Rigorous Bounds to Retarded Learning

We show that the lower bound to the critical fraction of data needed to infer (learn) the orientation of the anisotropy axis of a probability distribution, determined by Herschkowitz and Opper [Phys.Rev.Lett. 86, 2174 (2001)], is not always valid. If there is some structure in the data along the anisotropy axis, their analysis is incorrect, and learning is possible with much less data points.Comment: 1 page, 1 figure. Comment accepted for publication in Physical Review Letter

Are There Opportunities to Increase Social Security Progressivity Despite Underfunding?

Reviews the payroll tax, Social Security's benefit formula, and outcomes by race, gender, and earnings level, and explores why low-income and minority groups do not receive greater returns on contributions. Simulates the effects of progressive reforms

Finite size scaling of the bayesian perceptron

We study numerically the properties of the bayesian perceptron through a gradient descent on the optimal cost function. The theoretical distribution of stabilities is deduced. It predicts that the optimal generalizer lies close to the boundary of the space of (error-free) solutions. The numerical simulations are in good agreement with the theoretical distribution. The extrapolation of the generalization error to infinite input space size agrees with the theoretical results. Finite size corrections are negative and exhibit two different scaling regimes, depending on the training set size. The variance of the generalization error vanishes for $N \rightarrow \infty$ confirming the property of self-averaging.Comment: RevTeX, 7 pages, 7 figures, submitted to Phys. Rev.

Tariff Wars and Trade Deals With Costly Government

We study a simple model of tariff wars and trade deals in which government revenue collection and disbursement uses resources. The introduction of a costly government leads to lower non-cooperative tariffs, the possibility that a less costly government may win a tariff war, and fully cooperative trade deals where countries lower tariffs but do not eliminate them, even with lump-sum taxes and transfers.

Tariff Wars and Trade Deals with Costly Government

We study a simple model of tariff wars and trade deals in which government revenue collection and disbursement uses resources. The introduction of costly governments leads to lower non–cooperative tariffs, the possibility that a less costly government may win a tariff war, and fully cooperative trade deals where countries lower tariffs but do not eliminate them, even with lump–sum taxes and transfers.

Are Countercyclical Fiscal Policies Counterproductive?

Economists generally believe that countercyclical fiscal policies have stabilizing effects that work through automatic stabilizers and discretionary actions. Analyses underlying this conventional wisdom focus on intratemporal margins: how employment and personal income respond in the short run to changes in government expenditures and taxes. But in economic downturns, countercyclical policies increase government indebtedness, raising future debt service obligations. These new expenditure commitments must be financed by some mix of higher taxes, lower spending, or higher money growth in the future. Expectations of how future policies will adjust change current savings rates and the efficacy of countercyclical policies. It is thus possible for responses to expected future policies to exacerbate and prolong recessions. This paper highlights these expectations effects. Connecting the theory to U.S. data we find: (1) through this expectations channel, countercyclical policies may create a business cycle when there would be no cycle in the absence of countercyclical policies; (2) nontrivial fractions of variation in investment and velocity can be explained by variation in macro policies alone---without any nonpolicy sources of fluctuation; and (3) persistence in key macro variables can arise solely from expectations of policy.

The Price Level, the Quantity Theory of Money, and the Fiscal Theory of the Price Level

We consider price level determination from the perspective of portfolio choice. Arbitrages among money balances, bonds, and investment goods determine their relative demands. Returns to real balance holdings (transactions services), the nominal interest rate, and after-tax returns to investment goods determine the relative values of nominal and real assets. Since expectations of government policies ultimately determine the expected returns to both nominal and real assets, monetary and fiscal policies jointly determine the price level. Special cases of the fiscal and monetary policies considered produce the quantity theory of money and the fiscal theory of the price level.

Trends in velocity and policy expectations

U.S. velocity of base money exhibits three distinct trends since 1950. After rising steadily for thirty years, it flattens out in the 1980s and falls substantially in the 1990s. This paper explores whether the observed secular movements in velocity can be accounted for exclusively by endogenous responses to changing expectations about monetary and fiscal policy. We use a model with two key features: a substitute for money in transactions and an array of assets that includes money, nominal bonds, and physical capital. The model maps policy expectations into portfolio decisions, making equilibrium velocity a function of expected future money growth, tax rates, and government spending. When expectations are estimated using Bayesian updating, simulated velocity matches the trends in actual velocity surprisingly well.Macroeconomics ; Money supply ; Monetary policy ; Velocity of money

Dynamical control of quantum state transfer within hybrid open systems

We analyze quantum state-transfer optimization within hybrid open systems, from a "noisy" (write-in) qubit to its "quiet" counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy)