Stochastic Economic Model Research Articles

Yet more on a stochastic economic model: Part 5: a vector autoregressive (VAR) Model for retail prices and wages

AbstractIn this paper we develop a vector autoregressive model for retail prices and wages within the Wilkie model. The results turn out to be a slight improvement over the original model, but the simulated results are not very different.

Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs

Data envelopment analysis (DEA) is a well-known non-parametric technique primarily used to estimate radial efficiency under a set of mild assumptions regarding the production possibility set and the production function. The technical efficiency measure can be complemented with a consistent radial metrics for cost, revenue and profit efficiency in DEA, but only for the setting with known input and output prices. In many real applications of performance measurement, such as the evaluation of utilities, banks and supply chain operations, the input and/or output data are often stochastic and linked to exogenous random variables. It is known from standard results in stochastic programming that rankings of stochastic functions are biased if expected values are used for key parameters. In this paper, we propose economic efficiency measures for stochastic data with known input and output prices. We transform the stochastic economic efficiency models into a deterministic equivalent non-linear form that can be simplified to a deterministic programming with quadratic constraints. An application for a cost minimizing planning problem of a state government in the US is presented to illustrate the applicability of the proposed framework.

Double-uncertainty optimal operation of hybrid AC/DC microgrids with high proportion of intermittent energy sources

This paper applies double-uncertainty optimization theory to the operation of AC/DC hybrid microgrids to deal with uncertainties caused by a high proportion of intermittent energy sources. A fuzzy stochastic expectation economic model for day-ahead scheduling based on uncertain optimization theory is proposed to minimize the operational costs of hybrid AC/DC microgrids. The fuzzy stochastic alternating direction multiplier method is proposed to solve the double-uncertainty optimization problem. A real-time intra-day unbalanced power adjustment model is established to minimize real-time adjustment costs. Through comparative analysis of deterministic optimization, stochastic optimization and fuzzy stochastic optimization of day-ahead scheduling and real-time adjustment, the validity of fuzzy stochastic optimization based on a fuzzy stochastic expectation model is proved.

Efficient Uncertainty Quantification in Stochastic Economic Dispatch

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate evaluations of expectations or higher order moments for quantities of interest, e.g., generating cost, can require a prohibitively large number of samples. We propose an alternative to Monte Carlo sampling based on polynomial chaos expansions. These representations enable efficient and accurate propagation of uncertainties in model parameters, using sparse quadrature methods. We also use Karhunen–Loeve expansions for efficient representation of uncertain renewable energy generation that follows geographical and temporal correlations derived from historical data at each wind farm. Considering expected production cost, we demonstrate that the proposed approach can yield several orders of magnitude reduction in computational cost for solving stochastic economic dispatch relative to Monte Carlo sampling, for a given target error threshold.

Stochastic economic model predictive control for Markovian switching systems

The optimization of process economics within the model predictive control (MPC) formulation has given rise to a new control paradigm known as economic MPC (EMPC). Several authors have discussed the closed-loop properties of EMPC-controlled deterministic systems, however, little have uncertain systems been studied. In this paper we propose EMPC formulations for nonlinear Markovian switching systems which guarantee recursive feasibility, asymptotic performance bounds and constrained mean square (MS) stability.

Yet more on a stochastic economic model: Part 4: a model for share earnings, dividends, and prices

AbstractIn this paper, we develop an extension to the Wilkie model, introducing share earnings and cover (earnings/dividends) as new variables, and deriving share dividends from them. Earnings are available from April 1962, but only for the Non-Financial index, and for the All-Share one only from 1992. We construct a Composite Earnings Index from these series. We then find a suitable annual time series model for changes in earnings, and then for cover, which is mean-reverting. We compare this new model with the original model, in which changes in dividends were modelled directly. We also investigate monthly data to give parameters for stochastic interpolation. We observe an unusual change in earnings over 2015–2016, consider the implications of this and show specimen simulations.

Machine Learning for High-Dimensional Dynamic Stochastic Economies

We present the first computational framework that can compute global solutions to very-high-dimensional dynamic stochastic economic models on arbitrary state space geometries. This framework can also resolve value and policy functions' local features and perform uncertainty quantification, in a self-consistent manner. We achieve this by combining Gaussian process machine learning with the active subspace method; we then embed this into a massively parallelized discrete-time dynamic programming algorithm. To demonstrate the broad applicability of our method, we compute solutions to stochastic optimal growth models of up to 500 continuous dimensions. We also show that our framework can address parameter uncertainty and can provide predictive confidence intervals for policies that correspond to the epistemic uncertainty induced by limited data. Finally, we propose an algorithm, based on this framework, that is capable of learning irregularly shaped ergodic sets as well as performing dynamic programming on them.

Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system

As the installed capacity of wind power is growing, the stochastic variability of wind power leads to the mismatch of demand and generated power. Employing the regulating capability of demand to improve the utilization of wind power has become a new research direction. Meanwhile, the micro combined heat and power (micro-CHP) allows residential consumers to choose whether generating electricity by themselves or purchasing from the utility company, which forms a residential hybrid energy system. However, the impact of the demand response with hybrid energy system contained micro-CHP on the large-scale wind power utilization has not been analyzed quantitatively. This paper proposes an operation optimization model of the residential hybrid energy system based on price response, integrating micro-CHP and smart appliances intelligently. Moreover, a novel load aggregation method is adopted to centralize scattered response capability of residential load. At the power grid level, a day-ahead stochastic economic dispatch model considering demand response and wind power is constructed. Furthermore, simulation is conducted respectively on the modified 6-bus system and IEEE 118-bus system. The results show that with the method proposed, the wind power curtailment of the system decreases by 78% in 6-bus system. In the meantime, the energy costs of residential consumers and the operating costs of the power system reduced by 10.7% and 11.7% in 118-bus system, respectively.

Yet more on a stochastic economic model: Part 3C: stochastic bridging for share yields and dividends and interest rates

AbstractThis is the third and last subpart of a long paper in which we consider stochastic interpolation for the Wilkie asset model, considering both Brownian bridges and Ornstein–Uhlenbeck (OU) bridges. In Part 3A, we developed certain properties for both these types of stochastic bridge, and in Part 3B we investigated retail prices and wages. In this paper, we investigate the remainder of many of our data series, relating to shares and interest rates. We conclude that, regardless of the form of the annual model, the monthly data within each year can be modelled by Brownian bridges, usually on the logarithm of the principal variable. But in no case is a simple Brownian bridge enough, and all series have their own peculiarities. Overall, however, our modelling produces simulations that are realistic in comparison with the known data. Many of our findings would apply to any similar model used for simulation over time. Our results have considerable importance for financial economics. We reconcile the conflict between the long-term mean-reverting modelling of Schiller and the short-term random walk modelling of Fama. This conclusion therefore has very wide significance.

Yet more on a stochastic economic model: Part 3B: stochastic bridging for retail prices and wages

AbstractThis is the second subpart of three in a long paper in which we consider stochastic interpolation for the Wilkie asset model, considering both Brownian bridges and Ornstein–Uhlenbeck (OU) bridges. In Part 3A, we developed certain properties for both these types of stochastic bridge, and we investigate the properties of many of our data series on the same lines. We have several economic or investment series, which all have their own peculiarities. In this paper, we cover only retail prices and wages. The other series are dealt with in Part 3C. We find that, although the annual series for the rate of inflation is generated by an AR(1) model, which is the discrete time equivalent of an OU process, an OU bridge is not suitable. We need to use a Brownian bridge on the logarithm of the Price Index. Further, the standard deviation of the monthly increments in any year is, as we find empirically from the data, a function of the change in the annual value, and further there is correlation between the monthly increments in successive years.

Yet more on a stochastic economic model: Part 3A: stochastic interpolation: Brownian and Ornstein–Uhlenbeck (OU) bridges

AbstractIn this paper, we develop certain properties for discrete Brownian bridges and Ornstein–Uhlenbeck bridges, which we use in the successor papers Part 3B and Part 3C to analyse real economic data series, with a view to constructing stochastic interpolation models for the Wilkie asset model.

The Economic Impact of the Introduction of Biosimilars in Inflammatory Bowel Disease

Inflammatory bowel disease [IBD] entails a high economic burden to society. We aimed to estimate the current and future impact of the introduction of biosimilars for infliximab on IBD-related health care costs. We designed a stochastic economic model to simulate the introduction of biosimilars in IBD, using a 5-year time horizon, based on the Dutch situation. Prevalence data on ulcerative colitis [UC] and Crohn's disease [CD] and IBD-related health care costs data were used as input. Assumptions were made on price reductions of anti-tumour necrosis factor [TNF] therapy, increase of anti-TNF prescription rate, and development of hospitalization costs. The base case scenario included a gradual decrease in prices of biosimilars up to 60%, a gradual decrease in prices of original anti-TNF compounds up to 50%, and an annual increase of anti-TNF prescription rate of 1%, and this was compared with no introduction of biosimilars. Sensitivity analyses were performed. For the base case, cost savings over the total of 5 years were on average €9,850 per CD patient and €2,250 per UC patient, yielding in €493 million total cost savings [a reduction of 28%] for The Netherlands. Results were predominantly determined by price reduction of anti-TNF therapy, threshold price reduction at which physicians switch patients towards biosimilars and the extent to which switching will take place. The introduction of biosimilars for infliximab can be expected to have a major impact on the cost profile of IBD. The economic impact will depend on local pricing, procurement policies and the physician's willingness to switch patients to biosimilars.

Stochastic security‐constrained economic dispatch for random responsive price‐elastic load and wind power

Price-elastic load (PEL) is a typical demand response resource. PEL provides an effective option to address the challenge of wind power output fluctuation. This study proposes a stochastic scheduling model, considering uncertainties of variable wind power and PEL response. A PEL stochastic security-constrained economic dispatch model using chance-constrained programming is presented for scheduling. The authors propose that the chance-constrained transmission interface flow constraints should be considered to control the probability of transmission interface flow limit violation via the parameter of security probability. An approach is suggested to transform the stochastic model into a deterministic quadratic programming problem via linearising the branch flow constraints and transmission interface flow constraints with sensitivity analysis method. Then, the probabilistic transmission interface flow constraints are equivalently transformed into conventional constraints. Case simulations on a provincial power system with 151 buses demonstrate the effectiveness and feasibility of the proposed mechanism, models, and methods.

Seeking ergodicity in dynamic economies

In estimation and calibration studies, the convergence of time series sample averages plays a central role. At the same time, a significant number of economic models do not satisfy the classical ergodicity conditions. Motivated by existing work on asymptotics of stochastic economic models, we develop a new set of results on limits of sample moments and other sample averages using an order-theoretic approach. Our results include a condition that is necessary and sufficient for convergence over a broad class of moment functions. We discuss implications, sufficient conditions and a range of economic applications.

How Jameel’s Advanced Stressed Economic and Financial Crises Models Dramatically Increases Markets Confidence and Drastically Decreases Markets Risks

Quantitative Financial Risk Management has tremendously change the way markets’ Practitioners, Regulators and Supervisors, Investors, Academics, Economists, Politicians, Policy Makers and Civil Society perceived financial and commodities markets. The generous invention of Black – Scholes – Merton (1973) Formula is of course the advanced turning point. The Normality Assumption (which causes overreliance, overconfidence, overvaluation or undervaluation of assets, overleveraging and underestimation of risks by the market participants) is the fundamental pillar in question, because returns are not normally distributed, returns have fat tails consisting bubbles and crashes for instance like IT-bubble, stock market bubble, housing bubble and commodities bubbles. Nassim N. Taleb (2007) called these Black Swans or Low – Probability, High – Impact events. The formulae in question receives serious criticisms especially in the United States of America to the extent of Tim Harford (2012) published an article entitled ‘The Black – Sholes: The Maths Formula linked to the Financial Crash’. Jamilu (2015) using his criterion and Advanced Methods attempted to capture the popular Black Swans (Low – Probability, High – Impact). The aim of this paper is to use Jameel’s Advanced Stressed Methods and Criterion to incorporate fat –tailed effects into the existing stochastic Economic and Financial Models thereby tremendously increasing markets confidence and drastically decreasing markets risks. Based on the various presentations of results and graphs obtained, it can be observed, the Jameel’s Advanced Stressed Economic and Financial Models can traces the trajectories of the past and future Economic and Financial Crises given reliable, accurate, sophisticated, valid and sufficient models’ independent variables.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

Economic and Mathematic Modeling of Labour Efficiency

The article is dedicated to the author’s methodology of economic and mathematic modeling of labour efficiency indicators. Conditions and type of labour determine social and economic efficiency of labour, the increasing of which is becoming necessary for any organization. Economic and mathematic modeling makes it possible to calculate planned indicators of labour efficiency according to different parameters. The research suggests methods of building one-factor and multifactor statistic and dynamic economic and mathematical models of labour effectiveness indicators. The efficiency of labour of different categories of workers can be presented by two groups of indicators: indicators of production efficiency (labour efficiency) and indicators of economic (financial) efficiency (profitability of labour). On the basis of the analysis of the studied factors the dependence was derived which can be expressed in a deterministic or stochastic factor economic and mathematical model. Advantages of a stochastic model of efficiency of work consist is that incomplete, vague and insufficiently formalized information is also taken into account through a complex factorial function with variable structure and the changing nature of dynamics. The presented method allows a high degree of reliability in modeling planned increase in efficiency of labour. Thus, when evaluating and planning the efficiency of labour of the workers of commercial enterprises not only productivity but also profitability of labour should be taken into account. DOI: 10.5901/mjss.2015.v6n6s3p527

Modeling the effects of mergers in procurement

In procurement settings, mergers among suppliers reduce buyers' choice sets and can harm buyers by eliminating their preferred supplier or reducing their negotiating leverage. I develop a stochastic economic model that predicts the effects of mergers based on information that commonly is available to antitrust authorities. I derive general expressions for the ex ante expected changes in price, buyer utility, and supplier profit. Each becomes tractable under certain distributional assumptions. The model predicts that average prices will increase by more than 40% due to the recently litigated acquisition of Power Reviews by Bazaarvoice, in the absence of an effective remedy.

Pediatric Crohn’s Disease, Unrealized Height, and Diminished Lifetime Earnings

Introduction: Crohn’s disease (CD) can have negative effects on height development in pediatric patients with CD [1]. An association between reduced adult height and wages in employed persons has previously been reported[2,3]. We calculated the potential reduction in lifetime earnings associated with unrealized adult height resulting from pediatric CD. Methods: Existing estimates of the effect of CD on adult height and the effect of reduced height on wages were combined to develop a stochastic economic model that predicts the reduction in lifetime wages associated with CD in the United States (U.S.). The model used data from a retrospective analysis [4] of adults who developed CD as children to estimate the impact of CD on unrealized height (mean unrealized adult height =2.4 cm; standard deviation [SD] =6.5). We relied on estimates of the association between height and wages [2] (mean % reduction in wage per cm =0.98%, SD=0.22%, including both sexes) to calculate the effect of unrealized height on wages. Earnings were adjusted downward to account for CD. Monte Carlo analysis was used to assess stochastic results. Future earnings were discounted at a rate of 3%. Results: The mean reduction in lifetime earnings (in 2012 U.S.$) associated with CD-attributed lower stature was $32,728 (95% confidence interval [CI]: $57,291 to $13,181). One-way sensitivity analysis varied assumptions for height loss observed in CD patients, indicating a range in lifetime losses of $23,270 to $88,228. When restricting unrealized adult height to the bottom quartile of observations in the data, mean reduction in lifetime earnings was $143,794 (95% CI: $81,920 to $206,954). Variation in assumptions about the size of the height-wage effect indicated losses of $18,466 to $32,131. Higher wage inflation increased reductions in lifetime earnings. If pediatric onset CD affects labor force participation, losses would be higher; for every 1% drop in labor force participation, lifetime earnings are reduced by an additional $39,233. Conclusion: To our knowledge, this is the first assessment of the cost of CD-mediated unrealized height on lifetime earnings in the U.S. Earlier diagnosis, medical, and/or surgical interventions that improve growth outcomes may improve lifetime earnings in patients with CD in the U.S.

An economic analysis of hyperketonemia testing and propylene glycol treatment strategies in early lactation dairy cattle

The purpose was to develop stochastic economic models which address variation in disease risks and costs in order to evaluate different simulated on-farm testing and propylene glycol (PG) treatment strategies based on herd hyperketonemia (HYK) incidence during the first 30 DIM. Data used in model development concerning the difference in health and production consequences between HYK and non-ketotic cows were based on results from 10 studies representing over 13,000 cows from 833 dairy farms in North America, Canada, and Europe. Inputs for PG associated variables were based on a large field trial using cows from 4 free-stall dairy herds (2 in New York and 2 in Wisconsin). Four simulated on-farm testing and treatment strategies were analyzed at herd HYK incidences ranging from 5% to 80% and included: 1) treating all cows with 5d of PG starting at 5 DIM, 2) testing all cows for HYK 1 day per week (e.g. Mondays) from 3 to 16 DIM and treating all positive cows with 5d of oral PG, 3) testing all cows for HYK 2 days per week (e.g. Mondays and Thursdays) from 3 to 9 DIM and treating all positive cows with 5d of oral PG, and 4) testing all cows for HYK 3 days per week (e.g. Mondays, Wednesdays, and Fridays) from 3 to 16 DIM and treating all positive cows with 5d of oral PG. Cost-benefit analysis included the costs associated with labor to test cows, β-hydroxybutyrate test strips, labor to treat cows, PG, and the associated gain in milk production, decrease in DA and early removal risks of PG treated HYK positive cows compared to non-treated HYK positive cows. Stochastic models were developed to account for variability in the distribution of input variables. Per 100 fresh cows in a herd with an HYK incidence of 40%, the mean economic benefits of the 4 different strategies were $1088, $744, $1166, and $760, respectively. Testing cows 2 days per week from 3 to 9 DIM was the most cost-effective strategy for herds with HYK incidences between 15% and 50%; above 50%, treating all fresh cows with 5d of PG was the most cost-effective strategy. These results show that for herds similar to those used in model, when herd HYK incidences rise above 25%, almost any HYK testing and treatment protocol will be economically beneficial for the farm.