Michal Fabinger

Pass-Through as an Economic Tool: Principles of Incidence under Imperfect Competition

We extend five principles of tax incidence under perfect competition to a general model of imperfect competition. The principles cover (1) the independence of physical and economic incidence, the (2) qualitative and (3) quantitative manner in which taxes are split between consumers and producers, (4) the determinants of tax pass-through, and (5) the integration of local incidence to determine the overall division of surplus. We show how these principles can be used to simplify and generalize the analysis of a range of economic questions such as the optimal procurement of new markets and the welfare effects of third-degree price discrimination.

Casimir Effect Between World-Branes in Heterotic M-Theory

We study a non-supersymmetric E_8 × E_8 compactification of M-theory on S^1/Z_2, related to the supersymmetric E_8 × E_8 theory by a chirality flip at one of the boundaries. This system represents an M-theory analog of the D-brane anti-D-brane systems of string theory. Alternatively, this compactification can be viewed as a model of supersymmetry breaking in the “brane-world” approach to phenomenology. We calculate the Casimir energy of the system at large separations, and show that there is an attractive Casimir force between the E_8 × E_8 boundary. We predict that a tachyonic instability develops at separations of order the Planck scale, and discuss the possibility that the M-theory fivebrane might appear as a topological defect supported by the E_8 × E_8 system. Finally, we analyze the eventual fate of the configuration, in the semiclassical approximation at large separations: the two ends of the world annihilate by nucleating wormholes between the two boundaries.

On Smooth Time-Dependent Orbifolds and Null Singularities

We study string theory on a non-singular time-dependent orbifold of flat space. The orbifold group, which involves only space-like identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.

Higher-Dimensional Quantum Hall Effect in String Theory

We construct a string theory realization of the 4+1d quantum Hall effect recently described by Zhang and Hu. The string theory picture contains coincident D4-branes forming an S4 and having D0-branes (i.e. instantons) in their world-volume. The charged particles are modelled as string ends. Their configuration space approaches in the large-N limit a CP3, which is an S2 fibration over S4, the extra S2 being made out of the Chan-Paton degrees of freedom. An alternative matrix theory description involves the fuzzy S4. We also find that there is a hierarchy of quantum Hall effects in odd-dimensional spacetimes, generalizing the known cases in 2+1d and 4+1d.

Stringy Resolutions of Null Singularities

We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form of the metric. As a result, the local nature of any such spacetime can be easily understood. We show that we can view any such geometry as a sequence of solutions to lower-dimensional Euclidean gravity. If we choose the lower-dimensional solutions to degenerate at some light-cone time, we obtain null singularities, which may be thought of as generalizations of the parabolic orbifold singularity. We find that in string theory, many such null singularities get repaired by � 0 -corrections - in particular, by worldsheet instantons. As a consequence, the resulting string theory solutions do not suffer from any instability. Even though the CFT description of these solutions is not always valid, they can still be well understood after taking the effects of light D-branes into account; the breakdown of the worldsheet conformal field theory is purely gauge-theoretic, not involving strong gravitational effects. SLAC-PUB-9636

A Tractable Approach to Pass-Through Patterns

Under imperfect competition the curvature of demand is central to the rate of cost pass-through and thus to incidence and other questions of economic interest. We show that standard functional forms for demand severely and often unrealistically restrict the behavior of pass-through rates. We propose an Adjustable pass-through (Apt) class of demand functions that avoids these restrictions while yielding closed-form solutions to standard models. To illustrate the utility of this generalized demand form we show how to embed it in monopolistic competition. This allows us to apply it to canonical international trade models with heterogeneous firms and provide a natural case in which standard results on the competitive effects of international trade reverse. Incidence (viz. the division between consumers and firms of gains from trade and losses from taxation of that trade) plays a central role in much economic analysis. As we show in Weyl and Fabinger (2012), it is pivotal in, among other things, the behavior of supply chains, the design of optimal procurement mechanisms and the optimal taxation of international commerce. While under perfect competition the pass-through rate is entirely determined by the elasticity of supply and demand, under imperfect competition the curvature of demand also plays a central role. Unfortunately, as we show below, standard demand forms restrict this curvature in ways that have little empirical or theoretical foundation, are hard to work with analytically. In this paper we propose a novel, simple and highly tractable class of demand functions that avoid these limitations and apply it to provide closed-form, yet flexible, ∗Some results in this paper were formerly circulated as part of “Pass-through as an Economic Tool”, as well as an earlier paper “Apt Demand: A Flexible, Tractable Adjustable Pass-Through Demand Function”. Many individuals who contributed to those papers also aided us on the results developed her, but given that we have thanked them there for brevity we omit further acknowledgement here. We are grateful to Eric Guan and Yali Miao for their assistance in creating the Apt Demand Toolkit and to Daichi Ueda for more general research assistance. †Department of Economics, Pennsylvania State University, University Park, PA 16802: fabinger@psu.edu. ‡Department of Economics, University of Chicago, 1126 E. 59th Street, Chicago, IL 60637: weyl@uchicago.edu.For tractability, researchers often use equilibrium models that can be solved in closed-form. In practice, this means imposing unintended substantive restrictions on incidence properties that are central to many policy questions. To overcome this limitation, we characterize a set of joint supply and demand systems yielding closed-form solutions. This class is broad enough to allow substantial flexibility and thus realism, and it nests virtually all other tractable systems in the literature. We apply these more realistic structures to bargaining and trade models typically solved in closed-form, thereby deriving several applied insights about the cyclicality of labor hoarding, the organization of supply chains and the welfare gains from international trade. Beyond parametric examples, the Laplace Transform, a standard tool used in applied mathematics and physics in analogous settings that we exploit, provides a general approach to characterizing and approximating incidence at any degree of desired tractability. The online appendix for this paper are available at the following URL: http://ssrn.com/abstract=2575471

The Average-Marginal Relationship and Tractable Equilibrium Forms

Under imperfect competition the curvature of demand is central to the rate of cost pass-through and thus to incidence and other questions of economic interest. We show that standard functional forms for demand severely and often unrealistically restrict the behavior of pass-through rates. We propose an Adjustable pass-through (Apt) class of demand functions that avoids these restrictions while yielding closed-form solutions to standard models. To illustrate the utility of this generalized demand form we show how to embed it in monopolistic competition. This allows us to apply it to canonical international trade models with heterogeneous firms and provide a natural case in which standard results on the competitive effects of international trade reverse. Incidence (viz. the division between consumers and firms of gains from trade and losses from taxation of that trade) plays a central role in much economic analysis. As we show in Weyl and Fabinger (2012), it is pivotal in, among other things, the behavior of supply chains, the design of optimal procurement mechanisms and the optimal taxation of international commerce. While under perfect competition the pass-through rate is entirely determined by the elasticity of supply and demand, under imperfect competition the curvature of demand also plays a central role. Unfortunately, as we show below, standard demand forms restrict this curvature in ways that have little empirical or theoretical foundation, are hard to work with analytically. In this paper we propose a novel, simple and highly tractable class of demand functions that avoid these limitations and apply it to provide closed-form, yet flexible, ∗Some results in this paper were formerly circulated as part of “Pass-through as an Economic Tool”, as well as an earlier paper “Apt Demand: A Flexible, Tractable Adjustable Pass-Through Demand Function”. Many individuals who contributed to those papers also aided us on the results developed her, but given that we have thanked them there for brevity we omit further acknowledgement here. We are grateful to Eric Guan and Yali Miao for their assistance in creating the Apt Demand Toolkit and to Daichi Ueda for more general research assistance. †Department of Economics, Pennsylvania State University, University Park, PA 16802: fabinger@psu.edu. ‡Department of Economics, University of Chicago, 1126 E. 59th Street, Chicago, IL 60637: weyl@uchicago.edu.For tractability, researchers often use equilibrium models that can be solved in closed-form. In practice, this means imposing unintended substantive restrictions on incidence properties that are central to many policy questions. To overcome this limitation, we characterize a set of joint supply and demand systems yielding closed-form solutions. This class is broad enough to allow substantial flexibility and thus realism, and it nests virtually all other tractable systems in the literature. We apply these more realistic structures to bargaining and trade models typically solved in closed-form, thereby deriving several applied insights about the cyclicality of labor hoarding, the organization of supply chains and the welfare gains from international trade. Beyond parametric examples, the Laplace Transform, a standard tool used in applied mathematics and physics in analogous settings that we exploit, provides a general approach to characterizing and approximating incidence at any degree of desired tractability. The online appendix for this paper are available at the following URL: http://ssrn.com/abstract=2575471

Cities as Solitons: Analytic Solutions to Models of Agglomeration and Related Numerical Approaches

Economic geography equilibria that represent spontaneous agglomeration in a featureless underlying geographic space have been solved only numerically, and the resulting spatial configurations were symmetric. This paper introduces a method of obtaining analytic solutions to similar models. In the case of continuum space, the multi-city equilibria are again symmetric. However, by working in discrete space it is possible to generate stable equilibria with multiple cities of various population levels and spatial extent, asymmetrically distributed across space. The properties of these equilibria may be understood in terms of deterministic chaos theory. The analytic approach makes it possible to find all equilibria, stable and unstable. There are two qualitative predictions that may be empirically tested: (1) the stability of an isolated city does not depend on its precise position, and (2) if two cities are too close to each other, the configuration becomes unstable and the space between the cities is filled with newcomers, turning the two cities into a megalopolis. In addition, the stable equilibria of the model are compared to population density in northern Chile. It is possible to find equilibria that match the real-world population density profile with correlation of 0.9 or more.

International Influences on Japanese Supply Chains

This paper investigates the transmission mechanism of Chinese productivity shocks through industry-level and firm-level networks in the Japanese manufacturing sector using an instrumental variable approach. We find that increased Chinese productivity in a particular industry negatively affects Japanese suppliers of Japanese firms in that industry (upstream propagation) and positively affects their Japanese corporate customers (downstream propagation). This contrasts the recently studied case of the United States, which did not lead to evidence for downstream propagation of such shocks.

Functional Forms for Tractable Economic Models and the Cost Structure of International Trade

Under imperfect competition the curvature of demand is central to the rate of cost pass-through and thus to incidence and other questions of economic interest. We show that standard functional forms for demand severely and often unrealistically restrict the behavior of pass-through rates. We propose an Adjustable pass-through (Apt) class of demand functions that avoids these restrictions while yielding closed-form solutions to standard models. To illustrate the utility of this generalized demand form we show how to embed it in monopolistic competition. This allows us to apply it to canonical international trade models with heterogeneous firms and provide a natural case in which standard results on the competitive effects of international trade reverse. Incidence (viz. the division between consumers and firms of gains from trade and losses from taxation of that trade) plays a central role in much economic analysis. As we show in Weyl and Fabinger (2012), it is pivotal in, among other things, the behavior of supply chains, the design of optimal procurement mechanisms and the optimal taxation of international commerce. While under perfect competition the pass-through rate is entirely determined by the elasticity of supply and demand, under imperfect competition the curvature of demand also plays a central role. Unfortunately, as we show below, standard demand forms restrict this curvature in ways that have little empirical or theoretical foundation, are hard to work with analytically. In this paper we propose a novel, simple and highly tractable class of demand functions that avoid these limitations and apply it to provide closed-form, yet flexible, ∗Some results in this paper were formerly circulated as part of “Pass-through as an Economic Tool”, as well as an earlier paper “Apt Demand: A Flexible, Tractable Adjustable Pass-Through Demand Function”. Many individuals who contributed to those papers also aided us on the results developed her, but given that we have thanked them there for brevity we omit further acknowledgement here. We are grateful to Eric Guan and Yali Miao for their assistance in creating the Apt Demand Toolkit and to Daichi Ueda for more general research assistance. †Department of Economics, Pennsylvania State University, University Park, PA 16802: fabinger@psu.edu. ‡Department of Economics, University of Chicago, 1126 E. 59th Street, Chicago, IL 60637: weyl@uchicago.edu.For tractability, researchers often use equilibrium models that can be solved in closed-form. In practice, this means imposing unintended substantive restrictions on incidence properties that are central to many policy questions. To overcome this limitation, we characterize a set of joint supply and demand systems yielding closed-form solutions. This class is broad enough to allow substantial flexibility and thus realism, and it nests virtually all other tractable systems in the literature. We apply these more realistic structures to bargaining and trade models typically solved in closed-form, thereby deriving several applied insights about the cyclicality of labor hoarding, the organization of supply chains and the welfare gains from international trade. Beyond parametric examples, the Laplace Transform, a standard tool used in applied mathematics and physics in analogous settings that we exploit, provides a general approach to characterizing and approximating incidence at any degree of desired tractability. The online appendix for this paper are available at the following URL: http://ssrn.com/abstract=2575471