Optimal Capital Taxation and Consumer Uncertainty

This paper analyzes the impact of consumer uncertainty on optimal fiscal policy in a model with capital. The consumers lack confidence about the probability model that characterizes the stochastic environment and so apply a max-min operator to their optimization problem. An altruistic fiscal authority does not face this Knightian uncertainty. We show analytically that, in responding to consumer uncertainty, the government no longer sets the expected capital tax rate exactly equal to zero, as is the case in the full-confidence benchmark model. Rather, our numerical results indicate that the government chooses to subsidize capital income, albeit at a modest rate. We also show that the government responds to consumer uncertainty by smoothing the labor tax across states and by making the labor tax persistent

Robust Predictions for DSGE Models with Incomplete Information

We study the quantitative potential of DSGE models with incomplete information. In contrast to existing literature, we offer predictions that are robust across all possible private information structures that agents may have. Our approach maps DSGE models with information-frictions into a parallel economy where deviations from fullinformation are captured by time-varying wedges. We derive exact conditions that ensure the consistency of these wedges with some information structure. We apply our approach to an otherwise frictionless business cycle model where firms and households have incomplete information. We show how assumptions about information interact with the presence of idiosyncratic shocks to shape the potential for confidence-driven fluctuations. For a realistic calibration, we find that correlated confidence regarding idiosyncratic shocks (aka “sentiment shocks”) can account for up to 51 percent of U.S. business cycle fluctuations. By contrast, confidence about aggregate productivity can account for at most 3 percent

Optimal Capital Taxation and Consumer Uncertainty

This paper analyzes the impact of consumer uncertainty on optimal fiscal policy in a model with capital. The consumers lack confidence about the probability model that characterizes the stochastic environment and so apply a max-min operator to their optimization problem. An altruistic fiscal authority does not face this Knightian uncertainty. We show analytically that, in responding to consumer uncertainty, the government no longer sets the expected capital tax rate exactly equal to zero, as is the case in the full-confidence benchmark model. Rather, our numerical results indicate that the government chooses to subsidize capital income, albeit at a modest rate. We also show that the government responds to consumer uncertainty by smoothing the labor tax across states and by making the labor tax persistent

Information-driven Business Cycles: A Primal Approach

We develop a methodology to characterize equilibrium in DSGE models, free of parametric restrictions on information. First, we define a “primal” economy in which deviations from full information are captured by wedges in agents' expectations. Then, we provide conditions ensuring some information-structure can implement these wedges. We apply the approach to estimate a business cycle model where firms and households have dispersed information. The estimated model fits the data, attributing the majority of fluctuations to a single shock to households' expectations. The responses are consistent with an implementation in which households become optimistic about local productivities and gradually learn about others' optimism

Information-driven Business Cycles: A Primal Approach

We develop a methodology to characterize equilibrium in DSGE models, free of parametric restrictions on information. First, we define a “primal” economy in which deviations from full information are captured by wedges in agents' expectations. Then, we provide conditions ensuring some information-structure can implement these wedges. We apply the approach to estimate a business cycle model where firms and households have dispersed information. The estimated model fits the data, attributing the majority of fluctuations to a single shock to households' expectations. The responses are consistent with an implementation in which households become optimistic about local productivities and gradually learn about others' optimism

Robust Predictions for DSGE Models with Incomplete Information

We study the quantitative potential of DSGE models with incomplete information. In contrast to existing literature, we offer predictions that are robust across all possible private information structures that agents may have. Our approach maps DSGE models with information-frictions into a parallel economy where deviations from fullinformation are captured by time-varying wedges. We derive exact conditions that ensure the consistency of these wedges with some information structure. We apply our approach to an otherwise frictionless business cycle model where firms and households have incomplete information. We show how assumptions about information interact with the presence of idiosyncratic shocks to shape the potential for confidence-driven fluctuations. For a realistic calibration, we find that correlated confidence regarding idiosyncratic shocks (aka “sentiment shocks”) can account for up to 51 percent of U.S. business cycle fluctuations. By contrast, confidence about aggregate productivity can account for at most 3 percent

Regularity of the Density of Surface States

We prove that the integrated density of surface states of continuous or discrete Anderson-type random Schroedinger operators is a measurable locally integrable function rather than a signed measure or a distribution. This generalize our recent results on the existence of the integrated density of surface states in the continuous case and those of A. Chahrour in the discrete case. The proof uses the new $L^p$-bound on the spectral shift function recently obtained by Combes, Hislop, and Nakamura. Also we provide a simple proof of their result on the Hoelder continuity of the integrated density of bulk states

Comparing Machine Learning and Interpolation Methods for Loop-Level Calculations

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman $D_0$ function, and the two-loop self-energy master integral $M$. We find that in low dimensions ($d = 3$), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions ($d=5, 6, 9$) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.Comment: 30 pages, 17 figures, v2:added a few references, v3: new title, added a few reference

Uniform existence of the integrated density of states for random Schr\"odinger operators on metric graphs over Zd\mathbb{Z}^d

We consider ergodic random magnetic Schr\"odinger operators on the metric graph $\mathbb{Z}^d$ with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss percolation models.Comment: 17 pages; typos removed, references updated, definition of subgraph densities explaine