Richard M. Todd

Periodic linear-quadratic methods for modeling seasonality

Optimal linear regulator methods are used to represent a class of models of endogenous equilibrium seasonality that has so far received little attention. Seasonal structure is built into these models in either of two equivalent ways: periodically varying the coefficient matrices of a formerly nonseasonal problem or embedding this periodic-coefficient problem in a higher-dimensional sparse system whose time-invariant matrices have a special pattern of zero blocks. The former structure is compact and convenient computationally; the latter can be used to apply familiar convergence results from the theory of time-invariant optimal regulator problems. The new class of seasonality models provides an equilibrium interpretation for empirical work involving periodically stationary time series.

Real effects of monetary policy in a world economy

We present a 2-country model with heterogeneous agents in which changes in a country?s monetary policy affect real interest rates, relative prices of traded and nontraded goods and real exchange rates. Nontransitory real effects of monetary policy stem solely from a friction (country-specific reserve requirements) that generates separate demands for a country?s money and bonds. Without violating the classical assumptions of individual rationality and flexible prices, the model?s implications seem qualitatively in accord with the U.S. experience of the 1980s: a monetary policy tightening leading to a rise in the real interest rate and to an initial rise in the real value of the dollar which is subsequently reversed. In the model a monetary policy change leads to different welfare effects for agents born at different times, living in different countries, or participating on different sides of a market. The welfare of some agents can be affected more by relative price changes than by real interest rate changes.

Consumer Credit on American Indian Reservations

This paper provides the first encompassing quantitative picture of consumer credit in Indian Country. Drawing on a unique large-scale consumer credit database, we find that Equifax Risk Scores and the use of certain forms of credit, especially mortgages, are low on reservations. However, usage of other forms of credit on reservations is not always low. Moreover, the gaps in credit usage on versus off reservations differ significantly across states and can change notably over time. Among predictors of consumer credit outcomes, the percentage of American Indian residents is robustly negatively associated with favorable credit outcomes. Furthermore, once controlling for racial composition, the effect of an areas location vis-a-vis a reservation often becomes statistically insignificant. Other socio-economic variables are generally poor predictors of credit outcomes on reservations. State jurisdiction over legal matters is, at least on average, associated with favorable credit outcomes on reservations.

The Role of Non-Owner-Occupied Homes in the Current Housing and Foreclosure Cycle

Non-occupant homeowners differ from owner occupants in that they tend to have lower-risk credit characteristics, such as higher credit scores, but may also have weaker incentives to maintain mortgage payments when housing values fall. During the recent housing boom, the share of mortgage borrowing by non-occupant owners was relatively high in states where home values appreciated relatively rapidly. After the housing boom, foreclosures on non-occupant mortgages in several Midwestern and Northeastern states reflected primarily a high rate of foreclosure per mortgage, not a high volume of mortgages to non-occupants. The reverse held true in some coastal and mountain states. Nevada and Florida have experienced the greatest impact overall, because they have both a high volume of mortgages to non-occupant owners and a high rate of foreclosure on those mortgages.

A GENERAL EQUILIBRIUM INTERPRETATION OF DAMAGE-CONTINGENT SECURITIES

ABSTRACT Cass, Chichilnisky, and Wu (1996) show in an endowment economy that mutual insurance and securities contingent on aggregate states support optimal risk-sharing. We extend their result to a model with production in which risk is endogenous and beliefs about the aggregate state vary across individuals. We use the model to interpret the role of new securities that are contingent on measures of total damage from natural catastrophes. Plausible special cases of the model predict the trade pattern in such securities across diverse regions and predict that such securities will not represent actuarially fair gambles. INTRODUCTION Cass, Chichilnisky, and Wu (1996) show in an endowment economy that if the structure of uncertainty resembles an individual insurance situation, then a combination of mutual insurance and securities contingent on aggregate states supports optimal risk-sharing. In other words, in such settings, a complete set of Arrow-Debreu markets is not needed. We extend their result to a model with production in which the amount of risk depends on individual decisions--as when houses are built in areas prone to hurricanes. Our model is of a static economy in which the aggregate amount of resources subject to risk is the result of individual investment decisions and in which beliefs about the aggregate state vary across individuals. For that model, we show that a Pareto efficient allocation can be supported by a competitive equilibrium with two types of securities: mutual insurance that provides for risk sharing among individuals who are ex ante similar, and a set of state-contingent securities that are indexed by the aggregate exogenous state. This extends the result in Cass, Chichilnisky, and Wu (1996) to the case of a productive economy where the level of aggregate risk is endogenous. We go on to show that the state-contingent securities can be replaced by securities contingent on aggregate losses rather than the exogenous state, despite the fact that aggregate losses are endogenous. For special cases of the model, we describe the implied pattern of trade in the contingent contracts and how they are priced. We show that there is no theoretical basis for believing that the damage-contingent securities are priced in an actuarially fair manner. If individuals have identical beliefs, then the price of a damage contingent security will in general include a risk premium that rewards individuals for taking on this risk. After presenting those results, we conclude with a brief discussion of recent policy initiatives and related discussion concerning losses from natural catastrophes. A MODEL WITH ENDOGENOUS DAMAGE We present a static model that is designed to represent, in a simple way, regions which end up being subject to different amounts of risk. The economy consists of a finite number of islands that are indexed by h from 1 to H. Island h is inhabited by [N.sub.h] people of type h. Each island is perfectly round and has a plateau in the middle of it. The land on the coast is subject to the risk of damage (from storms), while land located on the plateau is safe. Each person on island h is endowed with an ex ante identical slice of land, which includes some coastal land and some plateau land, and with a resource, [y.sub.h], which can be interpreted as labor. The only use of the resource is as an input into production of a single good, rice, on the coastal land or on the plateau land owned by that person. All type h people are identical in terms of von Neumann-Morgenstern utility function, endowments, and technologies. We let [u.sub.h]: [R.sub.+] [right arrow] R denote a type h persons von Neumann-Morgenstern utility function (for rice consumption), and we assume that [u.sub.h] is strictly increasing, strictly concave, and continuously differentiable. The technologies determine the distribution of output resulting from the decision about dividing [y. …

Neighborhood Racial Characteristics, Credit History, and Bankcard Credit in Indian Country

We draw on a large-scale dataset of individual-level credit bureau records to study bankcard credit limits in Indian Country. Utilizing approaches that aim to isolate supply from demand considerations, we find that residing in a predominantly American Indian neighborhood is ceteris paribus associated with lower awarded bankcard credit limits than residing in a neighborhood where the share of American Indian residents is low. Consumer’s credit history is a robust and quantitatively more important predictor of awarded credit limits than racial composition of the consumer’s neighborhood. Bankcard credit limits do not depend on the consumer’s location vis-à-vis a reservation.