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1、计量经济学导论电子教案英文版（伍德里奇）Welcome to Economics 20What is Econometrics?Economics 20 - Prof. AndersonWhy study Econometrics? Rare in economics (and many other areas without labs!) to have experimental data Need to use nonexperimental, or observational, data to make inferencesImportant to be able to apply ec
2、onomic theory to real world dataEconomics 20 - Prof. AndersonWhy study Econometrics? An empirical analysis uses data to test a theory or to estimate a relationship A formal economic model can be tested Theory may be ambiguous as to the effect of some policy change can use econometrics to evaluate th
3、e programEconomics 20 - Prof. AndersonTypes of Data Cross Sectional Cross-sectional data is a random sample Each observation is a new individual, firm, etc. with information at a point in time If the data is not a random sample, we have a sample-selection problemEconomics 20 - Prof. AndersonTypes of
4、 Data Panel Can pool random cross sections and treat similar to a normal cross section. Will just need to account for time differences. Can follow the same random individual observations over time known as panel data or longitudinal dataEconomics 20 - Prof. AndersonTypes of Data Time Series Time ser
5、ies data has a separate observation for each time period e.g. stock prices Since not a random sample, different problems to consider Trends and seasonality will be importantEconomics 20 - Prof. AndersonThe Question of Causality Simply establishing a relationship between variables is rarely sufficien
6、t Want to the effect to be considered causal If weve truly controlled for enough other variables, then the estimated ceteris paribus effect can often be considered to be causal Can be difficult to establish causalityEconomics 20 - Prof. AndersonExample: Returns to Education A model of human capital
7、investment implies getting more education should lead to higher earnings In the simplest case, this implies an equation likeEconomics 20 - Prof. AndersonExample: (continued) The estimate of b1, is the return to education, but can it be considered causal? While the error term, u, includes other facto
8、rs affecting earnings, want to control for as much as possible Some things are still unobserved, which can be problematicEconomics 20 - Prof. AndersonThe Simple Regression Modely = b0 + b1x + uEconomics 20 - Prof. AndersonSome Terminology In the simple linear regression model, where y = b0 + b1x + u
9、, we typically refer to y as theDependent Variable, orLeft-Hand Side Variable, orExplained Variable, orRegressandEconomics 20 - Prof. AndersonSome Terminology, cont. In the simple linear regression of y on x, we typically refer to x as theIndependent Variable, orRight-Hand Side Variable, orExplanato
10、ry Variable, orRegressor, orCovariate, orControl VariablesEconomics 20 - Prof. AndersonA Simple Assumption The average value of u, the error term, in the population is 0. That is, E(u) = 0 This is not a restrictive assumption, since we can always use b0 to normalize E(u) to 0Economics 20 - Prof. And
11、ersonZero Conditional Mean We need to make a crucial assumption about how u and x are related We want it to be the case that knowing something about x does not give us any information about u, so that they are completely unrelated. That is, that E(u|x) = E(u) = 0, which implies E(y|x) = b0 + b1xEcon
12、omics 20 - Prof. Anderson.x1x2E(y|x) as a linear function of x, where for any x the distribution of y is centered about E(y|x)E(y|x) = b0 + b1xyf(y)Economics 20 - Prof. AndersonOrdinary Least Squares Basic idea of regression is to estimate the population parameters from a sample Let (xi,yi): i=1, ,n
13、 denote a random sample of size n from the population For each observation in this sample, it will be the case that yi = b0 + b1xi + uiEconomics 20 - Prof. Anderson.y4y1y2y3x1x2x3x4u1u2u3u4xyPopulation regression line, sample data pointsand the associated error termsE(y|x) = b0 + b1xEconomics 20 - P
14、rof. AndersonDeriving OLS Estimates To derive the OLS estimates we need to realize that our main assumption of E(u|x) = E(u) = 0 also implies that Cov(x,u) = E(xu) = 0 Why? Remember from basic probability that Cov(X,Y) = E(XY) E(X)E(Y)Economics 20 - Prof. AndersonDeriving OLS continued We can write
15、our 2 restrictions just in terms of x, y, b0 and b1 , since u = y b0 b1x E(y b0 b1x) = 0 Ex(y b0 b1x) = 0These are called moment restrictionsEconomics 20 - Prof. AndersonDeriving OLS using M.O.M. The method of moments approach to estimation implies imposing the population moment restrictions on the sample moments What does this mean? Recall that for E(X), the mean of a population distribution, a sample estimator of E(X) is simply the arithmetic mean of
