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Lecture Notes 1a

Hans Lf, Lecture 1. 2. Lectures. 1. Introduction to the Course and to Econometrics (1/9,HL)REGRESSION ANALYSIS WITH CROSS SECTIONAL DATA2. Statistics and Simple Regression Analysis (2/9, HL)3. MultipleRegression Analysis (6/9, HL)4. Multiple Regression Analysis (9/9, HL)5. Multiple Regression

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Lecture Notes 1a

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    1. Hans Lööf, Lecture 1 1 Lecture Notes 1(a) Welcome to the Course & A Guide to Econometrics

    2. Hans Lööf, Lecture 1 2 Lectures 1. Introduction to the Course and to Econometrics (1/9,HL) REGRESSION ANALYSIS WITH CROSS SECTIONAL DATA 2. Statistics and Simple Regression Analysis (2/9, HL) 3. MultipleRegression Analysis (6/9, HL) 4. Multiple Regression Analysis (9/9, HL) 5. Multiple Regression analysis (13/9, HL&MW) 6. Workshop (20/9, HL) REGRESSION ANALYSIS WITH TIME SERIAL DATA 7. Time Serial Analysis (27/9, MW) 8. Time Serial Analysis (30/9, MW) 9. Instrumental Variables Estimation and 2SLS (5/10, HL) 10.Pooled Data Models, Panel Data Models. (11/10, HL) 11.Limited Dependent Variable Models and Sample Selection (12/10, HL) 12. Advanced Time Series Topics. (19/10, MW).

    3. Hans Lööf, Lecture 1 3 Exercises REGRESSION ANALYSIS WITH CROSS-SECTIONAL DATA Problem Sets 1. Simple regression Model. Chapter 2. (6/9) 2. Multiple Regression Model. Chapters 3-5. (13/9) 3. Multiple Regression Model. Chapters 6-9.(20/9) REGRESSION ANALYSIS WITH TIME-SERIES DATA Problem Sets 4. Time Series Analysis. Chapters 10-12 and 18. (30/9) 5. Instrumental Variables and 2SLS. Chapters 15 and 16. (5/10) 6. Panel Data Methods. Chapters 13-14. (11/10) 7 Limited Dependent Variable Models, Sample Selection Mod. Ch 17. (12/10) 8. Advanced Time Series Topics. Chapter 18. (19/12)

    4. Hans Lööf, Lecture 1 4 Data sets BWGHT, data on births to women in the US 401K, data to study the rerlationsship between participation in a pension plan and the generosity of the plan. CEOSAL2, data on chief executive officers for U.S corporations. WAGE2, data on monthly salary and an IQ score RDCEM, data on expenditures on research and developemnt, and sales HPRICE, data on house prices and various characteristics of the houses. VOTE1, data on election votes and campaign expensitures. LAWSCH85, data on rank of law schools and salaries ATTEND….

    5. Hans Lööf, Lecture 1 5

    6. Hans Lööf, Lecture 1 6

    7. Hans Lööf, Lecture 1 7 Requirement 3 Problem Sets (Probelems and Computer Exercises) Cross-Sectional Data 5 Problem Sets (Problems and Computer Exercises) Time Series Data 1 Written Project Final Exam

    8. Hans Lööf, Lecture 1 8 Why study Econometrics? Rare in economics (and many other areas without labs) to have experimental data. Need o use nonexperimental, or observational, data to make inference. Important to be able to apply economic theory to the real world data.

    9. Hans Lööf, Lecture 1 9 How to Learn? Introductory Econometrics (Wooldrige) ( If necessesary, Appendix A-C) STATA 9 (Axcess through Mimers Bar) 18 Data sets (Axcess through Mimers Bar) Lectures notes Group Dynamic learning, 3-person groups

    10. Hans Lööf, Lecture 1 10 Example: Returns to Education A model of human capital investment implies getting more education should lead to higher earnings In the simplest case, this implies an equation like

    11. Hans Lööf, Lecture 1 11 Example: (continued) The parameters of the model, b0 and b1, are constants to be estimated. In this case, they are intercept and slope as a function relating education to earnings. The estimate of b1, is the return to education. The error term, u, includes other factors affecting earnings, including unobserved factors.

    12. Hans Lööf, Lecture 1 12 Relationship?

    13. Hans Lööf, Lecture 1 13 Causality or correlation? Having added more factors to out model, we hope that we now have an estimate of ceteris paribus effect (every thing else equal) If we truly controlled for everyting (sex, age, ability etc) the estimated ceterisbus can be considered to be causal effect. Somethimes even if there are unobserved factors, the effect can be considered causal).

    14. Hans Lööf, Lecture 1 14 Introduction 1. What is Econometrics 2. The Disturbance Term 3. Estimates and estimators

    15. Hans Lööf, Lecture 1 15 Some Criteria for Estimators 1. Least Squares 2. Highest R2 3. Unbiasedness 4. Efficiency

    16. Hans Lööf, Lecture 1 16 What is Econometrics? There does not exit a generally accepted answer to this question! Why? Econometricians wear many different hats!

    17. Hans Lööf, Lecture 1 17 (1) Economists First, and foremost, they are economicts, capable of utilizing economic theory to improve their empirical analyses and the the problems they adresses.

    18. Hans Lööf, Lecture 1 18 (2) Mathematicians At times they are mathematicians, formulating economic theory in ways that make it appropriate for statistical testing.

    19. Hans Lööf, Lecture 1 19 (3) Accountants At times thay are accountants, concerned with the problem of finding and collecting economic data and relating theoretical economic variables to the observable ones

    20. Hans Lööf, Lecture 1 20 (4) Applied Statisticians At time they are applied statisticians, spending hours with the computer trying to estimate economic relationsships or predict economic events

    21. Hans Lööf, Lecture 1 21 (5) Theoretical Statisticians And at times they are theoretical statiticians, applying their skills to the development of statistical techniqies appropriate to the empirical problem characterizing the science of economics

    22. Hans Lööf, Lecture 1 22 What distinguishes an econometrican from a statistician? The formers preoccupation with problems caused by violation of the statisticians’ standard assumtions due to - The nature of economic relationships - The lack of controlled experimentation

    23. Hans Lööf, Lecture 1 23 What distinguish an econometrician from an economist? A major distinction between economists and econometricians is that the latter’s concern with the disturbance terms. An economist will specify that consumption is a function of income: C= f(Y). An econometrician will claim that this relationship must also include a disturbance (or error) term: C=f(Y)+e

    24. Hans Lööf, Lecture 1 24 Deterministic or Stochastic (1) Without the disturbance term, the relationsship is said to be exact or deterministic; With the disturbance term it is said to be stochastic.

    25. Hans Lööf, Lecture 1 25 Deterministic or Stochastic (2) A stochastic relationship is not always rigth on the target in the sense that it predistcs the presice value of the variable beeing explained just as a dart thrown at a target seldom hits the bull’s eye. The disturbance term is used to capture explicitly the size of these ”misses” or ”errors”.

    26. Hans Lööf, Lecture 1 26 Parameter, Estimate and Estimators Parameter: An unknown value that describes a population relationship. Estimate is a numerical value taken on by an estimator for a parameter in a particular sample data. The estimator is the formula or the ”recipe” by which the data are tranformed into an actual estimate.

    27. Hans Lööf, Lecture 1 27 Least Squares (1) Assume a relationship: Y=f(X)+e For any set of values of the parameters characterizing a relationship between the - * dependent variable (Y) Income (the veriable beeing explained) – Can be calculated using the values of the independet variable (s) [(X) for example R&D] in the data set.

    28. Hans Lööf, Lecture 1 28 Least Squares (2) The estimated values on Income (called ) of the dependent variable can be subtracted from the actual values of (y) of the dependent variable in the data set to produce what is calles residuals These residuals can be thougth of as estimates of the unknown disturbances inherent in the data set. In Econometrics, we are trying to minimize the sum of squared residuals. (Lecture 1, and 2!)

    29. Hans Lööf, Lecture 1 29 Highest R2 A statistic that appears frequently in economics is the coefficient of determination, R2. It is supposed to represent the proportion of the variation in the dependent variable (Y) ”explained” by variation in the independet variables (X1…Xn)

    30. Hans Lööf, Lecture 1 30 Unbiasedness Suppose we perform the conceptual experiment of what is called a repeated sample. This could be repeated, say 2000 times. For each of these repeated samples, we could use an estimator b* to calulate an estimate of b ( i.g the marginal impact on wage of education), The man ner in which these estimates are distributed is called the sampling distribution of b*

    31. Hans Lööf, Lecture 1 31 Unbiasedness An estimator b* is said to be an unbiased estimator of b if the mean of its sampling distribution is equal to b if the mean of its sampling distribution is equal to b. The mean of the sampling distribution of b* is called the expected value of b* and is written E b*. The bias of b* is the difference between E b* and b. (And if we could undertake repeated samling in an infinite number of times, we would get the correct estimate ”on the average”.

    32. Hans Lööf, Lecture 1 32 Efficiency In some econometric problems it is impossible to find an unbiased estimator. But whenever one unbiased estimator can be found, it is usually the case that a large number of ofther unbaised estimator also can be found. In this circumstance the unbaised estimator whose sampling distribution has the smallest variance is called the best unbiased estimator, or the efficient estimator.

    33. Hans Lööf, Lecture 1 33

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