Using difference equations to find optimal tax structures on the SugarScape

The use of equations to describe agent-based model dynamics allows access to mathematical theory that is not otherwise available. In particular, equation models can be effective at solving optimization problems—that is, problems concerning how an agent-based model can be most effectively steered into a particular state. In order to illustrate this strategy, we describe a modified version of the well-known SugarScape model and implement taxation. The optimization problem is to determine tax structures that minimize deaths but maximize tax income. Tax rates are dependent upon the amount of sugar available in a particular region; the rates change over time. A system of discrete difference equations is built to capture agent-based model dynamics. The equations are shown to capture the dynamics very well both with and without taxation. A multi-objective optimization technique known as Pareto optimization is then used to solve the problem. Rather than focusing on a cost function in which the two objectives are assigned weights, Pareto optimization is a heuristic method that determines a suite of solutions, each of which is optimal depending on the priorities of the researcher. In this case, Pareto optimization allows analysis of the tradeoff between taxes collected and deaths caused by taxation. The strategies contained here serve as a framework for a broad class of models.     

Spatial Vector Autoregressions

Abstract

A spatial vector autoregressive model (SpVAR) is defined as a VAR which includes spatial as well as temporal lags among a vector of stationary state variables. SpVARs may contain disturbances that are spatially as well as temporally correlated. Although the structural parameters are not fully identified in SpVARs, contemporaneous spatial lag coefficients may be identified by weakly exogenous state variables. Dynamic spatial panel data econometrics is used to estimate SpVARs. The incidental parameter problem is handled by bias correction rather than more popular alternatives such as generalised methods of moments (GMM). The interaction between temporal and spatial stationarity is discussed. The impulse responses for SpVARs are derived, which naturally depend upon the temporal and spatial dynamics of the model. We provide an empirical illustration using annual spatial panel data for Israel. The estimated SpVAR is used to calculate impulse responses between variables, over time, and across space. Finally, weakly exogenous instrumental variables are used to identify contemporaneous spatial lag coefficients.     

Popularity of reinforcement-based and belief-based learning models: An evolutionary approach

In an evolutionary model, players from a given population meet randomly in pairs each instant to play a coordination game. At each instant, the learning model used is determined via some replicator dynamics that respects payoff fitness. We allow for two such models: a belief-based best-response model that uses a costly predictor, and a costless reinforcement-based one. This generates dynamics over the choice of learning models and the consequent choices of endogenous variables. We report conditions under which the long run outcomes are efficient (or inefficient) and they support the exclusive use of either of the models (or their co-existence).     

Bayesian modeling of joint and conditional distributions

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.     

Computational techniques for analysis of system dynamics models of social systems

This paper presents a methodology for analysis of system dynamics models of social systems. The methodology consists of computational algorithms Specifically, the computational techniques of sensitivity analysis as extended to system dynamics models are shown to enhance an understanding of model behavior and to contribute to considerations of model validity, whereas optimization analyses are shown to contribute to model utility and policy formulation.     

Bayesian MCMC Mapping of Quantitative Trait Loci in a Half-sib Design: a Graphical Model Perspective

Graphical models provide a powerful and flexible approach to the analysis of complex problems in genetics. While task-specific software may be extremely efficient for any particular analysis, it is often difficult to adapt to new computational challenges. By viewing these genetic applications in a more general framework, many problems can be handled by essentially the same software. This is advantageous in an area where fast methodological development is essential. Once a method has been fully developed and tested, problem-specific software may then be required. The aim of this paper is to illustrate the potential use of a graphical model approach to genetic analyses by taking a very simple and well-understood problem by way of example.     

Outlier‐Robust Bayesian Multinomial Choice Modeling

A Bayesian method for outlier‐robust estimation of multinomial choice models is presented. The method can be used for both correlated as well as uncorrelated choice alternatives and guarantees robustness towards outliers in the dependent and independent variables. To account for outliers in the response direction, the fat‐tailed multivariate Laplace distribution is used. Leverage points are handled via a shrinkage procedure. A simulation study shows that estimation of the model parameters is less influenced by outliers compared to non‐robust alternatives. An analysis of margarine scanner data shows how our method can be used for better pricing decisions. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluating forecasts of political conflict dynamics

There is considerable interest today in the forecasting of conflict dynamics. Commonly, the root mean square error and other point metrics are used to evaluate the forecasts from such models. However, conflict processes are non-linear, so these point metrics often do not produce adequate evaluations of the calibration and sharpness of the forecast models. Forecast density evaluation improves the model evaluation. We review tools for density evaluation, including continuous rank probability scores, verification rank histograms, and sharpness plots. The usefulness of these tools for evaluating conflict forecasting models is explained. We illustrate this, first, in a comparison of several time series models’ forecasts of simulated data from a Markov-switching process, and second, in a comparison of several models’ abilities to forecast conflict dynamics in the Cross Straits. These applications show the pitfalls of relying on point metrics alone for evaluating the quality of conflict forecasting models. As in other fields, it is more useful to employ a suite of tools. A non-linear vector autoregressive model emerges as the model which is best able to forecast conflict dynamics between China and Taiwan.     

CO‐INTEGRATING VAR MODELS AND ECONOMIC POLICY

This paper surveys some relevant contributions to the economic literature on co‐integrating vector autoregressive (VAR) models [vector error correction mechanisms (VECMs)], emphasizing their usefulness for economic policy. It further discusses some theoretical aspects that are necessary for a complete understanding of their potential. The theoretical introduction of the co‐integrating VAR model is followed by an illustration of its applications to monetary policy, fiscal policy and exchanges rates as well as in establishing the effects of structural bilateral shocks between countries (the so‐called global VAR, or GVAR, models). Special attention is paid to the VECM capacities of being used in conjunction with dynamic stochastic general equilibrium models and of jointly specifying the short‐ and long‐run dynamics, thus representing the steady‐state of economic systems (by means of the co‐integration relations) and the short‐run dynamics around it.     

Simple,Efficient and Distribution-free Approach to Interaction Effects in Complex Structural Equation Models

Structural equation models with mean structure and non-linear constraints are the most frequent choice for estimating interaction effects when measurement errors are present. This article proposes eliminating the mean structure and all the constraints but one, which leads to a more easily handled model that is more robust to non-normality and more general as it can accommodate endogenous interactions and thus indirect effects. Our approach is compared to other approaches found in the literature with a Monte Carlo simulation and is found to be equally efficient under normality and less biased under non-normality. An empirical illustration is included.     

Unemployment,disequilibrium and the short run phillips curve: An econometric approach

The paper specifies a disequilibrium model for the aggregate labour market consisting of demand and supply functions for labour, an adjustment equation for wages as well as for prices, a transactions equation and, finally, an equation that relates measured unemployment to vacancies and to excess demand. The model has a more sophisticated treatment of dynamics than earlier disequilibrium models. The parameter estimates and the goodness-of-fit are satisfactory and the model's implications for the behaviour of several important variables are sensible. In particular, excess demand estimates computed in various ways are reasonable.     

Dynamic capacity planning of public schools in changing urban communities

A dynamic programming model is suggested as a core of a procedure to determine optimal number of classrooms and schools in a community which faces a trend of immigration. The model captures the dynamics of the expansion process and can handle, to a certain extent, uncertainty in future immigration. In certain conditions, the model is similar to inventory models for which computations can be efficiently carried out.     

Stochastic models of resonating markets

This paper describes a way to model a seasonally and irregularly peaking price dynamics, as that originated in commodity and energy markets, using a system of coupled nonlinear stochastic differential equations. The specific case of an electric power market is used to show which microeconomic features this approach is able to model. Critical point analysis is used in a simple way to show how the interaction between dynamic criticality and stochasticity can be used to develop further models, useful to explore more deeply other types of peaking price dynamics.     

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting,incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.     

Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model

The special functions are intensively used in mathematical physics to solve differential systems. We argue that they should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous economic growth models. We illustrate our argument on the famous Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of all variables in level. The parameters of the involved hypergeometric functions are identified using the Pontryagin conditions arising from the underlying optimization problems. In contrast to the pre-existing approaches, our method is global and does not rely on dimension reduction.     

NOMINAL AND REAL WAGE RIGIDITIES IN NEW KEYNESIAN MODELS: A CRITICAL SURVEY

Abstract The labour market is receiving increasing attention in the New Keynesian literature. In this paper, I critically survey this literature in order to highlight the role played by wage rigidities in the explanation of fluctuations caused by technology shocks. To this aim, I present a dynamic stochastic general equilibrium model with sticky prices, nominal wage rigidities and hiring costs. The comparison between this model and that of Blanchard and Gali highlights the non‐trivial differences which exist in the way nominal wage and real wage rigidities drive the economy's dynamics. My conclusion is that models incorporating nominal wage rigidities and some degree of price stickiness provide a better account of macroeconomic dynamics than models with real wage rigidities.     

Option pricing with discrete time jump processes

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.     

Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting

Wind power forecasts with lead times of up to a few hours are essential to the optimal and economical operation of power systems and markets. Vector autoregression (VAR) is a framework that has been shown to be well suited to predicting for several wind farms simultaneously by considering the spatio-temporal dependencies in their time series. Lasso penalisation yields sparse models and can avoid overfitting the large numbers of coefficients in higher dimensional settings. However, estimation in VAR models usually does not account for changes in the spatio-temporal wind power dynamics that are related to factors such as seasons or wind farm setup changes, for example. This paper tackles this problem by proposing a time-adaptive lasso estimator and an efficient coordinate descent algorithm for updating the VAR model parameters recursively online. The approach shows good abilities to track changes in the multivariate time series dynamics on simulated data. Furthermore, in two case studies it shows clearly better predictive performances than the non-adaptive lasso VAR and univariate autoregression.     

Finite sample evidence on the performance of stochastic frontier models using panel data

Most stochastic frontier models have focused on estimating average productive efficiency across all firms. The failure to estimate firm-specific effiicency has been regarded as a major limitation of previous stochastic frontier models. In this paper, we measure firm-level efficiency using panel data, and examine its finite sample distribution over a wide range of the parameter and model space. We also investigate the performance of the stochastic frontier approach using three estimators: maximum likelihood, generalized least squares and dummy variables (or the within estimator). Our results indicate that the performance of the stochastic frontier approach is sensitive to the form of the underlying technology and its complexity. The results appear to be quite stable across estimators. The within estimatoris preferred, however, because of weak assumptions and relative computational ease.The refereeing process of this paper was handled through J. van den Broeck.     

Impact of value-at-risk models on market stability

Financial institutions around the world use value-at-risk (VaR) models to manage their market risk and calculate their capital requirements under Basel Accords. VaR models, as any other risk management system, are meant to keep financial institutions out of trouble by, among other things, guiding investment decisions within established risk limits so that the viability of a business is not put unduly at risk in a sharp market downturn. However, some researchers have warned that the widespread use of VaR models creates negative externalities in financial markets, as it can feed market instability and result in what has been called endogenous risk, that is, risk caused and amplified by the system itself, rather than being the result of an exogenous shock. This paper aims at analyzing the potential of VaR systems to amplify market disturbances with an agent-based model of fundamentalist and technical traders which manage their risk with a simple VaR model and must reduce their positions when the risk of their portfolio goes above a given threshold. We analyse the impact of the widespread use of VaR systems on different financial instability indicators and confirm that VaR models may induce a particular price dynamics that rises market volatility. These dynamics, which we have called `VaR cycles’, take place when a sufficient number of traders reach their VaR limit and are forced to simultaneously reduce their portfolio; the reductions cause a sudden price movement, raise volatility and force even more traders to liquidate part of their positions. The model shows that market is more prone to suffer VaR cycles when investors use a short-term horizon to calculate asset volatility or a not-too-extreme value for their risk threshold.