OLS Estimates Research Articles

Regional convergence in Russia: Estimating an augmented Solow model

This paper studies convergence in per capita gross regional products across Russian regions in the period from 1996 to 2017. By applying the system GMM technique we estimate growth equations that are directly derived from the classic Solow model, augmented with human capital and migration and considering possible spatial effects. Our main estimates establish a convergence rate of around 2% per year. While interregional migration and interdependencies of the growth of Russian regions contribute to the convergence process, the role of human capital is ambiguous: when we employ system GMM we do not find any significant impact of human capital on regional growth no matter how we measure human capital, while pooled OLS estimates establish a positive contribution.

A robust counterpart approach for the ridge estimator to tackle outlier effect in restricted multicollinear regression models

In statistics, regression analysis is a method for predicting a target variable by establishing the optimal linear relationship between the dependent and independent variables. The ordinary least squares estimator (OLSE) is the optimal estimation method in classical regression analysis based on the Gauss–Markov theorem if the essential assumptions of normality, independence of error terms, and little or no multicollinearity in the covariates are satisfied. OLSE is profoundly affected by the collinearity between explanatory variables and outlier problems. Therefore, we require resilient strategies to resolve these challenges. Robust stochastic ridge regression is an alternative optimization problem to least squares regression when data are simultaneously contaminated by anomalies, influential observations, and multicollinearity. To combat outliers and multicollinearity problems, a robust stochastic ridge regression estimator based on the least squares trimmed method is proposed in this paper. Using simulated and real data sets, the efficacy of the proposed method with correlated and uncorrelated errors is then evaluated.

Монетарная бедность и образование в России

Russian economic literature on poverty abounds with empirically unsupported assertions about the positive relationship between education and living standards. The purpose of this study is to find empirical evidence of this relationship using panel data for 82 regions of the Russian Federation for 2000–2021. We applied a dynamic OLS estimator to estimate a panel cointegrating equation and found strong negative and statistically significant dependence of indicators of absolute and relative monetary poverty on the highest level of education of the regional working-age population. We also performed the Dumitrescu-Hurlin pairwise causality test, which shows that higher education does not homogeneously cause more absolute monetary poverty, but more absolute monetary poverty does homogeneously cause better education as people try to avoid poverty by raising their educational level. The results of these econometric procedures suggest that the purpose of the study has been achieved.

Impact of entrepreneurial governance and ease of doing business on economic growth: Evidence from ECOWAS economies (2000–2019)

We reignited the debate that developing countries still struggle to make the most of entrepreneurship due to institutional imbalances. The aim of this study is to empirically examine impact of entrepreneurial governance and ease of doing business on economic growth in a panel of 15 ECOWAS countries. The empirical evidence is based on secondary data from 2000 to 2019 estimated using the Pooled OLS Regression OLS estimator. Using institutional theory, we examined the chain of causality from institutions to entrepreneurship and from entrepreneurship to economic growth. Four findings emerged. Firstly, the regulatory pillar, represented by the indicators of ease of doing business (incorporation procedure, time required to set up a business, and cost of the business), is negatively and significantly related to economic growth. But the indicators of cost of doing business and start‐up costs are more detrimental to business and economic growth. Secondly, the normative pillar represented by entrepreneurial governance indicators (government integrity and business freedom) is positively and significantly associated with growth. But the impact of government integrity on economic growth is greater than that of business freedom. Third, the interaction between regulatory and normative pillars is negative and significant. Finally, the cognitive pillar shows mixed results. For example, indicators of investment, trade openness, education, and financial development have positive and significant effects on economic growth, while government size, inflation, and population have negative and significant effects on economic growth. We discuss policy implications for stakeholders in ECOWAS economies.

Effects of Property Rights on Entrepreneurship Development in the CEMAC Sub-Region

Objective: This article sought to investigate the effects of property rights on entrepreneurship development in the CEMAC Sub- region. Research Design & Methods: Data for this study was collected from the World Governance Indicators (WGI) for the six indicators of governance and World Bank data for entrepreneurship development and control variables. Pooled Ordinary Least Squares estimation technique was used to estimate the parameters of the model. Findings: The findings from the data analysis revealed that there was a negative and significant effect of democracy (captured by voice and accountability index) on entrepreneurship development in CEMAC. In accordance with theoretical expectation, results from data analysis further revealed that there was a positive and significant effect of government effectiveness on entrepreneurship development in the sub region. Results from the pooled OLS estimation showed that there was a negative and significant effect of control of corruption on entrepreneurship development in CEMAC. Contribution & Value Added: The fourth indicator of institutional quality used in this work is political stability. Thus, an improvement of public services by reducing bureaucratic bottlenecks, improvement in the fight against corruption and increasing the level of investments could enhance entrepreneurship development in the sub-region.

A modelling framework for regression with collinearity

This study addresses a fundamental, yet overlooked, gap between standard theory and empirical modelling practices in the OLS regression model y=Xβ+u with collinearity. In fact, while an estimated model in practice is desired to have stability and efficiency in its “individual OLS estimates”, y itself has no capacity to identify and control the collinearity in X and hence no theory including model selection process (MSP) would fill this gap unless X is controlled in view of sampling theory. In this paper, first introducing a new concept of “empirically effective modelling” (EEM), we propose our EEM methodology (EEM-M) as an integrated process of two MSPs with data (yo,X) given. The first MSP uses X only, called the XMSP, and pre-selects a class D of models with individually inefficiency-controlled and collinearity-controlled OLS estimates, where the corresponding two controlling variables are chosen from predictive standard error of each estimate. Next, defining an inefficiency-collinearity risk index for each model, a partial ordering is introduced onto the set of models to compare without using yo, where the better-ness and admissibility of models are discussed. The second MSP is a commonly used MSP that uses (yo,X), and evaluates total model performance as a whole by such AIC, BIC, etc. to select an optimal model from D. Third, to materialize the XMSP, two algorithms are proposed with applications.

Measuring Education Changes Between Generations: Evidence for 52 Developing Countries from 1870 to 2010

AbstractThis work measures the education changes between generations for a sample of 52 developing countries (Latin America, 15; Asia and the Pacific, 13; the Middle East, 6; and Africa, 18) from 1870 to 2010. Results show that the intergenerational correlations of Pearson-Spearman indices in the developing world are higher than ρ = 0.90, with those cases in which the existing correlation between individuals of the same gender exceeds values higher than ρ = 0.95 being especially noteworthy. The OLS estimations show intergenerational indices between 0.67 and 0.99, with Asia and Pacific being the region with the highest values, and Latin America being the developing region with the lowest indices. All four regions show a significantly high level of educational transmission between generations, with this lack of educational mobility appearing to be one reason for the stagnation of growth and economic development in these regions.

Return to education by ethnicity in Indonesia

Using data from the Indonesia Family Life Survey (IFLS) from 2014–2015, this study seeks to analyze the ethnic differences in the return to education in Indonesia. We discovered that IV models, as opposed to OLS estimation, are more suitable to evaluate returns to education in Indonesia. Additionally, rather than treating the ethnicity variable as an instrumental variable, it is preferable to use it as a grouping variable. After segmenting our samples into six ethnic groups, this study discovered that all ethnic groups, with the exception of the Chinese group, match the IV estimation. The non-Chinese groups with the best returns on schooling are Bataknese and Minangnese. The high return on education in these ethnic groups is attributed to the intense excitement for learning that permeates Bataknese and Minangnese cultures as native cultural assets. Earnings are also influenced favorably by marital status, masculinity, employment in the public sector, and urban-rural location. These findings suggest that ethnic and cultural topics should be covered in the national curriculum as well as local curricula. Since these characteristics have a direct impact on salaries, the government should also pay attention to gender segregation, career opportunities, and urban-rural growth.JEL Classification C26; I26; J15

Combating Multicollinearity: A New Two-Parameter Approach

The ordinary least square (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) when all linear regression model assumptions are valid. The OLS estimator, however, becomes inefficient in the presence of multicollinearity. Various one and two-parameter estimators have been proposed to circumvent the problem of multicollinearity. This paper presents a new twoparameter estimator called Liu-Kibria Lukman Estimator (LKL) estimator. The proposed estimator is compared theoretically and through Monte Carlo simulation with existing estimators such as the ordinary least square, ordinary ridge regression, Liu, Kibria-Lukman, and Modified Ridge estimators. The results show that the proposed estimator performs better than existing estimators considered in this study under some conditions, using the mean square error criterion. A real-life application to Portland cement and Longley datasets supported the theoretical and simulation results by giving the smallest mean square error compared to the existing estimators.

Review of Some Robust Estimators in Multiple Linear Regressions in the Presence of Outlier(s)

Linear regression has been one of the most important statistical data analysis tools. Multiple regression is a type of regression where the dependent variable shows a linear relationship with two or more independent variables. OLS estimate is extremely sensitive to unusual observations (outliers), with low breakdown point and low efficiency. This paper reviews and compares some of the existing robust methods (Least Absolute Deviation, Huber M-Estimator, Bisquare M-Estimator, MM Estimator, Least Median Square, Least Trimmed Square, S-Estimator); a simulation method is used to compare the selected existing methods. It was concluded based on the results that for y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.3 is MM; for x direction outlier, the best estimator in term breakdown point of at most 0.4 is S; for x, y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.2 is MM.

Robust Liu‐type estimator based on GM estimator

Ordinary Least Squares Estimator (OLSE) is widely used to estimate parameters in regression analysis. In practice, the assumptions of regression analysis are often not met. The most common problems that break these assumptions are outliers and multicollinearity problems. As a result of these problems, OLSE loses efficiency. Therefore, alternative estimators to OLSE have been proposed to solve these problems. Robust estimators are often used to solve the outlier problem, and biased estimators are often used to solve the multicollinearity problem. These problems do not always occur individually in the real‐world dataset. Therefore, robust biased estimators are proposed for simultaneous solutions to these problems. The aim of this study is to propose Liu‐type Generalized M Estimator as an alternative to the robust biased estimators available in the literature to obtain more efficient results. This estimator gives effective results in the case of outlier and multicollinearity in both dependent and independent variables. The proposed estimator is theoretically compared with other estimators available in the literature. In addition, Monte Carlo simulation and real dataset example are performed to compare the performance of the estimator with existing estimators.

Controlling for fixed effects in studies of income underreporting

AbstractThe expenditure method of Pissarides and Weber (J Public Econ 39(1):17–32, 1989) shows how one backs out measure of income underreporting by the self-employed by using food consumption as trace of true income. In this paper we make a case for using panel data and fixed effects estimation in such analysis, instead of OLS estimation. The main argument is that fixed effects estimation addresses the problem of omitted variable bias in the identification. We demonstrate the use of panel data and fixed effects estimation by using large-scale administrative register data on charitable donations, exploiting that the data can be turned into a panel dataset. The results suggest that the estimation technique matters—fixed effects estimates are smaller than OLS estimates.

Lagged Dependent Variable Predictors, Classical Measurement Error, and Path Dependency: The Conditions Under Which Various Estimators are Appropriate

Lagged dependent variables (LDVs) are often used as predictors in ordinary least squares (OLS) models in the social sciences. Although several estimators are commonly employed, little is known about their relative merits in the presence of classical measurement error and different longitudinal processes. We assess the performance of four commonly used estimators: (1) the standard OLS estimator, (2) an average of past measures (AVG), (3) an instrumental variable (IV) measured at one period previously (IV), and (4) an IV derived from information from more than one time before (IV2). We also propose a new estimator for fixed effects models—the first difference instrumental variable (FDIV) estimator. After exploring the consistency of these estimators, we demonstrate their performance using an empirical application predicting primary school test scores. Our results demonstrate that for a Markov process with classic measurement error (CME), IV and IV2 estimators are generally consistent; LDV and AVG estimators are not. For a semi-Markov process, only the IV2 estimator is consistent. On the other hand, if fixed effects are included in the model, only the FDIV estimator is consistent. We end with advice on how to select the appropriate estimator.

Consistency and asymptotic normality in a class of nearly unstable processes

This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $$A_{n}$$ with spectral radius $$\rho (A_{n}) < 1$$ satisfying $$\rho (A_{n}) \rightarrow 1$$ . This framework is particularly suitable to understand unit root issues by focusing on the inner boundary of the unit circle. Consistency is established for the empirical covariance and the OLS estimation together with asymptotic normality under appropriate hypotheses when A, the limit of $$A_n$$ , has a real spectrum, and a particular case is deduced when A also contains complex eigenvalues. The asymptotic process is integrated with either one unit root (located at 1 or $$-1$$ ), or even two unit roots located at 1 and $$-1$$ . Finally, a set of simulations illustrate the asymptotic behavior of the OLS. The results are essentially proved by $$L^2$$ computations and the limit theory of triangular arrays of martingales.

Circular Economy, Stock Volatility, and Resilience to the COVID-19 Shock: Evidence from European Companies

Background: By decoupling economic growth from an intensive use of resources, preventing the impairment of natural capital, and enhancing resilience to system-wide shocks, the Circular Economy (CE) is a powerful opportunity to hedge against “linear” risk factors. In fact, it helps shielding against the risk of assets becoming stranded, can generate fresh and non-speculative demand for investments, and can improve investment results at both individual and portfolio levels. Problem: Therefore, equity investors into circular undertakings could benefit from (H1) reduced stock return volatility, as well as (H2) a greater ability to withstand exogenous negative events. Approach: For testing these hypotheses, we constructed a sample of 644 listed companies across EU-15 countries, plus Switzerland, and 17 different industries. We retrieved their market data in 2019–2020, as well as their accounting fundamentals in 2018–2019. By controlling for the latter, we investigated whether equity risk—either in total terms (i.e., the standard deviation of returns) or circumscribed to the systematic component thereof (i.e., the Beta against a European or global market index)—may be explained by a company’s degree of circularity, measured by the Circularity Score (CS). This is a novel indicator originally proposed by Zara and Ramkumar (2022), based on Refinitiv ESG data, the methodology whereof we significantly amended. As a core innovation, in weighting an entity’s performance on a CE framework, we assessed the latter’s “financial materiality” (i.e., relevance to the company’s business) at sub-industry level, applying the SASB Materiality Maps. Via OLS estimation, we tested our hypotheses (i) over the whole-time horizon, in a panel model; (ii) on specific timeframes, in a standard cross-sectional model. The latter was applied to either the entire 2020 or subperiods thereof: namely, with respect to the COVID-19 outbreak, we distinguished between a pre-shock, a shock and a post-shock phase. Our quest was refined to conduct a deeper investigation into the Oil &amp; Gas industry, which is intrinsically the most exposed to linear risks and, also, did experience the widest volatility in 2020. Findings: Both H1 and H2 received widespread confirmation. The CS was found to exert a negative, significant and robust effect on all the three risk measures, over the whole timespan as well as in subperiods (particularly the post-shock phase). Also, amplifying effects were recorded on the Oil &amp; Gas industry. Conclusions: Our results lend remarkable support to the idea that the CE is a powerful enabler of de-risking, also in case of a severe shock, with a view to mitigating the negative consequences and building back better. They call on firms and policymakers to foster the circular transition, thereby accelerating economic recovery in the aftermath of the pandemic crisis.

Testing the Economic Growth Path “Green-Resilience” Under Natural Resources Constraint in Asia-Pacific Economies

This study investigates the existence of the environmental Kuznets curve hypothesis under natural resources (NRs) constraint in nine Asian-Pacific countries with data spanning from 2000 to 2019. Using Pooled OLS estimations, results show that economic growth is on a pathway from which environmental quality is improved. Hypothesising that NRs exploitation is a potential factor that can exacerbate environmental quality, the study shows that the Asian economic structure is on a “green-resilience” path when controlling for total and each NRs component. The magnitude of each NR component in the ability of increasing CO2 emissions is characterised. Results are robust with different methods of estimations (control variables, alternative dependent variable, Two Stages Least Squares (2SLS)-3SLS Instrumental Variables strategies, Panel-Corrected Standard Error (PCSE) and Driscoll and Kraay methods). As policy implications, Asia-Pacific countries should amplify eco-innovation, development of renewable energies and fiscal policies as they positively impact FDI on green growth.

Impact of Selected Macroeconomic Variables in Economic Growth: Empirical Study in the Philippines

This study investigates the relationship between foreign direct investment (FDI), household final consumption expenditure (HFCE), gross national income per capita (GNI), and the GDP growth rate in the Philippines. This study uses OLS estimation with annual time series data spanning 1981 to 2021 to assess the impact of these variables on the nation's economic progress. The Philippines' economy has developed significantly in recent years. Because the GDP growth rate is an important indicator of economic progress, policymakers must understand the factors that contribute to it in order to sustain economic growth. The study's findings offer important insights into the drivers of economic progress in the Philippines. Understanding the impact of FDI, HFCE, and GNI per capita on GDP growth rate enables policymakers to make informed decisions that encourage sustainable economic growth and increase the well-being of the entire population.

Some Modified Ridge Estimators for Handling the Multicollinearity Problem

Regression analysis is a statistical process that utilizes two or more predictor variables to predict a response variable. When the predictors included in the regression model are strongly correlated with each other, the problem of multicollinearity arises in the model. Due to this problem, the model variance increases significantly, leading to inconsistent ordinary least-squares estimators that may lead to invalid inferences. There are numerous existing strategies used to solve the multicollinearity issue, and one of the most used methods is ridge regression. The aim of this work is to develop novel estimators for the ridge parameter “γ” and compare them with existing estimators via extensive Monte Carlo simulation and real data sets based on the mean squared error criterion. The study findings indicate that the proposed estimators outperform the existing estimators.

Linear Probability Model Revisited: Why It Works and How It Should Be Specified

A linear model is often used to find the effect of a binary treatment [Formula: see text] on a noncontinuous outcome [Formula: see text] with covariates [Formula: see text]. Particularly, a binary [Formula: see text] gives the popular “linear probability model (LPM),” but the linear model is untenable if [Formula: see text] contains a continuous regressor. This raises the question: what kind of treatment effect does the ordinary least squares estimator (OLS) to LPM estimate? This article shows that the OLS estimates a weighted average of the [Formula: see text]-conditional heterogeneous effect plus a bias. Under the condition that [Formula: see text] is equal to the linear projection of [Formula: see text] on [Formula: see text], the bias becomes zero, and the OLS estimates the “overlap-weighted average” of the [Formula: see text]-conditional effect. Although the condition does not hold in general, specifying the [Formula: see text]-part of the LPM such that the [Formula: see text]-part predicts [Formula: see text] well, not [Formula: see text], minimizes the bias counter-intuitively. This article also shows how to estimate the overlap-weighted average without the condition by using the “propensity-score residual” [Formula: see text]. An empirical analysis demonstrates our points.

Residual Analysis in Simple Linear Regression: A Practical Application with the Jarque-Bera Test

This study provides a practical guide to residual analysis in ordinary linear regression, a basic statistical technique. Explains how to calculate and interpret residuals, which play a key role in assessing model validity. The study then focuses on the Jarque-Bera test, a diagnostic tool used to assess the normality of residuals. Through a step-by-step example, we show how to calculate the skewness and kurtosis of the residuals, and then calculate the Jarque-Bera test statistic. We highlight the importance of this test in determining whether residuals obey a normal distribution, helping researchers make reliable statistical inferences. This practical guide helps readers understand the importance of residual analysis in building robust regression models. Keywords: Residual analysis, simple linear regression, model assumptions, Ordinary Least Squares, OLS estimation, Jarque-Bera test, normality, validation, practical example.