# generated by /homes/nber/adrepec/bin/nbrred running on mysql0
Template-Type: ReDIF-Paper 1.0
Title: The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions
Classification-JEL: C32; G12
Author-Name: Yacine Ait-Sahalia
Author-Person: pai23
Author-Name: Per A. Mykland
Note: TWP
Number: 0276
Creation-Date: 2002-04
Order-URL: http://www.nber.org/papers/t0276
File-URL: http://www.nber.org/papers/t0276.pdf
File-Format: application/pdf
Publication-Status: published as "The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions", Econometrica, Vol. 71, pp. 483-549 (2003)
Abstract: High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuous-time model. In particular, we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data. We also examine the effect of simply ignoring the sampling randomness. We find that in many situations the randomness of the sampling has a larger impact than the discreteness of the data.
Handle: RePEc:nbr:nberte:0276
Template-Type: ReDIF-Paper 1.0
Title: Trimming for Bounds on Treatment Effects with Missing Outcomes
Classification-JEL: C10; C24
Author-Name: David S. Lee
Note: TWP
Number: 0277
Creation-Date: 2002-06
Order-URL: http://www.nber.org/papers/t0277
File-URL: http://www.nber.org/papers/t0277.pdf
File-Format: application/pdf
Abstract: Empirical researchers routinely encounter sample selection bias whereby 1) the regressor of interest is assumed to be exogenous, 2) the dependent variable is missing in a potentially non-random manner, 3) the dependent variable is characterized by an unbounded (or very large) support, and 4) it is unknown which variables directly affect sample selection but not the outcome. This paper proposes a simple and intuitive bounding procedure that can be used in this context. The proposed trimming procedure yields the tightest bounds on average treatment effects consistent with the observed data. The key assumption is a monotonicity restriction on how the assignment to treatment effects selection -- a restriction that is implicitly assumed in standard formulations of the sample selection problem.
Handle: RePEc:nbr:nberte:0277
Template-Type: ReDIF-Paper 1.0
Title: Econometric Methods for Endogenously Sampled Time Series: The Case of Commodity Price Speculation in the Steel Market
Classification-JEL: C1; C6
Author-Name: George Hall
Author-Person: pha118
Author-Name: John Rust
Author-Person: pru5
Note: TWP
Number: 0278
Creation-Date: 2002-08
Order-URL: http://www.nber.org/papers/t0278
File-URL: http://www.nber.org/papers/t0278.pdf
File-Format: application/pdf
Abstract: This paper studies the econometric problems associated with estimation of a stochastic process that is endogenously sampled. Our interest is to infer the law of motion of a discrete-time stochastic process {pt} that is observed only at a subset of times {t1,..., tn} that depend on the outcome of a probabilistic sampling rule that depends on the history of the process as well as other observed covariates xt . We focus on a particular example where pt denotes the daily wholesale price of a standardized steel product. However there are no formal exchanges or centralized markets where steel is traded and pt can be observed. Instead nearly all steel transaction prices are a result of private bilateral negotiations between buyers and sellers, typically intermediated by middlemen known as steel service centers. Even though there is no central record of daily transactions prices in the steel market, we do observe transaction prices for a particular firm -- a steel service center that purchases large quantities of steel in the wholesale market for subsequent resale in the retail market. The endogenous sampling problem arises from the fact that the firm only records pt on the days that it purchases steel. We present a parametric analysis of this problem under the assumption that the timing of steel purchases is part of an optimal trading strategy that maximizes the firm's expected discounted trading profits. We derive a parametric partial information maximum likelihood (PIML) estimator that solves the endogenous sampling problem and efficiently estimates the unknown parameters of a Markov transition probability that determines the law of motion for the underlying {pt} process. The PIML estimator also yields estimates of the structural parameters that determine the optimal trading rule. We also introduce an alternative consistent, less efficient, but computationally simpler simulated minimum distance (SMD) estimator that avoids high dimensional numerical integrations required by the PIML estimator. Using the SMD estimator, we provide estimates of a truncated lognormal AR(1) model of the wholesale price processes for particular types of steel plate. We use this to infer the share of the middleman's discounted profits that are due to markups paid by its retail customers, and the share due to price speculation. The latter measures the firm's success in forecasting steel prices and in timing its purchases in order to buy low and sell high'. The more successful the firm is in speculation (i.e. in strategically timing its purchases), the more serious are the potential biases that would result from failing to account for the endogeneity of the sampling process.
Handle: RePEc:nbr:nberte:0278
Template-Type: ReDIF-Paper 1.0
Title: Parametric and Nonparametric Volatility Measurement
Classification-JEL: C1
Author-Name: Torben G. Andersen
Author-Name: Tim Bollerslev
Author-Person: pbo66
Author-Name: Francis X. Diebold
Author-Person: pdi1
Note: TWP
Number: 0279
Creation-Date: 2002-08
Order-URL: http://www.nber.org/papers/t0279
File-URL: http://www.nber.org/papers/t0279.pdf
File-Format: application/pdf
Abstract: Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the ex-post sample-path return variability over a fixed time interval, (ii) the ex-ante expected volatility over a fixed time interval, and (iii) the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discrete-time ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete- and continuous-time stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recently-popularized realized volatility measures for (non-trivial) fixed-length time intervals.
Handle: RePEc:nbr:nberte:0279
Template-Type: ReDIF-Paper 1.0
Title: Identification and Inference in Nonlinear Difference-In-Differences Models
Author-Name: Susan Athey
Author-Person: pat6
Author-Name: Guido W. Imbens
Author-Person: pim4
Note: TWP
Number: 0280
Creation-Date: 2002-09
Order-URL: http://www.nber.org/papers/t0280
File-URL: http://www.nber.org/papers/t0280.pdf
File-Format: application/pdf
Publication-Status: published as Athey, Susan and Guido W. Imbens. "Identification and Inference in Nonlinear Difference-in-Differences Models." Econometrica 74, 2 (2006): 431-497.
Abstract: This paper develops an alternative approach to the widely used Difference-In-Difference (DID) method for evaluating the effects of policy changes. In contrast to the standard approach, we introduce a nonlinear model that permits changes over time in the effect of unobservables (e.g., there may be a time trend in the level of wages as well as the returns to skill in the labor market). Further, our assumptions are independent of the scaling of the outcome. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment, and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean-variance tradeoff. We provide conditions under which the model is nonparametrically identified and propose an estimator. We consider extensions to allow for covariates and discrete dependent variables. We also analyze inference, showing that our estimator is root-N consistent and asymptotically normal. Finally, we consider an application.
Handle: RePEc:nbr:nberte:0280
Template-Type: ReDIF-Paper 1.0
Title: Affine Processes and Application in Finance
Author-Name: D. Duffie
Author-Person: pdu341
Author-Name: D. Filipovic
Author-Name: W. Schachermayer
Note: TWP
Number: 0281
Creation-Date: 2002-09
Order-URL: http://www.nber.org/papers/t0281
File-URL: http://www.nber.org/papers/t0281.pdf
File-Format: application/pdf
Abstract: We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.
Handle: RePEc:nbr:nberte:0281
Template-Type: ReDIF-Paper 1.0
Title: Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function
Classification-JEL: E0; C63
Author-Name: Stephanie Schmitt-Grohe
Author-Person: psc44
Author-Name: Martin Uribe
Note: TWP
Number: 0282
Creation-Date: 2002-10
Order-URL: http://www.nber.org/papers/t0282
File-URL: http://www.nber.org/papers/t0282.pdf
File-Format: application/pdf
Abstract: This paper derives a second-order approximation to the solution of a general class of discrete- time rational expectations models. The main theoretical contribution of the paper is to show that for any model belonging to the general class considered, the coefficients on the terms linear and quadratic in the state vector in a second-order expansion of the decision rule are independent of the volatility of the exogenous shocks. In other words, these coefficients must be the same in the stochastic and the deterministic versions of the model. Thus, up to second order, the presence of uncertainty affects only the constant term of the decision rules. In addition, the paper presents a set of MATLAB programs designed to compute the coefficients of the second-order approximation. The validity and applicability of the proposed method is illustrated by solving the dynamics of a number of model economies.
Handle: RePEc:nbr:nberte:0282
Template-Type: ReDIF-Paper 1.0
Title: Simple and Bias-Corrected Matching Estimators for Average Treatment Effects
Classification-JEL: C10; C13
Author-Name: Alberto Abadie
Author-Person: pab7
Author-Name: Guido W. Imbens
Author-Person: pim4
Note: TWP
Number: 0283
Creation-Date: 2002-10
Order-URL: http://www.nber.org/papers/t0283
File-URL: http://www.nber.org/papers/t0283.pdf
File-Format: application/pdf
Abstract: Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. In this article, we develop a new framework to analyze the properties of matching estimators and establish a number of new results. First, we show that matching estimators include a conditional bias term which may not vanish at a rate faster than root-N when more than one continuous variable is used for matching. As a result, matching estimators may not be root-N-consistent. Second, we show that even after removing the conditional bias, matching estimators with a fixed number of matches do not reach the semiparametric efficiency bound for average treatment effects, although the efficiency loss may be small. Third, we propose a bias-correction that removes the conditional bias asymptotically, making matching estimators root-N-consistent. Fourth, we provide a new estimator for the conditional variance that does not require consistent nonparametric estimation of unknown functions. We apply the bias-corrected matching estimators to the study of the effects of a labor market program previously analyzed by Lalonde (1986). We also carry out a small simulation study based on Lalonde's example where a simple implementation of the biascorrected matching estimator performs well compared to both simple matching estimators and to regression estimators in terms of bias and root-mean-squared-error. Software for implementing the proposed estimators in STATA and Matlab is available from the authors on the web.
Handle: RePEc:nbr:nberte:0283
Template-Type: ReDIF-Paper 1.0
Title: Testing for Weak Instruments in Linear IV Regression
Classification-JEL: C2; C3
Author-Name: James H. Stock
Author-Person: pst148
Author-Name: Motohiro Yogo
Author-Person: pyo20
Note: TWP LS
Number: 0284
Creation-Date: 2002-11
Order-URL: http://www.nber.org/papers/t0284
File-URL: http://www.nber.org/papers/t0284.pdf
File-Format: application/pdf
Abstract: Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak instruments, and how does one detect them in practice? This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors. We tabulate critical values that enable using the first-stage F-statistic (or, when there are multiple endogenous regressors, the Cragg-Donald (1993) statistic) to test whether given instruments are weak. A technical contribution is to justify sequential asymptotic approximations for IV statistics with many weak instruments.
Handle: RePEc:nbr:nberte:0284
Template-Type: ReDIF-Paper 1.0
Title: Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity
Author-Name: Guido W. Imbens
Author-Person: pim4
Author-Name: Whitney K. Newey
Note: TWP
Number: 0285
Creation-Date: 2002-11
Order-URL: http://www.nber.org/papers/t0285
File-URL: http://www.nber.org/papers/t0285.pdf
File-Format: application/pdf
Abstract: This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors. We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components. We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function. For inference we propose a two-step series estimator. The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument. In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach. We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.
Handle: RePEc:nbr:nberte:0285
Template-Type: ReDIF-Paper 1.0
Title: Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions
Classification-JEL: G12; G13
Author-Name: Yacine Aït-Sahalia
Author-Person: pai23
Author-Name: Robert Kimmel
Note: TWP
Number: 0286
Creation-Date: 2002-12
Order-URL: http://www.nber.org/papers/t0286
File-URL: http://www.nber.org/papers/t0286.pdf
File-Format: application/pdf
Abstract: We develop and implement a technique for closed-form maximum likelihood estimation (MLE) of multifactor affine yield models. We derive closed-form approximations to likelihoods for nine Dai and Singleton (2000) affine models. Simulations show our technique very accurately approximates true (but infeasible) MLE. Using US Treasury data, we estimate nine affine yield models with different market price of risk specifications. MLE allows non-nested model comparison using likelihood ratio tests; the preferred model depends on the market price of risk. Estimation with simulated and real data suggests our technique is much closer to true MLE than Euler and quasi-maximum likelihood (QML) methods.
Handle: RePEc:nbr:nberte:0286
Template-Type: ReDIF-Paper 1.0
Title: Cointegration Vector Estimation by Panel DOLS and Long-Run Money Demand
Classification-JEL: C1; E4
Author-Name: Nelson C. Mark
Author-Person: pma186
Author-Name: Donggyu Sul
Author-Person: psu42
Note: TWP
Number: 0287
Creation-Date: 2002-12
Order-URL: http://www.nber.org/papers/t0287
File-URL: http://www.nber.org/papers/t0287.pdf
File-Format: application/pdf
Publication-Status: published as Mark, Nelson C. and Donggyu Sul. "Cointegration Vector Estimation By Panel DOLS And Long-Run Money Demand," Oxford Bulletin of Economics and Statistics, 2003, v65(5,Dec), 665-680.
Abstract: We study the panel DOLS estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individual-specific time trends, individual-specific fixed effects and time-specific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T approaches infinity, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of linear constraints has a limiting chi-square distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T go to infinity then letting N go to infinity. In a series of Monte Carlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel dynamic OLS to estimate coefficients of the long-run money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e.=0.26) and the estimated interest rate semi-elasticity is -0.02 (asymptotic s.e.=0.01).
Handle: RePEc:nbr:nberte:0287