Limited Information Maximum Likelihood Estimator Research Articles

ICT, Financial Inclusion and the Informal Economy: Evidence from Selected Latin American and Caribbean Countries

ABSTRACT Exploring effective tools to control the rampant expansion of the informal economy is critical to achieving the Sustainable Development Goals (SDGs). Based on balanced panel data for 19 selected Latin American and Caribbean countries for the period 2008–2017, this study employs fixed-effects estimation, limited information maximum likelihood estimation, and system generalized method of moments estimation to investigate the direct and indirect effects of information and communication technologies (ICT) diffusion on the size of the informal economy. The findings suggest that ICT diffusion can significantly reduce the size of the informal economy in LAC. Moreover, the dampening effect of ICT on the informal economy is more significant in countries with lower levels of financial inclusion. Accordingly, we recommend strengthening ICT sector development to enhance financial deepening and government efficiency and thus reduce informality in LAC.

A weighted average limited information maximum likelihood estimator

In this article, a Stein-type weighted limited information maximum likelihood (LIML) estimator is proposed. It is based on a weighted average of the ordinary least squares (OLS) and LIML estimators, with weights inversely proportional to the Hausman test statistic. The asymptotic distribution of the proposed estimator is derived by means of local-to-exogenous asymptotic theory. In addition, the asymptotic risk of the Stein-type LIML estimator is calculated, and it is shown that the risk is strictly smaller than the risk of the LIML under certain conditions. A Monte Carlo simulation and an empirical application of a green patent dataset from Nordic countries are used to demonstrate the superiority of the Stein-type LIML estimator to the OLS, two-stage least squares, LIML and combined estimators when the number of instruments is large.

Impact of institutional quality on ecological footprint: New insights from G20 countries

The complex relationship between institutional quality and ecological footprint (ECF) has been verified in prior literature; however, the subject is still inadequately explored and often disregarded to highlight areas where specific policy tensions exist. Therefore, this study aims to delve into the significance of institutional quality on ECF through a limited information maximum likelihood (LIML) panel analysis in the G20 countries from 2000 to 2022. For a precise evaluation, the study innovatively constructs a composite institutional quality index (IQI) and three indices under the accountability, transparency, and participation dimensions. Additionally, the study develops an economic uncertainty predictor to capture the effects of external economic shocks on the subject. The results obtained from the LIML estimation demonstrate that IQI is substantive in reducing ECF in the recipient panel. Further, the findings highlight that all three dimensions of IQI are significant in abating ECF, while the transparency index yields a higher influence on abating ECF. It is also observed that IQI plays an effective role in modulating the relationships between ECF, financial development, human development, growth, and energy consumption, while it is found to be insignificant in reducing the negative effects of globalization on ECF. Finally, the results indicate that IQI is highly influential in eliminating the adverse impact of external shocks on ECF. The results are robust and have specific policy implications.

R&D contribution in TFP growth of Greek industry: A limited information likelihood approach

ABSTRACTWe provide a novel panel model to decompose total factor productivity (TFP) growth in the Greek industry at the firm level while we tackle the contribution of R&D. We, therefore, opt for parametric methodology that provides statistical inference and would validate the results. Our modeling departs from prior strong assumptions such as error terms across firms being independent. In fact, we provide a novel limited information maximum likelihood (LIML) estimation method that adequately deals with the issue of endogeneity and model misspecification. We demonstrate that our model detects variability in terms of TFP growth components across industries and firms. Our results show that R&D would enhance TFP of Greek firms, albeit the crisis has had a detrimental impact. Financial ratios such as liquidity and solvency ratios also affect TFP as we demonstrate that both would enhance TFP. The solvency ratio is important as it provides an estimate of whether the firm can cope with debt. We also note variability across small versus medium and large firms and report that small firms are more productive and spend more of their revenues on R&D. In terms of policy, our evidence warrants higher R&D spending to enhance TFP growth, though R&D funding is a concern.

HIGHER-ORDER APPROXIMATION OF IV ESTIMATORS WITH INVALID INSTRUMENTS

This paper analyzes the higher-order approximation of instrumental variable (IV) estimators in a linear homoskedastic IV regression model when a large set of instruments with potential invalidity is present. We establish theoretical results on the higher-order mean-squared error (MSE) approximation of the two-stage least-squares (2SLS), the limited information maximum likelihood (LIML), the Fuller (FULL), the bias-adjusted 2SLS, and jackknife version of the LIML and FULL estimators by allowing for local violations of the instrument exogeneity conditions. Based on the approximation to the higher-order MSE, we consider the instrument selection criteria that can be used to choose among the set of available instruments. We demonstrate the asymptotic optimality of the instrument selection procedure proposed by Donald and Newey (2001, Econometrica 69, 1161–1191) in the presence of locally (faster than $N^{-1/2}$ ) invalid instruments in the sense that the dominant term in the MSE with the chosen instrument is asymptotically equivalent to the infeasible optimum. Furthermore, we propose instrument selection procedures to choose instruments among the sets of conservative (known) valid instruments and potentially locally ( $N^{-1/2}$ ) invalid instruments based on the higher-order MSE of the IV estimators by considering the bias-variance trade-off.

The Effect of Health on the Elderly's Labor Supply in Rural China: Simultaneous Equation Models With Binary, Ordered, and Censored Variables.

In this study, we examined the effect of health on the elderly's labor supply in rural China based on the data of the Chinese Health and Nutrition Survey (CHNS) from 1997 to 2006. We used simultaneous equations to address the endogeneity problem of health and estimate the models with censored data of labor supply by the full information maximum likelihood estimation. We found that the failing health does not significantly decrease the elderly's labor supply in rural areas when using both the subjective (self-reported health status) and objective (hypertension diagnosed or not) health indicators. Our finding indicates the phenomenon of “ceaseless toil” for the elderly in rural China, i.e., the elderly almost work their whole life even if they are not physically capable. The results remain robust when using a two-stage limited information maximum likelihood estimation.

Financial development and institutional quality among emerging economies

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.

The Impact of Globalization, Energy Use, and Trade on Ecological Footprint in Pakistan: Does Environmental Sustainability Exist?

Globalization has contributed to several advances in technology including linking people around the globe and driving us to modern economies. With fast economic growth and industrialization progress, the negative impact of globalization on biodiversity can be easily ignored. Globalization is an undeniable factor in our planetary devastation from pollution to global warming and climate change. The major intention of our recent analysis was to examine the globalization, energy consumption, trade, economic growth, and fuel importation to determine the ecological footprint in Pakistan by taking the annual data variables from 1974–2017. A linear ARDL (autoregressive distributed lag) technique with limited information maximum likelihood and linear Gaussian model estimation were utilized to check the variables association. Outcomes show that in the long run, globalization, energy usage, trade, and GDP growth have consistently productive interactions with the ecological footprint, while an examination of fuel importation uncovers an adversative linkage to impacts on the ecological footprint in Pakistan. Similarly, the findings of short-run interactions also reveal that globalization, energy usage, trade, and GDP growth have constructive linkages; however, an examination of fuel importation also uncovers an adversative linkage to impacts on the ecological footprint. The outcomes of limited information maximum likelihood also expose that the variables of globalization, energy usage, trade, and fuel importation have productive linkages, while an examination the GDP growth uncovers an adversative linkage to the ecological footprint. Furthermore, the outcomes of the linear Gaussian model estimation also uncover that globalization and energy usage demonstrate a constructive linkage, while other variables reveal an adverse linkage to the ecological footprint. Environmental pollution is now an emerging issue which causes the climatic variations associated with greenhouse gases emissions. The Pakistani government must adopt new strategies to ensure that CO2 emissions are reduced in order to stimulate economic growth.

Second-order refinements for [formula omitted]-ratios with many instruments

This paper studies second-order properties of the many instruments robust t-ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models with homoskedastic errors under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n, and proposes second-order refinements to the t-ratios to improve the size and power properties. Based on asymptotic expansions of the null and non-null distributions of the t-ratios derived under the many instruments asymptotics, we show that the second-order terms of those expansions may have non-trivial impacts on the size as well as the power properties. Furthermore, we propose adjusted t-ratios whose approximation errors for the null rejection probabilities are of order O(n−1) in contrast to the ones for the unadjusted t-ratios of order O(n−1/2), and show that these adjustments induce some desirable power properties in terms of the local maximinity. Although these results are derived under homoskedastic errors, we also establish a stochastic expansion for a heteroskedasticity robust t-ratio, and propose an analogous adjustment under slight deviations from homoskedasticity.

The impact of Say-on-Pay votes on firms' strategic policies: Insights from the Anglo-Saxon economy

This study examines evidences of executive reactions to say-on-pay (SOP) votes in terms of strategic policies which could affect firms' long-run growth and eventual survival. We employed an unbalanced panel data from 1932 firms taken from four countries in the Anglo-Saxon economy, covering time periods when different forms of SOP were implemented in these countries. Using Limited Information Maximum Likelihood (LIML) estimator to gauge the simultaneous determination of SOP votes and firm strategic policies, we find that, in line with shareholders preferences, US firms had increased capital expenditure ratio; Australian and US firms had reduced reliance on debt financing; US managers had shifted focus on current rather than long-term profit, but evidences emerged from other countries are unclear. Corroborations also suggest that excess liquidity was shunned by Canadian shareholders, but the reactions of their company executives were overly disproportionate. UK firm policies did not appear to have been affected by SOP, and vice versa. Overall, the varying effects of SOP votes on firms' strategic policies might be ascribed to either the adoption of a specific SOP practice or the effectiveness of the board.

Adaptive k-class estimation in high-dimensional linear models

In this paper, we explore the k-class estimator in high-dimensional linear models with potential endogeneity issues which are very common in empirical economics studies. K-class estimator has the advantage of incorporating many popular estimators such as the OLS estimator, two stage least squares (2SLS) estimator, limited information maximum likelihood (LIML) estimator, etc., as k takes on different values. Our main innovations are: 1) In the newly proposed high-dimensional k-class estimator, we allow the value of k (hence the level of endogeneity) to be determined by the data. Therefore, our method is very useful in empirical studies where the researcher do not know the severity of endogeneity or the importance of variables in a very large pool of candidate covariates. 2) In this paper, the adaptive LASSO method is incorporated into the generalized k-class estimation for variable selection and coefficient estimation in both the structural and reduced form equations. We show that the adaptive LASSO type k-class estimator has oracle properties. In simulation studies, we show that our new estimator can choose the optimal k value as well as achieving the minimum MSE among a set of popular estimators in finite samples where the number of potential endogenous variable is large.

TSLS and LIML Estimators in Panels with Unobserved Shocks

The properties of the two stage least squares (TSLS) and limited information maximum likelihood (LIML) estimators in panel data models where the observables are affected by common shocks, modelled through unobservable factors, are studied for the case where the time series dimension is fixed. We show that the key assumption in determining the consistency of the panel TSLS and LIML estimators, as the cross section dimension tends to infinity, is the lack of correlation between the factor loadings in the errors and in the exogenous variables—including the instruments—conditional on the common shocks. If this condition fails, both estimators have degenerate distributions. When the panel TSLS and LIML estimators are consistent, they have covariance-matrix mixed-normal distributions asymptotically. Tests on the coefficients can be constructed in the usual way and have standard distributions under the null hypothesis.

Minimum distance approach to inference with many instruments

I analyze a linear instrumental variables model with a single endogenous regressor and many instruments. I use invariance arguments to construct a new minimum distance objective function. With respect to a particular weight matrix, the minimum distance estimator is equivalent to the random effects estimator of Chamberlain and Imbens (2004), and the estimator of the coefficient on the endogenous regressor coincides with the limited information maximum likelihood estimator. This weight matrix is inefficient unless the errors are normal, and I construct a new, more efficient estimator based on the optimal weight matrix. Finally, I show that when the minimum distance objective function does not impose a proportionality restriction on the reduced-form coefficients, the resulting estimator corresponds to a version of the bias-corrected two-stage least squares estimator. I use the objective function to construct confidence intervals that remain valid when the proportionality restriction is violated.

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

This study assesses the relationship between quality of life (QOL), tourism specialization, and economic growth as applied to small island destinations. The study is grounded on a QOL model and translog production function and employs the limited information maximum likelihood estimator to investigate the nature of this relationship in Malta. Results indicate that the relationship between tourism specialization and both QOL and economic growth is only partial. Tourism specialization improves the residents QOL but, only on the short term. The study enhances the existing empirical evidence of the literature that examines the relationship between tourism specialization and residents' QOL in the medium- and long-term in that it controls for endogeneity. The translog production function methodology is novel as it allows for examining tourism returns and the factors that shape tourism preferences. This permits supply and demand variables to be combined into a production and consumption system.

Cascading effect of contagion in Indian stock market: Evidence from reachable stocks

The financial turbulence in a country percolates to another along the trajectories of reachable stocks owned by foreign investors. To indemnify the losses originating from the crisis country, foreign investors dispose of shares in other markets triggering a contagion in an unrelated market. This paper provides empirical evidence for the stock market crisis that spreads globally through investors owning international portfolios, with special reference to the global financial crisis of 2008–09. Using two-step Limited Information Maximum Likelihood estimation and Murphy-Topel variance estimate, the results show that reachability plays a crucial role in the transposal of distress from one country to another, explaining investor-induced contagion in the Indian stock market.

LIML estimation of import demand and export supply elasticities

ABSTRACTI apply limited-information maximum likelihood (LIML) to estimate import demand and export supply elasticities for a range of eurozone countries. The results highlight inconsistencies in the parameters estimated by LIML relative to an estimator that is robust to heteroskedasticity. The nature of the structural equations reveals complications generated by the limiting behavior of the parameters that can be replicated in finite samples. The results of simulations underscore improvements in parameter estimates in a three-dimensional panel, suggesting that the problem of limiting behaviour can be overcome in larger dataset/panels.

Tourism and financial development in small states

Tourism expenditure in Caribbean countries represents the single largest inflow of foreign exchange and is associated with a significant amount of international capital flows. Yet, the relationship between tourism and financial development (FD) has received scant attention in the academic literature. This article focuses on whether tourism promotes FD in Caribbean economies. We do so by using newly constructed data on tourism flows to the region during the period 1980–2013. We find that tourist expenditure, on average, has a positive and significant impact on various measures of FD. At our most conservative estimates, we find that by increasing tourism expenditures per capita by about $1200 (USD), depth in the financial system improves by about 10–15%, while efficiency increases by about 34%. Our results are robust to instrumental variables, system generalized method of moments, and limited information maximum likelihood estimation techniques as well as to a variety of measures of FD. Such findings may have important policy implications related to facilitating growth and development through an increase in efficiency in the system of FD.

The unconditional distributions of the OLS, TSLS and LIML estimators in a simple structural equations model

ABSTRACTThe exact distributions of the standard estimators of the structural coefficients in a linear structural equations model conditional on the exogenous variables have been shown to have some unexpected and quirky features. Since the argument for conditioning on exogenous (ancillary) variables has been weakened over the past 20 years by the discovery of an “ancillarity paradox,” it is natural to wonder whether such finite sample properties are in fact due to conditioning on the exogenous variables. This article studies the exact distributions of the ordinary least squares (OLS), two-stage least squares (TSLS), and limited information maximum likelihood (LIML) estimators of the structural coefficients in a linear structural equation without conditioning on the exogenous variables.

A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments

AbstractThe presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the ‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The ‐norm regularization with a regularized parameter O(n) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O(n), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed ‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.

Linear Model IV Estimation When Instruments Are Many or Weak

AbstractEconomists rely frequently on instrumental variables estimation to overcome biases that endogenous explanatory variables cause in ordinary least squares estimation. However, traditional instrumental variables estimators, such as two-stage least squares and limited information maximum likelihood estimation, can suffer persistent estimator biases and size-of-test biases in even very large samples if the instruments used are large in number or are only weakly correlated with an endogenous explanatory variable. This paper reviews strategies for grappling with weak instruments and with large numbers of instruments in linear regression models.