Sufficient Statistics Approach Research Articles

Trade and Inequality: A Sufficient-Statistics Approach

Trade and Inequality: A Sufficient-Statistics Approach

Valuing Financial Data

Abstract How should an investor value financial data? The answer is complicated because it depends on the characteristics of all investors. We develop a sufficient statistics approach that uses equilibrium asset return moments to summarize all relevant information about others’ characteristics. Our approach values public or private data, data about one or many assets, and data relevant for dividends or sentiment. While different data types, of course, have different valuations, heterogeneous investors also value the same data very differently. This finding suggests a low price elasticity for data demand. Heterogeneous investors’ data valuations are also affected very differentially by market illiquidity.

Partially observed optimal control of local and remote controllers

AbstractThe article investigates a networked optimal control problem with one remote controller and local controllers, where each local controller partially observes the local state and sends the observed information to remote controller through an unreliable channel and yet the channels from remote controller to local controllers are perfect. The objective of all the controllers is to cooperate to minimize a common cost function. In order to overcome the difficulties caused by partial observation of state, sufficient statistic of historical data is firstly investigated for a nonlinear non‐Gaussian partial observation model, which takes the same role as that of state in the full observation model. Then, a dynamic programming framework is given for solving the optimal control problem based on the sufficient statistic and common information approach. Furthermore, the explicit closed‐form solution is obtained for a linear‐quadratic‐Gaussian optimal control problem. Finally, a numerical example is given to show the effectiveness of the obtained results of this article.

The Two-Margin Problem in Insurance Markets.

Insurance markets often feature consumer sorting along both an extensive margin (whether to buy) and an intensive margin (which plan to buy). We present a new graphical theoretical framework that extends a workhorse model to incorporate both selection margins simultaneously. A key insight from our framework is that policies aimed at addressing one margin of selection often involve an economically meaningful trade-off on the other margin in terms of prices, enrollment, and welfare. Using data from Massachusetts, we illustrate these trade-offs in an empirical sufficient statistics approach that is tightly linked to the graphical framework we develop.

Sufficient statistics for frictional wage dispersion and growth

This paper develops a sufficient statistics approach for estimating the role of search frictions in wage dispersion and life‐cycle wage growth. We show how the wage dynamics of displaced workers are directly informative of both for a large class of search models. Specifically, the correlation between pre‐ and post‐displacement wages is informative of frictional wage dispersion. Furthermore, the fraction of displaced workers who suffer a wage loss is informative of frictional wage growth and job‐to‐job mobility, independent of the job‐offer distribution and other labor‐market parameters. Applying our methodology to US data, we find that search frictions account for less than 20% of wage dispersion. In addition, we estimate that between 40 to 80% of workers experience no frictional wage growth during an employment spell. Our approach allows us to estimate how frictions change over time. We find that frictional wage dispersion has declined substantially since 1980 and that frictional wage growth, while low, is more important toward the end of expansionary periods. We finish by estimating two versions of a random search model to show how at least two different mechanisms—involuntary job transitions or compensating differentials—can reconcile our results with the job‐to‐job mobility seen in the data. Regardless of the mechanism, the estimated models show that frictional wage growth accounts for about 15% of life‐cycle wage growth.

A sufficient statistics approach for welfare analysis of oligopolistic third‐degree price discrimination

This paper proposes a sufficient statistics approach to studying the welfare effects of third-degree price discrimination in differentiated oligopoly. Specifically, our sufficient conditions for price discrimination to increase or decrease social welfare simply entail a cross-market comparison of multiplications of such sufficient statistics as pass-through, conduct, and profit margin that are functions of first-order and second-order elasticities of the firm’s demand. Notably, these results are derived under a general class of market demand, and can be readily extended to accommodate heterogeneous firms. These features suggest that our approach has potential for conducting welfare analysis without a full specification of an oligopoly model.

Robots, Trade, and Luddism: A Sufficient Statistic Approach to Optimal Technology Regulation

Abstract Technological change, from the advent of robots to expanded trade opportunities, creates winners and losers. How should government policy respond? We provide a general theory of optimal technology regulation in a second-best world, with rich heterogeneity across households, linear taxes on the subset of firms affected by technological change, and a non-linear tax on labour income. Our first set of results consists of optimal tax formulas, with minimal structural assumptions, involving sufficient statistics that can be implemented using evidence on the distributional impact of new technologies, such as robots and trade. Our final results are comparative static exercises illustrating, among other things, that while distributional concerns create a rationale for non-zero taxes on robots and trade, the magnitude of these taxes may decrease as the process of automation and globalization deepens and inequality increases.

A first aid kit to assess welfare impacts

We develop a simple framework to measure the impacts of an economic shock on unemployed workers’ welfare quantitatively. We follow the sufficient statistics approach in consulting traditional economic models, and use a standard job search model to derive the sufficient statistics to identify the impacts. We then apply our framework to assess the impacts of the coronavirus disease 2019 (COVID-19) by using regional data of the United States, and international data. Analysis reveals the regions and countries that are severely damaged by the COVID-19.

Sufficient Statistics Revisited

This article reviews and generalizes the sufficient statistics approach to policy evaluation. The idea of the approach is that the welfare effect of policy changes can be expressed in terms of estimable reduced-form elasticities, allowing for policy evaluation without estimating the structural primitives of fully specified models. The approach relies on three assumptions: that policy changes are small, that government policy is the only source of market imperfection, and that a set of high-level restrictions on the environment and on preferences can be used to reduce the number of elasticities to be estimated. We generalize the approach in all three dimensions. It is possible to develop transparent sufficient statistics formulas under very general conditions, but the estimation requirements increase greatly. Starting from such general formulas elucidates that feasible empirical implementations are in fact structural approaches.

A Menu of Insurance Contracts for the Unemployed

Abstract Unemployment insurance (UI) programs traditionally take the form of a single insurance contract offered to job seekers. In this work, we show that offering a menu of contracts can be welfare improving in the presence of adverse selection and moral hazard. When insurance contracts are composed of (1) a UI payment and (2) a severance payment paid at the onset of unemployment, offering contracts with different ratios of UI benefits to severance payment is optimal under the equivalent of a single-crossing condition: job seekers in higher need of unemployment insurance should be less prone to moral hazard. In that setting, a menu allows the planner to attract job seekers with a high need for insurance in a contract with generous UI benefits, and to attract job seekers most prone to moral hazard in a separate contract with a large severance payment but little unemployment insurance. We propose a simple sufficient statistics approach to test the single-crossing condition in the data.

Second-Best Source-Based Taxation of Multinational Firms

I consider a continuum of multinational enterprises (MNEs), which differ in profitability. MNEs employ capital, shift profit to tax havens and may relocate their production facilities to other countries. Source countries provide public inputs and levy taxes. I derive optimal policy choices for different government objectives (to maximize tax revenue, national income or the representative household’s utility) allowing for an unrestricted set of tax policy instruments — in contrast to most existing work on corporate taxation. With observable productivity types, source governments set type-dependent lump-sum taxes and attain the first-best allocation. With unobservable productivity types, the optimum source-based tax system consists of a small lump-sum tax (driving low-profit types out of the market) and positive marginal taxes on reported profit. Optimal marginal tax rates on capital inputs are positive if more profitable firms employ more capital. Optimal public inputs are lower than in the first best if they are of higher value to more profitable firm types. I use a sufficient statistics approach (following Saez 2001) to express optimal tax and input choices as functions of elasticities of observable choice variables. Finally, I use the model to evaluate tax policy measures, e.g. the introduction of an effective minimum tax on profits in tax havens, and to derive the welfare properties of tax competition with an unrestricted set of tax instruments.

Taxing Capital in the Presence of Trickle Down Effects: A Sufficient Statistics Approach

Within a rich dynamic environment I derive a robust and testable condition for the optimality of capital income tax rates. I apply this condition to US data. Endogenous responses of factor prices mitigate welfare gains of capital tax increases for a large fraction of the population, who derives most of its disposable income from net wages. However, due to a positive revenue impact, the same price responses amplify the welfare gains of the very bottom of the income distribution, whose main income source are government transfers. As a consequence, general equilibrium forces may increase the optimal capital tax rate relative to its exogenous price counterpart, contradicting conventional wisdom.

Welfare Effects of Property Taxation

We analyze the welfare implications of property taxation. Using a sufficient statistics approach, we show that the tax incidence depends on how housing prices, labor and other types of incomes as well as public services respond to property tax changes. Empirically, we exploit the German institutional setting with 5,200 municipal tax reforms for identification. We find that higher taxes are fully passed on to rental prices after three years. The pass-through is lower when housing supply is inelastic. Combining reduced form estimates with our theoretical framework, we simulate the welfare effects of property taxes and show that they are regressive.

Demographics, Wealth, and Global Imbalances in the Twenty-First Century

We use a sufficient statistic approach to quantify the general equilibrium effects of population aging on wealth accumulation, expected asset returns, and global imbalances. Combining population forecasts with household survey data from 25 countries, we measure the compositional effect of aging: how a changing age distribution affects wealth-to-GDP, holding the age profiles of assets and labor income fixed. In a baseline overlapping generations model this statistic, in conjunction with cross-sectional information and two standard macro parameters, pins down general equilibrium outcomes. Since the compositional effect is positive, large, and heterogeneous across countries, our model predicts that population aging will increase wealth-to-GDP ratios, lower asset returns, and widen global imbalances through the twenty-first century. These conclusions extend to a richer model in which bequests, individual savings, and the tax-and-transfer system all respond to demographic change.

Demographics, Wealth, and Global Imbalances in the Twenty-First Century

We use a sufficient statistic approach to quantify the general equilibrium effects of population aging on wealth accumulation, expected asset returns, and global imbalances. Combining population forecasts with household survey data from 25 countries, we measure the compositional effect of aging: how a changing age distribution affects wealth-to-GDP, holding the age profiles of assets and labor income fixed. In a baseline overlapping generations model this statistic, in conjunction with cross-sectional information and two standard macro parameters, pins down general equilibrium outcomes. Since the compositional effect is positive, large, and heterogeneous across countries, our model predicts that population aging will increase wealth-to- GDP ratios, lower asset returns, and widen global imbalances through the twenty-first century. These conclusions extend to a richer model in which bequests, individual savings, and the tax-and-transfer system all respond to demographic change.

The cost of a global tariff war: A sufficient statistics approach

Tariff wars have reemerged as a serious threat to the global economy. Yet measuring the prospective cost of a global tariff war remains computationally prohibitive, unless we restrict attention to a small set of countries and industries. This paper develops a new methodology that measures the cost of a global tariff war in one simple step as a function of observable shares, industry-level trade elasticities, and markup wedges. Applying this methodology to data on 44 countries and 56 industries, I find that (i) the prospective cost of a global tariff war has more-than-doubled over the past fifteen years, with small downstream economies being the most vulnerable. (ii) Meanwhile, due to the rise of global markup distortions, the potential gains from cooperative tariff policies have also elevated to unprecedented levels.

Dynamic Taxation

This article reviews recent advances in the study of dynamic taxation, considering three main approaches: the dynamic Mirrlees, the parametric Ramsey, and the sufficient statistics approaches. In the first approach, agents’ heterogeneous abilities to earn income are private information and evolve stochastically over time. Dynamic taxes are not restricted ex ante and are set for redistribution and insurance considerations. Capital is taxed only in order to improve incentives to work. Human capital is optimally subsidized if it reduces posttax inequality and risk on balance. The Ramsey approach specifies ex ante restricted tax instruments and adopts quantitative methods, which allow it to consider more complex and realistic economies. Capital taxes are optimal when age-dependent labor income taxes are not possible. The newer and tractable sufficient statistics approach derives robust tax formulas that depend on estimable elasticities and features of the income distributions. It simplifies the transitional dynamics thanks to a newly defined criterion, the utility-based steady-state approach, which prevents the government from exploiting sluggish responses in the short run. Capital taxes are here based on the standard equity-efficiency trade-off.

Estimating the welfare costs of autarky: A sufficient statistics approach

This paper uses the Jeffersonian Embargo enacted in 1807 to estimate the welfare costs of autarky. I use an Armington trade model to compute the welfare losses using two sufficient statistics: the share of expenditures on domestic goods and the elasticity of substitution between domestic and imported goods. I use historical data from 1792 to 1807 to estimate the Armington elasticity, using import tariffs as instrument for relative prices. The empirical findings suggest welfare losses of 2.83–8.14% of real income.

Can global uncertainty promote international trade?

Common wisdom holds that uncertainty impedes trade—yet we show that uncertainty can fuel more trade in a simple general equilibrium trade model with information frictions. In equilibrium, increases in uncertainty increase both the mean and variance in returns to exporting. This implies that trade can increase or decrease with uncertainty, depending on preferences. Under general conditions on preferences, we characterize the importance of these forces using a sufficient statistics approach. Higher uncertainty leads to increases in trade because agents receive improved terms of trade, particularly in states of nature in which consumption is most valuable. Trade creates value, in part, by offering a mechanism for risk sharing, and risk sharing is most effective when both parties are uninformed.

Malas notches

This paper shows that the sufficient statistic approach to the welfare properties of income (and other) taxes does not easily extend to tax systems with notches, because with notches, changes in bunching induced by changes in tax rates have a first-order effect on tax revenues. In an income tax setting, we show that the marginal excess burden (MEB) of a change in the top rate of tax is given by the Feldstein (Rev Econ Stat 81(4):674–680, 1999) formula for the MEB of a proportional tax, plus a correction term. This formula applies even if there is tax evasion. These correction terms cannot be calculated just from knowledge of the elasticity of taxable income, and quantitatively, they can be large. An application to VAT is discussed; with a calibration to UK data, the MEB of the VAT is roughly three times what it would be if VAT was simply a proportional tax.