Social and Behavioral Sciences Commons^™

A Strategic Topology On Information Structures, Dirk Bergemann, Stephen Morris, Rafael Veiel

Cowles Foundation Discussion Papers

Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an “almost common knowledge topology” reflecting this notion of closeness. We show that it is the coarsest topology generating continuity of equilibrium outcomes. An information structure is said to be simple if each player has a finite set of types and each type has a distinct first-order belief about payoff states. We show that simple information structures are dense in the almost common knowledge topology and thus it is without loss …

Estimation And Inference In A Possibly Multi-Cointegrated System With A Fixed Number Of Instruments, Yixiao Sun, Peter C.B. Phillips, Igor Kheifets

Cowles Foundation Discussion Papers

This note shows that the mixed normal asymptotic limit of the trend IV estimator with a fixed number of deterministic instruments (fTIV) holds in both singular (multicointegrated) and nonsingular cointegration systems, thereby relaxing the exogeneity condition in (Phillips and Kheifets, 2024, Theorem 1(ii)). The mixed normality of the limiting distribution of fTIV allows for asymptotically pivotal F tests about the cointegration parameters and for simple efficiency comparisons of the estimators for different numbers K of instruments, as well as comparisons with the trend IV estimator when K → ∞ with the sample size.

Wealth, Marriage, And Sex Selection, Girija Borker, Jan Eeckhout, Nancy Luke, Shantidani Minz, Kaivan Munshi, Soumya Swaminathan

Cowles Foundation Discussion Papers

Two mechanisms have been proposed to explain sex selection in India: son preference in which parents desire a male heir and daughter aversion in which dowry payments make parents worse off with girls. Our model incorporates both mechanisms, providing micro-foundations, based on the organization of the marriage institution, for daughter aversion. Marital matching, sex selection, and dowries are jointly determined in the model, whose implications are tested on a representative sample of rural households. Simulations of the model indicate that existing policies targeting daughter aversion might exacerbate the problem, while identifying other policies that could be effective.

Gmm Estimation With Brownian Kernels Applied To Income Inequality Measurement, Jin Seo Cho, Peter C.B. Phillips

Cowles Foundation Discussion Papers

In GMM estimation, it is well known that if the moment dimension grows with the sample size, the asymptotics of GMM differ from the standard finite dimensional case. The present work examines the asymptotic properties of infinite dimensional GMM estimation when the weight matrix is formed by inverting Brownian motion or Brownian bridge covariance kernels. These kernels arise in econometric work such as minimum Cramer-von Mises distance estimation when testing distributional specification. The properties of GMM estimation are studied under different environments where the moment conditions converge to a smooth Gaussian or non-differentiable Gaussian process. Conditions are also developed for …

Welfare Accounting, Eduardo Dávila, Andreas Schaab

Cowles Foundation Discussion Papers

This paper develops a welfare accounting decomposition that identifies and quantifies the origins of welfare gains and losses in general economies with heterogeneous individuals and disaggregated production. The decomposition — exclusively based on preferences and technologies — first separates efficiency from redistribution considerations. Efficiency comprises i) exchange efficiency, which captures allocative efficiency gains due to reallocating consumption and factor supply across individuals, and ii) production efficiency, which captures allocative efficiency gains due to adjusting intermediate inputs and factors, as well as technical efficiency gains from primitive changes in technologies, good endowments, and factor endowments. Leveraging the decomposition, we provide a …

Herding With Heterogeneous Ability: An Application To Organ Transplantation, Stephanie De Mel, Kaivan Munshi, Soenje Reiche, Hamid Sabourian

Cowles Foundation Discussion Papers

There are many economic environments in which an object is offered sequentially to prospective buyers. It is often observed that once the object for sale is turned down by one or more agents, those that follow do the same. One explanation for this phenomenon is that agents making choices further down the line rationally ignore their own assessment of the object and herd behind their predecessors. Our research extends the canonical herding model by allowing agents to differ in their ability to assess the quality of the offered object. We develop novel tests of herding based on this ability heterogeneity …

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 …

Cyclical Time Series: An Empirical Analysis Of Temperatures In Central England Over Three Centuries, Liudas Giraitis, Fulvia Marotta, Peter C.B. Phillips

Cowles Foundation Discussion Papers

This paper builds on methodology that corrects for irregular spacing between realizations of unevenly spaced time series and provides appropriately corrected estimates of autoregressive model parameters. Using these methods for dealing with missing data, we develop time series tools for forecasting and estimation of autoregressions with cyclically varying parameters in which periodicity is assumed. To illustrate the robustness and flexibility of the methodology, an application is conducted to model daily temperature data. The approach helps to uncover cyclical (daily as well as annual) patterns in the data without imposing restrictive assumptions. Using the Central England Temperature (CET) time series (1772 …

Economic Development, Undernutrition And Diabetes, Kaivan Munshi, Swapnil Singh, Nancy Luke, Anu Mary Oommen

Cowles Foundation Discussion Papers

This research connects two seemingly unrelated facts that have recently been documented in developing countries, with important consequences for global health: (i) the weak association between nutritional status and income, and (ii) the elevated risk of diabetes among normalweight individuals. The model that we develop to reconcile these facts is based on a set point for body size that is adapted to (low) pre-modern food supply, but subsequently fails to adjust to rapid economic change. During the process of development, some individuals thus remain at their low-BMI set point, despite the increase in their income (food consumption), while others who …

Community Networks, Entrepreneurship And The Process Of Economic Development, Ruochen Dai, Dilip Mookherjee, Kaivan Munshi, Xiaobo Zhang

Cowles Foundation Discussion Papers

This research examines the determinants of entrepreneurship in China’s transition from agriculture to domestic production in the 1990’s and the subsequent transition to exporting in the 2000’s. The model that we develop and test to describe these transitions incorporates a productivity enhancing role for community (birth county) networks, which emerge in response to market imperfections at early stages of economic development. Using administrative data covering the universe of registered firms over the 1994-2012 period and the universe of exporters over the 2002-2012 period, we provide causal evidence that these networks of firms were active and were effective at increasing the …

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 …

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.

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 …

The Reallocation Effects Of Domestic Outsourcing, Mayara Felix, Michael B. Wong

Cowles Foundation Discussion Papers

This paper estimates the wage, employment, and reallocation effects of non-core activity outsourcing using Brazil’s unexpected 1993 court-ordered outsourcing legalization. We leverage North-South variation in pre-legalization court permissiveness and compare security guards to less affected occupations. We find that older incumbent security guards were adversely impacted through occupational layoffs, loss of firm-level wage premia, and exit from the occupation. At the same time, increased numbers of younger workers entered the formal sector and became employed at contract firms. On net, legalization increased guard employment by 5%, led by a 50% increase in employment for guards aged 18-24, and had no …

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 …

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.

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 …

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 …