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This module follows on from Introductory Econometrics and considers econometric theory and methods when Gauss Markov assumptions fail to hold. The first half of this module deals with time series and panel data. The second half introduces different examples of the endogeneity problem and their solutions. 

Macroeconomic policy and performance are fundamental to our daily lives. This course gives the students a systematic way of thinking about macroeconomic issues.  The students will be able to derive macroeconomic models based on the behaviour of economics agents.  The students will end up with a model that they could can use independently to understand macroeconomic behaviour and policy issues in the real world.

This module will build on, and extend, what students have learned in previous microeconomics courses.  We will continue to study how agents make optimising decisions, but here with a focus on how those decisions can be inefficient when there are market failures, as opposed to the perfectly competitive world that students have mostly studied before in, for example, the Microeconomics module in the previous semester. Some prominent real-world examples are environmental externalities, or the provision of public goods. We will also explore common mechanisms that have been developed to try and move decisions to more efficient outcomes; for example taxes, tradable permits, preference revelation mechanisms. We will study how societies, rather than individuals, can make collective decisions over resource allocations when preferences differ across the population – again, particularly relevant in the case of public goods. Some of the topics may have been touched on in level 4, but students will see how learning progresses by looking at topics in more detail and with more rigour. Paralleling this, the learning outcomes in this module will provide a basis upon which to build for some of level 6’s microeconomic-based modules.

By the end of the module students will have learnt how to carry out empirical analyses using appropriate econometric software to study economic and financial time series data; how to interpret the results of such analyses; and will have acquired an ability to critically assess empirical papers.  

This module develops equilibrium concepts for static, dynamic, complete and incomplete information. These are applied to various aspects of economic importance: markets, bargaining, job-market signalling, expert advice and electoral competition.  The module will advance students’ knowledge of microeconomics. 

This module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

The module broadly covers two parts. In the first part we concentrate on the theoretical foundations of international trade, i.e. address the questions “why do we trade” and “is trade good for us”. In the second part we focus on the policy instruments that are available to the designers of trade policy; our analysis involves issues related to the potential costs and/or benefits to a range of stakeholders of trade barriers, e.g. tariffs and quotas. We also investigate the issues of international trade agreements.

This module introduces students to the field of behavioural economics which incorporates psychological evidence into economics. The standard approach in economics explains market outcomes and economic decision-making using theoretical models which usually assume that people are fully rational. Behavioural economics, on the other hand, seeks to increase the explanatory power of traditional models by considering a number of real life decision making situations where some standard rationality assumptions on preferences do not hold. This module builds mainly on the individual decision making models taught in microeconomics and financial economics modules in year 1 and year 2, identifies departures from these classical models, and use them as an inspiration to create alternative theories of decision making.

This module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity, connectedness and compactness. In the second part smooth manifolds are introduced, together with different construction methods, concepts of orientability and transversality. Finally, in the third part key elements of analysis on manifolds are discussed, such as tensors, differential forms, and the Stokes theorem in full generality.MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.

This module looks at developments in microeconomic theory in relation to the role of information in the economy. It presents models of the basic contract theory and asymmetric information (moral hazard and adverse selection) as well as some of the applications of these models (e.g., insurance, labour market contracts). The module builds on the knowledge and skills the students have acquired in Levels 4 and 5 in terms of microeconomic theory, mathematical tools (algebra, calculus, constrained and unconstrained optimisation) and econometrics.

The module has the aim of introducing students to core concepts in the blockchain technology. Students will become familiar with applications of cryptography to financial transactions and the technicalities behind cryptocurrencies and their workings. Using case studies and simulations, students will be exposed to the use of software wallets and engage in blockchain and cryptocurrency related transactions.

Economics of Competition and Regulation Policy is a microeconomics course concerned with the performance of markets and the strategic behaviour of firms. The course draws on the fields of industrial organization and market design and focuses on imperfect competition, co-operation between firms, and common regulations such as anti-trust laws. This is a theory-based optional module for third year BSc students. The aim of the module is to provide a solid understanding of some of the core economic models of imperfect competition and to help students understand the challenges involved with designing and structuring markets.

The module introduces the workings of financial and commodity derivatives markets and securities. Securities such as forwards, futures, swaps, CDOs and options have been traded on organised exchanges and/or ‘over the counter’, for decades. Financial markets are innovative and new derivative instruments are frequently introduced to facilitate risk-hedging or speculative investor operations. However, financial innovation can bring about its own significant risks, as the link between securitisation, CDOs and the credit crisis of 2007/08 showed. The emphasis of this module is on the pricing of derivative securities, their risks, as well as their use in professional settings, such as executive boards and derivative trading firms for hedging or investment purposes. 

Bayesian Statistics is the branch of statistics that relies on subjective probability to create a wide range of statistical models. This module introduces Bayesian methodology and guides students to use prior to posterior analysis for modelling realistic problems. This module then tackles more difficult topics such as Bayesian point estimates, model selection and linear regression. 

This module builds on the econometrics foundation from the Introductory Econometrics and Intermediate Econometrics courses and emphasizes on introducing micro-econometric techniques used to analyse microeconomic data. The first half of this module considers techniques to achieve causal inference. The second half studies maximum likelihood estimation of limited dependent variable models (logit, probit, Poisson, censoring and selectivity), as well as basic machine learning methods. This will enable students to acquire the skill sets necessary to investigate important and intriguing empirical questions that have real-world impacts on society.

Utilising the material taught across different principal subjects in Economics, this module provides a comprehensive introduction to theoretical and applied issues related to the global banking industry. Understanding the role of the financial system in the economy in ensuring the efficient allocation of resources, its effect on policy making and the risks involved from a potential disruption of its operation are key learning outcomes from this module, especially for students who are interested in applying for employment in the financial sector.

The module incorporates the foreign exchange market into a macroeconomic setting in order to shed light on the constraints within which open economies operate. At the heart of the analysis is the exchange rate and its determinants, including the different types of possible government intervention. In this context, the role of inflation, interest rates and market expectations are discussed. In addition, the government may also intervene in the foreign exchange market to manage the exchange rate by, e.g., buying or selling the international reserve currency. The decision whether to undertake or not such operations impacts on how the economy responds to different types of shocks (internal or external). The module covers these issues in detail and, in addition, provides a historical context for international arrangements concerning the exchange rate, as well as a review of episodes of exchange-rate crises.

This unit introduces the students to the process of independent academic investigation and helps them develop research skills through the completion of a substantial research project. Students are expected to use the empirical and analytical skills that they acquired in other modules.

Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.

This module explores topics within macroeconomics around two themes: Economic growth and dynamic equilibrium modeling. The aim of the economic growth part of the module is to survey the main models which are currently used to describe the determinants of economic growth. This includes both exogenous and endogenous growth models. The module will also develop a micro-founded dynamic equilibrium model of the macro-economy by combining agents and firms which are forward-looking and rational. This allows students to understand the modern model of economic fluctuations that informs economists and policymakers; it will develop their thinking in a structured framework. The importance of rigorous arguments is highlighted and insights about fiscal and monetary policy are drawn.

This module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.

This module introduces students to computational methods for solving and simulating economic models. The student will learn basic results and techniques in numerical analysis, acquire a working knowledge of programming language, and learn how to apply these tools to analyse quantitative implications of macroeconomic dynamic models and macroeconometrics. Matlab will be the main language taught in the course, while learning other languages (e.g. Python, Julia, etc) will be optional.

Time series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.

This module follows on from Introductory Econometrics and considers econometric theory and methods when Gauss Markov assumptions fail to hold. The first half of this module deals with time series and panel data. The second half introduces different examples of the endogeneity problem and their solutions. 

Macroeconomic policy and performance are fundamental to our daily lives. This course gives the students a systematic way of thinking about macroeconomic issues.  The students will be able to derive macroeconomic models based on the behaviour of economics agents.  The students will end up with a model that they could can use independently to understand macroeconomic behaviour and policy issues in the real world.

This module will build on, and extend, what students have learned in previous microeconomics courses.  We will continue to study how agents make optimising decisions, but here with a focus on how those decisions can be inefficient when there are market failures, as opposed to the perfectly competitive world that students have mostly studied before in, for example, the Microeconomics module in the previous semester. Some prominent real-world examples are environmental externalities, or the provision of public goods. We will also explore common mechanisms that have been developed to try and move decisions to more efficient outcomes; for example taxes, tradable permits, preference revelation mechanisms. We will study how societies, rather than individuals, can make collective decisions over resource allocations when preferences differ across the population – again, particularly relevant in the case of public goods. Some of the topics may have been touched on in level 4, but students will see how learning progresses by looking at topics in more detail and with more rigour. Paralleling this, the learning outcomes in this module will provide a basis upon which to build for some of level 6’s microeconomic-based modules.

By the end of the module students will have learnt how to carry out empirical analyses using appropriate econometric software to study economic and financial time series data; how to interpret the results of such analyses; and will have acquired an ability to critically assess empirical papers.  

This module develops equilibrium concepts for static, dynamic, complete and incomplete information. These are applied to various aspects of economic importance: markets, bargaining, job-market signalling, expert advice and electoral competition.  The module will advance students’ knowledge of microeconomics. 

This module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

The module broadly covers two parts. In the first part we concentrate on the theoretical foundations of international trade, i.e. address the questions “why do we trade” and “is trade good for us”. In the second part we focus on the policy instruments that are available to the designers of trade policy; our analysis involves issues related to the potential costs and/or benefits to a range of stakeholders of trade barriers, e.g. tariffs and quotas. We also investigate the issues of international trade agreements.

This module introduces students to the field of behavioural economics which incorporates psychological evidence into economics. The standard approach in economics explains market outcomes and economic decision-making using theoretical models which usually assume that people are fully rational. Behavioural economics, on the other hand, seeks to increase the explanatory power of traditional models by considering a number of real life decision making situations where some standard rationality assumptions on preferences do not hold. This module builds mainly on the individual decision making models taught in microeconomics and financial economics modules in year 1 and year 2, identifies departures from these classical models, and use them as an inspiration to create alternative theories of decision making.

This module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity, connectedness and compactness. In the second part smooth manifolds are introduced, together with different construction methods, concepts of orientability and transversality. Finally, in the third part key elements of analysis on manifolds are discussed, such as tensors, differential forms, and the Stokes theorem in full generality.MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.

This module looks at developments in microeconomic theory in relation to the role of information in the economy. It presents models of the basic contract theory and asymmetric information (moral hazard and adverse selection) as well as some of the applications of these models (e.g., insurance, labour market contracts). The module builds on the knowledge and skills the students have acquired in Levels 4 and 5 in terms of microeconomic theory, mathematical tools (algebra, calculus, constrained and unconstrained optimisation) and econometrics.

The module has the aim of introducing students to core concepts in the blockchain technology. Students will become familiar with applications of cryptography to financial transactions and the technicalities behind cryptocurrencies and their workings. Using case studies and simulations, students will be exposed to the use of software wallets and engage in blockchain and cryptocurrency related transactions.

Economics of Competition and Regulation Policy is a microeconomics course concerned with the performance of markets and the strategic behaviour of firms. The course draws on the fields of industrial organization and market design and focuses on imperfect competition, co-operation between firms, and common regulations such as anti-trust laws. This is a theory-based optional module for third year BSc students. The aim of the module is to provide a solid understanding of some of the core economic models of imperfect competition and to help students understand the challenges involved with designing and structuring markets.

The module introduces the workings of financial and commodity derivatives markets and securities. Securities such as forwards, futures, swaps, CDOs and options have been traded on organised exchanges and/or ‘over the counter’, for decades. Financial markets are innovative and new derivative instruments are frequently introduced to facilitate risk-hedging or speculative investor operations. However, financial innovation can bring about its own significant risks, as the link between securitisation, CDOs and the credit crisis of 2007/08 showed. The emphasis of this module is on the pricing of derivative securities, their risks, as well as their use in professional settings, such as executive boards and derivative trading firms for hedging or investment purposes. 

Bayesian Statistics is the branch of statistics that relies on subjective probability to create a wide range of statistical models. This module introduces Bayesian methodology and guides students to use prior to posterior analysis for modelling realistic problems. This module then tackles more difficult topics such as Bayesian point estimates, model selection and linear regression. 

This module builds on the econometrics foundation from the Introductory Econometrics and Intermediate Econometrics courses and emphasizes on introducing micro-econometric techniques used to analyse microeconomic data. The first half of this module considers techniques to achieve causal inference. The second half studies maximum likelihood estimation of limited dependent variable models (logit, probit, Poisson, censoring and selectivity), as well as basic machine learning methods. This will enable students to acquire the skill sets necessary to investigate important and intriguing empirical questions that have real-world impacts on society.

Utilising the material taught across different principal subjects in Economics, this module provides a comprehensive introduction to theoretical and applied issues related to the global banking industry. Understanding the role of the financial system in the economy in ensuring the efficient allocation of resources, its effect on policy making and the risks involved from a potential disruption of its operation are key learning outcomes from this module, especially for students who are interested in applying for employment in the financial sector.

The module incorporates the foreign exchange market into a macroeconomic setting in order to shed light on the constraints within which open economies operate. At the heart of the analysis is the exchange rate and its determinants, including the different types of possible government intervention. In this context, the role of inflation, interest rates and market expectations are discussed. In addition, the government may also intervene in the foreign exchange market to manage the exchange rate by, e.g., buying or selling the international reserve currency. The decision whether to undertake or not such operations impacts on how the economy responds to different types of shocks (internal or external). The module covers these issues in detail and, in addition, provides a historical context for international arrangements concerning the exchange rate, as well as a review of episodes of exchange-rate crises.

This unit introduces the students to the process of independent academic investigation and helps them develop research skills through the completion of a substantial research project. Students are expected to use the empirical and analytical skills that they acquired in other modules.

Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.

This module explores topics within macroeconomics around two themes: Economic growth and dynamic equilibrium modeling. The aim of the economic growth part of the module is to survey the main models which are currently used to describe the determinants of economic growth. This includes both exogenous and endogenous growth models. The module will also develop a micro-founded dynamic equilibrium model of the macro-economy by combining agents and firms which are forward-looking and rational. This allows students to understand the modern model of economic fluctuations that informs economists and policymakers; it will develop their thinking in a structured framework. The importance of rigorous arguments is highlighted and insights about fiscal and monetary policy are drawn.

This module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.

This module introduces students to computational methods for solving and simulating economic models. The student will learn basic results and techniques in numerical analysis, acquire a working knowledge of programming language, and learn how to apply these tools to analyse quantitative implications of macroeconomic dynamic models and macroeconometrics. Matlab will be the main language taught in the course, while learning other languages (e.g. Python, Julia, etc) will be optional.

Time series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.