Innovation Efficiency

This study examines the relationship between external knowledge sourcing and firm innovation efficiency. We build on the organizational learning theory to propose that this relationship follows an inverted U‐shape: as the level of external knowledge sourcing increases from low to moderate, firm innovation efficiency increases; as the level of external knowledge sourcing increases from moderate to high, firm innovation efficiency declines. Further, we explore the moderating role of different contextual factors and contend that this inverted U‐shaped relationship is flattened in firms that operate in high‐tech sectors and in firms that face high internal constraints for innovation. Our empirical analysis is based on a sample of 3,204 Spanish firms over the period 2004–2015, and our results provide support for these contentions. We used data envelopment analysis methodology to estimate firm innovation efficiency relative to industry best performers, and truncated regression models for panel data with bootstrapped confidence intervals to test our hypotheses.     

Equilibrium Labor Turnover,Firm Growth,and Unemployment

This paper considers equilibrium quit turnover in a frictional labor market with costly hiring by firms, where large firms employ many workers and face both aggregate and firm specific productivity shocks. There is exogenous firm turnover as new (small) startups enter the market over time, while some existing firms fail and exit. Individual firm growth rates are disperse and evolve stochastically. The paper highlights how dynamic monopsony, where firms trade off lower wages against higher (endogenous) employee quit rates, yields excessive job‐to‐job quits. Such quits directly crowd out the reemployment prospects of the unemployed. With finite firm productivity states, stochastic equilibrium is fully tractable and can be computed using standard numerical techniques.     

The Impact of Costliness,Competitive Importance,and Modularity of Investments on Outsourcing

This study is motivated by examples of outsourcing that are not readily explained by widely established economic theories. We extend recent literature that develops the idea that outsourcing can help firms avoid overinvestment by specifying more precisely the conditions under which this thesis is likely to apply. Our extension is realized through a two‐period game theoretic model in which the outsourcing and in‐house investments are driven by (1) the cost required to develop a product or process module, (2) competitive relevance, defined as the module's share in the production cost or the module's importance to the customer, and (3) modularity, defined as the extent to which generic investments in the module can approach firm‐specific investments in terms of the overall product/process performance. The analysis generates predictions about what types of insourcing, outsourcing, and non‐sourcing behaviors are likely to emerge in different parts of the parameter space. Outsourcing to a more concentrated industry upstream emerges at equilibrium when modularity is high, relevance low to medium, and development cost high enough that none or only a subset of focal firms wants to invest. While firms are forced to insource and overinvest due to a prisoner's dilemma when the development cost is sufficiently high relative to the module's relevance, we do not find outsourcing equilibria that solve this problem in a two‐period game with no commitment. This result implies that some form of tacit coordination in a multi‐period game may be necessary. We conclude the study with a discussion of empirical implications.     

Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation

The widely used estimator of Berry, Levinsohn, and Pakes (1995) produces estimates of consumer preferences from a discrete‐choice demand model with random coefficients, market‐level demand shocks, and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLP's estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward‐looking demand models where the Bellman equation must also be solved repeatedly. Several Monte Carlo and real‐data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization. For static BLP, the constrained optimization approach can be as much as ten to forty times faster for large‐dimensional problems with many markets.     

Signaling to Partially Informed Investors in the Newsvendor Model

We analyze a signaling game between the manager of a firm and an investor in the firm. The manager has private information about the firm's demand and cares about the short‐term stock price assigned by the investor. Previous research has shown that under continuous decision choices and the Intuitive Criterion refinement, the least‐cost separating equilibrium will result, in which a low‐quality firm chooses its optimal capacity and a high‐quality firm over‐invests in order to signal its quality to investors. We build on this research by showing the existence of pooling outcomes in which low‐quality firms over‐invest and high‐quality firms under‐invest so as to provide identical signals to investors. The pooling equilibrium is practically appealing because it yields a Pareto improvement compared to the least‐cost separating equilibrium. Distinguishing features of our analysis are that: (i) we allow the capacity decision to have either discrete or continuous support, and (ii) we allow beliefs to be refined based on either the Undefeated refinement or the Intuitive Criterion refinement. We find that the newsvendor model parameters impact the likelihood of a pooling outcome, and this impact changes in both sign and magnitude depending on which refinement is used.     

The Role of the State in Explaining the Internationalization of Emerging Market Enterprises

While the competitive advantages of firms from developed economies are well understood, knowledge of the advantages that enable emerging market enterprises (EMEs) to expand overseas remains limited. Our analysis goes beyond theorizing that focuses on firm resources, enhancing the understanding of how EMEs expand abroad by internalizing home‐country institutional advantages that extend beyond the firm boundaries. More specifically, we examine how the state and institutional idiosyncrasies in the home country help EMEs internationalize. We demonstrate that state ownership has a strong independent effect on the international expansion of EMEs. This effect, however, is contingent upon firms' own resources and other location‐ and industry‐specific forces pertaining to the market orientation of each subnational region and the institutional policies within a given industry.     

A Theory of the Firm with Non‐binding Employment Contracts

This paper examines an employment relation in which individual workers enjoy some bargaining power vis‐a‐vis the firm although they are not unionized. The main elements of the situations studied here are that the employment contracts are non‐binding across periods of production and that the firm has opportunities to replace workers. The paper analyzes a dynamic model in which the processes of contracting and recontracting between the firm and its workers are intertwined with the dynamic evolution of the firm's workforce. The analysis of the model is somewhat complicated because the employment level is a nondegenerate state variable that evolves over time and is affected by past decisions. The main analytical results characterize certain important equilibria: the profit maximizing and stationary equilibria. The unique stationary equilibrium is markedly inefficient: it exhibits inefficient over‐employment and the steady state wages coincide with the workers' reservation wage. It confirms earlier results derived by Stole and Zwiebel (1996a, b) in the context of a static model and shows that they are very robust even when the firm has nearly frictionless hiring opportunities. In contrast, in the profit maximizing equilibrium the outcome is nearly efficient and the wage exhibits a mark‐up over the reservation wage.     

The Impact of Trade on Intra‐Industry Reallocations and Aggregate Industry Productivity

This paper develops a dynamic industry model with heterogeneous firms to analyze the intra‐industry effects of international trade. The model shows how the exposure to trade will induce only the more productive firms to enter the export market (while some less productive firms continue to produce only for the domestic market) and will simultaneously force the least productive firms to exit. It then shows how further increases in the industry's exposure to trade lead to additional inter‐firm reallocations towards more productive firms. The paper also shows how the aggregate industry productivity growth generated by the reallocations contributes to a welfare gain, thus highlighting a benefit from trade that has not been examined theoretically before. The paper adapts Hopenhayn's (1992a) dynamic industry model to monopolistic competition in a general equilibrium setting. In so doing, the paper provides an extension of Krugman's (1980) trade model that incorporates firm level productivity differences. Firms with different productivity levels coexist in an industry because each firm faces initial uncertainty concerning its productivity before making an irreversible investment to enter the industry. Entry into the export market is also costly, but the firm's decision to export occurs after it gains knowledge of its productivity.