Introduction

1. Introduction Ekonometri 2013 This is a wide” introduction” to econometrics. I will also talk about what you need to know and learn (on your own) during the next coming 5 days. Econometrics Introduction

2. Overview • General introduction • What you need to remember from econometrics 101 • Estimators • Properties of testing • Mathematical statistics for beginners • The Friday lecture will be longer! Econometrics Introduction

3. Econometrics second course • 1) What you should know about econometrics and statistics • 2) What you shoukld know and hopefully remember from your first course in econometrics • 3) Econometrics basics at little higher level Econometrics Introduction

4. How to study econometrics? • Always use more than one textbook • Use different programs • Download gretl and data for different books, inkl Verbeek. • Practice alone with the programs • Learn how to prepare data, estimate models, test models and interpretate results. • It is your responsibility. There is plenty of exercises, if you don’t do them you don’t learn anything. Econometrics Introduction

5. Econometric Software • Gretl (freeware) based on R from sourgeforce.net • Jmulti (freeware) • RATS, Eviews, Gauss • TSP, Microfit, SPSS • STATA – favoured by the World Bank • SAS: Statistical Analysis System • SPSS • PcGive (David Hendry & J. Doornik ) Shazam (Ken White), Ects (Davidsson), STAMP (Harvey), LIMDEP (Green) • Matlab ... + more Econometrics Introduction

6. Software • Most software is written by amatuer programmers who learnt econometrics on mainframe computers and requires effort to learn. Sic • Many offers programing of the user´s own routines. • PcGive is the only program with a modern interface • gretl is a nice budget version Econometrics Introduction

7. What to do with econometrics? • Some people think that capitalism is the root of evil. Get rid of capitalism and all problems will be solved. • Some thiks the same of economics, of economists, • And some don’t like econometrics.... Econometrics Introduction

8. “Measurement in Economics” • Econometrics – What is it? • “The application of statistical and mathematical methods to the analysis of econometric data, with the purpose of giving content to economic theories, and verifying or refuting them.” (Maddala) • Compare: Biometrics etc… • Is Maddala’s definition realistic? Econometrics Introduction

9. Why Econometrics - 1? • “History is nothing but a pack of tricks that we play upon the dead” (Voltaire) • For verification of economic theories - logical consistency is not enough, we need empirical research to verify the relevance of theories. • Observation without logic. Logic without observations? Econometrics Introduction

10. Why Econometrics - 2? • ”It is a capital mistake to theorise without emprical observations” Sherlock Holmes • ”Of course it might work in practice. But, the real question is - does it work in theory?” Unkown economist Econometrics Introduction

11. Why Econometrics - 3? • Forecasting – yes. • Evaluation of interventions, medical, social, economic – yes. • Scientific proof of theories? – Sorry cannot do. • Circumstancial evidence for or against at most. • Relevance of theories: • Describe relations, simulate, forecast, give policy recommendations - put flesh on the bones given by theory. • Those who seek hopefully with an open mind will find something to believe in. • Controversy: What can you really do with econometrics? Econometrics Introduction

12. Why Econometrics – 4 Controversies? • “Models are too simplified” • “Unrealistic assumptions” • “If you torture your data long enough it will confess to anything” • “No econometric work has ever changed or inspired economic theory” • Rational expectations …hmmm help? Econometrics Introduction

13. Look at the greater picture • The controversies are mainly related to • 1) Macroeconomic policy (monetary policy?) and • 2) How well are markets working, how are people behaving, are there causes for interventions? • ’Tons of results’ support the view that when people have to make choices they make very rational choices, given their (limited) information, given other restrictions, given that they maximise their welfare in the long run. The clever economist reveals this and are able to predict average and marginal human behavior far better than the man on the street, politicians, poets, priests and other social and natural scientists. Econometrics Introduction

14. Book Examples: Freakonomics Freakonomics [Revised and Expanded]: A Rogue Economist Explores the Hidden Side of Everything • Steven D. Levitt (Author) • Stephen J. Dubner (Author) • Super Freakonomics • The Undercover Economist Econometrics Introduction

15. Evaluation • To improve the welfare of people, especially the poor, politicians construct different social and economic interventions. But, do they work? • Banerjee and Duflo (2011) Poor Economics: A Radical Rethinking of the Way to Fight Global Poverty. • FT:s Business Book of the Year award 2011. • Research based (scientific) evaluations • Controlled randomised experiments • Impact evaluations - A rapidly growing area Econometrics Introduction

16. Time Series Econometrics • Changed views during the 1980s due to • Lucas: Rational expectations • Sargent and Sims: VAR models • Lars P Hansen: GMM to estimate ’euler equations’, models where the right hand side contains expectations of the future left hand variable. • Hendry: Error Correction Models, describe the data Econometrics Introduction

17. Before • Before? Simply transfered OLS for cross section (static) to time series. Now more based on Time Series statistics. • Bigger and bigger macroeconometric models • Models showed bad fit, low predictability • Also relatively few observations • Spurious regression results? Econometrics Introduction

18. Cross-section and Panel etc • During the last 30 years an explosion of methods related to estimation related to understanding of pepole, firms, social problems, desises etc etc. Evaluation and policy • Heckman, - Heckit model, how can you ask relevant questions as if your sample is from a random experiment, though the data is not. • Other disciples especially in Sweden and at LiU are so far behind. At LiU as a PhD student you are not expected to a basic course in statistics, nor econometrics or Heckit models as an example. Since they work behiond closed doors they don’t understand, and students and their supervisors are lazy. • Only economists study statistical methods for evaluating social programs. • It requires an intelletual effort to study econometrics. Econometrics Introduction

19. Two Principal Modeling Strategies Start from economic theory and impose theory on data. Or, start from the data and seek for theory. 1) Build a model based on much a priori information. Examples: financial applications + rational expectations, and DSGE models. • GMM, adjust the residuals in the equation to take care of dynamics and whatever. Econometrics Introduction

20. Sargent, Hansen • They worked from the perspective that you have a intertemporal theoretical model, with expectations. • Real busines cycle models, DSGE models where you need to estimate a few parameters under specific imposed restrictions from theory. The outcome you see and measure is based on expectations that you don’t measure directly. To make sense of estimates they to be put within a theory first => consequences for economtrics Econometrics Introduction

21. The Second Approach The other approach: Let the data speech • Describe the Data Generating Process (DGP) of the variables. • Then from the DGP forecast and identify economic behavior. • i) Vector autoregressive models (VAR) • ii) Structural models, single equation error correction (ECM) or Vector error correction models (VECM). Econometrics Introduction

22. Or to sum it up ... • One impose theoretical restrictions from the beginning, use economtrics to estimate specific parameters in the model, which is calibrated to the data. • Second, use time series statistics to describe and forecast only • Third, use time series statistics to model well-defined statistical models from which deeper economic paramters can be found as long as the data supports economic theory. Econometrics Introduction

23. Why not Statistics? • Economics - problems are interrelated with math and statistics and probability. • To study correlation is not enough, the question is what is the correlation representing? Can it be understood in economic terms? • Each area forms, or has it own statistical problems. • Stochastic variables are part of economic theory (expectations, growth, allocation over time etc.). • Bringing theory and empirics together - a discrepancy that is best described as stochastic process. Econometrics Introduction

24. The ‘Special Problems’ of Time Series Econometrics • Dependence between variables - multivariate systems. • Dependence over time • Small samples • Aggregation over time and individuals • Trend and Stochastic trends • Expectations and decisions into the future! • The sampling process cannot be controlled. Data is given. Econometrics Introduction

25. Econometric Modelling: Start • Theory gives relations and suggests parameters of interest • Data • Transformation of data (log, differencing) • Descripitive statistics • Build an econometric model that fits the data • By testing the model - critical • Test economic hypotheses • Simulate, make predictions, draw conclusions Econometrics Introduction

26. Your First Course in Statistics Descriptive statistics of a Population • Mean, variance (spread, dispersion) • From a population to a sample • Sampling model is critical • Estimation • Mean, variance etc. • Inference • Hypothesis testing, significance, confidence interval Econometrics Introduction

27. Time Series Econometricans –Do it backwards! • Since data is given: • Start from the sample and ask what type of population could have generated this data? Find the data generating process (the DGP) of the dependent variable(s). • You construct a model that fits the data. • You construct a white noise residual. • Higher level mathematical statistics. Econometrics Introduction

28. Repetition • Random Variables and their properties • Properties of OLS • When OLS breaks down • What not to do, what you should forget from your first econometric class. Econometrics Introduction

29. Random Variables • A random variable (X) is a variable that can take on more than one number, or outcomes xi. For each possible outcome xi there is a number between zero and one that describes the probability of observing that particular outcome. • Random variables = stochastic variables = variates Econometrics Introduction

30. Definition cont • Whether a variables is random or not depend on the available information set. • Intuition, with complete information you might be 100% certain of the outcome. But your information set is limited the outcome might be described in terms of probabilities. • Remember: A random variable can always be predicted. The outcome the value it takes on can be predicted. • Uncertainty is a different think that we do not handle here. In fact we question the existence of uncertainty. Econometrics Introduction

31. Random Variables • Random variables are described by their moments and/or their probability functions • The link between observations and probability: Mathematical function f(x;) called the density function. Econometrics Introduction

32. Random Variables • Discrete random variables take on a finite number of values (Heads or Tails, etc). • Probability distribution function • Continuous random variables can take on any value in a certain range. • Probability density function Econometrics Introduction

33. Continuous Random Variables • For discrete RVs we can link a specific outcome with a probability. • For continuous RVs the probability of a specific outcome (number) is zero. We can only state less than, greater than or between two given numbers. Econometrics Introduction

34. Mulivariate processes • One random variable, or a multivariate process = several random variables • Joint probability density function Econometrics Introduction

35. Random Variables can be described by their moments • The first moment of a random variable: The mean. • The second moment: The variance. • Higher moments: • Skewness (Third) and kurtosis (fourth) etc. • Differ between sample moments and population moments. Econometrics Introduction

36. Moments and Distributions • In practice, we often use moments to describe an observed random variable. • How do we know the probability of observing an outcome? • Answer: Assumptions about the distribution • Standard Distributions: Normal distribution Econometrics Introduction

37. Distributions • Joint, marginal and conditional p.d.f. • Standard probability (density) functions • The Normal Distribution (N) • CLT - The central limit theorem • The t-distribution (small sample N) • The Chi-square Distribution (square N) • The F-distribution (ratio of two squared N) • + more see my handout Econometrics Introduction

38. If I know the distrubution • We need to know the distribution to say something about the size, to do inference of our estimates. • From the distribution we can construct, estimators, or learn about estimators. • We can also create various tests • The maximum likelihood estimator is the king, which holds the key to understand econometrics at a higher level. Econometrics Introduction

39. The Normal Distribution • The normal distribution is standard. • It is symetrical around the mean and have only two moments. • Two moments are ok because we seldom need the higher moments in practice. Only if you have ’jumps’ in your data will the normal ’be very bad’ [Samuelsson 196?) • The central limit theorem says that, under quitegeneral assumption, estimates will asymptotically converge to the normal distribution. Econometrics Introduction

40. Estimators • In Econometrics OLS is the first step • Gauss-Markov theorem = basic assumptions • Method of Moments and Maximum likelihood estimators • MLE, FIML, IV, GMM etc. Econometrics Introduction

41. Which Estimator? • ML is the most basic, widely used in theoretical econometrics to derive for instance tests and properties of estimation under different assumptions. • OLS is the workhorse • Method of moments often when situation calls for modelling, or restricting, the residual process. Econometrics Introduction

42. Properties of Estimators Introduce Operators > Mean E(X), Var(X), etc. Properties of a good estimator: • Unbiasedness : E(X) =  • Efficiency : V(X) = 2 As small as possible, or smaller than what we use as a benchmark BLUE (Best linear unbiased) • Consistency : As the sample changes we should get the same estimates, and as the sample increases estimates should become more unbiased and more efficient Econometrics Introduction

43. Properties of OLS • The Gauss-Markov conditions: • yt = xt’i + t or matrix form y = x’  +  • t is a random variable (a process) • E{t} = 0 • E{t t} = 2 Homoskedasticity • E{t t/-k} = 0 for all k  t No autocorrelation • E{t | X} = 0 • Var {t | X} = 0 • If these conditions are fulfilled OLS is BLUE, and the estimated coefficients are good estimates of the true parameters of interest. Econometrics Introduction

44. Why? These will not be fulfilled we must either transform the data, change estimation method and or respecify the statistical model. A good econometrican knows what he or she must do to get good estimates. Econometrics is not about using software, it is to be able to understand the problems at hand and how to solve them. This requires knowledge of properties of estimators, matrix algebra, etc. Econometrics Introduction

45. Three Golden Rules of econometrics • Test • Test • Test • Testing is don to respicify the model so that it fits the data chosen, and becomes a well-defined statistical model. Econometrics Introduction

46. GLS and FGLS (or EGLS) • In you first course you learn how to understand the coefficients in a mutivariate linear regression model • You focus on ”the problems” of heteroscedasticity and autocorrelation. • These ”problems” can be analysed and ’solved’ with Generalized Least squares GLS. • Since GLS assumes that we know the covariance matrix, it must be replaced by a estimates, which leads to Feasible Generalized Least Squuares (FGLS) or Estimated Generalized Least Squares (EGLS). Econometrics Introduction

47. GLS • You want E{’} = 2I • Where I is the identity matrix • But got E{’} = 2 • To get what you want find P’P = -1 • So that -1  = I, find P use it to • Py = Px’  + P • y* = x*‘  + * where V{* } = 2I Econometrics Introduction

48. GLS and FGLS • Is mostly an illusion • It show how you can manipulate models • Works quite fine for heteroscedasticity • Works very rarely for autocorrelation Econometrics Introduction

49. When OLS Breaks down • Autocorrelation in combination with lagged dependent variable • No longer consistent • Measurment error in variables • A matter of degree • Omitted variables • Omitting a relevant variable is always bad for the interpretation of the estimated parameters – the model might still be fine though • Including an irrelvant (insignificant) variable is harmless • Simulataneity and reversed causality • Simulataneity bias. Again, the model might be ok but the parameter estimates might be wrong. Econometrics Introduction

50. What Not to DO! • Don’t use the DW test for autocorrelation! • It is biased against 2.0 with lagged dependent variables, there i an inconclusive region and there are better alternatives around. • Do not use Cochrane-Orcutt and similar procedures to cure first order autocorrelation. It will not work! • Don’t use partial adjustment models, so-called almon lags, or polynomial lag restrictions. Parameter restrictions should never be imposed on the data without tests that confirms that the restriction is valid. • You cannot really test for multicollinearity! • You cannot really test for exogeneity! The proof is in the pudding. Econometrics Introduction