Beyond Traditional Probabilistic Methods in Economics

This book presents recent research on probabilistic methods in economics, from machine learning to statistical analysis. Economics is a very important – and at the same a very difficult discipline. It is not easy to predict how an economy will evolve or to identify the measures needed to make an economy prosper. One of the main reasons for this is the high level of uncertainty: different difficult-to-predict events can influence the future economic behavior. To make good predictions and reasonable recommendations, this uncertainty has to be taken into account.

In the past, most related research results were based on using traditional techniques from probability and statistics, such as p-value-based hypothesis testing. These techniques led to numerous successful applications, but in the last decades, several examples have emerged showing that these techniques often lead to unreliable and inaccurate predictions. It is therefore necessary to come up with new techniques for processing the corresponding uncertainty that go beyond the traditional probabilistic techniques.

This book focuses on such techniques, their economic applications and the remaining challenges, presenting both related theoretical developments and their practical applications.

Methodology of economics

What do economists do? What are their goals? What methods do they use? Three terms—principles, policies and problems—guide us in answering the first two questions. Economists derive economic principles that are useful in the formulation of policies designed to solve economic problems. The methods of economic study used by the economist are summarised in Figure 1.1 . • The economist may collect and analyse the facts that are relevant to a specific economic problem. This task is sometimes called descriptive or empirical economics (see box 1 in Figure 1.1 ). • Economists may also generalise about the way individuals and institutions actually behave. Deriving such principles is called economic theory or ‘economic analysis’ (see box 2 in Figure 1.1 ). • Finally, the general knowledge of economic behaviour that economic principles provide can be used in formulating policies (or strategies). These policies are remedies or solutions for correcting or preventing the problem under scrutiny. This final aspect of the field is sometimes called applied economics , or policy economics or strategy (in the business sector). (See box 3 in Figure 1.1 .) INDUCTION AND DEDUCTION As we see in Figure 1.1 , economists—in studying economic behaviour—may move from facts to theory, or from theory to facts. Stated differently, economists may use inductive or deductive methods. With the inductive method , the economist begins with an accumulation of facts. These facts are then systematically arranged and analysed. The systematic analysis permits the derivation of a principle or a generalisation . Induction moves from facts to theory—that is, from the particular to the general). With the deductive method, the economist begins at the level of theory and proceeds to the verification (or rejection) of this theory by application of the facts. In this method, economists may draw on casual observation, insight or intuition to express a tentative, untested principle called a hypothesis . For example, they may infer, on casual observation, that it is rational for consumers to buy more of a product when its price is low and less when its price is high. The validity of this hypothesis must then be tested by the systematic and repeated examination of relevant facts. This is the deductive, or hypothetical, method . The deductive method goes from theory to facts—that is, from the general to the particular. p. 6 FIGURE 1.1 THE RELATIONSHIP BETWEEN FACTS, PRINCIPLES AND APPLICATION IN ECONOMICS (K) In analysing problems or aspects of the economy, economists may use the inductive method. In this method, they gather, systematically arrange and generalise from facts. Alternatively, the deductive method entails the development of hypotheses, which are then tested against facts. Generalisations derived from either method of inquiry can be useful in explaining economic behaviour, and also as a basis for formulating economic policies. Deduction and induction are complementary, rather than opposing, techniques of investigation. Hypotheses formulated by deduction provide guidelines for the economist in collecting and systematising empirical data. Conversely, some understanding of factual evidence—of the ‘real world’—is a prerequisite for the formulation of meaningful hypotheses. DESCRIPTIVE ECONOMICS All sciences are empirical. All sciences are based on facts—that is, they are based on observable and verifiable behaviour of certain data or subject matter. In the physical sciences, the factual data are inorganic. As a social science, economics is concerned with the behaviour of individuals, households, businesses and institutions that are engaged in the production, exchange and consumption of goods and services. Gathering facts can be an infinitely complex task. The world of reality is cluttered with countless interrelated facts. So, we must use good judgement in collecting facts. First, we must differentiate economic from non-economic facts. Then we must determine which economic facts are relevant to the problem under consideration. When this systematic categorisation has been completed, the relevant economic facts may appear diverse and unrelated. The next step is analysis to reach our analytical goal—that is, to test our hypothesis. ECONOMIC THEORY Accumulation of facts by itself is relatively useless. A description of what we observe is not enough. To be meaningful, facts must be systematically arranged and interpreted so that generalisations can be made. This is the task of economic theory or analysis. By connecting facts (arranging them in meaningful relationship to one another) and making generalisations, we derive economic principles and theories. This is the end result of economic analysis—to bring order and meaning to a collection of facts. ‘Theories without facts may be barren, but facts without theories are meaningless.’ 3 Principles and theories are meaningful statements drawn from facts; but facts, in turn, serve as a constant check on the validity of principles already established. Economic facts—how individuals and institutions actually behave in producing, exchanging and consuming goods and services—change with time. Thus, it is essential that economists continually check existing principles and theories against the changing economic environment. p. 7 TERMINOLOGY OF ECONOMIC THEORY Economists talk about ‘laws’, ‘principles’, ‘theories’ and ‘models’. These terms all mean essentially the same thing: generalisations (or statements of regularity) concerning the economic behaviour of individuals and institutions. The term ‘economic law’ suggests a high degree of exactness, universal application and even moral ‘rightness’—this is misleading. Similarly, the term ‘principle’ suggests a high degree of exactness. The term ‘theory’ may be associated with rules and ideas that do not match the realities of the world. In using these terms, we need to understand that they are generalisations—not rules or laws. The term ‘model’, however, it is a very practical one. A model is a simplified picture of reality, an abstract generalisation of how the relevant data actually behave. In this book, the terms ‘law’, ‘principle’, ‘theory’ and ‘model’ are used synonymously. The specific term chosen to label any particular generalisation reflects custom (convention) or convenience. Thus, for example, the relationship between the price of a product and the quantity of the product purchased by a consumer is called the ‘law’ of demand (rather than the ‘theory’ or ‘principle’ of demand)—because this is the convention. GENERALISATIONS IN ECONOMICS Economic principles are generalisations and, as the term implies, subject to exceptions and to quantitatively imprecise statements. Economic facts are usually diverse in nature—some individuals and institutions act in one way and some in another. Therefore, economic principles are often stated in terms of averages or statistical probabilities. For example, when economists say that the gross average household income was just over $50 500 in 2000–01, 4 they are making a generalisation. It is recognised that some households earned much more, and many others much less. But this generalisation—properly handled and interpreted—can be both meaningful and useful. Sometimes an economist states a generalisation in terms of probabilities. For example, research may suggest that there is a 95 per cent probability that every $1000 of cuts in personal income tax will result in a $900 increase in consumer spending. THE ‘OTHER THINGS BEING EQUAL’ ASSUMPTION Economists regularly use the ceteris paribus assumption (‘other things being equal’ assumption) when forming generalisations. That is, in order to simplify the process of analysis, economists assume that—other than the variable being considered—all other variables are constant. This helps the economist to focus on a particular factor. For example, consider the relationship between the price of Vegemite and the amount of Vegemite purchased. In studying the relationship, it is assumed that only the price of Vegemite varies. In fact, the factors that may influence the amount of Vegemite purchased would include consumer incomes and tastes and the prices of other goods (such as peanut butter). The ceteris paribus assumption allows the economist to focus on the relationship between the price of Vegemite and purchases of Vegemite—the analysis is not complicated by the intrusion of other variables. In the natural sciences, controlled experiments usually can be performed where ‘all other things’ are held constant (or nearly so)—and, therefore, the assumed relationship between two variables can be tested with high precision. Economics, however, is not a laboratory science. It is a social science. The economist's method of empirical verification is based on real-world data (statistics), generated by the actual operation of the economy. In this real-world environment, ‘other things’ do change. Sophisticated statistical techniques have been designed to hold other things contant, but such controls are imperfect. Thus, economic principles are less certain and less precise than those of the laboratory sciences. ABSTRACTIONS IN ECONOMICS An abstraction is the forming of general ideas (or concepts) from specific real examples. Economic principles or theories are abstractions. They do not present the full complexity of reality—they give a general picture (representation) of it. In the fact-collecting process (of studying economic behaviour), we identify ‘non-economic and irrelevant facts’. The process of doing this necessarily involves abstracting from reality. Why? Because, as economists studying a particular problem, we need to focus on particular facts. We may, for example, apply the ceteris paribus assumption—again abstracting from reality. (K)

p. 8 Business insight MODELS IN ECONOMICS—REPRESENTATION,NOT REALITIES Models are abstractions—that is, models are not meant to be fully realistic. They are meant to characterise and explain important aspects of a particular problem or issue. These stylised facts may confuse the beginner in economics who often looks for a full set of answers in a single framework. Umberto Eco provides a useful commentary on the purpose and limitations of models: 5 … [A] system is a structural model which arrests reality for an instant and tries to make it intelligible. But this arrest, necessary for communication, impoverishes the real instead of enriching it. The model is of value only if it stimulates an advance to a new level of understanding of reality, a level on which it then seems inadequate. Thus, the role of the model is to help us better understand what exists in reality, not to represent it accurately. Importantly, as new and better models develop, our understanding increases over time.

Unfortunately, the abstract nature of economic theory attracts the criticism that it is unrealistic and of little practical use. This is nonsense! Economic theories are useful for the simple reason that they are abstractions. Reality is too complex to allow meaningful analysis and interpretation of every detail. Economists theorise in order to meaningfully interpret a multitude of facts. These facts are studied, categorised and presented in a practical form for analysis. Thus, to generalise is to abstract, to form general ideas from real-world examples for the purpose of economic problem-solving. Generalisation (abstraction) for this purpose is practical. An economic theory is a model—a simplified picture or map—of some segment of the economy. This model enables us to understand reality better because it avoids the details of reality. Theories—good theories—are grounded in facts and, therefore, are realistic. (Theories that do not fit the facts are simply not good theories.) MACROECONOMICS AND MICROECONOMICS The economist may derive laws concerning economic behaviour at two different levels of analysis: macroeconomics and microeconomics. Macroeconomicsis concerned either with the economy as a whole or with the basic subdivisions or aggregates that make up the economy. is concerned with either the economy as a whole or with the basic subdivisions or aggregates (such as the government, household and business sectors) which constitute the economy. An aggregateA collection of specific economic units that are treated as if they were one unit. is a collection of specific economic units that are treated as if they were one unit. Thus, we may find it convenient to combine the more than seven million households in our economy and treat them as if they were one huge unit. In dealing with aggregates, macroeconomics is concerned with obtaining an overview of the structure of the economy and the relationships among the major aggregates that constitute the economy. The specific units that make up the various aggregates are not studied. In analysing economic problems, macroeconomics entails discussions of total output, the total level of employment, total income, aggregate expenditures, the general level of prices, and so on. It gives us an overview of the economy. On the other hand, microeconomicsis concerned with specific economic units and a detailed consideration of these individual units. is concerned with specific economic units and a detailed consideration of the behaviour of these individual units. At this level of analysis, the economist examines an economic unit, or a very small segment of the economy, to observe the details of its operation. Here, we mean an individual industry, firm or household. Our analysis concentrates on output or price of a specific product, the number of workers employed by a single firm, the revenue or income of a particular firm or household, the expenditures of a given firm or family, and so on. In microeconomics we examine the detail of some very specific component of our economic system. p. 9 In practice, however, not every topic can easily be labelled as ‘micro’ or ‘macro’: many topics and subdivisions of economics cover both. POLICY ECONOMICS: POSITIVE AND NORMATIVE As we move from the economic facts and principles levels (boxes 1 and 2 of Figure 1.1 ) to the application level (box 3), we make a critical leap from positive to normative economics. • Normative economics involves someone's value judgements about what the economy should be like or what particular policy action should be recommended, based on a given economic generalisation or relationship. • Positive economics , in contrast, deals with facts (and theories about these facts) and avoids value judgements. Positive economics attempts to set out scientific statements (models or theories) about economic behaviour. A common distinction between the two is to say that positive economics concerns what is—whereas normative economics represents subjective feelings about what should be (or ought to be). Positive economics deals with what the economy is actually like—whereas normative economics subjectively examines whether certain conditions or aspects of the economy are desirable or not. Consider these examples. The following statement is positive: ‘Unemployment is five per cent of the labour force’ (factual statement). The following statement is normative: ‘Unemployment should to be reduced’ (a desirable goal). The following statement is positive: ‘Other things being the same, if student fees are increased, enrolment at universities will fall’ (theory). The following statement is normative: ‘Student fees should be lowered at universities so that more people can obtain an education’ (goal). Whenever words such as ‘ought to’ or ‘should’ appear in a sentence, there is a strong chance that the statement is normative. Much of the apparent disagreement among economists involves normative, value-based policy questions. It may be true that various economists present and support different theories or models of the economy and its component parts. But mostly the biggest economic controversy reflects differing opinions or value judgements about what our society should be like. For example, there is greater agreement about what is the actual distribution of income in our society than about how income should be distributed. The point we re-emphasise is that value judgements or normative statements occur at the level of policy economics. ECONOMIC GOALS It is important to note a number of economic goals or values that are widely accepted in our own society and many other societies. They are not universally accepted, but common to many modern (especially western) economies. They include: 1. Economic growth: A higher standard of living the production and consumption of a greater amount and better quality of goods and services) is desirable. 2. Full employment: Suitable jobs should be available for people who are willing and able to work. 3. Economic efficiency: We desire maximum benefit at minimum cost from the limited productive resources available. 4. Price-level stability: Sizeable upswings or downswings in the general price level—that is, inflation and deflation—should be avoided. 5. Economic freedom: Consumers, business managers and workers should enjoy a high degree of freedom in which to conduct their economic activities. 6. An equitable distribution of income: No group should face severe poverty while another enjoys extreme luxury. 7. Economic security: Provision should be made for people who are chronically ill, have disabilities, are handicapped, are aged or are unable to earn sufficient income. 8. External balance: We seek a reasonable balance in our international trade and international financial transactions. p. 10 This list of goals provides the basis for several significant points. Interpretation The above list of basic economic goals inevitably entails problems of interpretation. What are ‘sizeable’ changes in the price level? What is a ‘high degree’ of economic freedom? What is an ‘equitable’ distribution of income? Most of us may accept these goals in general, but we may disagree substantially on their specific meanings. Furthermore, some goals cannot be accurately measured. Goals 1–4 and 8 are subject to reasonably accurate measurements, but goals 5–7 are hard to quantify. The problem of accurate measurement and quantification of goals contributes to the controversy over their precise meaning. Consequently, we may disagree significantly on the types of policy needed to attain these goals. Complementary goals Some of these economic goals are complementary—that is, when one goal is achieved, some other goal or goals are also likely to be achieved. For example, if we achieve full employment (goal 2), this means the elimination of unemployment. Employment is a basic cause of low incomes (goal 6) and economic insecurity (goal 7). Further, high levels of economic growth (goal 1) may help to achieve a more equal distribution of income (goal 6). This is particularly so if the growth favours low-income groups relative to high-income groups. Conflicting goals Many goals are conflicting or mutually exclusive. They involve trade-offs , implying that to achieve one goal we must sacrifice another. For example, some economists argue that those forces that lead to economic growth and full employment may be the same forces that cause inflation. In fact, the apparent conflict between goals 2 and 4 has been the focus of economic research. Goals 2 and 3 may also be in conflict. There are economists who argue that attempts to achieve greater efficiency (goal 3) may mean substitution of capital for labour which, without other job opportunities, may lead to unemployment (contrary to goal 2). Priorities When basic goals do conflict, society is forced to develop a system of priorities to achieve objectives. To illustrate, if full employment and price stability are mutually exclusive to some extent if full employment involves some inflation, and price stability involves some unemployment), society must decide on the relative importance of these two goals. Obviously, there is scope for disagreement here. Society must, however, somehow confront the trade-offs and make decisions to prioritise. FORMULATING ECONOMIC POLICY The design of specific policies to achieve the broad economic goals of our society is no simple matter. A brief examination of the basic steps in policy formulation is useful. 1. Stating goals: The first step is to define our goals clearly. If we say that we want ‘full employment’, do we mean that everyone over 16 and under 65 years of age should have a job? Or do we mean that everyone who wants to work should have a job? Should we allow some ‘normal’ unemployment caused by inevitable changes in the structure of industry and due to workers voluntarily changing jobs? 2. Policy options: Next, we must state and recognise the possible effects of alternative policies designed to achieve the goal. This requires a clear-cut understanding of the economic impact, benefits, costs and political feasibility of alternative programs. For example, economists may debate the relative merits and demerits of: • fiscal policy (which includes changing government spending and taxes), and • monetary policy (which involves altering interest rates) as alternative means of achieving and maintaining full employment. 3. Evaluation: It is essential to review our experiences with chosen policies and to evaluate their effectiveness. This is our duty—to our own generation and to future generations. It is only through such evaluation that we can hope to improve policy prescription. Did a given change in taxes or interest rates alter the level of employment to the extent predicted? Did deregulation of a particular industry (e.g. banking) yield the predicted benefits to society? If not, why not? (K)

p. 11 Business insight THE ‘DISMAL SCIENCE’? The reference to economic analysis as the ‘dismal science’ is attributed to controversial Scottish writer, historian and social commentator Thomas Carlyle (1795–1881). People incorrectly claim he was commenting (in the mid-1800s) on the prediction by Malthus that the growth in population will exceed food production. Apparently, this shortfall will result in widespread famines and misery. However, recent research has shown that Carlyle was arguing in favour of slavery in the Caribbean and elsewhere. He believed that lazy and inferior workers needed to be slaves to make them productive. 6 He was frustrated by his inability to use scientific economic methodology to prove this. Subsequently, he made the famous and inaccurate criticism concerning growth in population—which has since been incorrectly attributed to Malthus's dismal prediction (which economics has also shown to be wrong). 7

(K) Checkpoint

• The practice of economics usually combines three elements: – describing or gathering facts – developing principles or theories that make generalisations about economic behaviour – applying the insights gained from economic statistics and analysis in the form of policy or strategy prescription. • Two approaches are taken by economists to develop economic theories: – the deductive approach, where testable hypotheses about economic behaviour are developed as part of a logical argument based on observation, insight or intuition – the inductive approach, where accumulated information is arranged and systematically analysed in order to derive generalisations regarding economic behaviour. • Economic description and analysis are usually conducted at two levels: – macroeconomics is concerned with the behaviour of aggregates within the economy (e.g. the average level of prices, the total amount of unemployment) – microeconomics is concerned with the behaviour of specific units within the economy (e.g. the market for wheat, the price of housing in Noosa). • Policy prescription requires: – a movement from positive economics (what is) to normative economics (what should be), and the recognition of the importance and impact of value judgements on policy choices – the statement of economic goals (e.g. economic growth, full employment, economic efficiency, price-level stability, economic freedom, an equitable distribution of income, economic security and external balance) – recognition of the possible effects of alternative economic policies, their costs and benefits, and the political feasibility of their implementation – an intent and willingness to conduct an evaluation of the effectiveness and consequences of the chosen economic policies.

Learning objective 1.2 (K)

Statistical Methods in Economics

This is a year three module. It is taught intensively by Birmingham professors over eight weeks. There is continuous assessment and a final examination.

The course emphasizes the techniques for fundamentally empirical research, interpretation of quantitative results and model evaluations in finance and economics. It emphasizes the understanding of quantitative methods, model evaluations, and the techniques for empirical studies in economics and business.

The module starts with an introduction to general economic concepts, then it will cover the basics and extension of ordinary least square methods, heteroskedasticity, autocorrelation, multicollinearity, model specifications, and time series analysis. Furthermore, students will gain hands-on experience formulating and estimating models, interpreting results, and making forecasts using SAS. A tentative class schedule can be found on the last page of the syllabus.

By the end of the module students should be able to: