Working Papers
By Year:
Paper #  Author  Title  

97030 
Francis X. Diebold Andrew Hickman Atsushi Inoue Til Schuermann 
"Converting 1Day Volatility to hDay Volatility: Scaling by is Worse than You Think"  
We show that the common practice of converting 1day volatility estimates to hday estimates by scaling by the sqaure root of h is inappropriate and produces overestimates of the variability of longhorizon volatility. We conclude that volatility models are best tailored to tasks: if interest centers on longhorizon volatility, then a longhorizon volatility model should be used. Economic considerations, however, confound even that prescription and point to important directions for future research. Download Paper


97029 
Jeremy Berkowitz Francis X. Diebold Lee E. Ohanian 
"A Dynamic Equilibrium Economies: A Framework for Comparing Models and Data"  
We propose a constructive, multivariate framework for assessing agreement between (generally misspecified) dynamic equilibrium models and data, a framework which enables a complete secondorder comparison of the dynamic properties of models and data. We use bootstrap algorithms to evaluate the significance of deviations between models and data, and we use goodnessoffit criteria to produce estimators that optimize economically relevant loss functions. We provide a detailed illustrative application to modeling the U.S. cattle cycle. Download Paper


97028 
Filippo Altissimo Valentina Corradi 
"A LIL for mEstimators and Applications to Hypothesis Testing with Nuisance Parameters"  
The purpose of this paper is twofold: On one side we aim to provide easily computable almost sure bounds for inference in presence of nuisance parameters unidentified under the null. On the other hand, more generally, we aim to provide a flexible completely consistent procedure for inference in, possibly mispecified, parametric models, in the case of dependent and heterogeneous observationsl. With the term completely consistent we mean that the asymptotic size is zero and the asymptotic power is one. The small sample behavior of our procedures is analyzed via few Monte Carlo simulations, in particular we consider (i) conditional moment tests, (ii) testing for nonlinearities in the SETAR model. Overall the size approaches zerio relatively slowly, while the power approaches one very quickly. Download Paper


97027 
Valentina Corradi 
"Deciding Between I(0) and I(1) via FLILbased Bounds"  
We construct properly scaled functions of Rpvalued partial sums of demeaned data and derive bounds via the functional law of the iterated logarithm for strong mixing processes. If we obtain a value below or equal to the bound we decide in favor of I(0); otherwise we decide in favor of I(1). This provides a consistent rule for classifying time series as being I(1) or I(0). The nice feature of the procedure lies in the almost sure nature of the bound, guaranteeing a lim sup–type result. We finally provide conditions for the strong consistency of estimators of the variance in the dependent and heterogeneous case. The finite sample behavior of the procedure is analyzed via Monte Carlo simulations. Download Paper


97026 
Valentina Corradi Norman R. Swanson 
"Choosing Between Levels and Logs in the Presences of Deterministic and Stochastic Trends"  
In macroeconometrics, unit root tests are typically performed using logs. While this is sensible from a theoretical macroeconomic perspective, there is no clear reason, particularly from an empirical perspective, why logs should be used rather than levels. Further, standard unit root tests assume linearity under both the null and the alternative hypthesis. Violation of this linearity assumption can result in severe size and power distortion, both in finite and large samples. Finally, casual inspection of gnp per capita, for example, plotted against its fitted linear deterministic trend (see Figure 1) gives no clear indication that a loglinear specification should be preferred to a linear specification. thus, it is reasonable to address the problem of data transformation before running a unit root test. In this paper we propose a simple completely consistent procedure for choosing between levels and loglevels specifications in the presence of deterministic and/or stochastic trends. Download Paper


97025 
Jere R. Behrman 
"Mother's Schooling and Child Education: A Survey"  
This paper first discussed a general framework for thinking about the impact of mothers schooling on child education and then surveys what we know on the basis of all 237 estimates that have been located. Examination of available estimates in light of this general framework suggests that knowledge on the impact of women's schooling on child education generally could be improved with more clarity about what model is estimated, roles of possibly important unobserved variables such as preferences and abilities, distinctions between particular and more general total effects and use of broader indicators of both mother's and child's education that capture outcomes rather than primarily timeinschool inputs. Download Paper


97024 
Jere R. Behrman Andrew D. Foster Mark R. Rosenzweig Prem Vashishtha 
"Women's Schooling, Home Teaching, and Economic Growth"  
Increased investment in schooling is often promoted as a key development strategy aimed at promoting economic growth. Most of the micro evidence that has been used to support the importance of schooling in augmenting incomes in lowincome countries comes mainly from data describing the returns to schooling for men (e.g, Psacharopolous, 1994). Given the relatively low rates of participation by women in formalsector labor markets in such countries, information on the potential contribution of women’s schooling to income is less available and where found problematical to interpret due to labor market selectivity. Download Paper


97023 
Jere R. Behrman Victor Lavy 
"Child Health and Schooling Achievement: Association, Causality and Household Allocations"  
Child health is widely perceived to affect strongly schooling. But evidence is quite limited because numerous studies based on socioeconomic surveys fail to consider the endogeneity of child health, measurement error, and the impact of unobserved fixed and choice inputs. This paper shows that a priori the resulting biases may be positive or negative depending on which of a number of household allocation behaviors dominate and what is the nature of any unobserved choice inputs in educational production. Then illustrative empirical analysis, using rich data from Ghana, is presented, with the following results: (1) IV estimates based on observed family and community characteristics similar to those used in other studies suggest a downward bias in OLS. (2) Family and community fixed effects estimates suggest that the direction of the bias in standard estimates is upward and that the true effects of the range of observed child health on school success is not significant despite the strong association that leads to the appearance of an effect in standard OLS or IV estimates using family and community variables. (3) The usual assumption that there are no unobserved choice inputs in educational production probably leads to an upward bias in the estimated impact of child health on schooling even if there is good control for the endogeneity of child health and measurement error. (4) Child health also does not significantly affect child cognitive achievement through schooling attainment; consideration of the relations that usually have been used to investigate such a possibility, moreover, suggests that the coefficients that are usually estimated are not coefficients that represent the impact of child health on child schooling. (5) The preferred estimates control for unobserved family and community fixed effects and are robust to other estimation problems, so the standard estimates overstate the impact of child health in the observed range on child schooling success, which should strike a cautionary note about the interpretation of the many production function estimates in the literature, including, but not limited to those that focus on household production. Download Paper


97022 
Jere R. Behrman James C. Knowles 
"How Strongly is Child Schooling Associated with Household Income?"  
Schooling is widely seen as critical for income generation in all types of economies. A growing concern among many has been the possibility of increasing inequality in part due to children from higherincome households obtaining more schooling and reaping greater gains from schooling than children from lowerincome households. There are many empirical studies for various societies that tend to find significantly positive, but small associations between household income and schooling. But these studies generally have three major limitations for the purpose of characterizing the degree of association between household income and schoolingrelated investments: (1) use of income indicators that may be contaminated by relatively large measurement errors and endogeneity, (2) inclusion of other household, community and schooling variables that may represent part of the association with income in empirical estimates, and (3) use of limited indicators of schooling. This paper uses a rich new household surveycommuneschool facility survey from Viet Nam to illustrate how important these limitations may be. The estimates suggest: (1) predicted income (expenditure) tends to yield estimates of much stronger associations than does current income or expenditures, (2) controlling for variables such as in most previous studies reduces the estimated associations with income substantially, and (3) including a wide range of schoolingrelated variables leads to more nuanced understanding of incomeschooling associations, with some benefits for children from poorer households but a dominant tendency for school and private behaviors to favor significantly and in many cases substantially children from higherincome households. Download Paper


97021 
Harold Alderman Jere R. Behrman Victor Lavy Rekha Menon 
"Child Nutrition, Child Health, and School Enrollment: A Longitudinal Analysis"  
Better health and nutrition are thought to improve children's performance in school, and therefore their productivity after school. Most literature ignores the fact that child health and schooling reflect behavioral choices, so the estimated impact of health and nutrition on a child's schooling reflects biases in the studies. Using an explicit dynamic model for preferred estimates, the authors use longitudinal data to investigate how children's health and nutrition affect school enrollment in rural Pakistan. They use price shocks when children were of preschool age to control for behavior determining the measure of children's health and nutrition stock. The authors find that children's health and nutrition is three times more important for enrollment than is suggested by"naive estimates"that assume that children's health and nutrition is predetermined rather that determined by household choices. Not only does improved nutrition increase enrollments, it does so more for girls, thus closing a portion of the gender gap. These results strongly reinforce the importance of using estimation methods that are consistent with the economic theory of households to explore the impact of some choice variables on others, using socioeconomic behavioral data. Private behaviors and public policies that affect the health and nutrition of children have much greater effect on school enrollment and on eventual productivity than suggested by early literature methods. Download Paper


97020 
Peter F. Christoffersen Francis X. Diebold 
"Optimal Prediction Under Asymmetric Loss"  
Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric loss is not well developed. We study the optimal prediction problem under general loss structures and characterize the optimal predictor. We compute the optimal predictor analytically in two leading cases. Analytic solutions for the optimal predictor are not available in more complicated cases, so we develop numerical procedures for computing it. We illustrate the results by forecasting the GARCH(1,1) process which, although white noise, is nontrivially forecastable under asymmetric loss. Download Paper


97018 
Francis X. Diebold Todd A. Gunther Anthony S. Tay 
"Evaluating Density Forecasts"  
We propose several methods for evaluating and improving density forecasts. We focus primarily on methods that are applicable regardless of the particular user s loss function, but we also show how to use information about the loss function when and if it is known. Throughout, we take explicit account of the relationships between density forecasts, action choices, and the corresponding expected loss. Download Paper


97017 
Peter F. Christoffersen Francis X. Diebold 
"Cointegration and LongHorizon Forecasting"  
It is widely believed that imposing cointegration on a forecasting system, if cointegration is in fact present, will improve longhorizon forecasts. Contrary to this belief, we show that at long horizons nothing is lost by ignoring cointegration when the forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate BoxJenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures  they fail to value the maintenance of cointegrating relationships among variables  and we suggest alternatives that explicitly do so. Download Paper


97016 
Richard Rogerson Peter Rupert Randall Wright 
"Homework in Labor Economics: Household Production and Intertemporal Substitution"  
We argue that estimates of intertemporal substitution elasticities obtained from standard life cycle models are subject to a downward bias because they neglect changes in work done at home over the life cycle. We extend the standard life cycle model to include home production and estimate it using data from three time use surveys. We find that the downward bias is large. Download Paper


97015 
Alberto Trejos Randall Wright 
"Toward a Theory of International Currency: A Step Further"  
We generalize the twocountry, twocurrency, searchbased monetary model of Matsuyama, Kiyotaki and Matsui to resolve two "shortcomings" in their approach. First, we endogenize prices and exchange rates. Second, we discuss some policy considerations. We use the model to address several questions related to the determination of the realms of circulation and relative values of different monies. Download Paper


97014 
Yiting Li Randall Wright 
"Policy Analysis in SearchBased Models of Money"  
The objective of this paper is to study the effects of government policies described as a searchtheoretic (or random matching) model of money. A search model is the right tool for the job because it generates an endogenous transactions pattern that allows one to determine in equilibrium which objects are accepted in which trades, and at what relative prices. Our framework willi allow one to analyze the effects of government transactions policies on these outcomes, and to make precise how these effects depend on things like the size and influence of the government in the economy. Download Paper


97013 
Stephen Coate Stephen Morris 
"Policy Conditionality"  
If policy makers in developing countries pursue "bad" economic policies, policy conditionality may provide financial leverage which induces them not to choose these policies. When is such policy conditionality beneficial? We point out that whether conditionality has a beneficial short run impact depends critically on the political economy explanations of the particular "bad" economic policy in question. We also argue that conditionality can only have a longrun impact if there is a tendency for reforms to "persist" and discuss alternative explanations for policy persistence. Download Paper


97012 
Stephen Morris Hyun Song Shin 
"Unique Equilibrium in a Model of SelfFulfilling Currency Attacks"  
Even though selffulfilling currency attacks lead to multiple equilibria when fundamentals are common knowledge, we demonstrate the uniqueness of equilibrium when speculators face a small amount of noise in their signals about the fundamentals. This unique equilibrium depends not only on the fundamentals, but also on financial variables, such as the quantity of hot money in circulation and the costs of speculative trading. In contrast to multiple equilibrium models, our model allows analysis of policy proposals directed at curtailing currency attacks. Download Paper


97011 
George J. Mailath Larry Samuelson Jeroen M. Swinkels 
"How Proper is Sequential Equilibrium?"  
A strategy profile of a normal form game is proper if and only if it is quasiperfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of supporting trembles, while sequentiality only requires optimality in the limit. A decisiontheoretic implementation of sequential rationality, strategic independence respecting equilibrium (SIRE), is defined and compared to proper equilibrium, using lexicographic probability systems. Finally, we give tremblebased characterizations, which do not involve structural features of the game, of the rankings of strategies that underlie proper equilibrium and SIRE. Download Paper


97010 
F. Gerard Adams Peter A. Prazmowski 
"Why Are Saving Rates in East Asia So High? Reviving the Life Cycle Hypothesis"  
Why are saving rates in the East Asian countries so high? This paper represents an attempt to provide an explanation in terms of rapid income growth rates linked to the life cycle hypothesis. Empirial tests support the relatinship between saving rates and growth implied by the theory. This approach goes a long way toward explaining high saving rates in East Asis. Download Paper


97009 
Melvyn Coles Randall Wright 
"A Dynamic Equilibrium Model of Search, Bargaining, and Money"  
We characterize dynamic (not just steady state) equilibria in a searchtheoretic model of fiat money, where buyers and sellers, upon meeting, enter bargaining games to determine prices. Equilibrium in the bargaining game is approximated in terms of a tractable dynamical system, in much the same way that the Nash solution approximates equilibrium in bargaining games in stationary environments. The model with our dynamic bargaining solution can generate outcomes (such as limit cycles) that never arise in the same model if one imposes a myopic bargaining solution, as has been done in the past. Download Paper


97008 
Stephen Morris Hyun Song Shin 
"Approximate Common Knowledge and Coordination: Recent Lessons from Game Theory"  
97007 
Francois R. Velde Warren E. Weber Randall Wright 
"A Model of Commodity Money, With Application to Gresham's Law and the Debasement Puzzle"  
We develop a model of commodity money and use it to analyze the following two questions motivated by issues in monetary history: What are the conditions under which Gresham's Law holds? And, what are the mechanics of a debasement (lowering the metallic content of coins)? The model contains light and heavy coins, imperfect information, and prices determined via bilateral bargaining. There are equilibria with neither, both, or only one type of coin in circulation. When both circulate, coins may trade by weight or by tale. We discuss the extent to which Grsham's Law holds in the various cases. Following a debasement, the quantty of reminting depends ont the incentives offered by the sovereign. Equilibria exist with positive seigniorage and a mixtdure of old and new coins in circulation Download Paper


97006 
George J. Mailath 
"Correlated Equilibria and Local Interactions"  
This paper shows that Nash equilibria of a localinteraction game are equivalent to correlated equilibria of the underlying game. Download Paper
