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The chapter reviews and extends the theory of exact and superlative index numbers. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. These exact indexes can be used to measure changes in a consumer's cost of living or welfare. Two cases are considered: the case of homothetic preferences and the case of nonhomothetic preferences. In the homothetic case, exact index numbers are obtained for square root quadratic preferences, quadratic mean of order r preferences, and normalized quadratic preferences. In the nonhomothetic case, exact indexes are obtained for various translog preferences.

We analyze stochastic volatility effects in the context of the bond market. The short rate model is of Vasicek type and the focus of our analysis is the effect of multiple scale variations in the volatility of this model. Using a combined singular-regular perturbation approach we can identify a parsimonious representation of multiscale stochastic volatility effects. The results are illustrated with numerical simulations. We also present a framework for model calibration and look at the connection to defaultable bonds.

Most current modeling approaches identify very small gains from trade reform. In this chapter, we examine recent developments in the literature to assess whether standard modeling approaches are mis-specifying, understating, or overstating the gains from trade reform. Key areas where the impacts of trade barrier reduction appear to be understated include the measurement of barriers; the aggregation of these barriers; process productivity gains, particularly those resulting from reallocation of resources between firms; product quality improvements and expansion of product variety; factor supply; and investment of gains from trade.

A futures contract may rely upon physical delivery or cash settlement to liquidate open positions at the maturity date. Contract settlement specification has direct impacts on the behavior of the futures price, leading to different effects of liquidity risk on futures hedging. This chapter compares such effects under alternative settlement specifications with a simple analytical model of daily price change. Numerical simulation results demonstrate that capital constraint reduces hedging effectiveness and tends to produce a lower optimal hedge ratio. As the futures contract proceeds toward the maturity date, hedgers will take larger hedge position in order to achieve better hedging effectiveness. Finally, optimal hedge ratios are higher (resp. lower) under cash settlement for the bivariate normal (resp. lognormal) assumptions, whereas hedging effectiveness is almost always greater under cash settlement.

This paper generalizes the critical loss concept of Harris and Simons to account for a broader range of possible cost structures. Our analysis presents a specialized market-level equilibrium for a relatively homogeneous good in which the Harris and Simons’ critical loss structure is appropriate for market definition. Then, we broaden the equilibrium and propose a generalized critical loss analysis. Of course, for relatively differentiated goods, market definition analysis would use firm-level modeling and therefore the standard market-level critical loss modeling could be inappropriate.

The effect of changes in commodity prices on factor rewards is studied in the multi-commodity, multi-factor case. It is shown that the inverse of the distributive share matrix must satisfy the following restriction: it cannot be anti-symmetric in its sign pattern. This means that one cannot partition the commodities into two groups (I and II) and factors into two groups (A and B), such that all factors in group A benefit (nominally) from all commodity price increases in group I, and simultaneously all factors in group B suffer from all commodity price increases in group II. It turns out that this is also the only sign-pattern restriction imposed by the general nature of the relationship of commodity prices and factor rewards.

There are two main dimensions in which the performance of a production unit can be assessed. The first is the dimension of time. The basic question here is: how is this or that production unit doing over time? Assessing a unit's performance over time is called monitoring. The second dimension is characterized by the question: how is this or that production unit doing relative to other, similar units? To answer this question one needs to specify the reference set of units and one needs sufficient information on each of the members of this set. This activity is usually called benchmarking. A combination of the two dimensions in the setting of a panel is also possible.