On the Normalization of Structural Equations: Properties of Direction Estimators

The limited information maximum likelihood (LIML) estimator is shown to be inadmissible in terms of asymptotic expansions of the distributions of the estimators. The LIML estimator is improved by combining it linearly with the two-stage or the ordinary least squares estimator.

We derive asymptotic expansions of the distributions of the maximum likelihood (ML) estimator and the ordinary least squares (OLS) estimator in a linear functional relationship model as the sample size increases infinitely. These expansions are equivalent to the asymptotic expansions of the distributions of the limited information maximum likelihood (LIML) estimator when the covariance is known to within a proportionality constant and the two-stage least squares (TSLS) estimator as the number of excluded exogenous variables increases in a simultaneous equations system.

PurposeThis study examines how institutional quality influences variability in financial development among economies in Sub-Saharan Africa (SSA).Design/methodology/approachEmpirical estimations verifying various relationships are performed using the limited information maximum likelihood (LIML) estimation technique.FindingsThe results suggest that institutional quality enhances the pace of financial development among economies in the sub-region all things being equal. In a further micro-level analysis where components of institutional quality index are examined separately, the study’s results suggest that effective governance, regulatory quality, rule of law and accountability tend to have a significant positive impact on financial sector development.Research limitations/implicationsFindings of the study suggest that policies geared towards improving governance and regulatory institutions can augment development of the financial sector among economies in SSA; governments and policymakers are therefore encouraged to resource noted institutions to play effective roles for the development of the financial sector.Originality/valueCompared to related studies, this study reorients existing paradigm, which emphasizes the role of governance and institutional variables in the economic growth discourse. The authors’ empirical inquiry rather focuses on how governance and institutional structures influence regional financial development dynamics. Specifically, this study differs from most macro-level studies found in literature because it examines the impact of hitherto unexamined governance and institutional variables on financial development among economies in SSA.

We study the small sample properties of the simultaneous equation estimators by a Monte Carlo approach. The four methods of estimation considered are: least squares, two-stage least squares, unbiased and minimumsecond-moment. The last of these four methods possesses the smallest secondorder sampling moments about the true parameter value in a majority of cases, while two-stage least squares shows the smallest bias in all cases. It is also founld that the usual asymptotic standard errors of two-stage least squares give a rather satisfactory picture of the variability of the estimates about the true value. This is not true for the least squares method in all cases considered. Instead, it seems that the classical least squares standard errors measure the variability of the estimates about the biased expectation, not about the true value. In some cases this makes a very large difference. IN A RECENT article Wagner [4] examined certain small-sample properties of limited-information maximum-likelihood, least squares, and instrumentalvariables estimates for two models by a Monte Carlo approach. Although these models are very simple-which is natural enough for a sampling experiment-it seems appropriate for a variety of reasons to consider them somewhat further. First, there are now several alternative estimation procedures available, and it is worth-while to analyse these too. Secondly, by using Wagner's models we can disregard certain methods of estimation for the simple reason that they were already considered by him. Thirdly, it appears that the two equations of both models are in a certain sense of extreme types, so that we may hope that a Monte Carlo approach will shed some light on the particular problems raised by such extremes. Wagner considered only one equation in each model, and one which is over identified. We shall consider also the second equation, which is just-identified. Just-identification implies that the two-stage least squares estimator is identical with the limited information maximum likelihood estimator. Hence we may disregard the latter estimation procedure, the limited

Optimizing in the class of Fuller modified limited information maximum likelihood estimators

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance restriction.

In this paper we propose a new estimator for a model with one endogenous regressor and many instrumental variables. Our motivation comes from the recent literature on the poor properties of standard instrumental variables estimators when the instrumental variables are weakly correlated with the endogenous regressor. Our proposed estimator puts a random coefficients structure on the relation between the endogenous regressor and the instruments. The variance of the random coefficients is modelled as an unknown parameter. In addition to proposing a new estimator, our analysis yields new insights into the properties of the standard two-stage least squares (TSLS) and limited-information maximum likelihood (LIML) estimators in the case with many weak instruments. We show that in some interesting cases, TSLS and LIML can be approximated by maximizing the random effects likelihood subject to particular constraints. We show that statistics based on comparisons of the unconstrained estimates of these parameters to the implicit TSLS and LIML restrictions can be used to identify settings when standard large sample approximations to the distributions of TSLS and LIML are likely to perform poorly. We also show that with many weak instruments, LIML confidence intervals are likely to have under-coverage, even though its finite sample distribution is approximately centered at the true value of the parameter. In an application with real data and simulations around this data set, the proposed estimator performs markedly better than TSLS and LIML, both in terms of coverage rate and in terms of risk.

Connecting quality of life, tourism specialization, and economic growth in small island destinations: The case of Malta

If the ordinary least squares (OLS) diagnostics discussed in the previous chapter indicate the existence of spatial lag or spatial error dependence, the researcher will wish to model the type of dependence indicated by these diagnostics. If the OLS diagnostics indicate the presence of a diffusion process, the researcher will wish to estimate a spatial lag model via maximum likelihood (ML) estimation or an instrumental variables specification incorporating instruments for the spatially lagged dependent variable. Alternatively, if the OLS diagnostics indicate the existence of spatial error dependence, the researcher may choose to estimate a more fully specified OLS model to model the spatial dependence or may choose to employ a ML or generalized method of moments (GMM) approach incorporating the spatial dependence in the errors. The spatial dependence diagnosed via the diagnostics discussed in Chapter 5 may alternatively be produced by spatial heterogeneity in the effects of covariates. If this is the only source of spatial dependence, modeling this heterogeneity will be sufficient to capture the spatial dependence. As a consequence, any specification search should also consider the possibility of spatial heterogeneity, which is the focus of Chapter 7. This chapter will first, however, examine alternative approaches for modeling spatial dependence if spatial heterogeneity is not present. This chapter begins by examining ML estimation of spatial lag models that derives from Ord (1975). Next, I explore alternative instrumental variables and GMM estimators for spatial lag dependence. Next, I turn to approaches for estimating spatial error models. I conclude by considering areas of concern in the estimation of spatial models. These include estimators for large sample sizes and diagnostics for continued spatial dependence. MAXIMUM LIKELIHOOD SPATIAL LAG ESTIMATION The mixed regressive, spatial autoregressive model, or spatial lag model, extends the pure spatial autoregressive model considered in Section 3.2 to include also the set of covariates and associated parameters: y = ρ W y +Xβ+e where X is again an N by K matrix of observations on the covariates, β is a K by 1 vector of parameters, and the remaining notation is as discussed in Section 3.2.

Recent studies have explored the role of firm dynamics and the connection to job reallocation. However, limited attention has been devoted to the role of micro and small firms in this process, particularly about the quality of the jobs generated. Therefore, this article aims to measure the impact of micro and small firm dynamics on occupation diversification in Brazil, with specific emphasis on job quality. The study used data from 558 microregions within the Brazilian industrial sector between 2003 and 2015. Panel data were applied to three econometric models: Feasible Generalized Least Squares (FGLS), Driscoll–Kraay (DK) and Instrumental Variable (IV) models for robustness analysis, including Two-Stage Least Squares (2SLS), Limited Information Maximum Likelihood (LIML), and the Generalized Method of Moments with Continuously Updating Estimators (GMM-CUE). Our main finding reveals that the dynamics of micro and small firms positively impact occupation diversity in Brazil, leading to the creation of a wider range of job types. Furthermore, the frequency of change of firms from microenterprises to small businesses increases the occupation diversity in the Brazilian industrial sector. Our findings are significant in providing policy recommendations for developing countries to achieve a more diverse labor market.

The aims of this study is to verify the effect of the exploitation of mineral resources on human capital in CEMAC countries. Our analysis made use of panel data sets of all these members countries, over the period of 2002 to 2016, which is a period where the prices of natural resources weakness frequent fluctuation in the world market. The econometric model formulated in relation to mineral rent in CEMAC countries has three indicators of human capital, measured by the rate of school enrolment, infant mortality rate and life expectancy. Three regression techniques have been used for this purpose: the ordinary least squared (OLS); two stages least squared (2SLS) and Limited Information Maximum Likelihood (LIML). The results of our analysis shows that rent from mineral resources has a negative effect on schooling rate and life expectancy rate in CEMAC. Similarly, our result demonstrates that, mineral rent increases infant mortality rate in CEMAC members countries. Keywords: Mineral rent, human capital and panel data DOI : 10.7176/JESD/10-24-05 Publication date: December 31 st 2019

Market response models based on field-generated data need to address potential endogeneity in the regressors to obtain consistent parameter estimates. Another requirement is that market response models predict well in a holdout sample. With both requirements combined, it may seem reasonable to subject an endogeneity-corrected model to a holdout prediction task, and this is quite common in the academic marketing literature. One may be inclined to expect that the consistent parameter estimates obtained via instrumental variables (IV) estimation predict better than the biased ordinary least squares (OLS) estimates. This paper shows that this expectation is incorrect. That is, if the holdout sample is similar to the estimation sample so that the regressors are endogenous in both samples, holdout sample validation favors regression estimates that are not corrected for endogeneity (i.e., OLS) over estimates that are corrected for endogeneity (i.e., IV estimation). We also discuss ways in which holdout samples may be used sensibly in the presence of endogeneity. A key takeaway is that if consistent parameter estimates are the primary model objective, the model should be validated with an exogenous (rather than endogenous) holdout sample.

We extend our 2003 paper on instrumental variables and generalized method of moments estimation, and we test and describe enhanced routines that address heteroskedasticity- and autocorrelation-consistent standard errors, weak instruments, limited-information maximum likelihood and k-class estimation, tests for endogeneity and Ramsey's regression specification-error test, and autocorrelation tests for instrumental variable estimates and panel-data instrumental variable estimates.

Identification of suitable instruments is a critical step for the implementation of instrumental variable (IV) estimation. A challenge is that, as the level of correlation between the instruments and the endogenous variable increases, so also do the chances that the instruments themselves will be correlated with the error terms. Contrariwise, when the correlation with the endogenous variable is low, the instruments may be weak and perform poorly. The objective of this paper is to explore the use of synthetic variables in IV estimation when the analysis is of spatial data series. The point of departure is the use of eigenvector analysis of the usual spatial weights matrix used in spatial statistics. Eigenvectors obtained from a transformed weights matrix are known to represent latent map patterns. Our proposal is to use these patterns to obtain synthetic variables for use as instruments in IV estimation. By their very nature, instruments based on synthetic variables are exogenous. Furthermore, they can provide relatively high levels of correlation with the endogenous variable. In this paper we consider two situations of interest: First, the case where there are no clear candidates for instrumentation and the instruments are comprised of purely synthetic variables; second, the case when there are substantive but weak instruments that can be enhanced by the addition of synthetic variables. The approach proposed is illustrated with an empirical example.

Purpose – The purpose of this paper is to investigate the relationship between corporate governance mechanism and firm value of the listed companies in China. Does the better corporate governance lead to the higher firm value? Or does the higher firm value make it easy to choose a better governance mechanism? Or they affect each other? In other words, this paper tries to answer whether the corporate governance mechanism is only decided by institutional arrangement, or by market choice according to firm value or performance or by the interaction of institutional arrangement and market choice? It tries to answer whether institutional arrangement maximizes the firm value, or an invisible hand pushes them to arrive at its maximum. Design/methodology/approach – This paper establishes an analytic framework of simultaneous equations based on causality, which includes five endogenous variables: ownership of larger shareholders, managerial ownership, director compensation, debt financing and firm value. It adopts 1,644 data samples from 274 Chinese listed companies in Shanghai and Shenzhen Stock Exchange during 2007- 2012 after the non-tradable shares reform. Ordinary least squares (OLS) estimation of single equation, 2SLS and 3SLS estimation of simultaneous equations are respectively done to show the differences of these three kinds of estimations. Findings – The empirical results show that differences exist among OLS, 2SLS and 3SLS estimation. Finally, 3SLS estimation should be adopted because the OLS and 2SLS estimation are biased. There are endogenous relationships between corporate governance mechanism and firm value. Through the 3SLS estimation, it is found that first, ownership concentration and firm value affect each other positively. Second, managerial ownership and firm value affect each other positively; third, director compensation and firm value affect each other negatively, while director compensation and firm performance affect each other positively. Finally, debt financing level and firm value are negatively related to each other. Practical implications – It means that ownership of large shareholders, managerial ownership, director compensation and debt financing in the Chinese listed companies are found to have a root in the interaction between institutional arrangement and market choice. It is also found that adverse selection occurs when creditors loan to the listed companies. Managerial compensation is positively related to accounting profit, but it is negatively related to firm value because managers increase profit due by earning management. This could only increase the accounting profits and obtain huge cash compensation, but not increase firm value and even harm the interests of shareholders. Originality/value – This paper not only shows the difference between OLS and 2SLS estimation but also compares the estimation of 2SLS and 3SLS in terms of empirical methods. It gives answers to the following questions: whether the relationship is one-way causality or bilateral causality between ownership concentration, managerial ownership, director compensation and firm value; whether governance mechanism affects firm value by institutional arrangement, or market drives both of them to strike a balance by an invisible hand. In other words, does it make them arrive at equilibrium through the competitive selection process when shareholders, directors, managers and creditors attempt to maximize themselves of their interests?