OLS Estimates Research Articles

Testing for Coefficient Distortion due to Outliers with an Application to the Economic Impacts of Climate Change

Outlying observations can bias regression estimates, requiring the use of robust estimators. Comparing robust estimates to those obtained using OLS is a common robustness check, however, such comparisons have been mostly informal due to the lack of available tests. Here we introduce a formal test for coefficient distortion due to outliers in regression models. Our proposed test is based on the difference between OLS and robust estimates obtained using a class of Huber-skip M-type estimators (such as Impulse Indicator Saturation or Robustified Least Squares). Establishing asymptotics of the corresponding Huber-skip M-estimators using an empirical process CLT recently developed by Berenguer-Rico et al. (2019), we show that our distortion test has an asymptotic chi-squared distribution, and is valid for cross-sectional as well as panel and time series models. To improve finite sample performance and to alleviate concerns on distributional assumptions, we further introduce and explore three bootstrap testing schemes. We apply our outlier distortion test to estimates of the macro-economic impacts of climate change allowing for adaptation. We find that OLS estimates are significantly different to those obtained using a robust estimator and provide evidence of income-driven adaptation. Projecting the resulting damage curve to the end of the century shows that outlier-robust estimates dampen projected GDP losses and reduce the estimated marginal impacts of additional warming under adaptation.

Comparison of estimation methods for one-inflated positive Poisson distribution

This paper aims to propose estimation methods for one-inflated positive Poisson (OIPP) distribution and compare their properties in terms of unbiasedness, consistency, efficiency and deficiency. All estimators considered in the study are asymptotically unbiased and consistent. The maximum likelihood estimator (MLE) for the OIPP distribution is asymptotically normal. When compared to the MLE, the ordinary least square estimator (OLSE) is the most efficient, followed by the method of moments estimator (MME) and the ratio of probability estimator (RPE). A novel one-inflation index was also proposed to assess the presence of excess ones in the dataset for the positive Poisson distribution to determine whether a one-inflated distribution is required for model fitting. A real dataset with a large number of ones, as identified by the proposed one-inflation index, was used for model fitting. It is found that the OLSE and MLE are the best estimators for an OIPP distribution.

Trade impacts of the New Silk Road in Africa: Insight from Neural Networks Analysis

The Belt and Road Initiative (BRI) is aimed to strengthen the preferential reciprocal trade between China and the Belt-Road nations. Quantitative evaluations of BRI to determine whether it can explicitly provide more insight into China’s bilateral trade among its partners are needed. Hence, improving prediction accuracy while using more superior algorithms for sustainable decision-making remains essential since decision-makers have been interested in predicting the future. Machine learning algorithms, such as supervised artificial neural networks (ANN), outperform several econometric procedures in predictions; therefore, they are potentially powerful techniques to evaluate BRI. This study uses detailed China’s bilateral export data from 1990 to 2017 to analyze and evaluate the impact of BRI on bilateral trade using gravity model estimations and ANN analysis techniques. The finding suggests that China’s bilateral export flow among the BRI countries results in a slight increase in inter-regional trade. The study provides a comparison view on the different estimation procedures of the gravity model – ordinary least squares (OLS) and Poisson pseudo-maximum likelihood (PPML) with the ANN. The ANN associated with fixed country effects reveals a more accurate estimation compared to a baseline model and with country-year fixed effects. Contrarily, the OLS estimator and PPML showed mixed results. Grounded on the study dataset, the ANN estimation of the gravity equation was superior over the other procedures to explain the variability of the dependent variable (export) regarding the prediction accuracy using root mean squared error (RMSE) and R-square.

The Random Walk and Trend Stationary Models with an Analysis of the US Real GDP: Can We Distinguish between the Two Models?

The unit root can lead to major problems in economic time series analyses. I obtain the asymptotic distributions of the ordinary least squares (OLS) estimator when the true model is trend stationary for the following three cases: 1) the null model is a random walk without drift, and the auxiliary regression model does not contain a constant; 2) the null model is a random walk with drift, and the auxiliary regression model contains a constant; and 3) the null model is a random walk with drift, and the auxiliary regression model contains both a constant and a time trend. In the third case, the asymptotic distribution of the OLS estimator is determined by the first order of the autocorrelation, and we can distinguish between the random walk and trend stationary models, unlike in previous studies. Based on these results, the real US gross domestic product is analyzed. A time trend model with autoregressive error terms is chosen. The results suggest that the impacts of a shock can become larger than the original shock in some periods and then gradually decline. However, the impacts continue for a long period, and policy makers should account for this to design better economic policies.

One Instrument to Rule Them All: The Bias and Coverage of Just-Id IV

Two-stage least squares estimates in heavily over-identified instrumental variables (IV) models can be misleadingly close to the corresponding ordinary least squares (OLS) estimates when many instruments are weak. Just-identified (just-ID) IV estimates using a single instrument are also biased, but the importance of weak-instrument bias in just-ID IV applications remains contentious. We argue that in microeconometric applications, just-ID IV estimators can typically be treated as all but unbiased and that the usual inference strategies are likely to be adequate. The argument begins with contour plots for confidence interval coverage as a function of instrument strength and explanatory variable endogeneity. These show undercoverage in excess of 5% only for endogeneity beyond that seen even when IV and OLS estimates differ by an order of magnitude. Three widely cited microeconometric applications are used to explain why endogeneity is likely low enough for IV estimates to be reliable. We then show that an estimator that’s unbiased given a population first-stage sign restriction has bias exceeding that of IV when the restriction is imposed on the data. But screening on the sign of the estimated first stage is shown to halve the median bias of conventional IV without reducing coverage. To the extent that sign-screening is already part of empirical workflows, reported IV estimates enjoy the minimal bias of sign-screened just-ID IV.

Topp-Leone odd log-logistic exponential distribution: Its improved estimators and applications.

In this paper, a new three-parameter lifetime model called the Topp-Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be monotone, unimodal, constant, J-shaped, constant-increasing-decreasing and decreasing-increasing-decreasing and bathtub-shaped. Our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the proposed model are derived. We briefly describe different estimators namely, the maximum likelihood estimators, ordinary least-squares estimators, weighted least-squares estimators, percentile estimators, maximum product of spacings estimators, Cramér-von-Mises minimum distance estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimation for both small and large samples. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to some other well-known distributions.

“The Good, the Bad and the Ugly”? The influence of dark triad personality traits on formation of entrepreneurial intentions

This article examines the influence of the “dark triad” personality traits — narcissism, Machiavellianism and psychopathy — on the development of entrepreneurial intentions through the prism of the theory of planned behavior. The theory explains entrepreneurial intentions formation trough emergence and development of the attitude towards entrepreneurship, relevant subjective norms, and perceived behavioral control. These personality traits are considered in the study in their non-clinical manifestations. The proposed theoretical model has been tested on a sample of 191 students and graduates from 13 Russian universities. The empirical data were collected through an online survey. The analysis was carried out with OLS estimation. To assess the mediation effects, the PROCESS macro for the SPSS data analysis package was employed. The study identifies the key role of narcissism as an antecedent of intention to start one’s own business, while the main element of the theory of planned behavior mediating psychological effects is the attitude towards entrepreneurship. In addition, a negative relationship between psychopathy and subjective norms as well as perceived behavioral control has been established. With this study, we contribute to the theory of personality traits in the context of entrepreneurship and expand knowledge about the role of negatively perceived individual psychological characteristics in the entrepreneurial process. In addition, this work details the theory of planned behavior in terms of identifying possible antecedents of attitudes towards entrepreneurship, subjective norms, and perceived behavioral control. The results of this study can be used by entrepreneurship educators, especially in courses and trainings on the psychology of entrepreneurship.

"Study Hard and Make Progress Every Day": Updates on Returns to Education in China

In this paper, we apply Generalized Propensity Score Matching (GPSM) method, which deals with a continuous treatment variable, to estimate the returns to education in China from 2010 to 2017. Results are compared with OLS estimates from the classical Mincerian equation, as well as estimates from two instrumental variable methods (i.e., 2SLS and Lewbel). We use the Chinese General Social Survey data, including a subset newly released in 2020. We find that returns to education in China experienced a slight decrease in 2010-2015, but reverted back in 2017. With the more flexible GPSM method, we also find that returns to university education remain higher than returns to secondary or compulsory education. The GPSM estimates are also closer to OLS estimates, compared to both instrumental variable methods.

Interconnectedness between Commodity Futures and Spot Prices: A Comparative Analysis between Ordinary Least Square (OLS) and Quantile Regression (QR)

The study sought to contribute to the extant literature on the interconnectedness between commodity spot prices and futures prices by covering daily data from 2001-2019. Employing the OLS and the QR, different dynamics of the relationship between commodity spot and futures prices emerged from the study. For oil and gold prices, OLS estimator revealed that neither spot nor futures prices of the commodities had a significant effect on the other. Quantile regression estimators however suggested otherwise. For oil prices, futures prices were found to have a significant positive effect on spot oil prices at the 60th and 75th percentile whereas spot oil prices were found to have a significant positive effect on the futures oil prices at the lower tail (0.1, 0.2, and 0.25 quantiles). For gold prices, futures gold prices had a significant positive effect on spot gold prices at the 75th percentile (3rd quantile) marked as the upper tail of the distribution whereas a significant negative effect was revealed at the middle quantile (50th percentile). For cocoa prices, both the OLS and the QR estimators were significant in either direction. A significant positive effect of futures (spot) cocoa price on spot (futures) cocoa price was observed across all quantiles in both directions. The results suggest that speculators and arbitrageurs in the commodity market must be concerned about the causality moving from one direction to another and take appropriate investment positions that protect their interests.

Generalized Class of Mean Estimators with Known Measures for Outliers Treatment

In estimation theory, the researchers have put their efforts to develop some estimators of population mean which may give more precise results when adopting ordinary least squares (OLS) method or robust regression techniques for estimating regression coefficients. But when the correlation is negative and the outliers are presented, the results can be distorted and the OLS-type estimators may give misleading estimates or highly biased estimates. Hence, this paper mainly focuses on such issues through the use of non-conventional measures of dispersion and a robust estimation method. Precisely, we have proposed generalized estimators by using the ancillary information of non-conventional measures of dispersion (Gini’s mean difference, Downton’s method and probability-weighted moment) using ordinary least squares and then finally adopting the Huber M-estimation technique on the suggested estimators. The proposed estimators are investigated in the presence of outliers in both situations of negative and positive correlation between study and auxiliary variables. Theoretical comparisons and real data application are provided to show the strength of the proposed generalized estimators. It is found that the proposed generalized Huber-M-type estimators are more efficient than the suggested generalized estimators under the OLS estimation method considered in this study. The new proposed estimators will be useful in the future for data analysis and making decisions.

Research on the Path of China Cities Service Consumption Upgrading

Based on the panel data of “first-line cities” and “new first-line” cities from 2006 to 2018, this paper constructs an extended linear expenditure system model (ELES) to empirically study the path law of service sub-consumption upgrade. Based on the full-sample OLS estimation, it is found that the overall marginal propensity for service consumption in the sample cities is 0.418, of which the sub-consumption propensity for cultural, entertainment and education services is the most obvious, followed by medical and health services, and transportation and communication services are the lowest. Based on service subconsumption, the research on price and income elasticity found that the expenditure and income elasticity of cultural entertainment and education, which has the most significant marginal propensity to consume, is the largest, while the price and income elasticity of health care services is the smallest. An empirical test based on sub-samples found that the marginal service consumption propensity of “first-line cities” and “new firstline cities” are 0.558 and 0.379, respectively; in terms of service breakdown, “first-line cities” have propensity to consume cultural entertainment and education services Significantly higher than the “new first-line cities”, the sub-item propensity to consume in medical and health services is slightly higher, and the sub-item propensity to consume in transportation and communication services is slightly lower.

Modelling of Index System of Economic Vitality During the COVID-19 Epidemic

Economic vitality is an important indicator to measure the level and potential of economic development. The paper puts forward three social problems about economic vitality and establishes a model to solve them. We build panel data model to analyze the influencing factors of economic vitality. Based on the section data of Beijing, the VAR-VEC model is established to analyze the long-term and short-term effects of economic policies on economic vitality. The development strategy of ORT is put forward, and the scheme to promote the growth of economic vitality is given during the COVID-19 epidemic. For the first problem, the paper preprocess panel data, and test its independence, and find that each factor is not independent of each other. Through the correlation analysis, we found that there is a strong correlation between the various elements. After Random Effect Test and Fixed Effect Test combined with Hausman Test, the data panel conforms to fixed effect model. Population change and enterprise vitality have a positive impact on economic vitality, the influencing factors are 0.01 and 0.07 respectively. We put forward the strategy of adjusting the overall structure of enterprises to improve economic vitality. For the second problem, the paper select the section data of Beijing city and construct the VARVEC model. Based on ADF unit root test and Johansen cointegration test, we find that there are at least three cointegration relationships between time series. We use Ais-Sc Criterion to determine the order of delay as the third order. We use OLS estimation method to get the coefficients of VEC Model. Through the IRF response, we find that the long-term impact of economic policy on economic vitality is positive correlation effect. Due to the effect of experience accumulation, the economic vitality presents a W-shaped trend. For the third problem, the paper use the minimum average deviation method to preprocess the index data, and get 9 representative indexes. We extract two main factors by factor analysis and build an index system of economic vitality. The economic vitality of each city from 2009 to 2017 is calculated according to the index system. Beijing, Shanghai, Guangzhou and Shenzhen often rank first, while Kunming and Dongguan often rank last. Based on the same data, the panel data model test results are similar to index system. For the fourth problem, we review the previous conclusions and put forward the ORT development strategy to improve economic vitality based on the established model

Welfare implications of solving the distance puzzle: global evidence from the last two centuries

This paper theoretically shows that changes in the distance elasticity of trade can be connected to welfare changes that depend on bilateral distance measures and expenditure shares of countries. Empirical results based on international and domestic trade data from the last two centuries show that the negative effects of distance on trade have increased over time when zero trade observations are ignored in inconsistent OLS estimations, confirming the distance puzzle in the literature. The corresponding welfare implications suggest that the world economy has experienced a cumulative welfare loss (about ) due to this puzzle in the last two centuries. When the puzzle is solved by considering zero trade observations in PPML estimations, the tables turn such that there are significant welfare gains from trade (about ) during the same period due to the decreasing negative effects of distance on trade over time. Welfare gains from further reductions in the negative effects of distance are investigated as well, suggesting significant potential gains from trade in the future.

Empirical Analysis of External Debt Exposure to Exchange Rate Risk in Nigeria

The study investigates external debt exposure to exchange rate risk in Nigeria. The Secondary data used were sourced from World Bank Development Indicators for all the variables from the period 1981 to 2019. By employing the Augmented Dickey-Fuller Unit root test and OLS estimation technique, the study found that external debt service payment (EXTDSP), total payment on external debt (TPEXTD), and trade openness (TROP) is significant. While External debt service payment (EXTDSP) and trade openness (TROP) is negatively impacting the exchange rate (EXCHR). TPEXTD has a positive significant impact on EXCHR at a 5% level of significance. The rest of the explanatory variables: external debt stock (EXTDS), gross domestic product growth rate (GDPGR), and real interest rate (RINTR) are all positive and insignificant at all levels of significance. The study, therefore, recommends that the government should go for concessional loans which has low-interest rate and are long-term in nature and as well encourage international trade with other countries of the world.

Do You Really Want to Share Everything? The Wellbeing of Work-Linked Couples

Work as well as family life are crucial sources of human wellbeing, which however often interfere. This is especially so if partners work in the same occupation or industry. At the same time, being work-linked may benefit their career success. Still, surprisingly little is known about the wellbeing of work-linked couples. Our study fills this gap by examining the satisfaction differences between work-linked and non-work-linked partners. Using data from the German Socio-Economic Panel (SOEP, 2019), we estimate the effect of working in the same occupation and/or industry on life satisfaction as well as satisfaction with four areas of life: income, work, family and leisure. In the process, we employ pooled OLS estimations and instrumental variable strategies, for instance based on the gender disparity in industries and occupations. Our results suggest that being work-linked increases satisfaction with life as well as income and job satisfaction. These findings are consistent with positive assortative matching and mutual career support between work-linked partners. Our conclusions concern hiring couples as a means of recruiting exceptional talent.

Cumulative Distribution Function and Probability Density Function of the Continuous Transitional Limiting Distribution of Normalized OLS Estimator

Cumulative Distribution Function and Probability Density Function of the Continuous Transitional Limiting Distribution of Normalized OLS Estimator

Do You Really Want to Share Everything? The Wellbeing of Work-Linked Couples

Work as well as family life are crucial sources of human wellbeing, which however often interfere. This is especially so if partners work in the same occupation or industry. At the same time, being work-linked may benefit their career success. Still, surprisingly little is known about the wellbeing of work-linked couples. Our study fills this gap by examining the satisfaction differences between work-linked and non-work-linked partners. Using data from the German Socio-Economic Panel (SOEP, 2019), we estimate the effect of working in the same occupation and/or industry on life satisfaction as well as satisfaction with four areas of life: income, work, family and leisure. In the process, we employ pooled OLS estimations and instrumental variable strategies, for instance based on the gender disparity in industries and occupations. Our results suggest that being work-linked increases satisfaction with life as well as income and job satisfaction. These findings are consistent with positive assortative matching and mutual career support between work-linked partners. Our conclusions concern hiring couples as a means of recruiting exceptional talent.

Bayesian Model Averaging for Satellite Models in Bank's Credit Risk Projections

Satellite Models are usually used by banks to project the impact of a given scenario, usually expressed in terms of macroeconomic and financial covariates, of various risk parameters, such as Loss Given Default (LGD) and Probability of Default (PD). These projections are needed in various contexts (ICAAP, Stress Testing, IFRS9 Provisioning, Recovery Plan) where usually the problem at hand is often sparse: we have relatively few observations of the risk parameter compared to the number of covariates available. To overcome the criticism of cherry picking related to any specific model, i.e. subset of covariates, a Bayesian Model Average approach has been suggested, as in [Gross and Poblacion, 2004] and [Sala-i Martin et al., 2004], where one samples the model space and an average projection is taken weighting the sampled models in terms of a penalized likelihood as in the Bayesian Information Criterion (BIC). The advantage of this approach lies in its ease of implementation involving OLS estimates. Also from a theoretical standpoint the suggested approach can be considered an asymptotic proxy of any bayesian model for a wide class of prior distributions on the covariates parameters. Here we will test the approach proposed in [Gross and Poblacion, 2004] and [Sala-i Martin et al., 2004] against a hierarchical empirical bayesian model on both simulated and real credit risk datasets showing how the two approaches give similar results in terms of fit and forecast distribution. Nevertheless the weights associated to the sampled models can significantly differ making the bayesian model a safer choice.

Impact of Unemployment, Inflation and Households Consumption on Economic Growth

The challenges imposed by the rising cases of unemployment, inflationary rate and less purchasing power in households have stirred considerable interest amongst researchers and actors in contemporary times in designing agreeable mechanism that engenders economic growth. This paper examined the impact of unemployment, inflation and household’s consumption on economic growth for 1960 to 2018. OLS estimation technique was adopted. From the findings, unemployment, inflation and household’s consumption impacted on economic growth. But it was observed that inflation (INF) significantly influence economic growth in Nigeria. However, controlling for the influence of consumer price index (CPI), we observed that it is a key determinant of economic growth. The study therefore recommends for efficient and effective policy mix that may monitor the inflation rate in Nigeria.

Ordinary least squares estimation of parameters of linear model

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.