Social and Behavioral Sciences Commons^™

Physical Decline Rates: Men Versus Women, Ray C. Fair

Cowles Foundation Discussion Papers

This paper uses world records by age in running, swimming, and rowing to estimate a biological frontier of decline rates for both men and women. Decline rates are assumed to be linear in percent terms up to a certain age and then quadratic after that, where the transition age is estimated. The use of world records avoids the possible problem of survivor bias in a sample. The decline rates are smallest for rowing, followed by swimming and then running. Decline rates for women are roughly the same as those for men for the swimming events. They are slightly larger for …

Inflation Expectations, Price Equations, And Fed Effects, Ray C. Fair

Cowles Foundation Discussion Papers

This paper makes three main contributions. First, inflation expectation equations are estimated using quarterly time series data. Second, a price equation in level form is estimated that is consistent with the data, unlike Phillips-curve equations. Third, the case is considered in which an expectation variable in an inflation or price equation is not causal.

The results suggest that household inflation expectations are mostly affected by current and past inflation. The Fed through interest rates has a modest effect. In the estimated price equation a measure of the expected future price level is significant, although it may not be causal. Whether …

A Non-Envelope Theorem With Linearly Homogeneous Constraints, Eduardo Dávila, Andreas Schaab

Cowles Foundation Discussion Papers

This paper shows that it is possible to define an unambiguous notion of the direct effect of a parameter perturbation on the value of an optimization problem’s objective away from an optimum for problems with linearly homogeneous constraints. This notion of the direct effect relies on reformulating the optimization problem using shares as choice variables, and has the interpretation of holding choice variables — when formulated as shares — fixed. This short paper contains one formal “non-envelope” theorem and four applications to i) consumer demand, ii) cost minimization, iii) planning in exchange economies, and iv) planning in production economies.

Labor Market Matching, Wages, And Amenities, Thibaut Lamadon, Jeremy Lise, Costas Meghir, Jean-Marc Robin

Cowles Foundation Discussion Papers

This paper develops the nonparametric identification of models with production complementarities, worker-firm specific disutility of labor and search frictions. Mobility in the model is subject to preference shocks, and we assume that firms can write wage contracts. We develop a constructive proof for the nonparametric identification of the model primitives from matched employer-employee data. We use the estimated model to decompose the sources of wage dispersion into worker heterogeneity, compensating differentials, and search frictions that generate between-firm and within-firm dispersion. We find that compensating differentials are substantial on average, but the contribution differs greatly between the lowest and highest types …

Direct And Indirect Taxes In Pollution Dynamics, Vladimir Smirnyagin, Aleh Tsyvinski, Xi Wu

Cowles Foundation Discussion Papers

Analyzing the universe of federal environmental regulations in the U.S., we construct a measure of regulations—direct taxes on pollution. Analyzing the universe of firms’ investor disclosures, we construct a measure of material environmental concerns—indirect taxes on pollution. These two empirical measures are new to the environmental regulations literature. Thirdly, we document an important new fact that the cross-sectional distribution of pollution changes is lumpy. We build a dynamic heterogeneous firm model with non-convex adjustment costs that fits the cross-sectional pollution evidence. The model explains half of the pollution decline in U.S. manufacturing over the last two decades due to direct …

Inefficiencies Of Carbon Trading Markets, Nicola Borri, Yukun Liu, Aleh Tsyvinski, Xi Wu

Cowles Foundation Discussion Papers

The European Union Emission Trading System is a prominent market-based mechanism to reduce emissions. While the theory is well-understood, we are the first to study the whole cap-and-trade mechanism as a financial market. Analyzing the universe of transactions in 2005-2020 (more than one million records of granular transaction data), we show that this market features significant inefficiencies undermining its goals. First, about 40% of firms never trade in a given year. Second, many firms only trade during surrendering months, when compliance is immediate and prices are predictably high. Third, a number of operators engage in speculative trading, exploiting private information.

A General Limit Theory For Nonlinear Functionals Of Nonstationary Time Series, Peter C. B. Phillips, Qiying Wang

Cowles Foundation Discussion Papers

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self normalized statistics …

Intrahousehold Welfare: Theory And Application To Japanese Data, Pierre-André Chiappori, Costas Meghir, Yoko Okuyama

Cowles Foundation Discussion Papers

In this paper we develop a novel approach to measuring individual welfare within house-holds, recognizing that individuals may have both different preferences (particularly regarding public consumption) and differential access to resources. We construct a money metric mea-sure of welfare that accounts for public goods (by using personalized prices) and the allocation of time. We then use our conceptual framework to analyse intrahousehold inequality in Japan, allowing for the presence of two public goods: expenditures on children and other public goods including housing. We show empirically that women have much stronger preferences for both public goods and this has critical implications …

Limit Theory Of Local Polynomial Estimation In Functional Coefficient Regression, Ying Wang, Peter C. B. Phillips

Cowles Foundation Discussion Papers

Limit theory for functional coefficient cointegrating regression was recently found to be considerably more complex than earlier understood. The issues were explained and correct limit theory derived for the kernel weighted local constant estimator in Phillips and Wang (2023b). The present paper provides complete limit theory for the general kernel weighted local p-th order polynomial estimator of the functional coefficient and the coefficient deriva-tives. Both stationary and nonstationary regressors are allowed. Implications for bandwidth selection are discussed. An adaptive procedure to select the fit order p is proposed and found to work well. A robust t-ratio is constructed following the …

Dynamic Price Competition With Capacity Constraints, Jose M. Betancourt, Ali Hortaçsu, Aniko Öry, Kevin R. Williams

Cowles Foundation Discussion Papers

We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with …

On The Alignment Of Consumer Surplus And Total Surplus Under Competitive Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

Producers of heterogeneous goods with heterogeneous costs compete in prices. When producers know their own production costs and the consumer knows their values, consumer surplus and total surplus are aligned: the information structure and equilibrium that maximize consumer surplus also maximize total surplus. We report when alignment extends to the case where either the consumer is uncertain about their own values or producers are uncertain about their own costs, and we also give examples showing when it does not. Less information for either producers or consumer may intensify competition in a way that benefits the consumer but results in inefficient …

Stride: A Tool-Assisted Llm Agent Framework For Strategic And Interactive Decision-Making, Chuanhao Li, Runhan Yang, Tiankai Li, Milad Bafarassat, Kourosh Sharifi, Dirk Bergemann, Zhuoran Yang

Cowles Foundation Discussion Papers

Large Language Models (LLMs) like GPT-4 have revolutionized natural language processing, showing remarkable linguistic proficiency and reasoning capabilities. However, their application in strategic multi-agent decision-making environments is hampered by significant limitations including poor mathematical reasoning, difficulty in following instructions, and a tendency to generate incorrect information. These deficiencies hinder their performance in strategic and interactive tasks that demand adherence to nuanced game rules, long-term planning, exploration in unknown environments, and anticipation of opponents’ moves. To overcome these obstacles, this paper presents a novel LLM agent framework equipped with memory and specialized tools to enhance their strategic decision-making capabilities. We deploy …

Approximating Choice Data By Discrete Choice Models, Haoge Chang, Yusuke Narita, Kota Saito

Cowles Foundation Discussion Papers

We obtain a necessary and sufficient condition under which random-coefficient discrete choice models, such as mixed-logit models, are rich enough to approximate any nonparametric random utility models arbitrarily well across choice sets. The condition turns out to be the affine-independence of the set of characteristic vectors. When the condition fails, resulting in some random utility models that cannot be closely approximated, we identify preferences and substitution patterns that are challenging to approximate accurately. We also propose algorithms to quantify the magnitude of approximation errors.

Algorithm As Experiment: Machine Learning, Market Design, And Policy Eligibility Rules, Yusuke Narita, Kohei Yata

Cowles Foundation Discussion Papers

Algorithms make a growing portion of policy and business decisions. We develop a treatment-effect estimator using algorithmic decisions as instruments for a class of stochastic and deterministic algorithms. Our estimator is consistent and asymptotically normal for well-defined causal effects. A special case of our setup is multidimensional regression discontinuity designs with complex boundaries. We apply our estimator to evaluate the Coronavirus Aid, Relief, and Economic Security Act, which allocated many billions of dollars worth of relief funding to hospitals via an algorithmic rule. The funding is shown to have little effect on COVID-19-related hospital activities. Naive estimates exhibit selection bias.

Meritocracy And Its Discontents: Long-Run Effects Of Repeated School Admission Reforms, Chiaki Moriguchi, Yusuke Narita, Mari Tanaka

Cowles Foundation Discussion Papers

What happens if selective colleges change their admission policies? We study this question by analyzing the world’s first implementation of nationally centralized meritocratic admissions in the early twentieth century. We find a persistent meritocracy-equity tradeoff. Compared to the decentralized system, the centralized system admitted more high-achievers and produced more occupational elites (such as top income earners) decades later in the labor market. This gain came at a distributional cost, however. Meritocratic centralization also increased the number of urban-born elites relative to rural-born ones, undermining equal access to higher education and career advancement.

Inference In A Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model, Donald W.K. Andrews, Ming Li

Cowles Foundation Discussion Papers

This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in some time periods, time-varying nonstationarity (i.e., unit root or local-to-unit root behavior) in other periods, and smooth transitions between the two. The estimation of the AR parameter at any time point is based on a local least squares regression method, where the relevant initial condition is endogenous. We obtain limit distributions for the AR parameter estimator and t-statistic at a given point τ in time when the parameter exhibits unit …

Teaching Financial Econometrics To Students Converting To Finance, Stan Hurn, Peter C. B. Phillips, Vance Martin, Jun Yu

Cowles Foundation Discussion Papers

Financial econometrics is a dynamic discipline that began to take on its present form around the turn of the century. Since then it has found a permanent position as a popular course sequence in both undergraduate and graduate teaching programs in economics, finance, and business schools. Because of the breadth of the subject’s foundations, its extensive coverage in applications and because these courses attract a wide range of students with accompanying interests and skill sets that cover diverse areas and technical capabilities, teaching financial econometrics presents many challenges to the university educator. This chapter addresses some of these challenges, provides …

Supply Chain Disruptions And Supplier Capital In U.S. Firms, Ernest Liu, Vladimir Smirnyagin, Aleh Tsyvinski

Cowles Foundation Discussion Papers

We empirically and quantitatively study the impact of supply chain disruptions on U.S. businesses. Leveraging granular shipment-level data on the universe of U.S. seaborne imports with nearly 200 million observations, we construct a measure of disruptions at the individual firm level for the time period 2013-2023. We document a significant heterogeneity in disruption rates among U.S. public firms, with a notable increase observed in recent years. We introduce a notion of supplier capital and investigate the effect of supply disruptions on firms’ investment decisions. In the data, firms tend to increase investment in supplier capital following the shock, however, financially …

Self-Weighted Estimation For Local Unit Root Regression With Applications, Zhishui Hu, Nan Liu, Peter C. B. Phillips, Qiying Wang

Cowles Foundation Discussion Papers

A new self-weighted least squares (LS) estimation theory is developed for local unit root (LUR) autoregression with heteroskedasticity. The proposed estimator has a mixed Gaussian limit distribution and the corresponding studentized statistic converges to a standard normal distribution free of the unknown localizing coefficient which is not consistently estimable. The estimator is super consistent with a convergence rate slightly below the OP (n) rate of LS estimation. The asymptotic theory relies on a new framework of convergence to the local time of a Gaussian process, allowing for the sample moments generated from martingales and many other integrated dependent sequences. A …

Personalization And Privacy Choice, Andrew Rhodes, Jidong Zhou

Cowles Foundation Discussion Papers

This paper studies consumers’ privacy choices when firms can use their data to make personalized offers. We first introduce a general framework of personalization and privacy choice, and then apply it to personalized recommendations, personalized prices, and personalized product design. We argue that due to firms’ reaction in the product market, consumers who share their data often impose a negative externality on other consumers. Due to this privacy-choice externality, too many consumers share their data relative to the consumer optimum; moreover, more competition, or improvements in data security, can lower consumer surplus by encouraging more data sharing.

Limit Theory And Inference In Non-Cointegrated Functional Coefficient Regression, Ying Wang, Yundong Tu, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Functional coefficient (FC) cointegrating regressions offer empirical investigators flexibility in modeling economic relationships by introducing covariates that influence the direction and intensity of comovement among nonstationary time series. FC regression models are also useful when formal cointegration is absent, in the sense that the equation errors may themselves be nonstationary, but where the nonstationary series display well-defined FC linkages that can be meaningfully interpreted as correlation measures involving the covariates. The present paper proposes new nonparametric estimators for such FC regression models where the nonstationary series display linkages that enable consistent estimation of the correlation measures between them. Specifically, we …

Technology And The Global Economy, Jonathan Eaton, Samuel Kortum

Cowles Foundation Discussion Papers

Interpreting individual heterogeneity in terms of probability theory has proved powerful in connecting behaviour at the individual and aggregate levels. Returning to Ricardo's focus on comparative efficiency as a basis for international trade, much recent quantitative equilibrium modeling of the global economy builds on particular probabilistic assumptions about technology. We review these assumptions and how they deliver a unified framework underlying a wide range of static and dynamic equilibrium models.

Earnings Dynamics And Firm-Level Shocks, Benjamin Friedrich, Lisa Laun, Costas Meghir, Luigi Pistaferri

Cowles Foundation Discussion Papers

We use matched employer-employee data from Sweden to study the role of the firm in affecting the stochastic properties of wages. Our model accounts for endogenous participation and mobility decisions. We find that firm-specific permanent productivity shocks transmit to individual wages, but the effect is mostly concentrated among the high-skilled workers. The pass-through of temporary shocks is smaller in magnitude and similar for high- and low-skilled workers. The updates to worker-firm specific match effects over the life of a firm-worker relationship are small. Substantial growth in earnings variance over the life cycle for high-skilled workers is driven by firms. In …

Trade And Domestic Distortions: The Case Of Informality, Rafael Dix-Carneiro, Pinelopi K. Goldberg, Costas Meghir, Gabriel Ulyssea

Cowles Foundation Discussion Papers

We examine the effects of international trade in the presence of a set of domestic distortions giving rise to informality, a prevalent phenomenon in developing countries. In our quantitative model, the informal sector arises from burdensome taxes and regulations that are imperfectly enforced by the government. Consequently, smaller, less productive firms face fewer distortions than larger, more productive ones, potentially leading to substantial misallocation. We show that in settings with a large informal sector, the gains from trade are significantly amplified, as reductions in trade barriers imply a reallocation of resources from initially less distorted to more distorted firms. We …

Bidder-Optimal Information Structures In Auctions, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

We characterize the bidders' surplus maximizing information structure in an optimal auction for a single unit good and related extensions to multi-unit and multi-good problems. The bidders seek to find a balance between participation (and the avoidance of exclusion) and efficiency. The information structure that maximizes the bidders' surplus is given by a generalized Pareto distribution at the center of demand distribution, and displays complete information disclosure at either end of the Pareto distribution.

A Unified Approach To Second And Third Degree Price Discrimination, Dirk Bergemann, Tibor Heumann, Michael C. Wang

Cowles Foundation Discussion Papers

We analyze the welfare impact of a monopolist able to segment a multiproduct market and offer differentiated price menus within each segment. We characterize a family of extremal distributions such that all achievable welfare outcomes can be reached by selecting segments from within these distributions. This family of distributions arises as the solution to the consumer maximizing distribution of values for multigood markets. With these results, we analyze the effect of segmentation on consumer surplus and prices in both interior and extremal markets, including conditions under which there exists a segmentation benefiting all consumers. Finally, we present an efficient algorithm …

Aiming For The Goal: Contribution Dynamics Of Crowdfunding, Joyee Deb, Aniko Öry (Oery), Kevin R. Williams

Cowles Foundation Discussion Papers

We study a dynamic contribution game where investors seek private benefits that are offered in exchange for contributions and a single, publicly-minded donor values project success. We show that donor contributions serve as costly signals that encour-age socially-productive contributions by investors who face a coordination problem. Investors and the donor prefer different equilibria but all benefit in expectation from the donor’s ability to dynamically signal his valuation. We explore various contexts in which our model can be applied and delve empirically into the case of Kickstarter. We calibrate our model and quantify the coordination benefits of dynamic signaling in counterfactuals.

Bidder-Optimal Information Structures In Auctions, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

We characterize the bidders' surplus maximizing information structure in an optimal auction for a single unit good and related extensions to multi-unit and multi-good problems. The bidders seeks to find a balance between participation (and the avoidance of exclusion) and efficiency. The information structure that maximizes the bidders surplus is given by a generalized Pareto distribution at the center of demand distribution, and displays complete information disclosure at either end of the Pareto distribution.

An Interview Study Of Pricing, Truman F. Bewley

Cowles Foundation Discussion Papers

Why do the prices of some products change little during business cycles while the prices of others vary wildly and tend to rise during economic booms and fall during recessions? In particular, why do the prices of some products not fall or fall only a little when the demand for them declines dramatically. It is not surprising that in highly competitive industries prices fluctuate with shifts in demand and supply, but what explains the stability of prices in markets where firms have more direct control of prices? These questions are central to an understanding of business cycles, and good answers …

On The Alignment Of Consumer Surplus And Total Surplus Under Competitive Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

A number of producers of heterogeneous goods with heterogeneous costs compete in prices. When producers know their own production costs and consumers know their values, consumer surplus and total surplus are aligned: the information structure and equilibrium that maximize consumer surplus also maximize total surplus. We report when alignment extends to the case where either consumers are uncertain about their own values or producers are uncertain about their own costs, and we also give examples showing when it does not. Less information for either producers or consumers may intensify competition in a way that benefits consumers but results in inefficient …