nep-cmp New Economics Papers
on Computational Economics
Issue of 2021‒12‒13
seventeen papers chosen by
Stan Miles
Thompson Rivers University

  1. Algorithmic Collusion: Insights from Deep Learning By Matthias Hettich
  2. Forecasting Regional Milk Production Quantity: A Comparison of Regression Models and Machine Learning By Baaken, Dominik; Hess, Sebastian
  3. Deep Structural Estimation:With an Application to Option Pricing By Hui Chen; Antoine Didisheim; Simon Scheidegger
  4. Forecasting Crude Oil Price Using Event Extraction By Jiangwei Liu; Xiaohong Huang
  5. Home sweet home: Assessment of Readiness of Croatian Companies to Introduce I4.0 Technologies By Rajka Hrbić; Tomislav Grebenar
  6. Assessing the effects of VAT policies with an integrated CGE-microsimulation approach: evidence on Italy By Ali Bayar; Barbara Bratta; Silvia Carta; Paolo Di Caro; Marco Manzo; Carlo Orecchia
  7. Machine Learning, Behavioral Targeting and Regression Discontinuity Designs By Narayanan, Sridhar; Kalyanam, Kirthi
  8. FinRL: Deep Reinforcement Learning Framework to Automate Trading in Quantitative Finance By Xiao-Yang Liu; Hongyang Yang; Jiechao Gao; Christina Dan Wang
  9. Taxing income or consumption: macroeconomic and distributional effects for Italy By D'ANDRIA Diego; DEBACKER Jason; EVANS Richard W.; PYCROFT Jonathan; ZACHLOD-JELEC Magdalena
  10. Assessing Short‑Term and Long‑Term Economic and Environmental Effects of the COVID‑19 Crisis in France By Paul Malliet; Frédéric Reynés; Gissela Landa; Meriem Hamdi‑cherif; Aurélien Saussay
  11. Coping with increasing tides: technological change, agglomeration dynamics and climate hazards in an agent-based evolutionary model By Alessandro Taberna; Tatiana Filatova; Andrea Roventini; Francesco Lamperti
  12. A Universal End-to-End Approach to Portfolio Optimization via Deep Learning By Chao Zhang; Zihao Zhang; Mihai Cucuringu; Stefan Zohren
  13. Free Trade Agreements and the Movement of Business People By Thierry Mayer; Hillel Rapoport; Camilo Umana Dajud
  14. Optimal Model Selection in Contextual Bandits with Many Classes via Offline Oracles By Krishnamurthy, Sanath Kumar; Athey, Susan
  15. Quantum Computing and the Financial System: Spooky Action at a Distance? By Tahsin Saadi Sedik; Mr. Michael Gorbanyov; Majid Malaika
  16. Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms By Nikitas Stamatopoulos; Guglielmo Mazzola; Stefan Woerner; William J. Zeng
  17. Fiscal rules’ compliance and Social Welfare. By Kea BARET

  1. By: Matthias Hettich
    Abstract: Increasingly, firms use algorithms powered by artificial intelligence to set prices. Previous research simulated interactions among Q-learning algorithms in an oligopoly model of price competition. The algorithms learn collusive strategies but require a long time that corresponds to several years to do so. We show that pricing algorithms using deep learning (DQN) can collude significantly faster. The availability of these more powerful pricing algorithms enables simulations in larger markets. Collusion disappears in wide oligopolies with up to 10 firms. However, incorporating knowledge of the learning behavior by reformulating the state representation increases the ability to collude effectively.
    Keywords: Algorithmic Pricing, Collusion, Artificial Intelligence, Reinforcement Learning, DQN
    JEL: D21 D43 D83 L12 L13
    Date: 2021–11
    URL: http://d.repec.org/n?u=RePEc:cqe:wpaper:9421&r=
  2. By: Baaken, Dominik; Hess, Sebastian
    Keywords: Livestock Production/Industries
    Date: 2021–08
    URL: http://d.repec.org/n?u=RePEc:ags:iaae21:315117&r=
  3. By: Hui Chen; Antoine Didisheim; Simon Scheidegger
    Abstract: We propose a novel structural estimation framework in which we train a surrogateof an economic model with deep neural networks. Our methodology alleviates the curse of dimensionality and speeds up the evaluation and parameter estimation by orders of magnitudes, which significantly enhances one's ability to conduct analyses that require frequent parameter re-estimation. As an empirical application, we compare two popular option pricing models (the Heston and the Bates model with double-exponential jumps)against a non-parametric random forest model. We document that: a) the Bates model produces better out-of-sample pricing on average, but both structural models fail to outperform random forest for large areas of the volatility surface; b) random forest is more competitive at short horizons (e.g., 1-day), for short-dated options (with less than 7 days to maturity), and on days with poor liquidity; c) both structural models outperform random forest in out-of-sample delta hedging; d) the Heston model's relative performance has deteriorated significantly after the 2008 financial crisis.
    Keywords: Deep Learning, Structural Estimation, Option Pricing, Parameter Stability
    JEL: C45 C52 C58 C61 G17
    Date: 2021–02
    URL: http://d.repec.org/n?u=RePEc:lau:crdeep:21.14&r=
  4. By: Jiangwei Liu; Xiaohong Huang
    Abstract: Research on crude oil price forecasting has attracted tremendous attention from scholars and policymakers due to its significant effect on the global economy. Besides supply and demand, crude oil prices are largely influenced by various factors, such as economic development, financial markets, conflicts, wars, and political events. Most previous research treats crude oil price forecasting as a time series or econometric variable prediction problem. Although recently there have been researches considering the effects of real-time news events, most of these works mainly use raw news headlines or topic models to extract text features without profoundly exploring the event information. In this study, a novel crude oil price forecasting framework, AGESL, is proposed to deal with this problem. In our approach, an open domain event extraction algorithm is utilized to extract underlying related events, and a text sentiment analysis algorithm is used to extract sentiment from massive news. Then a deep neural network integrating the news event features, sentimental features, and historical price features is built to predict future crude oil prices. Empirical experiments are performed on West Texas Intermediate (WTI) crude oil price data, and the results show that our approach obtains superior performance compared with several benchmark methods.
    Date: 2021–11
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2111.09111&r=
  5. By: Rajka Hrbić (The Croatian National Bank, Croatia); Tomislav Grebenar (The Croatian National Bank, Croatia)
    Abstract: The main topic of this paper is to estimate the possibility and inclination of Croatian companies towards technology and inovation as well as to analize advantages, limitations and risks involved with this significant technological leap. In this paper, we analized 7.147 of Croatian business entities operating in different industries. Starting point in this research is to identify other subjects which could be users of I4.0 or its elements, based on the simmilarity of indicators with indicators of a sample of 58 identified I4.0 companies. We developed machine learning model by using eXtreme Gradient Boosting algoritm (XGBoost) for this purpose, an approach which has not been used in any similar reserches. This research shows that the main difference between I4.0 and traditional industry is mostly observable in significantly better businesess performance of investment indicators, cost efficiency, technical equipment and market competitivness. Riskiness of I4.0 companies is significantly lower than the riskiness of traditional ones. We identified 141 companies (1,97% of total analized sample) as potential users of I4.0, which make around 27% of total assets of the analised sample and around 26% of revenues.
    Keywords: Industry 4.0, eXtreme Gradient Boosting (XGBoost), artificial intelligence, robotics, high-tech companies, machine learning, impacts of I4.0 on bussines results
    JEL: C45 D22 D24 O14 O32 O33
    Date: 2021–03
    URL: http://d.repec.org/n?u=RePEc:hnb:wpaper:63&r=
  6. By: Ali Bayar (EcoMode CESifo); Barbara Bratta (Department of Finance Italian Ministry of Economy and Finance); Silvia Carta (Department of Finance Italian Ministry of Economy and Finance); Paolo Di Caro (Department of Law University of Catania Italy - Tax Administration Research Centre University of Essex Business School United Kingdom); Marco Manzo (Department of Finance Italian Ministry of Economy and Finance); Carlo Orecchia (Department of Finance Italian Ministry of Economy and Finance)
    Abstract: Reforming the structure of the Value Added Tax (VAT) is an open issue in different countries, mostly for raising revenues and improving the efficiency of the tax system. However, most of the existing analyses do not combine micro- and macro-modelling tools for assessing the welfare and redistributive effects of VAT reforms. Aspects like tax evasion and erosion, moreover, are usually of secondary importance when studying VAT changes. The objective of this paper is twofold. First, we propose an integrated approach, based on the new dynamic multi-sector, multi-household tax computable general equilibrium (CGE) model (ITAXCGE) recently developed at the Italian Ministry of Economy and Finance, to study a uniform VAT rate reform in Italy. Our empirical approach has the merit of including new information when evaluating VAT reforms: tax evasion and erosion, irregular labour, different household groups, and a detailed structure of taxation. Second, we simulate the effects of a uniform VAT rate reform on welfare and redistribution, by taking into consideration the consequences of such reform on VAT gap changes. Our results suggest that the equity-efficiency trade-off deriving from the reform under investigation is reduced when including information on tax evasion in the analysis. The policy implications of our study are finally discussed
    Keywords: Microsimulation, CGE-Modelling, integrated approach, VAT, tax gap.
    JEL: H31 D58 J22
    Date: 2021–12
    URL: http://d.repec.org/n?u=RePEc:ahg:wpaper:wp2021-14&r=
  7. By: Narayanan, Sridhar (Stanford University); Kalyanam, Kirthi (Santa Clara University)
    Abstract: The availability of behavioral data on customers and advances in machine learning methods have enabled scoring and targeting of customers in a variety of domains, including pricing, advertising, recommendation and personal selling. Typically, such targeting involves first training a machine learning algorithm on a training dataset, using that algorithm to score current or potential customers, and when the score crosses a threshold, a treatment such as an offer, an advertisement or a recommendation is assigned. In this paper, we highlight regression discontinuity designs (RDD) as a low-cost alternative to obtaining causal estimates in settings where machine learning is used for behavioral targeting. Our investigation leads to several new insights. Under appropriate conditions, RDD recovers the local average treatment effect (LATE). Further, we show that RDD recovers the average treatment effect (ATE) when: (1) The score is orthogonal to the slope of the treatment and (2) When the selection threshold is equal to the mean value of the score. We also show that RDD can estimate the bounds on the ATE even if we are unable to get point estimates of the ATE. That RDD can estimate ATE or bounds on ATE is a novel perspective that has been understudied in the literature. We also distinguish between two types of scoring: Intercept versus slope based and highlight the practical value of RDD in each context. Finally, we apply RDD in an empirical context where a machine learning based score was used to select consumers for retargeted display advertising. We obtain LATE estimates of the impact of the retargeted advertising program on both online and offline purchases, and also estimate bounds on the ATE. Our LATE estimates and ATE bounds add to the understanding of the effectiveness of retargeting programs in particular on offline purchases which has received less attention.
    Date: 2021–10
    URL: http://d.repec.org/n?u=RePEc:ecl:stabus:3992&r=
  8. By: Xiao-Yang Liu; Hongyang Yang; Jiechao Gao; Christina Dan Wang
    Abstract: Deep reinforcement learning (DRL) has been envisioned to have a competitive edge in quantitative finance. However, there is a steep development curve for quantitative traders to obtain an agent that automatically positions to win in the market, namely \textit{to decide where to trade, at what price} and \textit{what quantity}, due to the error-prone programming and arduous debugging. In this paper, we present the first open-source framework \textit{FinRL} as a full pipeline to help quantitative traders overcome the steep learning curve. FinRL is featured with simplicity, applicability and extensibility under the key principles, \textit{full-stack framework, customization, reproducibility} and \textit{hands-on tutoring}. Embodied as a three-layer architecture with modular structures, FinRL implements fine-tuned state-of-the-art DRL algorithms and common reward functions, while alleviating the debugging workloads. Thus, we help users pipeline the strategy design at a high turnover rate. At multiple levels of time granularity, FinRL simulates various markets as training environments using historical data and live trading APIs. Being highly extensible, FinRL reserves a set of user-import interfaces and incorporates trading constraints such as market friction, market liquidity and investor's risk-aversion. Moreover, serving as practitioners' stepping stones, typical trading tasks are provided as step-by-step tutorials, e.g., stock trading, portfolio allocation, cryptocurrency trading, etc.
    Date: 2021–11
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2111.09395&r=
  9. By: D'ANDRIA Diego (European Commission - JRC); DEBACKER Jason; EVANS Richard W.; PYCROFT Jonathan (European Commission - JRC); ZACHLOD-JELEC Magdalena (European Commission - JRC)
    Abstract: We study a set of tax reforms introducing a budget-neutral tax shift in Italy, from labour income to consumption taxes. To this end we use a microsimulation model to provide the output with which to estimate the parameters of tax functions in an overlapping-generations computable general equilibrium model. In doing so we make marginal and average tax rates bivariate non-linear functions of capital income and labour income. The methodology allows for the representation of the non-linearities of the tax and social benefit system and interactions between capital and labour incomes. The linked macro model then simulates labour supply, consumption and savings in a dynamic setting, thus accounting for behavioural and general equilibrium effects within a life-cycle optimization framework. Our simulations show that a tax shift made by cutting personal income tax rates might bring significant efficiency gains in Italy, with limited regressive effects, notwithstanding the revenue-compensating increase in consumptions taxes.
    Keywords: computable general equilibrium, overlapping generations, taxation, microsimulation, Italy, tax shift
    Date: 2021–12
    URL: http://d.repec.org/n?u=RePEc:ipt:taxref:202113&r=
  10. By: Paul Malliet (OFCE - Observatoire français des conjonctures économiques - Sciences Po - Sciences Po); Frédéric Reynés (OFCE - Observatoire français des conjonctures économiques - Sciences Po - Sciences Po); Gissela Landa (OFCE - Observatoire français des conjonctures économiques - Sciences Po - Sciences Po); Meriem Hamdi‑cherif; Aurélien Saussay (OFCE - Observatoire français des conjonctures économiques - Sciences Po - Sciences Po)
    Abstract: In response to the COVID-19 health crisis, the French government has imposed drastic lockdown measures for a period of 55 days. This paper provides a quantitative assessment of the economic and environmental impacts of these measures in the short and long term. We use a Computable General Equilibrium model designed to assess environmental and energy policies impacts at the macroeconomic and sectoral levels. We find that the lockdown has led to a significant decrease in economic output of 5% of GDP, but a positive environmental impact with a 6.6% reduction in CO2 emissions in 2020. Both decreases are temporary: economic and environmental indicators return to their baseline trajectory after a few years. CO2 emissions even end up significantly higher after the COVID-19 crisis when we account for persistently low oil prices. We then investigate whether implementing carbon pricing can still yield positive macroeconomic dividends in the post-COVID recovery. We find that implementing ambitious carbon pricing speeds up economic recovery while significantly reducing CO2 emissions. By maintaining high fossil fuel prices, carbon taxation reduces the imports of fossil energy and stimulates energy efficiency investments while the full redistribution of tax proceeds does not hamper the recovery.
    Keywords: Carbon tax,CO2 emissions,Macroeconomic modeling,Neo-Keynesian CGE model,Post-COVID economy
    Date: 2020
    URL: http://d.repec.org/n?u=RePEc:hal:journl:hal-03403038&r=
  11. By: Alessandro Taberna; Tatiana Filatova; Andrea Roventini; Francesco Lamperti
    Abstract: By 2050 about 70% of the worldùs population is expected to live in cities. Cities offer spatial economic advantages that boost agglomeration forces and innovation, fostering further concentration of economic activities. For historic reasons urban clustering occurs along coasts and rivers, which are prone to climate-induced flooding. To explore trade-offs between agglomeration economies and increasing climate-induced hazards, we develop an evolutionary agent-based model with heterogeneous boundedly-rational agents who learn and adapt to a changing environment. The model combines migration decision of both households and firms between safe Inland and hazard-prone Coastal regions with endogenous technological learning and economic growth. Flood damages affect Coastal firms hitting their labour productivity, capital stock and inventories. We find that the model is able to replicate a rich set of micro- and macro-empirical regularities concerning economic and spatial dynamics. Without climate-induced shocks, the model shows how lower transport costs favour the waterfront region leading to self-reinforcing and path-dependent agglomeration processes. We then introduce five scenarios considering flood hazards characterized by different frequency and severity and we study their complex interplay with agglomeration patterns and the performance of the overall economy. We find that when shocks are mild or infrequent, they negatively affect the economic performance of the two regions. If strong flood hazards hit frequently the Coastal region before agglomeration forces trigger high levels of waterfront urbanization, firms and households can timely adapt and migrate landwards, thus absorbing the adverse impacts of climate shocks on the whole economy. Conversely, in presence of climate tipping points which suddenly increase the frequency and magnitude of flood hazards, we find that the consolidated coastal gentrification of economic activities locks-in firms on the waterfront, leading to a harsh downturn for the whole economy.
    Keywords: Agglomeration; path-dependency; climate; flood; shock; relocation; migration; agent-based model; tipping point; resilience; lock in.
    Date: 2021–11–29
    URL: http://d.repec.org/n?u=RePEc:ssa:lemwps:2021/44&r=
  12. By: Chao Zhang; Zihao Zhang; Mihai Cucuringu; Stefan Zohren
    Abstract: We propose a universal end-to-end framework for portfolio optimization where asset distributions are directly obtained. The designed framework circumvents the traditional forecasting step and avoids the estimation of the covariance matrix, lifting the bottleneck for generalizing to a large amount of instruments. Our framework has the flexibility of optimizing various objective functions including Sharpe ratio, mean-variance trade-off etc. Further, we allow for short selling and study several constraints attached to objective functions. In particular, we consider cardinality, maximum position for individual instrument and leverage. These constraints are formulated into objective functions by utilizing several neural layers and gradient ascent can be adopted for optimization. To ensure the robustness of our framework, we test our methods on two datasets. Firstly, we look at a synthetic dataset where we demonstrate that weights obtained from our end-to-end approach are better than classical predictive methods. Secondly, we apply our framework on a real-life dataset with historical observations of hundreds of instruments with a testing period of more than 20 years.
    Date: 2021–11
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2111.09170&r=
  13. By: Thierry Mayer; Hillel Rapoport; Camilo Umana Dajud
    Abstract: Many of the measures to contain Covid-19 severely reduced business travel. Using provisions to ease the movement of business visitors in trade agreements, we show that removing barriers to the movement of business people promotes trade. To do this, we first document the increasing complexity of Free Trade Agreements. We then develop an algorithm that combines machine learning and text analysis techniques to examine the content of FTAs. We use the algorithm to determine which FTAs include provisions to facilitate the movement of business people and whether those provisions are included in dispute settlement mechanisms. Using these data and accounting for the overall depth of FTAs, we show that provisions facilitating business travel indeed facilitate business travel (but not permanent migration) and, eventually, increase bilateral trade flows.
    Keywords: Covid-19;Business travel;Free Trade Agreements;Machine Learning;Text Analysis
    JEL: F10 F13 F14 F15 F20
    Date: 2021–12
    URL: http://d.repec.org/n?u=RePEc:cii:cepidt:2021-10&r=
  14. By: Krishnamurthy, Sanath Kumar (Stanford University); Athey, Susan (Stanford University)
    Abstract: We study the problem of model selection for contextual bandits, in which the algorithm must balance the bias-variance trade-off for model estimation while also balancing the exploration-exploitation trade-off. In this paper, we propose the first reduction of model selection in contextual bandits to offline model selection oracles, allowing for flexible general purpose algorithms with computational requirements no worse than those for model selection for regression. Our main result is a new model selection guarantee for stochastic contextual bandits. When one of the classes in our set is realizable, up to a logarithmic dependency on the number of classes, our algorithm attains optimal realizability-based regret bounds for that class under one of two conditions: if the time-horizon is large enough, or if an assumption that helps with detecting misspecification holds. Hence our algorithm adapts to the complexity of this unknown class. Even when this realizable class is known, we prove improved regret guarantees in early rounds by relying on simpler model classes for those rounds and hence further establish the importance of model selection in contextual bandits.
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:ecl:stabus:3971&r=
  15. By: Tahsin Saadi Sedik; Mr. Michael Gorbanyov; Majid Malaika
    Abstract: The era of quantum computing is about to begin, with profound implications for the global economy and the financial system. Rapid development of quantum computing brings both benefits and risks. Quantum computers can revolutionize industries and fields that require significant computing power, including modeling financial markets, designing new effective medicines and vaccines, and empowering artificial intelligence, as well as creating a new and secure way of communication (quantum Internet). But they would also crack many of the current encryption algorithms and threaten financial stability by compromising the security of mobile banking, e-commerce, fintech, digital currencies, and Internet information exchange. While the work on quantum-safe encryption is still in progress, financial institutions should take steps now to prepare for the cryptographic transition, by assessing future and retroactive risks from quantum computers, taking an inventory of their cryptographic algorithms (especially public keys), and building cryptographic agility to improve the overall cybersecurity resilience.
    Keywords: quantum computing; quantum-safe encryption; cybersecurity; fintech.; fintech; functioning quantum computer; computing technology; quantum machine; encryption standard; hardware capability; cloud service; Computer science; Migration; Financial sector; Global
    Date: 2021–03–12
    URL: http://d.repec.org/n?u=RePEc:imf:imfwpa:2021/071&r=
  16. By: Nikitas Stamatopoulos; Guglielmo Mazzola; Stefan Woerner; William J. Zeng
    Abstract: We introduce a quantum algorithm to compute the market risk of financial derivatives. Previous work has shown that quantum amplitude estimation can accelerate derivative pricing quadratically in the target error and we extend this to a quadratic error scaling advantage in market risk computation. We show that employing quantum gradient estimation algorithms can deliver a further quadratic advantage in the number of the associated market sensitivities, usually called greeks. By numerically simulating the quantum gradient estimation algorithms on financial derivatives of practical interest, we demonstrate that not only can we successfully estimate the greeks in the examples studied, but that the resource requirements can be significantly lower in practice than what is expected by theoretical complexity bounds. This additional advantage in the computation of financial market risk lowers the estimated logical clock rate required for financial quantum advantage from Chakrabarti et al. [Quantum 5, 463 (2021)] by a factor of 50, from 50MHz to 1MHz, even for a modest number of greeks by industry standards (four). Moreover, we show that if we have access to enough resources, the quantum algorithm can be parallelized across 30 QPUs for the same overall runtime as the serial execution if the logical clock rate of each device is ~30kHz, same order of magnitude as the best current estimates of feasible target clock rates of around 10kHz. Throughout this work, we summarize and compare several different combinations of quantum and classical approaches that could be used for computing the market risk of financial derivatives.
    Date: 2021–11
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2111.12509&r=
  17. By: Kea BARET
    Abstract: This paper studies the side-effects of fiscal rules’ compliance on social welfare. It considers national Budget Balance Rules’ (BBR) compliance effects on macroeconomic indicators and social welfare proxy indicators in OECD countries between 2004 and 2015. Instead of fiscal rules strength or fiscal rules presence effectiveness, we focus on fiscal rules’ compliance to assess the impact of fiscal rules’ performance on social welfare. The paper shows that governments seem to operate a reallocation of their spending to ensure both BBR’s compliance and economic objectives. Nevertheless, governments choices regarding their public spending composition seem leading to an increase in social inequalities suggesting that governments finally face a trade-off between fiscal rules’ compliance and social objectives. The analysis constitutes the first use of a causal Machine Mearning approach, namely the Double/Debiased Machine Learning recently developed by Chernozhukov et al. [2018], applied to fiscal rules’ performance assessment issues. This method allows us to highlight the key determinants of national BBR’s compliance as well as assessing the compliance’s effect on different macroeconomic and social indicators. We take care of voter preferences by computing a new proxy variable through Latent Factor Analysis approach and show that voter preferences appear as a key determinant for BBR’s compliance, giving an empirical proof that Wyplosz [2012]’s bias may matter when assessing fiscal rules’ performance.
    Keywords: Fiscal rules’ compliance; Social Welfare; Fiscal Surveillance; Machine learning.
    JEL: E61 H11 H50 H61 H62
    Date: 2021
    URL: http://d.repec.org/n?u=RePEc:ulp:sbbeta:2021-50&r=

This nep-cmp issue is ©2021 by Stan Miles. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at http://nep.repec.org. For comments please write to the director of NEP, Marco Novarese at <director@nep.repec.org>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.