This innovative and multi-layered study of the music and culture of Renaissance instrumentalists spans the early institutionalization of instrumental music from c.1420 to the rise of the basso ...continuo and newer roles for instrumentalists around 1600. Employing a broad cultural narrative interwoven with detailed case studies, close readings of eighteen essential musical sources, and analysis of musical images, Victor Coelho and Keith Polk show that instrumental music formed a vital and dynamic element in the artistic landscape, from rote function to creative fantasy. Instrumentalists occupied a central role in courtly ceremonies and private social rituals during the Renaissance, and banquets, dances, processions, religious celebrations and weddings all required their participation, regardless of social class. Instrumental genres were highly diverse artistic creations, from polyphonic repertories revealing knowledge of notated styles, to improvisation and flexible practices. Understanding the contributions of instrumentalists is essential for any accurate assessment of Renaissance culture.
Plausibly exogenous Conley, Timothy G; Hansen, Christian B; Rossi, Peter E
The review of economics and statistics,
02/2012, Volume:
94, Issue:
1
Journal Article
Peer reviewed
Instrumental variable (IV) methods are widely used to identify causal effects in models with endogenous explanatory variables. Often the instrument exclusion restriction that underlies the validity ...of the usual IV inference is suspect; that is, instruments are only plausibly exogenous. We present practical methods for performing inference while relaxing the exclusion restriction. We illustrate the approaches with empirical examples that examine the effect of 401(k) participation on asset accumulation, price elasticity of demand for margarine, and returns to schooling. We find that inference is informative even with a substantial relaxation of the exclusion restriction in two of the three cases.
We consider estimation of and inference about coefficients on endogenous variables in a linear instrumental variables model where the number of instruments and exogenous control variables are each ...allowed to be larger than the sample size. We work within an approximately sparse framework that maintains that the signal available in the instruments and control variables may be effectively captured by a small number of the available variables. We provide a LASSO-based method for this setting which provides uniformly valid inference about the coefficients on endogenous variables. We illustrate the method through an application to demand estimation.
When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables (IV) estimation and inference become unreliable. A large literature in econometrics ...has developed procedures for detecting weak instruments and constructing robust confidence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for nonhomoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the
American Economic Review
from 2014 to 2018 that use IV. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps that researchers can take to better handle weak instruments in applications.
We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. ...Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic "beta-min" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.
BACKGROUND:Investigators often support the validity of Mendelian randomization (MR) studies, an instrumental variable approach proposing genetic variants as instruments, via subject matter knowledge. ...However, the instrumental variable model implies certain inequalities, offering an empirical method of falsifying (but not verifying) the underlying assumptions. While these inequalities are said to detect only extreme assumption violations in practice, to our knowledge they have not been used in settings with multiple proposed instruments.
METHODS:We applied the instrumental inequalities to an MR analysis of the effect of maternal pregnancy Vitamin D on offspring psychiatric outcomes, proposing four independent maternal genetic variants as instruments. We assessed whether the proposed instruments satisfied the instrumental inequalities separately and jointly and explored the instrumental inequalities’ properties via simulations.
RESULTS:The instrumental inequalities were satisfied (i.e., we did not falsify the MR model) when considering each variant separately. However, the inequalities were violated when considering four variants jointly and for some combinations of two or three variants (2 of 36 two-variant combinations and 18 of 24 three-variant combinations). In simulations, the inequalities detected structural biases more often when assessing proposed instruments jointly, while falsification in the absence of structural bias remained rare.
CONCLUSIONS:The instrumental inequalities detected violations of the MR assumptions for genetic variants jointly proposed as instruments in our study, though the instrumental inequalities were satisfied when considering each proposed instrument separately. We discuss how investigators can assess instrumental inequalities to eliminate clearly invalid analyses in settings with many proposed instruments and provide appropriate code
We investigate the behavior of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang ...et al. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator that is consistent when less than 50% of the instruments are invalid, and its consistency does not depend on the relative strength of the instruments, or their correlation structure. We show that this estimator can be used for adaptive Lasso estimation, with the resulting estimator having oracle properties. The methods are applied to a Mendelian randomization study to estimate the causal effect of body mass index (BMI) on diastolic blood pressure, using data on individuals from the UK Biobank, with 96 single nucleotide polymorphisms as potential instruments for BMI. Supplementary materials for this article are available online.
The focus of this paper is the nonparametric estimation of an instrumental regression function defined by conditional moment restrictions that stem from a structural econometric model EY — (Z) | W = ...0, and involve endogenous variables Y and Z and instruments W. The function is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.
Authors often add covariates to a base model sequentially either to test a particular coefficient’s “robustness” or to account for the “effects” on this coefficient of adding covariates. This is ...problematic, due to sequence sensitivity when added covariates are intercorrelated. Using the omitted variables bias formula, I construct a conditional decomposition that accounts for various covariates’ role in moving base regressors’ coefficients. I also provide a consistent covariance formula. I illustrate this conditional decomposition with NLSY data in an application that exhibits sequence sensitivity. Related extensions include instrumental variables, the fact that my decomposition nests the Oaxaca-Blinder decomposition, and a Hausman test result.
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