Economics and Mathematics

Each year students receive specific training by the Management School Career Team, to prepare them for the graduate labour market. In the first year the focus is on growing the student’s awareness of labour market dynamics and his or her professional aspirations and inclinations. The second year focuses on goal setting, action planning, and the development of a personalised career plan. The third year focuses on one-to-one sessions with career advisors. The Career Team is based in the Management School, organises events with employers and alumni, and coaches students on how to best perform in the graduate job market through seminars, surgeries, mock interviews and one-to-one advice.

Students will gain a solid understanding of computation and computer programming within the context of maths and statistics. This module expands on five key areas:

• Programming and R
• Numerical solutions of equations
• Numerical differentiation and integration
• Monte Carlo methods
• Numerical solutions to ODEs

Under these headings, students will study a range of complex mathematical concepts, such as: data structures, fixed-point iteration, higher dimensions, first and second derivatives, non-parametric bootstraps, and modified Euler methods.

Throughout the module, students will gain an understanding of general programming and algorithms. They will develop a good level of IT skills and familiarity with computer tools that support mathematical computation.

Over the course of this module, students will have the opportunity to put their knowledge and skills into practice. Workshops, based in dedicated computing labs, allow them to gain relatable, practical experience of computational mathematics.

Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.

They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

Probability provides the theoretical basis for statistics and is of interest in its own right.

Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.

Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.

The focus will be on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.

Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.

This module helps you improve your strategic thinking. Over the course of this module, you will learn how to use ‘games’ to model strategic situations in the real world, and how to analyse and find out solutions to these games in situations in which players are intelligent and rational. Games including “normal form games”, “extensive form games”, “Bayesian games”, “repetitive games”, and “games with correlation device” will be introduced. Opportunities for playing games with the lecturer and other students will also be provided. The module requires a basic knowledge of algebra, calculus, and economics.

This module uses the tools of economics to study various macroeconomic variables (inflation, consumption, output, unemployment) and particularly their short-run and long-run dynamics. It covers topics related to fiscal policy and the sustainability of public debt in the intermediate run. In addition, students will study unemployment and labour market dynamics and more in general economic stability in the short run.

The module requires algebra, elementary calculus, logical thinking and general problem-solving ability.

This module first explores some of the key insights of New Keynesian economics, particularly that the monetary policy effectively influences output in the short-run but not in the long run. We will examine the crucial role of how the public formulates expectations for the economy’s stability, e.g. expectations about inflation and the importance of credible monetary policy. The second part of the module will cover topics explaining the “mysteries” of long-run economic growth. For example, how did we arrive at the vast degree of disparity between countries we observe today? This module covers topics like exogenous and endogenous growth, optimal growth, and dualism.

Note that this module is available only to students majoring in Economics.

Markets consist of individual buyers and sellers, each facing choices. A buyer must decide what, and how much, to purchase. A seller must decide how much to produce, how to produce it, and what price to charge. But how are these choices made? In this course, we will explore this question formally, with the aid of economic models. The topics include consumer choice, profit maximization and cost minimization. The module requires a basic knowledge of algebra and calculus.

By the end of the course, you will improve your logical thinking and problem-solving abilities.

This module builds on learning gained in Intermediate Microeconomics 1 (ECON220), developing on the theories and concepts covered as well as focusing on a range of new topics.

Topics include:

• analysis of monopoly behaviour and regulation

• price and quantity setting in duopoly markets

• introduction to game theory and strategic behaviour by firms

• auctions (including a study of eBay)

• general equilibrium and welfare economics

The module is normally taken in conjunction with ECON220.

The objective of the course is to train students to use macroeconomic models to understand real-world economic phenomena. The students will learn how to interpret macroeconomic data and understand the implications of economic policies. The course will put emphasis on major issues related to economic growth, the causes of economic fluctuations, and the effectiveness of economic policy. We will investigate the link between financial openness and economic growth, and we will explain why emerging countries experience capital outflows. We will study the impact of the exchange rate regime on the effectiveness of fiscal policy, we will rationalise the increase of current account deficits in Europe after the beginning of the nineties, and we will analyse the cause(s) of cross-country differences in hours worked.

The module requires basic knowledge of basic calculus, logical thinking and problem-solving skills.

This module provides the tools necessary to produce the rigorous economic analyses that form the core of both microeconomics and macroeconomics.

During the first part of the course, the attention is on the dynamic analysis of systems, which is key to understanding how economic variables change over time, especially in response to shifts in government economic policy.

The second part of the course studies constrained optimization which is central to understanding how households and firms make their consumption and production decisions when faced with limited budgets. Throughout the whole course, we focus our analysis on concrete examples and intuition, with an emphasis on how to frame economic problems using the mathematical tools you will acquire in the course.

We will require you to apply the concepts learned in class, and to translate informal problems into formal language.

Various topics of interest to prospective managers are covered within this module, including production and demand, competition and strategic behaviour, advertising and distribution, capital budgeting and inventories, the foreign exchange market, the economics of the multinational enterprise and the politics of corporate economics. The module provides knowledge of aspects of microeconomics relevant to general management, and also emphasises techniques and tools of analysis alongside relevant theory.

The module is designed to as an introduction to aspects of the firm and its environment which are of particular relevance to management. The topics selected aim to bridge the gap between the traditional approach to managerial economics and the more modern study of the organisation.

Each year students receive specific training by the Management School Career Team, to prepare them for the graduate labour market. In the first year the focus is on growing the student’s awareness of labour market dynamics and his or her professional aspirations and inclinations. The second year focuses on goal setting, action planning, and the development of a personalised career plan. The third year focuses on one-to-one sessions with career advisors. The Career Team is based in the Management School, organises events with employers and alumni, and coaches students on how to best perform in the graduate job market through seminars, surgeries, mock interviews and one-to-one advice.

Statistical inference is the theory of the extraction of information about the unknown parameters of an underlying probability distribution from observed data. Consequently, statistical inference underpins all practical statistical applications.

This module reinforces the likelihood approach taken in second year Statistics for single parameter statistical models, and extends this to problems where the probability for the data depends on more than one unknown parameter.

Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?

The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

The course introduces state-of-the-art methods used in current macroeconomics research to understand short-run business cycle and inflation dynamics, as well as economic stabilisation policies.

We will develop a broad and deep knowledge of modern Dynamic Stochastic General Equilibrium (DSGE) macroeconomic models that employ microeconomic foundations and rational expectations. These models will be solved using advanced analytical and numerical-computational approaches. More specifically, we will use the DSGE neoclassical Real Business Cycle and New Keynesian frameworks to understand the different sources of aggregate economic fluctuations, and to examine the positive and normative roles of fiscal and monetary policies.

Finally, the course examines contemporary issues such as inflationary shocks, government debt financing through distortionary taxation, optimal (un)conventional monetary and fiscal policies in a zero interest rate-liquidity trap environment, and financial frictions.

This module explores how the theoretical and mathematical tools of advanced microeconomic theory can be used to understand and model individual and strategic decision making. Topics it covers include advanced concepts of decision making of the main economic agents (consumers and firms), as well as specialised topics on game theory. The module requires algebra and calculus, along with logical thinking and problem-solving ability.

Bayesian statistics provides a mechanism for making decisions in the presence of uncertainty. Using Bayes’ theorem, knowledge or rational beliefs are updated as fresh observations are collected. The purpose of the data collection exercise is expressed through a utility function, which is specific to the client or user. It defines what is to be gained or lost through taking particular actions in the current environment. Actions are continually made or not made depending on the expectation of this utility function at any point in time.

Bayesians admit probability as the sole measure of uncertainty. Thus Bayesian reasoning is based on a firm axiomatic system. In addition, since most people have an intuitive notion about probability, Bayesian analysis is readily communicated.

Behavioural Economics is the interface between economics and psychology. It is one of the fastest-growing fields in economics, and since the past decade, it is regarded as a standard tool for policymaking. The course will survey the empirical tools used by behavioural economists and in particular lab and field experiments. We will explore behavioural biases affecting economic and financial decision making, and the role of trust and cooperation in teamwork. We will discuss models and experimental results explaining how we make decisions in various contexts such as choice under uncertainty, intertemporal choice or decision making in a social framework.

This course focuses on the economics of growth and development, both from a theoretical and empirical perspective. Using examples from developing countries, it explores wide-ranging, policy-relevant topics such as investments in health, education and infrastructure, microeconomics of credit markets, corruption and other determinants of economic development.

This module introduces up-to-date quantitative econometric methods used in applied research/empirical work. We will discuss various economic applications, including “returns to schooling” and “the effect of minimum wages on employment”. The module will also provide students with the data analytical skills necessary to conduct applied research in economics/policy analysis using popular statistical software, STATA. Key topics include linear regression, instrumental variables, causal inferences, binary choice models, panel data, time series modelling, and forecasting.

This module allows students the freedom to explore a research topic of their choice. It combines all of the previous skills acquired throughout the course of study. Students will be expected to write an original work of approximately 7,500 words. While the research topic will vary from student to student, each student will be assigned a supervisor to help guide them through the process of their first large scale research project in economics.

This module is essential for any student wishing to engage in graduate study in economics or for students wishing to work as a professional economist.

This applied module is an introduction to the economics of health and health care and will develop your awareness of the main policy issues in this field. It provides a comprehensive set of economic tools for critically appraising fundamental issues in the economics of health while offering a broad overview of the UK’s National Health Service and other health care systems around the world. The emphasis is on the use and interpretation of microeconomic models and the latest empirical evidence.

This module builds on basic microeconomics concepts to explore competition between firms and the evolution of market structure. It focuses on understanding the way firms make decisions and the effects of those decisions on market outcomes like prices, quantities, the type of products offered, and social welfare. The module first introduces basic concepts in Industrial Organisation to study imperfect competition and the determinants of market power. It then proceeds to analyse important topics in competition policy, such as cartels and merger policy.

The module requires an understanding of intermediate microeconomics (especially production/cost theory), basic concepts of game theory, and basic calculus.

This module develops your understanding of concepts and theories of international trade and factor flows, with particular reference to the way in which such material can inform policymaking. Topics covered include the Ricardian model, the Heckscher-Ohlin model, international trade under imperfect competition, outsourcing and offshoring, trade models based on heterogeneous firms and multinational firms, and trade policy under perfect and imperfect competition. Throughout the module we emphasise the applicability of the models learned, and their relevance to real-world events. Examples include the relationship between labour productivity and wages, opinions toward free trade, and the impact of immigration.

Focusing on the microeconomics of labour and personnel, this module covers topics such as the economics of migration, wage determination, job search and labour market discrimination.

There is a particular emphasis on principal agent problems in human resources and the design of incentives within firms.

Economics theory is used to analyse the operation of labour markers and assess the empirical evidence. Areas covered include:

• the firm's demand for labour
• labour supply at an individual and aggregate level
• causes of wage rigidity
• the economic impact of trade unions
• inflation and unemployment

This course aims at training ambitious economists to formal mathematical methods used in economic modelling and beyond. These techniques are necessary for students interested in pursuing postgraduate studies in Economics or working in analytically demanding jobs in the private sector. The course will cover material that usually is outside the scope of the regular mathematics education for economists, like decisions over time.

By the end of this course, students should have a good knowledge and understanding of these relevant mathematical techniques.

The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.

Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.

They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

Policymakers at Central Banks lie in a unique position to influence economic activity. This module examines the role of monetary policy in influencing the expectations and behaviour of agents in the economy and the implications this has for outcomes such as inflation, GDP and household welfare. Students will focus on applications of monetary theory to central banks problems and the recent objectives of the Bank of England Monetary Policy Committee. Topics include Central Bank independence, inflation targeting and the zero lower bound on interest rates, money creation and quantitative easing, and the macroeconomics of pandemics.

This module presents an overview of the interactions between the government, firms, and citizens, using a mix of theory and empirical work. Sometimes, markets are not efficient, and government intervention is necessary. Sometimes, markets are efficient, but equity concerns create the need for government. There is often a tension between the socially optimal policy and the outcome of the democratic process.

Some questions we study in this module:

• What is the role of government in the economy?
• Is it fair to redistribute money through taxation?
• Are some taxes better than others?
• How to deal with pollution, discriminations, and other inefficiencies of the market?
• How to make multinational companies pay taxes?
• Is there such a thing as an ideal voting system?

The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).

Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.

As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).

The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

Modern statistics is characterised by computer-intensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.

Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.

Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.

Lastly,students will spend time looking at Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.