Lecture 01Introduction to Econometrics Outline Features of Modern Economics?1. modelling (math)2. empirical veri…cation (statistics) Role of Quantitative Analysis1. Role of Modeling2. Role of Econometrics Limitations of Econometrics Conclusion1I. What is Economics? What is Economics?– Resource allocation in an uncertain environment Karl Marx: Study on production relationship Alfred Marshall: Study on human behavior in daily life Keynes divided Economics into three categories:– Normative Economics:– Positive Economics:– Technical/Engineering-style (e.g., Econometrics): What is the mainstream Economics? Modern economics studies resource allocation in a market economy.– Macroeconomicse.g., Rational Expectations, Business Cycles– Microeconomicse.g., Game Theory– Finance,e.g., Asset/derivative pricing, risk management– Econometricse.g.,Cross-sectional econometricsTime series econometricsMicroeconometrics (panel data analysis)2II. Features of Modern Economics? General Methodology of Modern Economics:1. Data collection and Summary of empirical stylized facts;— Stylized facts are often summarized from economic data.e.g., Phillip’s curve:negative correlation between in‡ation rate and unemployment rate.2. Theory/modelling an in attempt to explain stylized facts;3. Empirical veri…cation.— Check whether theory/model can explain stylized facts and predict future patterns.4. Applications. Modern economics has two important features:1. Modelization/Mathematization— Mathematical Economicse.g., General equilibrium theory:Whether multiple markets can achieve a competitive equilibrium.— Mathematical Financecontinuous-time calculuse.g., Black-Scholes formula for options pricing andFinancial engineering2. Empiricalization— Any theory/model needs empirical veri…cation.— New theory/model arise after empirical rejection of the existing theory/model.e.g., Positive-sloped Phillips curve in 1970s-1980s and macroeconomic theory of stag‡a-tion– e.g., Business cycles and new economyU.S. had the longest booming in the 1990s since WWII. Remark: Mathematization and empirical veri…cation arise from the e¤ort of economists tomake economics a "science".3 What is science?– Logical consistency and coherency in theory;– Consistency between theory and stylized facts.4MATHEMATIZATION AND MODELING First of all, there are many ways (e.g., verbal description, math) to describe economictheory. Math is just one of them. To ensure logical consistency of theory, there may notbe necessary to use math. However, mathematics is well-known as the most rigorous logical language. Any theory, when it can be expressed by mathematical language, will indicate that it hasachieved a sophisticated level. Remark: All leading economic PHD programs say that they emphasize on quantitativeanalysis. Why does Economics need math? This is determined by the features of economics.1. Math can summarize the essence of a theory in a concise manner.For example, Macroeconomics studies relationships between aggregate economic vari-ables (e.g., DGP, consumption, unemployment, in‡ation, interest rate, tax, exchangerate, etc.)Standard Keynesian theory can be summarized by two simple math equations:Y = C + I + G + EC =  + Y;where = marginal propensity to consume.Multiplier e¤ects of government spending:@Y@G=11  = 5:2. Complicated logical analysis can be greatly simpli…ed by using mathematicsIn most cases, sophisticated economic analysis cannot be done by verbal language.e.g., general equilibrium theory needs to study whether there exists an equilibriumwhen there exists mutual interaction between di¤erent markets.5Suppose there are n goods. Do there exist n prices (P1; :::; Pn) such that all themarkets are clear:Di(P1; :::; Pn) = Si(P1; :::; Pn);i = 1; :::; n:This is proved by using the so-called …xed point theorem in mathematics.Remark: Paul Samulson: I’d also like to use verbal languages to express economictheory, but I’m afraid that I’m not smart enough to do it without math.3. Modelization is a necessary path to empirical veri…cation of economic theory.Most economic/…nancial phenomena are in form of data.Need model economic theory so as to link the theory to data. Of course, modelization has its limitation. Question: What is the limitation of math/modelling?1. Unable to consider all possible factors that produce data.2. Rationale of a well-de…ned objective function (e.g., a utility function of the represen-tative agent)?6EMPIRICAL VERIFICATION The second feature of modern economics: Empirical veri…cation Question: Why is empirical veri…cation important? The use of math, or logical consistency of theory cannot ensure that economics is a science. Economic theory would be useless if the underlying assumptions are wrong. To be a science, economic theory should be able to:1. explain historical stylized facts and2. predict future economic phenomena. Reliable Economic theory/model can provide important guidance in economic policy-making,economic agents’decision-making under uncertainty. Question: How to check a theory/model empirically? Methods of empirical veri…cation– Econometrics— statistical analysis of economic/…nancial data Econometrics has a rather rapid development in the past few decades.1. the need of empirical veri…cation of economic theory;2. increasingly available high-quality data.Information era3. advance in computing technology. Question: What Roles Can Econometrics Play in Economics?1. Examine how well economic theory can explain historical economic data;2. Test economic hypotheses;3. Predict future evolution of the economy. Remark: New methods can lead to new discovery and to new development of economictheory.Question: What roles can econometrics play in economic research?7Some Motivating ExamplesExample 1 [Macroeconomics] Keynes Model, Multiplier and Policy RecommendationThe simplest Keynes model:Yt= Ct+ It+ Gt;Ct=  + Yt;Y =  + Y + I + G(1  )Y =  + I + GY =1  +I1  +G1  whereYt= aggregate income,Ct= private consumption,It= private investment,Gt= government spending.Economic interpretation for the consumption function: = survival level consumption, =dCtdYt= marginal propensity to consume.The multiplier of the income with respect to government spending is@Yt@Gt=11  = 5; (if  = 0:8)which dep