Showing papers in "Econometrica in 2014"

Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs

Abstract: In the regression-discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a “large” bandwidth, leading to data-driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory-based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias-corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close-to-correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).

Hazardous times for monetary policy : What do twenty-three million bank loans say about the effects of monetary policy on credit risk-taking?

Abstract: We identify the effects of monetary policy on credit risk-taking with an exhaustive credit register of loan applications and contracts. We separate the changes in the composition of the supply of credit from the concurrent changes in the volume of supply and quality, and the volume of demand. We employ a two-stage model that analyzes the granting of loan applications in the first stage and loan outcomes for the applications granted in the second stage, and that controls for both observed and unobserved, time-varying, firm and bank heterogeneity through time*firm and time*bank fixed effects. We find that a lower overnight interest rate induces lowly capitalized banks to grant more loan applications to ex ante risky firms and to commit larger loan volumes with fewer collateral requirements to these firms, yet with a higher ex post likelihood of default. A lower long-term interest rate and other relevant macroeconomic variables have no such effects.

A Model of the Consumption Response to Fiscal Stimulus Payments

Abstract: A wide body of empirical evidence, based on randomized experiments, finds that 20-40 percent of fiscal stimulus payments (e.g. tax rebates) are spent on nondurable household consumption in the quarter that they are received. We develop a structural economic model to interpret this evidence. Our model integrates the classical Baumol-Tobin model of money demand into the workhorse incomplete-markets life-cycle economy. In this framework, households can hold two assets: a low-return liquid asset (e.g., cash, checking account) and a high-return illiquid asset (e.g., housing, retirement account) that carries a transaction cost. The optimal life-cycle pattern of wealth accumulation implies that many households are “wealthy hand-to-mouth”: they hold little or no liquid wealth despite owning sizeable quantities of illiquid assets. They therefore display large propensities to consume out of additional income. We document the existence of such households in data from the Survey of Consumer Finances. A version of the model parameterized to the 2001 tax rebate episode is able to generate consumption responses to fiscal stimulus payments that are in line with the data.

What explains the 2007-2009 drop in employment?

Abstract: We show that deterioration in household balance sheets, or the housing net worth channel, played a significant role in the sharp decline in U.S. employment between 2007 and 2009. Counties with a larger decline in housing net worth experience a larger decline in non-tradable employment. This result is not driven by industry-specific supply-side shocks, exposure to the construction sector, policy-induced business uncertainty, or contemporaneous credit supply tightening. We find little evidence of labor market adjustment in response to the housing net worth shock. There is no significant expansion of the tradable sector in counties with the largest decline in housing net worth. Further, there is little evidence of wage adjustment within or emigration out of the hardest hit counties.

Optimal Taxes on Fossil Fuel in General Equilibrium

Abstract: We analyze a dynamic stochastic general-equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO2 concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well-known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.

Trade Liberalization and Labor Market Dynamics

Abstract: This paper estimates a structural dynamic equilibrium model of the Brazilian labor market in order to study trade-induced transitional dynamics. The model features a multi-sector economy with overlapping generations, heterogeneous workers, endogenous accumulation of sector-specific experience, and costly switching of sectors. The model's estimates yield median costs of mobility ranging from 1.4 to 2.7 times annual average wages, but a high dispersion of these costs across the population. In addition, sector-specific experience is imperfectly transferable across sectors, leading to additional barriers to mobility. Using the estimated model for counterfactual trade liberalization experiments, the main findings are: (1) there is a large labor market response following trade liberalization but the transition may take several years; (2) potential aggregate welfare gains are significantly reduced due to the delayed adjustment; (3) trade-induced welfare effects depend on initial sector of employment and on worker demographics such as age and education. The experiments also highlight the sensitivity of the transitional dynamics with respect to assumptions regarding the mobility of capital.

Dynamic Mechanism Design: A Myersonian Approach

Abstract: We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent's equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by �impulse response functions.� The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (�revenue equivalence�). Third, we characterize perfect Bayesian equilibrium-implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (�bandit auctions�).

Underinvestment in a Profitable Technology: The Case of Seasonal Migration in Bangladesh

Abstract: Hunger during pre-harvest lean seasons is widespread in the agrarian areas of Asia and Sub-Saharan Africa. We randomly assign an $8.50 incentive to households in rural Bangladesh to temporarily out-migrate during the lean season. The incentive induces 22% of households to send a seasonal migrant, their consumption at the origin increases significantly, and treated households are 8–10 percentage points more likely to re-migrate 1 and 3 years after the incentive is removed. These facts can be explained qualitatively by a model in which migration is risky, mitigating risk requires individual-specific learning, and some migrants are sufficiently close to subsistence that failed migration is very costly. We document evidence consistent with this model using heterogeneity analysis and additional experimental variation, but calibrations with forward-looking households that can save up to migrate suggest that it is difficult for the model to quantitatively match the data. We conclude with extensions to the model that could provide a better quantitative accounting of the behavior.

Understanding Mechanisms Underlying Peer Effects: Evidence From a Field Experiment on Financial Decisions

Abstract: Using a high‐stakes field experiment conducted with a financial brokerage, we implement a novel design to separately identify two channels of social influence in financial decisions, both widely studied theoretically. When someone purchases an asset, his peers may also want to purchase it, both because they learn from his choice (“social learning”) and because his possession of the asset directly affects others' utility of owning the same asset (“social utility”). We randomize whether one member of a peer pair who chose to purchase an asset has that choice implemented, thus randomizing his ability to possess the asset. Then, we randomize whether the second member of the pair: (i) receives no information about the first member, or (ii) is informed of the first member's desire to purchase the asset and the result of the randomization that determined possession. This allows us to estimate the effects of learning plus possession, and learning alone, relative to a (no information) control group. We find that both social learning and social utility channels have statistically and economically significant effects on investment decisions. Evidence from a follow‐up survey reveals that social learning effects are greatest when the first (second) investor is financially sophisticated (financially unsophisticated); investors report updating their beliefs about asset quality after learning about their peer's revealed preference; and, they report motivations consistent with “keeping up with the Joneses” when learning about their peer's possession of the asset. These results can help shed light on the mechanisms underlying herding behavior in financial markets and peer effects in consumption and investment decisions.

Stochastic Choice and Consideration Sets

Abstract: We model a boundedly rational agent who suers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximises a prefer- ence relation within the set of considered alternatives. We show that this random choice rule is the only one for which the impact of removing an alternative on the choice probability of any other alternative is asymmetric and menu independent. Both the preference relation and the attention parameters are identi…ed uniquely by stochastic choice data. J.E.L. codes: D0.

Information Frictions in Trade

Abstract: It is costly to learn about market conditions elsewhere, especially in developing countries. This paper examines how such information frictions affect trade. Using data on regional agricultural trade in the Philippines, I first document a number of observed patterns in trade flows and prices that suggest the presence of information frictions. I then incorporate information frictions into a perfect competition trade model by embedding a process whereby heterogeneous producers engage in a costly sequential search process to determine where to sell their produce. I show that introducing information frictions reconciles the theory with the observed patterns in the data. Structural estimation of the model finds that information frictions are quantitatively important: roughly half the observed regional price dispersion is due to information frictions. Furthermore, incorporating information frictions improves the out-of-sample predictive power of the model.

Short-run subsidies and long-run adoption of new health products: evidence from a field experiment.

Abstract: Short-run subsidies for health products are common in poor countries. How do they affect long-run adoption? A common fear among development practitioners is that one-off subsidies may negatively affect long-run adoption through reference-dependence: People might anchor around the subsidized price and be unwilling to pay more for the product later. But for experience goods, one-off subsidies could also boost long-run adoption through learning. This paper uses data from a two-stage randomized pricing experiment in Kenya to estimate the relative importance of these effects for a new, improved antimalarial bed net. Reduced form estimates show that a one-time subsidy has a positive impact on willingness to pay a year later inherit. To separately identify the learning and anchoring effects, we estimate a parsimonious experience-good model. Estimation results show a large, positive learning effect but no anchoring. We black then discuss the types of products and the contexts inherit for which these results may apply.

Land Use Regulation and Welfare

Abstract: We evaluate the effect of land use regulation on the value of land and on welfare. Our estimates are based on a decomposition of the effects of regulation into three components: an own-lot effect, which reflects the cost of regulatory constraints to the owner of a parcel; an external effect, which reflects the value of regulatory constraints on one's neighbors; a supply effect, which reflects the effect of regulated scarcity of developable land. Using this decomposition, we arrive at a novel strategy for estimating a plausibly causal effect of land use regulation on land value and welfare. This strategy exploits cross-border changes in development, prices, and regulation in regions near municipal borders. Our estimates suggest large negative effects of regulation on the value of land and welfare in these regions.

Structural Change and the Kaldor Facts in a Growth Model With Relative Price Effects and Non‐Gorman Preferences

Abstract: U.S. data reveal three facts: (1) the share of goods in total expenditure declines at a constant rate over time, (2) the price of goods relative to services declines at a constant rate over time, and (3) poor households spend a larger fraction of their budget on goods than do rich households. I provide a macroeconomic model with non-Gorman preferences that rationalizes these facts, along with the aggregate Kaldor facts. The model is parsimonious and admits an analytical solution. Its functional form allows a decomposition of U.S. structural change into an income and substitution effect. Estimates from micro data show each of these effects to be of roughly equal importance.

Firms, Destinations, and Aggregate Fluctuations

Abstract: This paper uses a database covering the universe of French rms for the period 1990{ 2007 to provide a forensic account of the role of individual rms in generating aggregate uctuations. We set up a simple multi-sector model of heterogeneous rms selling to multiple markets to motivate a theoretically-founded decomposition of rms’ annual sales growth rate into dierent components. We nd that the rm-specic component

Consistency of Higher Order Risk Preferences

Abstract: Risk aversion (a second-order risk preference) is a time-proven concept in economic models of choice under risk. More recently, the higher order risk preferences of prudence (third-order) and temperance (fourth-order) also have been shown to be quite important. While a majority of the population seems to exhibit both risk aversion and these higher order risk preferences, a significant minority does not. We show how both risk-averse and risk-loving behaviors might be generated by a simple type of basic lottery preference for either (1) combining �good� outcomes with �bad� ones, or (2) combining �good with good� and �bad with bad,� respectively. We further show that this dichotomy is fairly robust at explaining higher order risk attitudes in the laboratory. In addition to our own experimental evidence, we take a second look at the extant laboratory experiments that measure higher order risk preferences and we find a fair amount of support for this dichotomy. Our own experiment also is the first to look beyond fourth-order risk preferences, and we examine risk attitudes at even higher orders.

Inferring Labor Income Risk and Partial Insurance From Economic Choices

Abstract: This paper uses the information contained in the joint dynamics of individuals' labor earnings and consumption-choice decisions to quantify both the amount of income risk that individuals face and the extent to which they have access to informal insurance against this risk. We accomplish this task by using indirect inference to estimate a structural consumption�savings model, in which individuals both learn about the nature of their income process and partly insure shocks via informal mechanisms. In this framework, we estimate (i) the degree of partial insurance, (ii) the extent of systematic differences in income growth rates, (iii) the precision with which individuals know their own income growth rates when they begin their working lives, (iv) the persistence of typical labor income shocks, (v) the tightness of borrowing constraints, and (vi) the amount of measurement error in the data. In implementing indirect inference, we find that an auxiliary model that approximates the true structural equations of the model (which are not estimable) works very well, with negligible small sample bias. The main substantive findings are that income shocks are moderately persistent, systematic differences in income growth rates are large, individuals have substantial amounts of information about their income growth rates, and about one-half of income shocks are smoothed via partial insurance. Putting these findings together, the amount of uninsurable lifetime income risk that individuals perceive is substantially smaller than what is typically assumed in calibrated macroeconomic models with incomplete markets.

The intrinsic value of decision rights

Abstract: Philosophers, psychologists, and economists have long argued that certain decision rights carry not only instrumental value but may also be valuable for their own sake. The ideas of autonomy, freedom, and liberty derive their intuitive appeal—at least partly—from an assumed positive intrinsic value of decision rights. Providing clean evidence for the existence of this intrinsic value and measuring its size, however, is intricate. Here, we develop a method capable of achieving these goals. The data reveal that the large majority of our subjects intrinsically value decision rights beyond their instrumental benefit. The intrinsic valuation of decision rights has potentially important consequences for corporate governance, human resource management, and optimal job design: it may explain why managers value power, why employees appreciate jobs with task discretion, why individuals sort into self-employment, and why the reallocation of decision rights is often very difficult and cumbersome. Our method and results may also prove useful in developing an empirical revealed preference foundation for concepts such as "freedom of choice" and "individual autonomy."

Islamic Rule and the Empowerment of the Poor and Pious

Abstract: Does Islamic political control affect women's empowerment? Several countries have recently experienced Islamic parties coming to power through democratic elections. Due to strong support among religious conservatives, constituencies with Islamic rule often tend to exhibit poor women's rights. Whether this reflects a causal relationship or a spurious one has so far gone unexplored. I provide the first piece of evidence using a new and unique data set of Turkish municipalities. In 1994, an Islamic party won multiple municipal mayor seats across the country. Using a regression discontinuity (RD) design, I compare municipalities where this Islamic party barely won or lost elections. Despite negative raw correlations, the RD results reveal that, over a period of six years, Islamic rule increased female secular high school education. Corresponding effects for men are systematically smaller and less precise. In the longer run, the effect on female education remained persistent up to 17 years after, and also reduced adolescent marriages. An analysis of long-run political effects of Islamic rule shows increased female political participation and an overall decrease in Islamic political preferences. The results are consistent with an explanation that emphasizes the Islamic party's effectiveness in overcoming barriers to female entry for the poor and pious.

Random Choice as Behavioral Optimization

Abstract: We develop an extension of Luce's random choice model to study violations of the weak axiom of revealed preference. We introduce the notion of a stochastic preference and show that it implies the Luce model. Then, to address well-known difficulties of the Luce model, we define the attribute rule and establish that the existence of a well-defined stochastic preference over attributes characterizes it. We prove that the set of attribute rules and random utility maximizers are essentially the same. Finally, we show that both the Luce and attribute rules have a unique consistent extension to dynamic problems.vskip=-17.5pt]Author: please provide at least three Key Words that describe the article.

Forced Coexistence and Economic Development: Evidence From Native American Reservations

Abstract: There are large differences in economic development across Native American reservations today. This paper asks whether these differences can be in part explained by the forced integration of historically autonomous sub-tribal bands in the 19th century. To measure forced integration, I combine anthropological data on intra-tribal political integration in pre-reservation times with historical information on the constituent bands of each reservation. Exploring variation in how politically integrated tribes were before reservations and variation in how politically integrated reservations were at the time of their formation, I find that forced integration lowers per capita incomes today by about 30 percent. To account for potential selection into forced integration, I exploit historical mining rushes as a source of exogenous variation in the government’s incentive to combine bands onto reservations. The IV strategy confirms the baseline results. I also provide quantitative evidence on the channels through which forced integration affects incomes today.

The elite illusion: achievement effects at boston and new york exam schools

Abstract: Parents gauge school quality in part by the level of student achievement and a school's racial and socioeconomic mix. The importance of school characteristics in the housing market can be seen in the jump in house prices at school district boundaries where peer characteristics change. The question of whether schools with more attractive peers are really better in a value-added sense remains open, however. This paper uses a fuzzy regression-discontinuity design to evaluate the causal effects of peer characteristics. Our design exploits admissions cutoffs at Boston and New York City's heavily over-subscribed exam schools. Successful applicants near admissions cutoffs for the least selective of these schools move from schools with scores near the bottom of the state SAT score distribution to schools with scores near the median. Successful applicants near admissions cutoffs for the most selective of these schools move from above-average schools to schools with students whose scores fall in the extreme upper tail. Exam school students can also expect to study with fewer nonwhite classmates than unsuccessful applicants. Our estimates suggest that the marked changes in peer characteristics at exam school admissions cutoffs have little causal effect on test scores or college quality.

Endogenous Liquidity and Defaultable Bonds

Abstract: This paper studies the interaction between default and liquidity for corporate bonds that are traded in an over-the-counter secondary market with search frictions. Bargaining with dealers determines a bond's endogenous liquidity, which depends on both the firm fundamental and the time-to-maturity of the bond. Corporate default decisions interact with the endogenous secondary market liquidity via the rollover channel. A default-liquidity loop arises: Assuming a relative illiquid secondary bond market in default, earlier endogenous default worsens a bond's secondary market liquidity, which amplifies equity holders' rollover losses, which in turn leads to earlier endogenous default. Besides characterizing in closed form the full interdependence between liquidity and default for credit spreads, our calibrated model can jointly match empirically observed credit spreads and liquidity measures of bonds across different rating classes.

Bounded Memory and Biases in Information Processing

Abstract: Before choosing among two actions with state-dependent payoffs, a Bayesian decision-maker with a finite memory sees a sequence of informative signals, ending each period with fixed chance. He summarizes information observed with a finite-state automaton. I characterize the optimal protocol as an equilibrium of a dynamic game of imperfect recall; a new player runs each memory state each period. Players act as if maximizing expected payoffs in a common finite action decision problem. I characterize equilibrium play with many multinomial signals. The optimal protocol rationalizes many behavioral phenomena, like �stickiness,� salience, confirmation bias, and belief polarization.

Price Setting with menu cost for Multi-product firms

Abstract: We model the decisions of a multiproduct firm that faces a fixed �menu� cost: once it is paid, the firm can adjust the price of all its products. We characterize analytically the steady state firm's decisions in terms of the structural parameters: the variability of the flexible prices, the curvature of the profit function, the size of the menu cost, and the number of products sold. We provide expressions for the steady state frequency of adjustment, the hazard rate of price adjustments, and the size distribution of price changes, all in terms of the structural parameters. We study analytically the impulse response of aggregate prices and output to a monetary shock. The size of the output response and its duration both increase with the number of products; they more than double as the number of products goes from 1 to 10, quickly converging to the response of Taylor's staggered price model.

Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection

Abstract: In this paper, we describe a series of laboratory experiments that implement specific examples of a general network structure. Specifically, actions are either strategic substitutes or strategic complements, and participants have either complete or incomplete information about the structure of a random network. Since economic environments typically have a considerable degree of complementarity or substitutability, this framework applies to a wide variety of settings. We examine behavior and equilibrium selection. The degree of equilibrium play is striking, in particular with incomplete information. Behavior closely resembles the theoretical equilibrium whenever this is unique; when there are multiple equilibria, general features of networks, such as connectivity, clustering, and the degree of the players, help to predict informed behavior in the lab. People appear to be strongly attracted to maximizing aggregate payoffs (social efficiency), but there are forces that moderate this attraction: (1) people seem content with (in the aggregate) capturing only the lion's share of the efficient profits in exchange for reduced exposure to loss, and (2) uncertainty about the network structure makes it considerably more difficult to coordinate on a demanding, but efficient, equilibrium that is typically implemented with complete information.

Stable Matching With Incomplete Information

Abstract: We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of complete-information stable outcomes. We then provide sucient conditions for incomplete-information stable matchings to be ecient. Lastly, we dene a notion of price sustainable allocations and show that the set of incomplete- information stable matchings is a subset of the set of such allocations.

On Confidence Intervals for Autoregressive Roots and Predictive Regression

Abstract: Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + c/n), but are shown here to be invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Failure at the boundary implies that these CIs have zero asymptotic coverage probability in the stationary case and vicinities of unity that are wider than O(n−1/3). The inversion methods of Hansen (1999) and Mikusheva (2007) are asymptotically valid in such cases. Implications of these results for predictive regression tests are explored. When the predictive regressor is stationary, the popular Campbell and Yogo (2006) CIs for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious cautionary implications for the use of the procedures in empirical practice.

No‐Betting‐Pareto Dominance

Abstract: We argue that the notion of Pareto dominance is not as compelling in the presence of uncertainty as it is under certainty. In particular, voluntary trade based on differences in tastes is commonly accepted as desirable, because tastes cannot be wrong. By contrast, voluntary trade based on incompatible beliefs may indicate that at least one agent entertains mistaken beliefs. We propose and characterize a weaker, No-Betting, notion of Pareto domination which requires, on top of unanimity of preference, the existence of shared beliefs that can rationalize such preference for each agent.

Identification in Differentiated Products Markets Using Market Level Data

Abstract: We present new identification results for nonparametric models of differentiated products markets, using only market level observables. We specify a nonparametric random utility discrete choice model of demand allowing rich preference heterogeneity, product/market unobservables, and endogenous prices. Our supply model posits nonparametric cost functions, allows latent cost shocks, and nests a range of standard oligopoly models. We consider identification of demand, identification of changes in aggregate consumer welfare, identification of marginal costs, identification of firms' marginal cost functions, and discrimination between alternative models of firm conduct. We explore two complementary approaches. The first demonstrates identification under the same nonparametric instrumental variables conditions required for identification of regression models. The second treats demand and supply in a system of nonparametric simultaneous equations, leading to constructive proofs exploiting exogenous variation in demand shifters and cost shifters. We also derive testable restrictions that provide the first general formalization of Bresnahan's (1982) intuition for empirically distinguishing between alternative models of oligopoly competition. From a practical perspective, our results clarify the types of instrumental variables needed with market level data, including tradeoffs between functional form and exclusion restrictions.