Learning Exercise: Econometrics: The First Lesson
This lesson introduces the core of Econometrics, How we can apply Econometrics, Where can we Apply Econometrics and Basic of Data Analysis.
Course: Econometrics Theory and Analysis Using R, Matlab and Stata
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Introduction to the Lesson This first lesson in the course Econometric Modeling Using Matlab will guide the students to know about the notion of Econometrics, types of data and variables, how to select a proper model to analyse the data at hands, what tools can be used to analyse this data and how Matlab will assist professionally in dealing any type of datasets. The context of the course is to develop skills in theory of Econometric Modeling and Application and how to use Matlab for the modeling and data analysis. Rest of course will then enable the student besides doing advanced modeling but also the students will develop a sense of modeling and simulations. Learning Objectives The lesson aims to: * Introduce Econometrics and the use of Matlab for Econometric Modeling * Introduce the Types of Models in Econometrics and how Matlab can help us. * Introduce the tips and tricks that one needs to decide what models to use and How Matlab can be used for the specific models * Introduce the New paths from here and How Matlab will show us the Path. Learning Outcomes After reading these pages and listening to the Video lecture, the students would know: * What is Econometrics exactly? How Matlab can assist us in doing Econometric Analysis. * How to develop Basic Econometric Models. * How these Models can be tested and validated using Matlab Applications. * How useful these models could be in developing a sense of Interpreting Economic Theories using Real World Data * Extend their developed skills to other branches of sciences like Health Sciences, Business and Management and Educational Research. Introduction to the Lecture Econometrics is the study of: testing Economic Theories, Mathematical definition/modeling of these theories and testing these theories statistically using relevant, reliable and representative datasets. We can explain this definition by keeping one example theory of Business and Economics; Production Function: which related the inputs and output in a system. The economic theories roughly indicate production will increase when increasing the input levels. Thus there seems a positive relationship between inputs and output. What is the possible mathematical explanation for such theories? There might a straight linear relation or also there might be quadratic or other types of relation. We can test these in next lessons by comparing what mathematical models to use to best represent the theory. Next, we collect information from different firms about the input levels used and the production levels and apply a relevant technique to estimate the mathematical function describing the economic relationship between inputs and out. The results will show the estimated type of relationship. Changing the relation types, using the same statistical information would give us further estimates which we can use to compare the two functions for the same economic theories. Is not there any picture built in your mind? Yes, there seems we are following three parallel streams, economic theories, mathematical relations and statistical data. All this combinational science is what we know as Econometrics. Now the type of statistical data, the nature of the variables and mathematical relations all will affect what we do in Econometrics. For example if our mathematical function is such that it contains endogenous variables and thus estimating the economic theory would not be that much reliably estimated so we need an approach they accommodates such information. Also the nature of variables can affect our estimation strategies as we cannot use the techniques for numerical variables for those variables showing some attributes or behaviours. We will discuss these in detail in the coming lectures. What is Econometrics? The following extract is taken as it is from Gujarati text titled "Basic Econometrics". Econometrics, the result of a certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results.1 ....econometrics may be defined as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference.2 Econometrics may be defined as the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena.3 Econometrics is concerned with the empirical determination of economic laws.4 The following Extract is taken from the Greens Book to explain what we should know about Econometrics: In the first issue of Econometrica, the Econometric Society stated that: its main object shall be to promote studies that aim at a unification of the theoretical- quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking similar to that which has come to dominate the natural sciences. But there are several aspects of the quantitative approach to economics, and no single one of these aspects taken by itself, should be confounded with econometrics. Thus, econometrics is by no means the same as economic statistics. Nor is it identical with what we call general economic theory, although a considerable portion of this theory has a definitely quantitative character. Nor should econometrics be taken as synonomous [sic] with the application of mathematics to economics. Experience has shown that each of these three viewpoints, that of statistics, economic theory, and mathematics, is a necessary, but not by itself a sufficient, condition for a real understanding of the quantitative relations in modern economic life. It is the unification of all three that is powerful. And it is this unification that constitutes econometrics. Frisch (1933) and his society responded to an unprecedented accumulation of statistical information. They saw a need to establish a body of principles that could organize what would otherwise become a bewildering mass of data. Neither the pillars nor the objectives of econometrics have changed in the years since this editorial appeared. Econometrics is the field of economics that concerns itself with the application of mathematical statistics and the tools of statistical inference to the empirical measurement of relationships postulated by economic theory. What are different Econometric Models? Econometric analysis will usually begin with a statement of a theoretical proposition. Consider, for example, a canonical application: Example 1.1 Keynes's Consumption Function From Keynes's (1936) General Theory of Employment, Interest and Money: We shall therefore define what we shall call the propensity to consume as the functional relationship f between X, a given level of income and C, the expenditure on consumption out of the level of income, so that C = f ( X) . The amount that the community spends on consumption depends (i) partly on the amount of its income, (ii) partly on other objective attendant circumstances, and (iii) partly on the subjective needs and the psychological propensities and habits of the individuals composing it. The fundamental psychological law upon which we are entitled to depend with great confidence, both a priori from our knowledge of human nature and from the detailed facts of experience, is that men are disposed, as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.1 That is, . . . dC/dX is positive and less than unity. But, apart from short period changes in the level of income, it is also obvious that a higher absolute level of income will tend as a rule to widen the gap between income and consumption. . . . These reasons will lead, as a rule, to a greater proportion of income being saved as real income increases. The theory asserts a relationship between consumption and income, C = f ( X) , and claims in the third paragraph that the marginal propensity to consume (MPC), dC/dX, is between 0 and 1. The final paragraph asserts that the average propensity to consume (APC), C/X, falls as income rises, or d(C/X)/dX = (MPC - APC)/X < 0. It follows that MPC < APC. The most common formulation of the consumption function is a linear relationship, C =a + ßX, that satisfies Keynes's "laws" if ß lies between zero and one and if a is greater than zero. These theoretical propositions provide the basis for an econometric study. Given an appropriate data set, we could investigate whether the theory appears to be consistent with the observed "facts." For example, we could see whether the linear specification appears to be a satisfactory description of the relationship between consumption and income, and, if so, whether a is positive and ß is between zero and one. Some issues that might be studied are (1) whether this relationship is stable through time or whether the parameters of the relationship change from one generation to the next (a change in the average propensity to save, 1-APC, might represent a fundamental change in the behavior of consumers in the economy); (2) whether there are systematic differences in the relationship across different countries, and, if so, what explains these differences; and (3) whether there are other factors that would improve the ability of the model to explain the relationship between consumption and income. For example, Figure 1.1 presents aggregate consumption and personal income in constant dollars for the U.S. for the 10 years of 1970-1979. (See Appendix Table F1.1.) Apparently, at least superficially, the data (the facts) are consistent with the theory. The relationship appears to be linear, albeit only approximately, the intercept of a line that lies close to most of the points is positive and the slope is less than one, although not by much. Statistical Data Types and Econometric Models The connection between underlying behavioral models and the modern practice of econometrics is increasingly strong. Practitioners rely heavily on the theoretical tools of microeconomics including utility maximization, profit maximization, and market equilibrium. Macroeconomic model builders rely on the interactions between economic agents and policy makers. The analyses are directed at subtle, difficult questions that often require intricate, complicated formulations. A few applications: • What are the likely effects on labor supply behavior of proposed negative income taxes? [Ashenfelter and Heckman (1974).] • Does a monetary policy regime that is strongly oriented toward controlling inflation impose a real cost in terms of lost output on the U.S. economy? [Cecchetti and Rich (2001).] • Did 2001's largest federal tax cut in U.S. history contribute to or dampen the concurrent recession? Or was it irrelevant? (Still to be analyzed.) • Does attending an elite college bring an expected payoff in lifetime expected income sufficient to justify the higher tuition? [Krueger and Dale (2001) and Krueger (2002).] • Does a voluntary training program produce tangible benefits? Can these benefits be accurately measured? [Angrist (2001).] The horizontal orange arrow shows a cross section element and the overtime orange arrow shows a time series element. The cross sectional element clearly indicates that different or multiple or many individuals are observed to have one or other bit of information on a single point in time scale. On the other hand, the vertical arrow shows that a single individual is traced over time to have one or the other bit of information. It is then called the time series element in Statistical Data. While the blue triangular arrows shows multiple individuals selected are traced for bits of information over a few periods of time. This element is called Panel Data. On the basis of the observed characteristics on the basis of cross sectional, time series or panel data, the type of measurability of the characteristic further divides the data into different types. We name a few here but will describe each type of data in details in relevant lessons. Continues variables measuring nominal observations which are quantifiable, qualitative variables which are also known as categorical data but cannot be directly measured quantitatively. How to Decide what Econometric Method to Use The field of econometrics is large and rapidly growing. In one dimension, we can distinguish between theoretical and applied econometrics. Theorists develop new techniques and analyze the consequences of applying particular methods when the assumptions that justify them are not met. Applied econometricians are the users of these techniques and the analysts of data (real world and simulated). Of course, the distinction is far from clean; practitioners routinely develop new analytical tools for the purposes of the study that they are involved in. This book contains a heavy dose of theory, but it is directed toward applied econometrics. I have attempted to survey techniques, admittedly some quite elaborate and intricate, that have seen wide use "in the field." Another loose distinction can be made between microeconometrics and macroeconometrics. The former is characterized largely by its analysis of cross section and panel data and by its focus on individual consumers, firms, and micro-level decision makers. Macroeconometrics is generally involved in the analysis of time series data, usually of broad aggregates such as price levels, the money supply, exchange rates, output, and so on. Once again, the boundaries are not sharp. The very large field of financial econometrics is concerned with long-time series data and occasionally vast panel data sets, but with a very focused orientation toward models of individual behavior. The analysis of market returns and exchange rate behavior is neither macro- nor microeconometric in nature, or perhaps it is some of both. Another application that we will examine in this text concerns spending patterns of municipalities, which, again, rests somewhere between the two fields. Applied econometric methods will be used for estimation of important quantities, analysis of economic outcomes, markets or individual behavior, testing theories, and for forecasting. The last of these is an art and science in itself, and (fortunately) the subject of a vast library of sources. Though we will briefly discuss some aspects of forecasting, our interest in this text will be on estimation and analysis of models. The presentation, where there is a distinction to be made, will contain a blend of microeconometric and macroeconometric techniques and applications.
Additional Information: http://www.aneconomist.com/firstlesson/
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