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Articles 1 - 30 of 53
Full-Text Articles in Econometrics
The Impatience Of Winning: An Analysis Of Time Discounting, Predictive Modeling, And The Nba Draft, Alec R. Plante
The Impatience Of Winning: An Analysis Of Time Discounting, Predictive Modeling, And The Nba Draft, Alec R. Plante
Business and Economics Honors Papers
This paper examines whether NBA draft decisions can be better explained by incorporating non-geometric time discounting into a model of general manager decision making. Using a dataset of 285 NBA draft prospects over a 12-year period, the impact of college statistics on Value Over Replacement Player (VORP) is determined, and these impact values are then used to create a “predicted” VORP for the first 4 seasons of each player’s career: a projection of what a general manager might think of a prospect’s future value given their college statistics. Following this, geometric and hyperbolic time discounting models are applied to estimate …
Volatility Modeling With An Application To Risk Parity Portfolios, Kenneth Hou
Volatility Modeling With An Application To Risk Parity Portfolios, Kenneth Hou
CMC Senior Theses
This thesis studies volatility modeling in the context of risk parity portfolio construction. I compare three risk parity portfolios that differ only in their underlying volatility model: a historical covariance baseline, a Bayesian stochastic volatility model, and a GRU–GARCH hybrid neural network. Using daily returns on Kenneth French’s five industry portfolios from January 2016 through December 2025, I construct monthly rebalanced portfolios under each model, with the SV and GRU forecasts embedded in hybrid covariance matrices that combine forecasted volatilities with rolling historical correlations. The results document a divergence between forecast accuracy and portfolio performance: the SV model is the …
Multivariate Quantile Autoregression-Mixed Data Sampling (Mvqar-Midas) Modeling Of Cost Of Living And Supply Chain Dynamics In Canada., Patrick Gbolonyo
Multivariate Quantile Autoregression-Mixed Data Sampling (Mvqar-Midas) Modeling Of Cost Of Living And Supply Chain Dynamics In Canada., Patrick Gbolonyo
Theses and Dissertations (Comprehensive)
In recent years, the rising cost of living as a result of persistent inflationary pressures, disruptions in the global supply chains, and changes in the macroeconomic landscape has become a critical topic of discussion. To address this, we move beyond a mean-based framework and employ a quantile regression approach. This allows the persistence of each series and the transmis- sion of shocks between the Consumer Price Index (CPI) (the total CPI which is a percentage change over the past 12 months), the Interest Rate (IR)(the target for the overnight rate), the New Housing Price Index (NHPI), and high-frequency supply chain …
Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi
Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi
Electronic Theses & Dissertations (2024 - present)
In many scientific and financial contexts, we must reason and make predictions under conditions of incomplete information. This dissertation develops Entropic Dynamics (ED) as a unified framework for deriving dynamical laws directly from principles of inference. Within this approach, probability distributions represent states of knowledge, and their evolution is determined through entropy maximization subject to relevant constraints. This leads to a novel concept of entropic time and a formulation of dynamics as an inferential process. In this talk, I will present how ED provides a common foundation across multiple domains. In physics, quantum dynamics for particles and scalar fields in …
The Moderating Effect Of Income Inequality On The Income–Emissions Relationship In G20 Countries, Zahra Rizky Fadilah, Budiasih Budiasih
The Moderating Effect Of Income Inequality On The Income–Emissions Relationship In G20 Countries, Zahra Rizky Fadilah, Budiasih Budiasih
Economics and Finance in Indonesia
This study analyzes the moderating effect of income inequality on the income–emissions relationship in the environmental Kuznets curve (EKC) framework. Findings indicate that the relationship is inverted U-shaped in middle-income G20 countries, but monotonically increasing in high-income G20 countries. Interestingly, income inequality moderates this relationship only in the latter group. These findings suggest that middle-income G20 countries should focus on raising income per capita to mitigate environmental degradation, while their high-income counterparts need to prioritize reducing income inequality to effectively decouple income from emissions.
Comparative Evaluation Of Estimation Techniques For Purchasing Power Parity In African Countries Using The Country-Product-Dummy Regression Framework, Rokibat Adeola Tijani, Taiwo Abideen Lasisi, Dahud Kehinde Shangodoyin, Olasunkanmi James Oladapo
Comparative Evaluation Of Estimation Techniques For Purchasing Power Parity In African Countries Using The Country-Product-Dummy Regression Framework, Rokibat Adeola Tijani, Taiwo Abideen Lasisi, Dahud Kehinde Shangodoyin, Olasunkanmi James Oladapo
Al-Bahir
Purchasing Power Parity (PPP) is a popular macroeconomic analysis metric used to compare economic productivity and standards of living between countries. This study examines the estimation of PPP within the International Comparison Program (ICP) at Basic Heading (BH) level stage and leverages on the data from the 2011 ICP round. Focusing on five BHs out of 12 BHs across 50 Africa countries, to empirically evaluate the validity of the classical Ordinary Least Square (OLS) assumptions in the estimation of Country Product Dummy (CPD) regressions. Given the widespread use of OLS for BH level PPP computation, a rigorous examination of these …
Nba Player Types And Salaries: Assessing The Disparities In Pay, Nick Riccardi, Rodney J. Paul
Nba Player Types And Salaries: Assessing The Disparities In Pay, Nick Riccardi, Rodney J. Paul
Sport Management - All Scholarship
The purpose of this study was to identify player types that exist in the modern National Basketball Association (NBA), test whether player types are paid differently controlling for performance and other factors and construct successful rosters with cheaper payrolls.
We collected performance statistics and salary data for players and teams across five seasons (2018-19 to 2022-23). Cluster analysis is leveraged to group together player-seasons to identify the player types that exist in the NBA. Linear regression models are run to test for differences in pay by cluster membership while controlling for performance, age, and contractual details. Linear programming simulation models …
Welfare Implication Of Alternative Tax Rates Adjustment Policy In Nigeria: A Dsge Analysis, Umar B. Ibrahim, Isah F. Abubakar
Welfare Implication Of Alternative Tax Rates Adjustment Policy In Nigeria: A Dsge Analysis, Umar B. Ibrahim, Isah F. Abubakar
CBN Journal of Applied Statistics (JAS)
This study sets out to determine the desirable policy adjustment in the tax rate for Nigeria that ensures the least welfare cost. A calibrated small open-economy New Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model of the Nigerian economy is applied to achieve this objective. Within this framework, we examined the impact of an increase in value-added tax (VAT) rate from 7.5 to 15 percent on key macroeconomic variables relative to the impact of an increase in company income tax (CIT) rate from 30 to 35 percent on macroeconomic variables. Furthermore, we examined the welfare costs of the increases in the …
Mortgage Default Classification Modeling For Variable Analysis, Brendan R. Goggins
Mortgage Default Classification Modeling For Variable Analysis, Brendan R. Goggins
Honors College Theses
The financial crisis of the early 2000’s is a prime example of the severe consequences that mortgage default and borrower insolvency can have on economies at large. Mortgage default specifically is a prime case with the popularization of mortgage backed securities and the commonality of this loan structure. Multiple hypotheses and models have been formed to understand the reasons, causes, and consequences of mortgage default. This paper uses both machine learning and statistical classification models to inform an understanding of the variables most significant and impactful to the default outcome of mortgages. Consideration is given to both loan-level microeconomic variables …
Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information, Shujie Ma, Po-Yao Niu, Yichong Zhang, Yinchu Zhu
Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information, Shujie Ma, Po-Yao Niu, Yichong Zhang, Yinchu Zhu
Research Collection School Of Economics
This article investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent factors; the other part models the effects of the observed covariates through a coefficient matrix which is composed of high-dimensional column vectors. We model the observational pattern of the responses through a logistic regression of the covariates, and allow its probability to go to zero as the sample size increases. We apply an iterative least squares (LS) estimation approach in our considered context. The iterative LS …
Value Added Tax Rate Variation, Import Demand And Sectoral Output In Nigeria, Joshua K. Nomkuha, Aondoawase Asooso, Philip T. Abachi
Value Added Tax Rate Variation, Import Demand And Sectoral Output In Nigeria, Joshua K. Nomkuha, Aondoawase Asooso, Philip T. Abachi
CBN Journal of Applied Statistics (JAS)
This study employs computable general equilibrium (CGE) model to estimate the effect of increase in value added tax (VAT), from 5 per cent to 7.5 per cent, on import demand and sectoral output in Nigeria. The study uses 2020 as the base year for the data analysis. The results show that increase in VAT affects import demand negatively, based on import penetration ratios, with mixed effect across six sectors. The implication of the result is that the VAT policy discourage consumption of foreign products, and constitute excess burden to consumers of such products in Nigeria. The results further reveal that …
Trade Liberalization, Non-Oil Export And Economic Growth In Nigeria, Jerome T. Andohol, Terhemen Tarzoor, Dennis T. Nomor
Trade Liberalization, Non-Oil Export And Economic Growth In Nigeria, Jerome T. Andohol, Terhemen Tarzoor, Dennis T. Nomor
CBN Journal of Applied Statistics (JAS)
The study examines the impact of trade liberalization and non-oil exports on economic growth in Nigeria from 1986 to 2021. The study utilizes an autoregressive distributed lag model and found the combined effect of trade liberalization and non-oil exports to be positive and statistical significant. While trade liberalization alone may have negative consequences, its synergy with a robust non-oil export can drive sustainable economic growth. The study recommends that strategies to enhance non-oil exports should be encouraged to support the effectiveness of trade liberalization in promoting growth.
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
CBN Journal of Applied Statistics (JAS)
This paper investigates the time it would take for the FTSE-100 index to reach its post-COVID-19 peak. The paper utilises an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model that accounts for leverage effect and asymmetries. The preferred models amongst competing variants was the Autoregressive Moving Average (ARMA)-EGARCH(2,1) specification and was used to predict daily FTSE-100 data from 5th January 2000 to 21st June 2024. The empirical exercise showed that the COVID-19-induced financial crisis negatively affected the United Kingdom’s stock market performance. The results show that the FTSE100 index could reach its post-pandemic peak around 27th August, 2024 (two months after …
Impact Of Fiscal Policy On Financial Inclusion And Development In Nigeria, Okwanya Innocent, Taiwo A. Olusegun, Aimua E. Peace
Impact Of Fiscal Policy On Financial Inclusion And Development In Nigeria, Okwanya Innocent, Taiwo A. Olusegun, Aimua E. Peace
CBN Journal of Applied Statistics (JAS)
This paper examines the effect of fiscal policy on financial inclusion and development in Nigeria. The study employs the Autoregressive Distributed Lag (ARDL) model and impulse response function (IRF) to determine the extent and response of financial inclusion and development to fiscal policy changes in Nigeria. The study derives a financial inclusion index from three core indicators: access, usage and quality of financial services, while financial development is measured as the ratio of money supply to GDP (M2/GDP). The results show that government expenditure has a significant positive effect on financial inclusion and development, while tax revenue exerts a negative …
Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia
Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia
Journal of Nonprofit Innovation
Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.
Imagine Doris, who is …
Generalized Ratio-Product Cum Regression Variance Estimator In Two-Phase Sampling, Isah Muhammad
Generalized Ratio-Product Cum Regression Variance Estimator In Two-Phase Sampling, Isah Muhammad
CBN Journal of Applied Statistics (JAS)
This study develops a flexible and efficient generalized ratio-product cum regression type estimator of population variance utilizing auxiliary variable in two-phase sampling that incorporates the properties of ratio-type and product-type estimators. The properties of the estimator were derived using first order approximation. The theoretical conditions under which the precision and the flexibility of the estimator is better than some classical estimators are also provided. Empirical evidence from five real datasets suggests that the proposed estimator outperforms the classical variance, ratio variance, product, and exponential ratio type estimators in terms of precision and efficiency. The estimator can be utilized to provide …
Modelling The Naira Exchange Rate Dependence Using Static And Time-Varying Copula, Kabir Katata
Modelling The Naira Exchange Rate Dependence Using Static And Time-Varying Copula, Kabir Katata
CBN Journal of Applied Statistics (JAS)
This paper examines the dependence structure of different currencies versus the Nigerian Naira using constant and time-varying copula. Daily Naira/USD, Naira/Yuan, Naira/Pound, and Naira/Euro exchange rates from 23 December 2011 to 12 May 2020 were utilised. We fitted eight constant and time-varying copula families using the exchange rate standardised residuals. The study finds that the Naira exchange rate may be estimated with student t-copula, Symmetrized Joe-Clayton (SJC), or Rotated Gumbel copula models and Autoregressive (AR)– Glosten Jagannathan RunkleGeneralized Autoregressive Conditional Heteroscedastic (GJR-GARCH) (1,1) models with skewed t residuals for margins. The Naira exchange rate returns is timevarying, tail-dependent, and asymmetric. …
Improving The Efficiency Of Exponential Ratio-Type Estimator For Population Median: A Calibration Weight Adjustment Approach, Mathew J. Iseh, Kufre J. Bassey
Improving The Efficiency Of Exponential Ratio-Type Estimator For Population Median: A Calibration Weight Adjustment Approach, Mathew J. Iseh, Kufre J. Bassey
CBN Journal of Applied Statistics (JAS)
This paper modifies the Bahl and Tuteja exponential ratio-type estimator for population median under simple random and stratified sampling schemes using calibration weight adjustment technique with supplementary information to vary the stratum weights. The bias and mean square error of the modified estimator were obtained up to the second-order approximation, which satisfies the necessary conditions for efficiency. The findings show that the new estimator surpasses existing estimators in efficiency gain. This suggests the appropriateness of calibration weight modification in boosting the efficiency of a population parameter estimator under stratified random sampling especially where the population parameter of the auxiliary variable …
The Impact Of Subjective Risk Analysis On Real Estate Prices In The Nisqually Region Following The 2001 Nisqually Earthquake, Ryan Espedal
The Impact Of Subjective Risk Analysis On Real Estate Prices In The Nisqually Region Following The 2001 Nisqually Earthquake, Ryan Espedal
All Master's Theses
Earthquakes are an environmental hazard that pose great risks to communities almost every day. With earthquakes, the main cause of concern is physical destruction of property, however, there are also psychological effects that are researched and discussed much less. In 2001, the Nisqually area of western Washington experienced a substantial earthquake that produced minimal physical damage but caused a significant decrease in real estate prices. Studying single-family homes from 1986-2012, this research utilizes hedonic property models to measure the change in consumer’s subjective risk calculations with reference to real estate purchases after the Nisqually earthquake, measure the relationship between earthquake …
Application Of Sentiment Analysis And Machine Learning Techniques To Predict Daily Cryptocurrency Price Returns, Edward Wu
CMC Senior Theses
This paper examines the effects of social media sentiment relating to Bitcoin on the daily price returns of Bitcoin and other popular cryptocurrencies by utilizing sentiment analysis and machine learning techniques to predict daily price returns. Many investors think that social media sentiment affects cryptocurrency prices. However, the results of this paper find that social media sentiment relating to Bitcoin does not add significant predictive value to forecasting daily price returns for each of the six cryptocurrencies used for analysis and that machine learning models that do not assume linearity between the current day price return and previous daily price …
Fiscal And Monetary Policy Interactions In A Developing Economy: A Dsge-Based Evidence From Nigeria, Queen E. Oye, Philip O. Alege
Fiscal And Monetary Policy Interactions In A Developing Economy: A Dsge-Based Evidence From Nigeria, Queen E. Oye, Philip O. Alege
CBN Journal of Applied Statistics (JAS)
This study characterizes the nature of fiscal-monetary interaction in Nigeria and gauges its macroeconomic effects by estimating a New Keynesian Dynamic Stochastic General Equilibrium (NK DSGE) model. Two policy simulations were also conducted. The first experiment considers the desirable active-passive policy mix while the second experiment ranks alternative monetary policy rules among the differing objectives of price, output and exchange rate stabilization. The study finds that fiscal and monetary policies interact as complements in an active monetary and passive fiscal policy mix over the sample period. The result from the first policy simulation reveals that the active monetary and passive …
Market Risk Factors And Stock Returns In The Nigerian Bourse, Omorose A. Ogiemudia, Osagie Osifo, Igbinovia L. Eghosa
Market Risk Factors And Stock Returns In The Nigerian Bourse, Omorose A. Ogiemudia, Osagie Osifo, Igbinovia L. Eghosa
CBN Journal of Applied Statistics (JAS)
This study examines the link between market risk and equity return in Nigeria between 1980 to 2019. It employs the vector error correction model (VECM) to determine the short run dynamics and long run effect of market risk factors on stock return. The findings revealed that a dynamic relationship exists between market risk factors and stock returns in Nigeria. Also, exchange rate risk and oil price risks have significant influence on stock return, while inflation and interest rate risk, and political instability risks have a non-significant impact on stock return. Finally, a unidirectional relationship was detected between interest rate, oil …
Effect Of Monetary Policy Rate On Market Interest Rates In Nigeria: A Threshold And Nardl Approach, Oluwafemi E. Awopegba, Joseph O. Afolabi, Lydia T. Adeoye, Godwin O. Akpokodje
Effect Of Monetary Policy Rate On Market Interest Rates In Nigeria: A Threshold And Nardl Approach, Oluwafemi E. Awopegba, Joseph O. Afolabi, Lydia T. Adeoye, Godwin O. Akpokodje
CBN Journal of Applied Statistics (JAS)
This study examines the effect of monetary policy rate (MPR) on market interest rates in Nigeria. For parsimony, we develop two indexes called the short-term interest rate (SINT) and Lending interest rate (LINT) to represent deposit and lending rates respectively. The nonlinear autoregressive distributed lag (NARDL) and threshold regression models are adopted. The study uses monthly data from 2002:M1 to 2019:M12. The results of the threshold regression model indicate that the degree of the effect of MPR on SINT and LINT above the estimated threshold of 11 and 13 percent respectively is greater and significant than if MPR were to …
Social Dimension Of Inclusive Growth In Ecowas: Implication For Poverty Reduction, Toriola K. Anu, Goerge O. Emmanuel, Ajayi O. Felix
Social Dimension Of Inclusive Growth In Ecowas: Implication For Poverty Reduction, Toriola K. Anu, Goerge O. Emmanuel, Ajayi O. Felix
CBN Journal of Applied Statistics (JAS)
This study investigates the implication of the social dimension of inclusive growth on poverty reduction in Economic Community of West African States (ECOWAS) countries. It specifically examines how social indices of inclusive growth comprising of income inequality, education, and health outcomes affect poverty reduction. The study uses a panel dataset of the six (6) lower-middle income countries in ECOWAS which was analysed via panel Difference Generalised Method of Moment (D-GMM). The results show that GDP per capita exerts significant negative effect on poverty while inequality, education and health outcomes do not show significant effect on poverty. Although, the estimates of …
Effect Of Fdi Inflows On Employment Generation In Selected Ecowas Countries: Heterogeneous Panel Analysis, Timothy A. Aderemi, Olawunmi Omitogun, Bukonla G. Osisanwo
Effect Of Fdi Inflows On Employment Generation In Selected Ecowas Countries: Heterogeneous Panel Analysis, Timothy A. Aderemi, Olawunmi Omitogun, Bukonla G. Osisanwo
CBN Journal of Applied Statistics (JAS)
The aim of this study is to examine the effect of FDI on employment in ECOWAS sub region between 1990 and 2019. The study utilizes a panel autoregressive distributed lag model to analyse the short run and long run relationship between FDI and employment across ECOWAS sub region. In the short run, the impact of FDI on employment is negative and statistically not significant. Meanwhile, in the long run FDI has a positive and statistically significant impact on employment rate. This implies that FDI has the capacity to generate employment in countries in ECOWAS sub region. Therefore, this study recommends …
Impact Of Covid-19 Pandemic On The Nigeria Stock Market: A Sectoral Stock Prices Analysis, Peter A. Adekunle, Yakubu A. Bello, Udochukwu G. Nwachukwu
Impact Of Covid-19 Pandemic On The Nigeria Stock Market: A Sectoral Stock Prices Analysis, Peter A. Adekunle, Yakubu A. Bello, Udochukwu G. Nwachukwu
CBN Journal of Applied Statistics (JAS)
This study examines the impact of the COVID-19 pandemic on sectoral stock prices in Nigeria stock market using daily data covering from February 28, 2020 to June 26, 2020. Applying the autoregressive distributed lag (ARDL) bounds test, the study finds that COVID-19 pandemic had adverse impact on the stock market indices in the short run. Furthermore, the study documents negative response of sectoral stock prices to the pandemic while the stock prices of the banking sub-sector are the worst hit. Compared to the consumer goods, and industrial subsector indices, the speed of adjustment to long run equilibrium is faster for …
The Determinations Of Public Trust In The Government Of Egypt: An Empirical Study, Mohamed Elimam
The Determinations Of Public Trust In The Government Of Egypt: An Empirical Study, Mohamed Elimam
Theses and Dissertations
Trust is a concept that is usually studied in the context of social interactions. At varying levels, we trust our families and friends, we trust strangers who share some traits with us and even trust institutions like banks with our savings and to handle our personal finances. By expansion, political trust, or the public's trust in government as a whole and as individual agencies. Trust in government forms a basis for the legitimacy. High levels of political trust facilitates the implementation of policies with more willing compliance from the public. This is more evident in situations like global and national …
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Pitzer Senior Theses
This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …
Analyzing Competitive Balance In Professional Sport, Kevin Alwell
Analyzing Competitive Balance In Professional Sport, Kevin Alwell
Honors Scholar Theses
In this paper we review several measures to statistically analyze competitive balance and report which leagues have a wider variance of performance amongst its competitors. Each league seeks to maintain high levels of parity, making matches and overall season more unpredictable and appealing to the general audience. Here we quantify competitive advantage across major sports leagues in numbers using several statistical methods in order for leagues to optimize their revenue.
On Cluster Robust Models, José Bayoán Santiago Calderón
On Cluster Robust Models, José Bayoán Santiago Calderón
CGU Theses & Dissertations
Cluster robust models are a kind of statistical models that attempt to estimate parameters considering potential heterogeneity in treatment effects. Absent heterogeneity in treatment effects, the partial and average treatment effect are the same. When heterogeneity in treatment effects occurs, the average treatment effect is a function of the various partial treatment effects and the composition of the population of interest. The first chapter explores the performance of common estimators as a function of the presence of heterogeneity in treatment effects and other characteristics that may influence their performance for estimating average treatment effects. The second chapter examines various approaches …