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This paper considers the finite-sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite-sample unbiased k-class estimator, we introduce a double-k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperform Fuller (1977) estimators in terms of mean bias and MSE.

Principal component (PC) techniques are commonly used to improve the small sample properties of the linear instrumental variables (IV) estimator. Carrasco (2012) argue that PC type methods provide a natural ranking of instruments with which to reduce the size of the instrument set. This chapter shows how reducing the size of the instrument based on PC methods can lead to poor small sample properties of IV estimators. A new approach to ordering instruments termed ‘normalized principal components’ (NPCs) is introduced to overcome this problem. A simulation study shows the favourable small samples properties of IV estimators using NPC, methods to reduce the size of the instrument relative to PC. Using NPC we provide evidence that the IV setup in Angrist and Krueger (1992) may not suffer the weak instrument problem.

This chapter shows how a weighted average of a forward and reverse Jackknife IV estimator (JIVE) yields estimators that are robust against heteroscedasticity and many instruments. These estimators, called HFUL (Heteroscedasticity robust Fuller) and HLIM (Heteroskedasticity robust limited information maximum likelihood (LIML)) were introduced by Hausman, Newey, Woutersen, Chao, and Swanson (2012), but without derivation. Combining consistent estimators is a theme that is associated with Jerry Hausman and, therefore, we present this derivation in this volume. Additionally, and in order to further understand and interpret HFUL and HLIM in the context of jackknife type variance ratio estimators, we show that a new variant of HLIM, under specific grouped data settings with dummy instruments, simplifies to the Bekker and van der Ploeg (2005) MM (method of moments) estimator.

The authors generalize the standard linear-in-means model to allow for multiple types with between and within-type interactions. The authors provide a set of identification conditions of peer effects and consider a two-stage least squares estimation approach. Large sample properties of the proposed estimators are derived. Their performance in finite samples is investigated using Monte Carlo simulations.

In a recent paper, Hausman, Newey, Woutersen, Chao, and Swanson (2012) propose a new estimator, HFUL (Heteroscedasticity robust Fuller), for the linear model with endogeneity. This estimator is consistent and asymptotically normally distributed in the many instruments and many weak instruments asymptotics. Moreover, this estimator has moments, just like the estimator by Fuller (1977). The purpose of this note is to discuss at greater length the existence of moments result given in Hausman et al. (2012). In particular, we intend to answer the following questions: Why does LIML not have moments? Why does the Fuller modification lead to estimators with moments? Is normality required for the Fuller estimator to have moments? Why do we need a condition such as Hausman et al. (2012), Assumption 9? Why do we have the adjustment formula?

Structural models of demand founded on the classic work of Berry, Levinsohn, and Pakes (1995) link variation in aggregate market shares for a product to the influence of product attributes on heterogeneous consumer tastes. We consider implementing these models in settings with complicated products where consumer preferences for product attributes are sparse, that is, where a small proportion of a high-dimensional product characteristics influence consumer tastes. We propose a multistep estimator to efficiently perform uniform inference. Our estimator employs a penalized pre-estimation model specification stage to consistently estimate nonlinear features of the BLP model. We then perform selection via a Triple-LASSO for explanatory controls, treatment selection controls, and instrument selection. After selecting variables, we use an unpenalized GMM estimator for inference. Monte Carlo simulations verify the performance of these estimators.

This chapter studies the asymptotic properties of within-groups k-class estimators in a panel data model with weak instruments. Weak instruments are characterized by the coefficients of the instruments in the reduced form equation shrinking to zero at a rate proportional to nTδ, where n is the dimension of the cross-section and T is the dimension of the time series. Joint limits as (n,T)→∞ show that this within-group k-class estimator is consistent if 0≤δ<12 and inconsistent if 12≤δ<∞.

This paper evaluates how institutions of governance and macroeconomic uncertainty influence efficiency of financial institutions in the subregion of Sub-Saharan Africa (SSA). Data for the empirical inquiry were compiled from relevant sources for 33 countries in the subregion from 2002 to 2019. Empirical estimates verifying hypothesized relationships were carried out using the continuous updating estimator (CUE) by Hansen et al. (1996).

The purpose of this paper is to evaluates how institutions of governance and macroeconomic uncertainty influence efficiency of financial institutions in the subregion of Sub-Saharan Africa (SSA). Data for the empirical inquiry were compiled from relevant sources for 33 countries in the subregion from 2002 to 2019. Empirical estimates verifying hypothesized relationships were carried out using the continuous updating estimator (CUE) by Hansen et al. (1996).

The results suggest that institutional quality has significant positive effect on financial institution efficiency, supporting the view that improved and supportive structures of governance tend to promote operational efficiency among financial institutions among economies in SSA. In addition, improvement in individual governance indicators such as corruption control, government effectiveness, regulatory quality and rule of law was also found to support or enhance efficiency of financial institutions among economies in the subregion. Macroeconomic uncertainty on the other hand is found to impede efficiency of financial institutions; the same condition (macroeconomic uncertainty) is further found to negate any positive impact corruption control, government effectiveness, regulatory quality and rule of law have on operational efficiency among financial institutions in the subregion.

Unlike most of related studies, this study adopts a different approach on the dynamics of financial institutions. Approach pursued in this empirical inquiry examines how the regulatory environment within which financial institutions operate, the form of governance and the quality of government institutions influence efficiency of financial institutions among emerging economies in Sub-Sahara. Empirical analysis conducted examines effects of variables that are unique to this study; these variables are either constructed or econometrically derived specifically for various interactions verified in the study. For instance, institutional quality variable is an index constructed specifically for this study using principal component analysis approach.

It is shown in the literature that the Arellano–Bond type generalized method of moments (GMM) of dynamic panel models is asymptotically biased (e.g., Hsiao & Zhang, 2015; Hsiao & Zhou, 2017). To correct the asymptotical bias of Arellano–Bond GMM, the authors suggest to use the jackknife instrumental variables estimation (JIVE) and also show that the JIVE of Arellano–Bond GMM is indeed asymptotically unbiased. Monte Carlo studies are conducted to compare the performance of the JIVE as well as Arellano–Bond GMM for linear dynamic panels. The authors demonstrate that the reliability of statistical inference depends critically on whether an estimator is asymptotically unbiased or not.

This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in conditions such as growth convergence. Structural equation models are also considered and limit theory is derived for the corresponding instrumental variable (IV) estimator, Wald test statistic, and overidentification test when the regressors are endogenous. It is shown that near-singular designs of the type considered here are not completely fatal to least squares inference, but do inevitably involve size distortion except in special Gaussian cases. In the endogenous case, IV estimation is inconsistent and both the block Wald test and Sargan overidentification test are conservative, biasing these tests in favor of the null.