Ordinary Least-squares Techniques Research Articles

Evaluation of multiple linear regression function and generalized linear model types in estimating natural menopausal age: A cross-sectional study.

BackgroundSince women spend about one-third of their lifespan in menopause, accurate prediction of the age of natural menopause and its effective parameters are crucial to increase women's life expectancy.ObjectiveThis study aimed to compare the performance of generalized linear models (GLM) and the ordinary least squares (OLS) method in predicting the age of natural menopause in a large population of Iranian women.Materials and Methods This cross-sectional study was conducted using data from the recruitment phase of the Shahedieh Cohort Study, Yazd, Iran. In total, 1251 women who had the experience of natural menopause were included. For modeling natural menopause, the multiple linear regression model was employed using the ordinary least squares method and GLMs. With the help of the Akaike information criterion, root-mean-square error (RMSE), and mean absolute error, the performance of regression models was measured.ResultsThe mean age of menopausal women was 49.1 4.7 yr (95% CI: 48.8-49.3) with a median of 50 yr. The analysis showed similar Akaike criterion values for the multiple linear models with the OLS technique and the GLM with the Gaussian family. However, the RMSE and mean absolute error values were much lower in GLM. In all the models, education, history of salpingectomy, diabetes, cardiac ischemic, and depression were significantly associated with menopausal age.Conclusion To predict the age of natural menopause in this study, the GLM with the Gaussian family and the log link function with reduced RMSE and mean absolute error can be a good alternative for modeling menopausal age.

Statistical tools for water quality assessment and monitoring in river ecosystems – a scoping review and recommendations for data analysis

Abstract Robust scientific inference is crucial to ensure evidence-based decision making. Accordingly, the selection of appropriate statistical tools and experimental designs is integral to achieve accuracy from data analytical processes. Environmental monitoring of water quality has become increasingly common and widespread as a result of technological advances, leading to an abundance of datasets. We conducted a scoping review of the water quality literature and found that correlation and linear regression are by far the most used statistical tools. However, the accuracy of inferences drawn from ordinary least squares (OLS) techniques depends on a set of assumptions, most prominently: (a) independence among observations, (b) normally distributed errors, (c) equal variances of errors, and (d) balanced designs. Environmental data, however, are often faced with temporal and spatial dependencies, and unbalanced designs, thus making OLS techniques not suitable to provide valid statistical inferences. Generalized least squares (GLS), linear mixed-effect models (LMMs), and generalized linear mixed-effect models (GLMMs), as well as Bayesian data analyses, have been developed to better tackle these problems. Recent progress in the development of statistical software has made these approaches more accessible and user-friendly. We provide a high-level summary and practical guidance for those statistical techniques.

Robust least square approach for optimal development of quadratic fuel quantity function for steam power stations

Ordinary Least Square (OLS) and Robust Least Square (RLS) consisting of Least Absolute Residual and Bi-square approaches were deployed to obtain the fuel consumption characteristic curve and the coefficients of the quadratic fuel consumption function for thermal stations in Nigeria. Results were compared based on convergence property, Root Mean Square Error, R-Square value, Adjusted R-Square value, and Width Interval of coefficients. Valve Point loading effects of Egbin and Sapele power stations were used to develop the quadratic fuel consumption characteristic curve and function. The average difference in width interval for the coefficients a, b, c, d, and e of the two stations, after comparing Bi-square and OLS technique, were 0.02084, 8.5055, 1856.565, 520.8855, and 0.0082, respectively. The R-square values obtained from the Bi-Square technique were superior to the OLS technique with arithmetic differences of 0.6196 and 0.5254 for Egbin and Sapele generating stations, respectively. Bi-Square technique also offered better adjusted R-Square value for Egbin and Sapele stations with arithmetic differences of 0.622 and 0.5287, respectively. Bi-Square technique offered smaller Root Mean Square Error than the Ordinary Least Square technique for both stations. The coefficients obtained from Bi-Square technique were used to develop the fuel quantity function for the studied stations.

Live Crown Ratio Models for Loblolly Pine (Pinus taeda) with Beta Regression

The growth and production potential of a tree depends on its crown dimensions as these are closely related to a tree’s photosynthetic capacity. However, tree crowns have been studied less compared to their main stems because of their lower market value and because the measurement of crown dimensions, such as crown volume or surface area, is difficult. Frequently, an individual tree’s live crown ratio (LCR) is predicted by linear or nonlinear models that are a function of easy-to-measure dendrometric variables using ordinary least-squares techniques. Using the long-term data from established genetic and spacing trials, we developed and evaluated the predictive performance of three nonlinear models and introduced a new generalized linear model for predicting LCR. The nonlinear models were fit using exponential, Weibull, and Richards functions. The generalized linear model was based on beta regression. This resulted in a slightly smaller error than the other models in predicting the LCR of loblolly pine trees used in this study. Crown ratio is measured in percentage unit and should be modeled using generalized linear models that assume a beta distribution for error terms.

Allometric models for improving aboveground biomass estimates in West African savanna ecosystems

West African Sudanian savanna ecosystems greatly contribute to local peoples’ livelihoods and climate change mitigation. Yet, the contribution of these ecosystems to carbon storage remains poorly documented due to the lack of accurate biomass predictive tools. Therefore, biomass allometric models developed at both the species-level and site-level may greatly improve carbon stock estimation. In this study, we developed allometric models for estimating aboveground biomass (AGB) at the tree component-, species- and site-levels in Burkina Faso. Five woody species with high socio-economic significance (Anogeissus leiocarpa, Combretum nigricans, Isoberlinia doka, Mitragyna inermis and Pterocarpus erinaceus) were selected at two forest sites based on their dominance in the savanna ecosystem. A total of 150 trees (30 trees per dominant species) spanning a wide range of diameter at breast height (DBH) were destructively sampled. Models to predict tree component biomass at the species-level were independently built with the Ordinary Least Squares (OLS) technique. Allometric models to predict tree total aboveground biomass (TAGB) for each species and all species were developed using both the OLS technique and the Seemingly Unrelated Regression (SUR) method. Biomass estimates were regressed with DBH as a single predictor, DBH and height (H) as interacted variables, and DBH, H and wood density (ρ) as three independent-input variables. The performance of the validated allometric models were compared with the generalized pantropical equation model for African tropical forests (Chave et al., 2014). The findings revealed that biomass predictors varied between the five species. The goodness-of-fit statistics revealed that both the OLS and SUR methods provide accurate biomass allometric equations, with the SUR method being the most accurate. The developed allometric models provide more accurate estimation of AGB than the pantropical model. Therefore, we recommend the use of these local models to improve the quantification of AGB and carbon stocks in Sudanian savanna ecosystems. Furthermore, the established species-specific and mixed-species allometric equations may constitute a useful tool for the monitoring, reporting and verification of carbon stocks within the REDD+ framework in Burkina Faso.

Asymmetric Responses of Economic Growth to Daily Oil Price Changes: New Global Evidence from Mixed-data Sampling Approach

Abstract Our paper inspects empirically the asymmetric impact of daily oil price shocks on the quarterly real domestic product in eight countries during the period (1983–2016). We employ two methodologies Ordinary Least Squares (OLS) and Asymmetric Mixed Data Sampling (AMIDAS). The OLS technique shows that the positive oil price shocks have a statistically significant negative effect on economic growth in all the countries and vice versa. In addition, it reveals that this relationship could be either symmetric or asymmetric in all the countries. On the contrary, the AMIDAS gives more important details and proves that all the relationships in our sample data are asymmetric. Thus, we think that the AMIDAS technique leads to more accurate results which enhances a better insightful of an energy policy. The policy implication of our paper demonstrates that the energy policies are significant procedures to improve economic performance.

The Role of State Budget Expenditure on Economic Growth: Empirical Study in Vietnam

Many authors have examined the impact of public spending on economic growth. This study uses ordinary least-squares technique to test the effect of state budget expenditure with two major components: development investment expenditure and recurrent expenditure on Vietnamese economy for the period 2000-2017. The empirical results show that the state budget expenditure of Vietnam has positive effect on the economy, however each main component has different impacts. Recurrent expenditure has significant positive impact on Vietnamese economy while there has no evidence to affirm the relationship between the development investment expenditure and the economic growth. Vietnamese government should restructure the state budget to enhance the positive effect on the economy. In the short run, Vietnam should not increase development investment expenditure due to low efficency in public investment. In the long run, it is necessary to economize recurrent expenditure to reserve a reasonable proportion of state budget for development investment expenditure to build infrastructure for developing the economy. The state budget expenditure should be restructured towards prioritizing recurrent expenditure on human and social relief, reducing public administration expenditure, allocating investment capital from the state budget for key and pervasive projects, avoiding spreading out investments as well as crowding out private investments.

Spatial Modelling of Air Pollution from PM10 and SO2 concentrations during Winter Season in Marmara Region (2013-2014)

It was aimed to characterize spatial variations of air pollutants in Marmara region, Turkey for determining contribution to air pollution status in this study. We used spatial data analysis for measured sulfur dioxide (SO2) and particulate matter (PM10) concentrations recorded in Marmara, which is the most industrialized region of Turkey. GIS technique was used for monitoring air pollution and spatial analyses of these pollutants measured with the period during between October 1, 2013 and March 31, 2014 known as winter (heating) season obtained from 61 air quality monitoring stations located in this region. Spatial distribution maps for these pollutants were generated to determine emission patterns for the study area with the aid of geostatistical techniques. Additionally standard and spatial regression models were employed on the measured emissions to reveal possible factors of air quality in the region using standard ordinary least squares (OLS) and spatially autoregressive (SAR) regression models. The two regression models revealed that all the four explanatory meteorological variables (i.e. temperature, wind speed, humidity and atmospheric pressure) used to depict the pollution levels in relation to air quality. After the definition of the final model parameters, the model was fit to the entire data set and the residuals were examined for the presence of spatial autocorrelation with Moran’s I. Compared to the OLS technique, SAR is found to be more appropriate when dependent variables exhibit spatial autocorrelation resulting in a valid model.

Polynomial Piece-Wise Stiffness in Cable-Based Transmissions for Robots: Modeling and Identification

This paper deals with cable-based motor-to-joint transmissions of multi-link robots chain. Their effects on robots flexibility have to be taken into account for modeling and control design. More in details, slack cables do not provide any force during compression (unlike springs), may present an initial nonzero elongation (preload) and, depending on the material, could exhibit non-constant stiffness. Those features may lead to non-trivial piece-wise elastic torques in a mechanical transmission. In this context, we present a framework to generate a more general (piece-wise) elastic torque model which can be embedded in the classical flexible-joint robot model, coherently with the Lagrangian approach. Moreover, we propose a model based on polynomial stiffness, whose parameters can be identified with ordinary least-squares techniques. Experimental results conducted on a flexible transmission show the usage and the utility of this work.

Causal nexus between foreign direct investment and economic growth

Purpose– The purpose of this paper is to determine cause and effect relationship between foreign direct investment (FDI) and economic growth (gross domestic product (GDP) taken as proxy) for Brazil, Russia, India, China and South Africa (BRICS nations) individually for the period 1992-2013. Also, the study tries to explore the reasons behind the linkage between FDI and GDP by estimating a linear regression model consisting of both macro-economic and institutional variables.Design/methodology/approach– Johansen cointegration technique followed by vector error correction model (VECM) and standard Granger causality test are employed to investigate the causal linkage between FDI and GDP. To delve into the reasons behind this linkage, an ordinary least square (OLS) technique is also applied to test the linear regression model consisting of net FDI inflows as dependent variable and nine macro- economic and institutional variables. Residual diagnostics is also conducted using Breusch-Godfrey Lagrange Multiplier test for diagnosing the problem of serial correlation, Breusch-Pagan-Godfrey test for examining heteroskedasticity and Jarque Bera test for verifying the normality of residuals.Findings– The Johansen cointegration result establishes a single cointegrating vector (long run relationship) between FDI and GDP for India, China and Brazil. After proving a cointegration, VECM results revealed that there exists unidirectional long run causality running from GDP to FDI in case of Brazil, India and China. Also, it is confirmed that there exists short run causality between FDI and GDP in China, i.e. the past lags of FDI jointly impact the value of GDP. However, for Russia and South Africa, where there is no cointegration in the long run, standard Granger causality test is conducted which reveals that in both the nations, FDI and GDP are independent of one another. The results of OLS technique reveal different country-specific factors causing this linkage between FDI inflows and economic growth.Originality/value– Various researchers in the past have examined this issue of linkage between FDI and GDP in the context of various developing or developed nations. This reveals a gap in the existing literature pertaining to this causal linkage in the context of the BRICS. Thus, this study fills this gap by analyzing not just this causal nexus with the help of VECM and Granger causality techniques but also tries to explore further the reasons for such strong/weak/no link with the help of fitting a regression model which comprises of both macro-economic and institutional country-specific variables influencing this causation.

On Bayesian Conjugate Normal Linear Regression and Ordinary Least Square Regression Methods: A Monte Carlo Study

In this study,  comparison between the classical ordinary least square (OLS) regression technique and the Bayesian conjugate normal linear regression method when the data satisfy all the necessary assumptions of OLS technique is presented. The Bayesian normal linear regression model was fitted using Normal-Gamma conjugate prior. Results from Monte Carlo study showed that the OLS estimator is as good as the Bayesian estimator in terms of the closeness of their estimated parameters to the true values. However, using the criteria of the mean square errors of parameters’ estimates and other performance indices, the results showed that Bayesian estimator is more efficient,  more consistent and relatively more stable than the classical least squares method even when the sample data satisfy all the necessary assumptions of the OLS method. The apparent better performance of Bayesian estimator over the OLS is justified by the prior information about the data that Bayesian technique employed in its estimation. Therefore, it could be concluded that if reliable information about the data under investigation is available, Bayesian regression technique(s) that would make use of such information should be preferred for efficient model’s estimation and better inference. The R statistical package (www.cran.org) was employed for all the analysis in this study.

Examining HIV-related stigma and discrimination in Ghana: what are the major contributors?

Although AIDS-related stigma and discrimination are considered detrimental to HIV prevention activities, not many studies have attempted to understand stigma and discrimination in sub-Saharan Africa, particularly Ghana. Using the 2008 Ghana Demographic and Health Survey and applying the ordinary least-squares technique, this study examined what influences AIDS-related stigma and discrimination among men and women in Ghana. The results indicate that Ghanaian men and women with relatively high knowledge about HIV/AIDS had low stigmatising and discriminatory attitudes (b=-0.097, P<0.01; b=-0.083, P<0.01), respectively. On the other hand, respondents who endorsed more myths about HIV transmission had high stigma and discriminatory attitudes. Women who had ever tested for their HIV serostatus reported significantly lower levels of stigma and discrimination (b=-0.085, P<0.01) compared with those who had not tested for HIV. Individuals who are highly educated, employed and in wealthy households all reported significantly lower levels of stigma and discrimination compared with those who are uneducated, unemployed and in poorer households. AIDS-related stigma and discrimination can be reduced by encouraging HIV testing, and ensuring that Ghanaians understand and have factual knowledge regarding the transmission of the disease.

On-line detection of toxic components using a microbial fuel cell-based biosensor

Safe drinking water without toxic chemicals is crucial for people's health. A recently developed sensor for the detection of toxic components in water is the microbial fuel cell (MFC)-based biosensor. In this biosensor, substrate consumption rate and metabolic activity of bacteria are directly related to the electric current. A reduction in current under otherwise similar conditions is an indication of toxic inhibition. Under steady state conditions, current can be described by the Butler–Volmer–Monod (BVM) model. Knowing which parameters of this model change under toxic contamination can give an indication on the type of toxicity. The model requires that the substrate concentration is known. It is shown in this paper that is not possible to estimate both the substrate concentration as well as the BVM parameters on-line from current data at constant overpotential. However, it appears that substrate concentration and substrate consumption rate can be estimated on-line, and that after a linear reparametrization the BVM parameters can be estimated by ordinary least-squares techniques from a polarization curve that is generated as soon as a suspect change in current occurs. Analysis shows that a weighted least-squares method is necessary to secure a good fit at the overpotentials where current is most sensitive to changes in kinetic parameters. A protocol for on-line detection of toxicity and for detection of the type of kinetic inhibition is provided.

Multi‐level models of stress and well‐being

tional stress researchers may investigate individual factors related to stress and well-being (e.g. personality, work-life balance, emotions, coping skills, etc.); job and organizational factors (e.g., work hours and schedules, role overload/underload/ambiguity, emotional labour, job insecurity, organizational climate); and even societal and national factors (e.g. cultural values; social, economic and environmental indicators). Yet, all too often, these variables are all measured at a single level, usually at the individual level. Thus, while we acknowledge that individual, group, organizational and even cultural variables are theoretically necessary to understand and predict stress outcomes, we rarely measure these variables at their appropriate level. The purpose of this editorial is to encourage researchers to take a multilevel approach to considering the relationships between occupational stress and wellbeing. This entails intentionally refl ecting on the individual, job, organizational and macroeconomic antecedents of employee stress. Such a multilevel framework can be fruitful not only for understanding the stress-strain process, but also crucial in developing and conceptualizing stress interventions. Thus, a multilevel approach can enhance both our theoretical and empirical understanding of occupational stress as well as the practical implications stemming from our research. Using a multi-level modelling (MLM) approach means explicitly taking into account the often hierarchical nature of our data structure (e.g. individuals working in groups, students in classrooms, children in families). Such a hierarchical dataset has traditionally posed three problems within an ordinary least squares (OLS) regression approach: (1) the units of analysis problem; (2) the violation of independent observations assumption problem; and (3) the heterogeneity of slopes problem. Let us consider each in turn. Most behavioural science models of stress acknowledge that a complete understanding of the structure and process of stress invariably requires a consideration of individual, group and environmental/situational characteristics (Sulsky & Smith, 2005). Such models originally arose from an awareness that purely biological models of stress fail to reliably predict which potential stressors will be perceived as stressful and how this process is infl uenced by personal and contextual factors. For example, the cognitive-transactional model of stress (Lazarus & Launier, 1978) posits that there are few, if any, universal stressors. Rather, the perception of and reactions to a potential stressor will vary within and across individuals and may differ over occasions and time. Whether the potential stressor is perceived to be stressful, therefore, intimately depends on characteristics of the individual (e.g. needs, abilities, personality) and the situation (e.g. demands, resources). As a result, most contemporary models of stress include some variation of a person-environment (P-E) fi t perspective [e.g. Karasek’s (1979) demands-control model; Hobfall’s (1989) Conservation of Resources theory; French and colleagues’ P-E fi t model, (French, Caplan, & Van Harrison, 1982, Van Harrison, 1978)]. Despite the fact that our models of stress explicitly consider individual and contextual factors, researchers often do not appropriately model these environmental and individual factors either in their research design, data collection or subsequent analyses. Thus, organiza-

Urban property values and contaminated sites: A hedonic analysis of Sydney, Nova Scotia

This study examines the impact of contaminated sites on urban property values in Sydney, Nova Scotia, Canada. The property value effects are examined using an inverse distance specification from the property to the site. A hedonic method employing ordinary least-square technique was used for model estimation. The results show that the presence of contaminated sites has had significant negative effect on the value of residential property. This negative effect, however, is largely localized to within few hundred metres of the sites. The total property value loss in urban Sydney from the contaminated sites is estimated to be $CDN 36 million.

Estimation of Dynamic Rate Parameters in Insect Populations Undergoing Sublethal Exposure to Pesticides

With newer, more environmentally friendly and, subsequently less lethal, pesticides in use, evaluating efficacy of a pesticide now requires more than simply counting deaths after treatment. A discrete, age-structured matrix model that incorporates a species' life history traits (such as birth rate, death rate and fecundity) has previously been used by ecologists. This model will be presented and discussed along with an alternative continuous, age-structured model which offers significant advantage in considering sublethal damage. We use this continuous model to estimate time-dependent mortality parameters in an ordinary least-squares technique. Confidence intervals are given and results from tests for statistical significance of added parameters are presented.

Constrained Minimization for Parameter Estimation of Induction Motors in Saturated and Unsaturated Conditions

This paper presents the analytical solution of the application of the constrained least-squares (LS) minimization to the online parameter estimation of induction machines. This constrained minimization is derived from the classical linear dynamical model of the induction machine, and therefore it is able to estimated the steady-state value of the electrical parameters of the induction motor under different magnetization levels. The methodology has been verified in simulation with a dynamical model which takes into account iron path saturation effects. After a description of the experimental setup and its signal processing systems, the methodology is verified experimentally under saturated and unsaturated working conditions, and the results are discussed and compared to those obtained with a classical unconstrained ordinary LS technique.

Donor Characteristics and the Dispersion of Foreign Assistance

What motivates states to provide foreign aid? Many, sometimes contradictory, answers have been offered. This study seeks to contribute to the debate in two ways: First, while most studies have sought to explain the amount of aid given, we seek to explain the distribution of that aid. Whether aid is concentrated on a few recipients or dispersed widely among many reflects the policy priorities of the donor. Second, previous studies have rarely employed time series cross-section data. We include data for 17 members of the Development Assistance Committee for 13 years (1983–1995) and employ an ordinary least-squares technique with panel-corrected standard errors. We find that the proportion of parliamentary seats held by left parties is the only variable in our model that provides a statistically significant explanation of the dispersion of development aid.

Experimental Determination and Computer Fitting of Desorption Isotherms of D. Joaquina Pears

Desorption isotherms at different operating temperatures provide valuable information for the design and control of drying processes. In the present work the desorption isotherms of pears are determined according to two equivalent forms of the GAB model at temperatures of 20, 25 and 30°C. These cover the range of summer average daily temperatures in Portugal, when the solar drying of pears is carried out. Two different computer fitting methodologies are used, namely, Ordinary Least Squares (OLS) and Orthogonal Distance Regression (ODR), in order to evaluate the above mentioned forms of the GAB model. From the results obtained it is possible to conclude that the ODR fitting is clearly more adequate than the OLS technique for this kind of experimental problem. Moreover, it is advisable to exploit the full form of the GAB model instead of its simplified and restricted version. Finally, the desorption isotherms do not vary significantly in the temperature range under study.

Trade and International R&amp;D Spillovers among OECD Countries

1. Introduction Does a country's trading partners affect its long-run growth? While many authors such as Edwards (1998) have found that relatively open economies tend to grow faster than relatively closed economies, it is less clear whether a country's trading partners affect its long-run growth. One plausible way trade partners may influence long-run growth is through the transfer of knowledge. Recent empirical work reveals an apparent link between international research spillovers and import patterns. Coe and Helpman (1995) uncover empirical evidence of a relationship between domestic productivity and import-weighted foreign research stocks. Using slightly different approaches, Coe, Helpman, and Hoffmaister (1997); Engelbrecht (1997a, b); and Lichtenberg and van Pottelsberghe de la Potterie (1998) find similar results. By linking knowledge transmission to import patterns, these results suggest that trade partners do influence long-run growth. However, these results have come under some criticism. Keller (1998) questions whether any of these results can be interpreted as indicating a link between knowledge flows and imports. He finds that significant international spillovers are still estimated from foreign research-anddevelopment (R&D) stocks constructed using randomly assigned weights. He interprets this result to imply that the choice of weights is not indicative of the knowledge transmission mechanism. While this is an ingenious test, Keller is careful to point out that his results may be due to the time-series properties of the data. As with the other studies, Keller focuses on the longrun relationship between the nonstationary total factor productivity and R&D data series but estimates the relationship using standard OLS techniques. Kao and Chiang (1998) demonstrate that the ordinary-least-squares (OLS) estimator in a cointegrated panel is asymptotically normal but with a nonzero mean. Kao, Chiang, and Chen (1999) apply panel cointegration methods to Coe and Helpman's estimation and conclude that the evidence of a relationship between imports and research spillovers is weak. This paper reexamines the empirical relationship between trade and R&D spillovers using the panel cointegration techniques developed by Kao and Chiang (1998). As this paper shows, accurate estimates and inference tests of the cointegrating relationship indicate no long-run relationship between imports and international flows of knowledge, confirming Kao, Chiang, and Chen's (1999) results. Keller's experiment is reconsidered next. This paper finds that when panel cointegration techniques are employed, the choice of weights used in the construction of the foreign R&D stocks is informative. As a final contribution, this paper considers exports as an alternative transmission mechanism. Ben-David and Loewy (1998) describe how even the technological leaders may gain knowledge spillovers from their export relationships. The very strong evidence presented here supports their model. The new evidence suggests that previous studies may have overstated the role of imported inputs in international R&D spillovers while understating other transmission mechanisms. The rest of the paper proceeds as follows. Section 2 outlines a simple model of innovation and productivity growth. Section 3 discusses the nonstationary nature of the data and the recent advances in panel unit root tests and panel cointegration. A reevaluation of the relationship between randomly generated import patterns and international spillovers appears in section 4. Section 5 assesses the role of exports in transmitting international research spillovers. Section 6 concludes with a brief summary and suggestions for further research. 2. Model While the existence and transmission of international research spillovers plays a role in a variety of models of trade and growth, the empirical tests of international research spillovers are usually motivated by appeals to endogenous growth models, such as those in Grossman and Helpman (1991). …