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Inference with Many Weak Instruments

众多弱工具变量下的统计推断

Abstract We develop a concept of weak identification in linear instrumental variable models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson–Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator.…

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Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives to Random Bernoulli Sequences

热手谬误中的不确定性:识别偏离随机伯努利序列的连胜模式

Abstract We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive dependence—the hot hand fallacy. In particular, we study permutation tests of the null hypothesis of randomness (i.e. that trials are i.i.d.) based on test statistics that compare the proportion of successes that directly follow $k$ conse…

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Quasi-Experimental Shift-Share Research Designs

准实验移位份额研究设计

Abstract Many studies use shift-share (or “Bartik”) instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual…

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Identifying Shocks via Time-Varying Volatility

利用时变波动率识别结构冲击

Abstract I propose to identify an SVAR, up to shock ordering, using the autocovariance structure of the squared innovations implied by an arbitrary stochastic process for the shock variances. These higher moments are available without parametric assumptions on the variance process. In contrast, previous approaches exploiting heteroskedasticity rely on the path of innovation covariances, which can only be recovered from the data under specific parametric assumptions on the…

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On the Iterated Estimation of Dynamic Discrete Choice Games

动态离散选择博弈的迭代估计

Abstract We study the first-order asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider $K$-stage policy iteration (PI) estimators, where $K$ denotes the number of PIs employed in the estimation. This class nests several estimators proposed in the literature. By considering a “pseudo likelihood” criterion function, our estimator becomes the $K$-pseudo maximum likelihood (PML) estimator in Aguirregabiria and…

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Likelihood Ratio-Based Tests for Markov Regime Switching

马尔可夫机制转换的似然比检验

Abstract Markov regime-switching models are very common in economics and finance. Despite persisting interest in them, the asymptotic distributions of likelihood ratio-based tests for detecting regime switching remain unknown. This study examines such tests and establishes their asymptotic distributions in the context of nonlinear models, allowing multiple parameters to be affected by regime switching. The analysis addresses three difficulties: (i) some nuisance parameters…

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Abatement Strategies and the Cost of Environmental Regulation: Emission Standards on the European Car Market

减排策略与环境监管成本:欧洲汽车市场的排放标准

Abstract This article studies the introduction of an EU-wide emission standard on the automobile market. Using panel data from 1998 to 2011, I find that firms decreased emission ratings by 14%. Firms use technology adoption and gaming of emission tests to decrease emissions, rather than shifting the sales mix or downsizing. I find that the standard missed its emission target, and from estimating a structural model, I find that the standard was not welfare improving. The…

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Long-Run Effects of Lottery Wealth on Psychological Well-Being

彩票财富对心理福祉的长期影响

Abstract We surveyed a large sample of Swedish lottery players about their psychological well-being 5–22 years after a major lottery event and analysed the data following pre-registered procedures. Relative to matched controls, large-prize winners experience sustained increases in overall life satisfaction that persist for over a decade and show no evidence of dissipating over time. The estimated treatment effects on happiness and mental health are significantly smaller.…

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A Bias Bound Approach to Non-parametric Inference

非参数推断的偏差界方法

Abstract The traditional approach to obtain valid confidence intervals for non-parametric quantities is to select a smoothing parameter such that the bias of the estimator is negligible relative to its standard deviation. While this approach is apparently simple, it has two drawbacks: first, the question of optimal bandwidth selection is no longer well-defined, as it is not clear what ratio of bias to standard deviation should be considered negligible. Second, since the…

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Identification and Estimation in Non-Fundamental Structural VARMA Models

非基本结构VARMA模型的识别与估计

Abstract The basic assumption of a structural vector autoregressive moving average (SVARMA) model is that it is driven by a white noise whose components are uncorrelated or independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to non-correlation and these models face two identification issues. The first identification problem is “static” and is due to the fact that there is an infinite…

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Estimation with Aggregate Shocks

存在总量冲击时的估计

Abstract Aggregate shocks affect most households’ and firms’ decisions. Using three stylized models, we show that inference based on cross-sectional data alone generally fails to correctly account for decision making of rational agents facing aggregate uncertainty. We propose an econometric framework that overcomes these problems by explicitly parameterizing the agents’ decision problem relative to aggregate shocks. Our framework and examples illustrate that the…

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International Shocks, Variable Markups, and Domestic Prices

国际冲击、可变加成与国内价格

Abstract How strong are strategic complementarities in price setting across firms? In this article, we provide a direct empirical estimate of firms’ price responses to changes in competitor prices. We develop a general theoretical framework and an empirical identification strategy, taking advantage of a new micro-level dataset for the Belgian manufacturing sector. We find strong evidence of strategic complementarities, with a typical firm adjusting its price with an…

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Regional Transfer Multipliers

区域转移支付乘数

Abstract A series of discontinuities in the allocation mechanism of federal transfers to municipal governments in Brazil allow us to identify the causal effect of public spending on local labour markets, using a “fuzzy” Regression Discontinuity Design (RDD). Our estimates imply a cost per job of about 8,000 US dollars per year and a local income multiplier around two. The effect comes mostly from employment in services and is more pronounced among less financially developed…

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Inference on Causal and Structural Parameters using Many Moment Inequalities

利用大量矩不等式对因果参数与结构参数进行推断

Abstract This article considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters; a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly…

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Automobile Prices in Market Equilibrium with Unobserved Price Discrimination

存在不可观测价格歧视时的汽车市场均衡价格

Abstract In markets where sellers are able to price discriminate, individuals pay different prices that may be unobserved by the econometrician. This article considers the structural estimation of a demand and supply model of differentiated products with such price discrimination and limited information on prices taking the form of, e.g., observing list prices from catalogues or average prices. Within this framework, identification is achieved not only with usual moment…

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Estimating the Elasticity of Intertemporal Substitution Using Mortgage Notches

利用抵押贷款利率跳跃估计跨期替代弹性

Using a novel source of quasi-experimental variation in interest rates, we develop a new approach to estimating the Elasticity of Intertemporal Substitution (EIS). In the U.K., the mortgage interest rate features discrete jumps—notches—at thresholds for the loan-to-value (LTV) ratio. These notches generate large bunching below the critical LTV thresholds and missing mass above them. We develop a dynamic model that links these empirical moments to the underlying structural…

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Two-Step Estimation and Inference with Possibly Many Included Covariates

可能包含大量协变量时的两步估计与推断

We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first-order bias emerges when the number of included covariates is “large” relative to the square-root of sample size, rendering standard inference procedures invalid. We show that the jackknife is able to estimate this “many covariates” bias consistently, thereby delivering a new automatic bias-corrected two-step point estimator. The…

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Identification and Estimation of Dynamic Games When Players’ Beliefs Are Not in Equilibrium

参与者信念不处于均衡时动态博弈的识别与估计

This article deals with the identification and estimation of dynamic games when players’ beliefs about other players’ actions are biased, that is, beliefs do not represent the probability distribution of the actual behaviour of other players conditional on the information available. First, we show that an exclusion restriction, typically used to identify empirical games, provides testable non-parametric restrictions of the null hypothesis of equilibrium beliefs in dynamic…

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The Effectiveness of Hiring Credits

招聘税收抵免的有效性

This article analyses the effectiveness of hiring credits. Using comprehensive administrative data, we show that the French hiring credit, implemented during the Great Recession, had significant positive employment effects and no effects on wages. Relying on the quasi-experimental variation in labour cost triggered by the hiring credit, we estimate a structural search and matching model. Simulations of counterfactual policies show that the effectiveness of the hiring credit…

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Inference on Directionally Differentiable Functions

方向可微函数的统计推断

This article studies an asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\phi$ is a known directionally differentiable function and $\theta_0$ is estimated by $\hat \theta_n$. In these settings, the asymptotic distribution of the plug-in estimator $\phi(\hat \theta_n)$ can be derived employing existing extensions to the Delta method. We show, however, that (full) differentiability of $\phi$ is a necessary and sufficient…

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Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design

断点回归中的近似置换检验与诱导次序统计量

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing whether the means of baseline covariates do not change at the cut-off (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cut-off. We propose a permutation test based on…

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Non-parametric Panel Data Models with Interactive Fixed Effects

具有交互固定效应的非参数面板数据模型

This article studies non-parametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed. I focus on models where the unobservables have a factor structure and enter an unknown structural function non-additively. The setup allows the individual effects to impact outcomes differently in different time periods and it allows for heterogeneous marginal effects. I provide sufficient conditions for point identification of…

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Fuzzy Differences-in-Differences

模糊双重差分

Difference-in-differences (DID) is a method to evaluate the effect of a treatment. In its basic version, a “control group” is untreated at two dates, whereas a “treatment group” becomes fully treated at the second date. However, in many applications of the DID method, the treatment rate only increases more in the treatment group. In such fuzzy designs, a popular estimator of the treatment effect is the DID of the outcome divided by the DID of the treatment. We show that this…

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A Simple Adjustment for Bandwidth Snooping

带宽窥探的简单校正

Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals (CIs) may not have correct coverage, even if the estimator is unbiased. This article proposes a simple adjustment that gives correct coverage in such situations: replace the…

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