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1.
    
We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite‐sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is not known. When the function class is centrosymmetric, these efficiency bounds imply that minimax CIs are close to efficient at smooth regression functions. This implies, in particular, that it is impossible to form CIs that are substantively tighter using data‐dependent tuning parameters, and maintain coverage over the whole function class. We specialize our results to inference on the regression discontinuity parameter, and illustrate them in simulations and an empirical application.  相似文献   

2.
    
We investigate the role of uncertainty in business cycles. First, we demonstrate that microeconomic uncertainty rises sharply during recessions, including during the Great Recession of 2007–2009. Second, we show that uncertainty shocks can generate drops in gross domestic product of around 2.5% in a dynamic stochastic general equilibrium model with heterogeneous firms. However, we also find that uncertainty shocks need to be supplemented by first‐moment shocks to fit consumption over the cycle. So our data and simulations suggest recessions are best modelled as being driven by shocks with a negative first moment and a positive second moment. Finally, we show that increased uncertainty can make first‐moment policies, like wage subsidies, temporarily less effective because firms become more cautious in responding to price changes.  相似文献   

3.
    
We develop a new quantile‐based panel data framework to study the nature of income persistence and the transmission of income shocks to consumption. Log‐earnings are the sum of a general Markovian persistent component and a transitory innovation. The persistence of past shocks to earnings is allowed to vary according to the size and sign of the current shock. Consumption is modeled as an age‐dependent nonlinear function of assets, unobservable tastes, and the two earnings components. We establish the nonparametric identification of the nonlinear earnings process and of the consumption policy rule. Exploiting the enhanced consumption and asset data in recent waves of the Panel Study of Income Dynamics, we find that the earnings process features nonlinear persistence and conditional skewness. We confirm these results using population register data from Norway. We then show that the impact of earnings shocks varies substantially across earnings histories, and that this nonlinearity drives heterogeneous consumption responses. The framework provides new empirical measures of partial insurance in which the transmission of income shocks to consumption varies systematically with assets, the level of the shock, and the history of past shocks.  相似文献   

4.
    
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite‐dimensional nuisance parameter. We introduce a sufficient statistic for this nuisance parameter in a Gaussian problem and propose conditional tests. These conditional tests have uniformly correct asymptotic size for a large class of models and test statistics. We apply our approach to construct tests based on quasi‐likelihood ratio statistics, which we show are efficient in strongly identified models and perform well relative to existing alternatives in two examples.  相似文献   

5.
    
In the regression‐discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a “large” bandwidth, leading to data‐driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory‐based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias‐corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close‐to‐correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).  相似文献   

6.
    
This paper develops asymptotic approximations for kernel‐based semiparametric estimators under assumptions accommodating slower‐than‐usual rates of convergence of their nonparametric ingredients. Our first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias. This bias is nonnegligible in general, and therefore poses a challenge for inference. Our second main result shows that some (but not all) nonparametric bootstrap distributional approximations provide an automatic method of correcting for the bias. Our general theory is illustrated by means of examples and its main finite sample implications are corroborated in a simulation study.  相似文献   

7.
    
This paper develops a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of future τ‐quantile utilities, for τ ∈ (0,1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, including the ability to capture heterogeneity and allowing the separation between risk aversion and elasticity of intertemporal substitution. Although quantiles do not share some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, this value function is concave and differentiable, and the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well‐known quantile regression methods for estimating and testing the economic model. In this way, the parameters of the model can be interpreted as structural objects. Therefore, the proposed methods provide microeconomic foundations for quantile regression methods. To illustrate the developments, we construct an intertemporal consumption model and estimate the discount factor and elasticity of intertemporal substitution parameters across the quantiles. The results provide evidence of heterogeneity in these parameters.  相似文献   

8.
    
It is costly to learn about market conditions elsewhere, especially in developing countries. This paper examines how such information frictions affect trade. Using data on regional agricultural trade in the Philippines, I first document a number of observed patterns in trade flows and prices that suggest the presence of information frictions. I then incorporate information frictions into a perfect competition trade model by embedding a process whereby heterogeneous producers engage in a costly sequential search process to determine where to sell their produce. I show that introducing information frictions reconciles the theory with the observed patterns in the data. Structural estimation of the model finds that information frictions are quantitatively important: roughly half the observed regional price dispersion is due to information frictions. Furthermore, incorporating information frictions improves the out‐of‐sample predictive power of the model.  相似文献   

9.
    
We analyze the implications of household‐level adjustment costs for the dynamics of aggregate consumption. We show that an economy in which agents have “consumption commitments” is approximately equivalent to a habit formation model in which the habit stock is a weighted average of past consumption if idiosyncratic risk is large relative to aggregate risk. Consumption commitments can thus explain the empirical regularity that consumption is excessively sensitive and excessively smooth, findings that are typically attributed to habit formation. Unlike habit formation and other theories, but consistent with empirical evidence, the consumption commitments model also predicts that excess sensitivity and smoothness vanish for large shocks. These results suggest that behavior previously attributed to habit formation may be better explained by adjustment costs. We develop additional testable predictions to further distinguish the commitment and habit models and show that the two models have different welfare implications.  相似文献   

10.
    
We propose a bootstrap‐based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of θ, not θ itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately, and we establish its rate of convergence. The algorithm is of independent interest for optimization problems with simple objectives and complicated constraints. An empirical application estimating an entry game illustrates the usefulness of the method. Monte Carlo simulations confirm the accuracy of the solution algorithm, the good statistical as well as computational performance of calibrated projection (including in comparison to other methods), and the algorithm's potential to greatly accelerate computation of other confidence intervals.  相似文献   

11.
    
This paper provides conditions under which the inequality constraints generated by either single agent optimizing behavior or the best response condition of multiple agent problems can be used as a basis for estimation and inference. An application illustrates how the use of these inequality constraints can simplify the analysis of complex behavioral models.  相似文献   

12.
    
A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi‐experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery‐generated randomization integral to such designs from non‐random preferences and priorities remains open. This paper develops easily‐implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.  相似文献   

13.
    
The bootstrap is a convenient tool for calculating standard errors of the parameter estimates of complicated econometric models. Unfortunately, the fact that these models are complicated often makes the bootstrap extremely slow or even practically infeasible. This paper proposes an alternative to the bootstrap that relies only on the estimation of one‐dimensional parameters. We introduce the idea in the context of M and GMM estimators. A modification of the approach can be used to estimate the variance of two‐step estimators.  相似文献   

14.
    
In this paper, we develop algorithms to independently draw from a family of conjugate posterior distributions over the structural parameterization when sign and zero restrictions are used to identify structural vector autoregressions (SVARs). We call this family of conjugate posteriors normal‐generalized‐normal. Our algorithms draw from a conjugate uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization and transform the draws into the structural parameterization; this transformation induces a normal‐generalized‐normal posterior over the structural parameterization. The uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization has been prominent after the work of Uhlig (2005). We use Beaudry, Nam, and Wang's (2011) work on the relevance of optimism shocks to show the dangers of using alternative approaches to implementing sign and zero restrictions to identify SVARs like the penalty function approach. In particular, we analytically show that the penalty function approach adds restrictions to the ones described in the identification scheme.  相似文献   

15.
    
Internet advertising has been the fastest growing advertising channel in recent years, with paid search ads comprising the bulk of this revenue. We present results from a series of large‐scale field experiments done at eBay that were designed to measure the causal effectiveness of paid search ads. Because search clicks and purchase intent are correlated, we show that returns from paid search are a fraction of non‐experimental estimates. As an extreme case, we show that brand keyword ads have no measurable short‐term benefits. For non‐brand keywords, we find that new and infrequent users are positively influenced by ads but that more frequent users whose purchasing behavior is not influenced by ads account for most of the advertising expenses, resulting in average returns that are negative.  相似文献   

16.
    
Propensity score matching estimators (Rosenbaum and Rubin (1983)) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators, and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATET). The adjustment for the ATE estimator is negative (or zero in some special cases), implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples. However, for the ATET estimator, the sign of the adjustment term depends on the data generating process, and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small.  相似文献   

17.
    
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18.
    
We document that consumption growth rates are far from i.i.d. and have a highly persistent component. First, we estimate univariate and multivariate models of cash‐flow (consumption, output, dividends) growth that feature measurement errors, time‐varying volatilities, and mixed‐frequency observations. Monthly consumption data are important for identifying the stochastic volatility process; yet the data are contaminated, which makes the inclusion of measurement errors essential for identifying the predictable component. Second, we develop a novel state‐space model for cash flows and asset prices that imposes the pricing restrictions of a representative‐agent endowment economy with recursive preferences. To estimate this model, we use a particle MCMC approach that exploits the conditional linear structure of the approximate equilibrium. Once asset return data are included in the estimation, we find even stronger evidence for the persistent component and are able to identify three volatility processes: the one for the predictable cash‐flow component is crucial for asset pricing, whereas the other two are important for tracking the data. Our model generates asset prices that are largely consistent with the data in terms of sample moments and predictability features. The state‐space approach allows us to track over time the evolution of the predictable component, the volatility processes, the decomposition of the equity premium into risk factors, and the variance decomposition of asset prices.  相似文献   

19.
    
This paper develops a simple model of firm entry, competition, and exit in oligopolistic markets. It features toughness of competition, sunk entry costs, and market‐level demand and cost shocks, but assumes that firms' expected payoffs are identical when entry and survival decisions are made. We prove that this model has an essentially unique symmetric Markov‐perfect equilibrium, and we provide an algorithm for its computation. Because this algorithm only requires finding the fixed points of a finite sequence of contraction mappings, it is guaranteed to converge quickly.  相似文献   

20.
    
We develop a new parametric estimation procedure for option panels observed with error. We exploit asymptotic approximations assuming an ever increasing set of option prices in the moneyness (cross‐sectional) dimension, but with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estimators converge stably to a mixed‐Gaussian law and we develop feasible estimators for the limiting variance. We also provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and one constructed nonparametrically from high‐frequency data on the underlying asset. Furthermore, we develop new tests for the day‐by‐day model fit over specific regions of the volatility surface and for the stability of the risk‐neutral dynamics over time. A comprehensive Monte Carlo study indicates that the inference procedures work well in empirically realistic settings. In an empirical application to S&P 500 index options, guided by the new diagnostic tests, we extend existing asset pricing models by allowing for a flexible dynamic relation between volatility and priced jump tail risk. Importantly, we document that the priced jump tail risk typically responds in a more pronounced and persistent manner than volatility to large negative market shocks.  相似文献   

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