Divisible E-Cash from Constrained Pseudo-Random Functions

International audienceElectronic cash (e-cash) is the digital analogue of regular cash which aims at preservingusers’ privacy. Following Chaum’s seminal work, several new features were proposed for e-cash toaddress the practical issues of the original primitive. Among them,divisibilityhas proved very usefulto enable efficient storage and spendings. Unfortunately, it is also very difficult to achieve and, todate, quite a few constructions exist, all of them relying on complex mechanisms that can only beinstantiated in one specific setting. In addition security models are incomplete and proofs sometimeshand-wavy.In this work, we first provide a complete security model for divisible e-cash, and we study the linkswith constrained pseudo-random functions (PRFs), a primitive recently formalized by Boneh andWaters. We exhibit two frameworks of divisible e-cash systems from constrained PRFs achievingsome specific properties: either key homomorphism or delegability. We then formally prove theseframeworks, and address two main issues in previous constructions: two essential security notionswere either not considered at all or not fully proven. Indeed, we introduce the notion ofclearing,which should guarantee that only the recipient of a transaction should be able to do the deposit,and we show theexculpability, that should prevent an honest user to be falsely accused, was wrongin most proofs of the previous constructions. Some can easily be repaired, but this is not the casefor most complex settings such as constructions in the standard model. Consequently, we providethe first construction secure in the standard model, as a direct instantiation of our framework

Modeling Small Change: A Review Article

In The Big Problem of Small Change, Sargent and Velde apply a cash-in-advance model to the history of coinage and to contemporary thought about coinage. They assert that their model accounts for puzzling observations involving the depreciation and disappearance of small coins. I question its usefulness for that purpose and for other issues pertaining to coinage. My main concern is that their model does not depict the problems usually associated with full-bodied coinage systems-problems that stem from the technological difficulties of having a full-bodied coinage system in which money is portable, divisible, durable, and recognizable.

“On the ‘Hot Potato Effect’ of Inflation: Intensive versus Extensive Margins”

Conventional wisdom is that inflation makes people spend money faster, trying to get rid of it like a “hot potato,” and this is a channel through which inflation affects velocity and welfare. Monetary theory with endoge- nous search intensity seems ideal for studying this. However, in standard models, inflation is a tax that lowers the surplus from monetary exchange and hence reduces search effort. We replace search intensity with a free entry (participation) decision for buyers - i.e., we focus on the extensive rather than intensive margin - and prove buyers always spend their money faster when inflation increases. We also discuss welfare.Search, Money, Inflation, Velocity, Free Entry

Policy Uncertainty and Informational Monopolies: The Case of Monetary Policy.

In this paper we have presented a model in which perfectly enticipated inflation is superneutral: if the variance of the money (or the growth rate of the money supply in the dynamic interpretation) supply is zero, the real equilibrium is independent of the mean of the money supply.ECONOMIC MODELS ; INFLATION ; MONETARY POLICY

The Housing Market(s) of San Diego

This paper uses an assignment model to understand the cross section of house prices within a metro area. Movers’ demand for housing is derived from a lifecycle problem with credit market frictions. Equilibrium house prices adjust to assign houses that differ by quality to movers who differ by age, income and wealth. To quantify the model, we measure distributions of house prices, house qualities and mover characteristics from micro data on San Diego County during the 2000s boom. The main result is that cheaper credit for poor households was a major driver of prices, especially at the low end of the market.

Recent developments in monetary economics: a summary of the 2004 Workshop on Money, Banking, and Payments

We provide a summary and an overview of the papers presented at the Federal Reserve Bank of Cleveland’s 2004 Workshop on Money, Banking, and Payments, held during the weeks of August 3-7 and August 23-27, 2004.Monetary policy ; Monetary theory ; Banks and banking ; Payment systems

Money and Price Posting under Private Information

We study price posting with undirected search in a search-theoretic monetary model with divisible money and divisible goods. Ex ante homogeneous buyers experience match specific preference shocks in bilateral trades. The shocks follow a continuous distribution and the realization of the shocks is private information. We show that generically there exists a unique price posting monetary equilibrium. In equilibrium, each seller posts a continuous pricing schedule that exhibits quantity discounts. Buyers spend only when they have high enough preferences. As their preferences are higher, they spend more till they become cash constrained. Since inflation reduces the future purchasing power of money and the value of retaining money, buyers tend to spend their money faster in response to higher inflation. In particular, more buyers choose to spend money and buyers spend on average a higher fraction of their money. The model naturally captures the hot potato effect of inflation along both the intensive margin and the extensive margin.Economic models; Inflation and prices

Precautionary balances and the velocity of circulation of money

Inflation, as a tax on money, gives buyers an incentive to reduce their money balances. Sellers are aware of this incentive and try to attract buyers by announcing price offers that induce buyers to spend a larger fraction of their money. We examine the effect of inflation on equilibrium price offers and associated trades in a competitive search environment where buyers experience preference shocks after they are matched with a seller. With full information,equilibrium price offers consist of a flat fee applied equally to all buyers independently of the quantities they purchase. If buyers'preferences are private information, sellers must charge more to buyers who purchase larger quantities due to incentive compatibility restrictions. In this case, equilibrium price offers consist of a non-linear price schedule. However, as inflation rises, price schedules become relatively flat. This implies that buyers with a low desire to consume purchase higher quantities and spend their cash more rapidly. Buyers with a high desire to consume purchase lower quantities because, as their money balances fall, they become liquidity constrained. This is in contrast with the full information benchmark where inflation reduces the quantities purchased by all buyers. The equilibrium is efficient at the Friedman rule and inflation reduces welfare both with full and private information

Search theory and applied economic research

In the summer of 2002, the Swiss National Bank (SNB) hosted the “SNB-Fed Cleveland Workshop on Monetary Economics”. Recent years have seen the development of the search-theoretic approach to monetary theory. It has established itself as an important strand of monetary theory in a very short space of time, although it has yet to exert a significant influence on the empirical models that are typically used for monetary policy analysis. This is why the conference organisers, David Altig (Federal Reserve Bank of Cleveland), Aleksander Berentsen (University of Basel) and Thomas Jordan (SNB) decided that the event should focus on linking search theory with applied economic research. This summary article first briefly examines the objectives and challenges of search theory before discussing briefly the conference papers.Search Theory; Monetary Policy; Applied Economic Research