Covariance regularization by thresholding

This paper considers regularizing a covariance matrix of $p$ variables estimated from $n$ observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and $(\log p)/n\to0$, and obtain explicit rates. The results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity. We discuss an intuitive resampling scheme for threshold selection and prove a general cross-validation result that justifies this approach. We also compare thresholding to other covariance estimators in simulations and on an example from climate data.Comment: Published in at http://dx.doi.org/10.1214/08-AOS600 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Foreign Currency Pricing

A special case of dollarization is analyzed: quotation of prices in dollars. The proposed explanation is price stickiness: when price adjustment is costly, forms can prefer to fix their prices in a stable foreign currency rather than in an unstable domestic one in order to avoid frequent price changes. The proposed model shows how the choice of price-setting currency made by a firm depends on the in ation rate, exchange rate volatility, the pricing currency of competitors and input suppliers, and the shape of the demand function. The model predicts that there are two Nash equilibria in the economy populated by symmetric firms: an equilibrium with uniform ruble pricing and an equilibrium with uniform dollar pricing. It is shown that in economy with less competition a smaller increase in inflation is needed to make an individual firm deviate from the equilibrium with uniform ruble pricing and turn to pricing in dollars.

Understanding smart contracts as a new option in transaction cost economics

Among different concepts associated with the term blockchain, smart contracts have been a prominent one, especially popularized by the Ethereum platform. In this study, we unpack this concept within the framework of Transaction Cost Economics (TCE). This institutional economics theory emphasizes the role of distinctive (private and public) contract law regimes in shaping firm boundaries. We propose that widespread adoption of the smart contract concept creates a new option in public contracting, which may give rise to a smart-contract-augmented contract law regime. We discuss tradeoffs involved in the attractiveness of the smart contract concept for firms and the resulting potential for change in firm boundaries. Based on our new conceptualization, we discuss potential roles the three branches of government – judicial, executive, and legislative – in enabling and using this new contract law regime. We conclude the paper by pointing out limitations of the TCE perspective and suggesting future research directions