Using Genetic Algorithms to Develop Strategies for the Prisoners Dilemma

The Prisoner’s Dilemma, a simple two-person game invented by Merrill Flood & Melvin Dresher in the 1950s, has been studied extensively in Game Theory, Economics, and Political Science because it can be seen as an idealized model for real-world phenomena such as arms races (Axelrod 1984). In this paper, I describe a GA to search for strategies to play the Iterated Prisoner’s Dilemma, in which the fitness of a strategy is its average score in playing 100 games with itself and with every other member of the population. Each strategy remembers the three previous turns with a given player, by using a population of 20 strategies, fitness-proportional selection, single-point crossover with Pc=0.7, and mutation with Pm=0.001.GA, Crossover, Mutation and Fitness-proportional

Neural Network Models for Inflation Forecasting: An Appraisal

We assess the power of artificial neural network models as forecasting tools for monthly inflation rates for 28 OECD countries. For short out-of-sample forecasting horizons, we find that, on average, for 45% of the countries the ANN models were a superior predictor while the AR1 model performed better for 21%. Furthermore, arithmetic combinations of several ANN models can also serve as a credible tool for forecasting inflation.Artificial Neural Networks; Forecasting; Inflation

The Direction of Causality between Health Spending and GDP: The Case of Pakistan

Relevant literature suggests that the most important determinant of health care spending is real GDP. Moreover, there is considerable evidence that health care spending rises at a faster rate than real GDP. This paper uses recently developed tests for the existence of a long run relationship to analyze the links between health care spending and GDP. We are, particularly, interested in estimating the elasticity parameter. The aim of the paper is to provide a new method of analysis to those used in recent papers on this subject. Typically in applied analysis, testing for the existence of cointegration and causality can only be carried out once the time series properties of the data have been established. For example, tests for cointegration require the variables to integrated of the same order, typically I(1), prior to estimation. By eliminating the need for unit root pre-testing, the tests applied here considerably simplify the inference procedure. They also reduce the potential for distortions in the inference due to the unknown properties of the testing sequence. Our findings include robust evidence that, for Pakistan, the income elasticity for health care spending is greater than one and that the elasticity value is stable over the estimation period.Health Spending; GDP; Causality

A Small Open Economy DSGE Model for Pakistan

This paper estimates a small open economy Dynamic Stochastic General Equilibrium (DSGE) model for Pakistan using Bayesian simulation approach. Model setup is based on new Keynesian framework, characterized by nominal rigidity in prices with habit formation in household’s consumption. The core objective is to study whether an estimated small open economy DSGE model provides a realistic behavior about the structure Pakistan economy with fully articulated description of the monetary policy transmission mechanism vis-à-vis domestic firm’s price setting behavior. To do so, we analyze the impulse responses of key macro variables; domestic inflation, imported inflation, output, consumption, interest rate, exchange rate, term of trade to different structural/exogenous shocks. From several interesting results, few are; (a) high inflation in Pakistan do not hit domestic consumption significantly; (b) Central bank of Pakistan responds to high inflation by increasing the policy rate by 100 to 200 bps; (c) exchange rate appreciates in both the cases of high domestic and imported inflation; (d) tight monetary policy stance helps to curb domestic inflation as well as imported inflation but appreciates exchange rate significantly (f) pass through of exchange rate to domestic inflation is very low; finally parameter value of domestic price stickiness shows that around 24 percent domestic firms do not re-optimize their prices which implies averaged price contract is about two quarters.New-Keynesian economics; open economy DSGE models; nominal rigidities; monetary policy transmission mechanism; Bayesian Approach

What is Hidden, in the Hidden Economy of Pakistan? Size, Causes, Issues and Implications

There is a worldwide contemporary debate about the role of the hidden economy in achieving the goal of sustained and inclusive economic growth and development, especially in the context of its spillover effects on the formal economy. For this purpose, policy makers and academicians have made concerted efforts to estimate the size of the hidden economy and to analyze its causes, issues and implications on key macroeconomic variables. However, there is a consensus among the policy makers that a better macroeconomic policy formulation and its true implementation are subject to the proper management of the associated issues of the hidden economy with suitable policy measures. In Pakistan, it is generally assumed that the hidden economy contributes about 30% to 50% to the overall GDP. The purpose of this paper is to estimate more precisely the size of the hidden economy with the determination of its potential causes and implications. Five statistical and structural modeling approaches namely; simple monetary approach, modified monetary approach using dynamic ordinary least square (DOLS), multiple-indicators multiple-causes (MIMIC) approach, electricity consumption approach and labor market survey based approach are used to estimate the size of the hidden economy and to analyze the characteristic nature of its growth over the period. The study also investigates the potential determinants of the hidden economy and various interrelated socio-economic issues in perspective of achieving national goal of inclusive growth and development. Finally, policy implications are provided consistent with pervading facts of the hidden economy in Pakistan especially in the context of the 18th Amendment and the 7th NFC Award.Hidden Economy, Size, Causes, Socio-Economic Implications, Inclusive Growth and Development, 18th Amendment and 7th NFC Award of Pakistan

A Small Open Economy DSGE Model for Pakistan

This paper estimates a small open economy Dynamic Stochastic General Equilibrium (DSGE) model for Pakistan using Bayesian simulation approach. Model setup is based on new Keynesian framework, characterised by nominal rigidity in prices with habit formation in household’s consumption. The core objective is to study whether an estimated small open economy DSGE model provides a realistic behavior about the structure Pakistan economy with fully articulated description of the monetary policy transmission mechanism vis -à-vis domestic firm’s price setting behavior. To do so, we analyse the impulse responses of key macro variables; domestic inflation, imported inflation, output, consumption, interest rate, exchange rate, term of trade to different structural/exogenous shocks. From several interesting results, few are; (a) high inflation in Pakistan do not hit domestic consumption significantly; (b) Central bank of Pakistan responds to high inflation by increasing the policy rate by 100 to 200 bps; (c) exchange rate appreciates in both the cases of high domestic and imported inflation; (d) tight monetary policy stance helps to curb domestic inflation as well as imported inflation but appreciates exchange rate significantly (f) pass through of exchange rate to domestic inflation is very low; finally parameter value of domestic price stickiness shows that around 24 percent domestic firms do not re-optimise their prices which implies averaged price contract is about two quarters.New-Keynesian Economics, Open Economy DSGE Models, Nominal Rigidities, Monetary Policy, Transmission Mechanism, Bayesian Approach

Optimisation Methods For Training Deep Neural Networks in Speech Recognition

Automatic Speech Recognition (ASR) is an example of a sequence to sequence level classification task where, given an acoustic waveform, the goal is to produce the correct word level hypotheses. In machine learning, a classification problem such as ASR is solved in two stages: an inference stage that models the uncertainty associated with the choice of hypothesis given the acoustic waveform using a mathematical model, and a decision stage which employs the inference model in conjunction with decision theory to make optimal class assignments. With the advent of careful network initialisation and GPU computing, hybrid Hidden Markov Models (HMMs) augmented with Deep Neural Networks (DNNs) have shown to outperform traditional HMMs using Gaussian Mixture Models (GMMs) in solving the inference problem for ASR. In comparison to GMMs, DNNs possess a better capability to model the underlying non-linear data manifold due to their deep and complex structure. While the structure of such models gives rich modelling capability, it also creates complex dependencies between the parameters which can make learning difficult via first order stochastic gradient descent (SGD). The task of finding the best procedure to train DNNs continues to be an active area of research and has been made even more challenging by the availability of ever more training data. This thesis focuses on designing better optimisation approaches to train hybrid HMM-DNN models using sequence level discriminative criterion which is a natural loss function that preserves the sequential ordering of frames within a spoken utterance. The thesis presents an implementation of the second order Hessian Free (HF) optimisation method, and shows how the method can made efficient through appropriate modifications to the Conjugate Gradient algorithm. To achieve better convergence than SGD, this work explores the Natural Gradient method to train DNNs with discriminative sequence training. In the DNN literature, the method has been applied to train models for the Maximum Likelihood objective criterion. A novel contribution of this thesis is to extend this approach to the domain of Minimum Bayes Risk objective functions for discriminative sequence training. With sigmoid models trained on a 50hr and 200hr training set from the Multi-Genre Broadcast 1 (MGB1) transcription task, the NG method applied in a HF styled optimisation framework is shown to achieve better Word Error Rate (WER) reductions on the MGB1 development set than SGD from sequence training. This thesis also addresses the particular issue of overfitting between the training criterion and WER, that primarily arises during sequence training of DNN models that use Rectified Linear Units (ReLUs) as activation functions. It is shown how by scaling with the Gauss Newton matrix, the HF method unlike other approaches can overcome this issue. Seeing that different optimisers work best with different models, it is attractive to have a consistent optimisation framework that is agnostic to the choice of activation function. To address the issue, this thesis develops the geometry of the underlying function space captured by different realisations of DNN model parameters, and presents the design considerations for an optimisation algorithm to be well defined on this space. Building on this analysis, a novel optimisation technique called NGHF is presented that uses both the direction of steepest descent on a probabilistic manifold and local curvature information to effectively probe the error surface. The basis of the method relies on an alternative derivation of Taylor’s theorem using the concepts of manifolds, tangent vectors and directional derivatives from the perspective of Information Geometry. Apart from being well defined on the function space, when framed within a HF style optimisation framework, the method of NGHF is shown to achieve the greatest WER reductions from sequence training on the MGB1 development set with both sigmoid and ReLU based models trained on the 200hr MGB1 training set. The evaluation of the above optimisation methods in training different DNN model architectures is also presented.IDB Cambridge International Scholarshi