Adv Macroeconomic Theory
Adv Macroeconomic Theory ECON 200A
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This 4 page Class Notes was uploaded by Marge Hansen on Monday October 5, 2015. The Class Notes belongs to ECON 200A at California State University - Sacramento taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/218859/econ-200a-california-state-university-sacramento in Economcs at California State University - Sacramento.
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Date Created: 10/05/15
California State University Sacramento ECON 200A Advanced Macroeconomic Theory Prof Van Gaasbeck Econometrics Primer Econometrics Primer This supplement provides a very terse review of econometrics from ECON l4l Introduction to Econometrics We will not cover this material in class but this outline is designed to help guide you with reading the Studenmund chapters assigned as background reading What is econometrics 39 Measurement quantitative measurement of economic phenomena 39 Uses 0 Describequantify economic reality 0 Testing hypotheses of economic theory 0 Forecasting future economic activity 39 Explainquantify the behavior of dependent variable using explanatory variables ll Fundamentals A Correlation vs causation 39 Empirically we can only quantify relationships in terms of correlation 39 Causation is based on our underlying model 39 Example Relationship between real GDP capital and labor Empirically we can see how these variables are related We assume a causal relationship based on the production function we assume capital and labor are determined exogenously B Singleequation linear model i Variables 39 X explanatory variable independent variable I Y dependent variable 2 Function 39 Theoretical model Y 50 5 1X 39 DataY o 1Xe 3 Residuale l Specification error a Influences omitted from the equation b Nonlinear relationship 2 Measurement error 3 Unpredictable variation C Cross section vs time series data l Notation 39 common to use to denote cross section for individual 39 common to use t to denote time series time interval 2 Example Consumption Function 39 C 30 5 1Dl 39 Cross section data on individual household consumption and household disposable income 39 Time series data on aggregate consumption and disposable income California State University Sacramento ECON 200A Advanced Macroeconomic Theory Prof Van Gaasbeck Econometrics Primer D Estimated relationship 1 Predicted value of Y Yhat EYi I Xi 2 Estimated value of e ehat Yhat Y I OLS A Overview 1 Objective 1 Summation Notation Minimize the sum of squared errors Choose 30 and 51 to minimize the sum of squared residuals min el gt2 minim we we gt2 Firstorder conditions a 6 00 leY N o IZXIl 0 ZK 2X1 S O T 1T 3 0Y 1y 02 2ZY1 0 1XxZXIO f lf 1XzZle0 ZKK Xx Yl IZXI if 0 ZK Xx Yi 1 2Xz if 2 Matrix Notation Y X e where Y is an n x 1 vector e is an n x 1 vector X is an n x k matrix 5 is a k x 1 vector mine39e minY X Y X minY Y Z X Y X X 1 0 2X Y2X X 0 6 3 X X X Y 3 X39Xle39Y California State University Sacramento ECON 200A Advanced Macroeconomic Theory Prof Van Gaasbeck Econometrics Primer B Features 1 YbarbOlebar 2 SumeO 3 OLS is BLUE C Evaluating the regresion i R2 2 Ftest 3 Ttest of individual coefficients IV CLM A Assumptions let T 2 sample size 39 Linear and correctly specified 39 EeO 39 EXeO 39 EeesO no autocorrelation 39 Ee262 no heteroskedasticity 39 No perfect correlation 39 e NO62 B OLS is BLUE Gauss Markov Theorem implies the following for the estimated 5 39 Unbiased E5hat 5 39 Minimum variance efficient var5hat is as small as possible 39 Consistent im E5hat gt 5 as Tgt 00 39 Normal distribution 5hat N5var5hat V Hypothesis Testing A Overview 39 It s almost never possible to prove something theory correct or true in the same way we can in mathematics 39 Strategy Take a random sample to see whether it conforms to a hypothesis o If we can reject a hypothesis with a certain degree of confidence then it s very unlikely the sample result would have been observed if the theory were correct B Steps 1 Set up null and alternative hypothesis Ho 51 0 Hg 51 O Analogy guilt or innocence of the accused 2 Determine degree of confidence w which to reject the null Type I error reject a true null hypothesis 2 find an innocent person guilty Colifornio Stote University Sacrament ECON 20 C o GA Advanced Mocroeconomic Theory Prof Von Goosbeck Econometrics Primer Type II error fail to reject a false null I find the guilty person innocent We face a tradeoff which type of error do we want to avoid Eliminate Type I error never reject the null I find everyone innocent Reject the null only when we re very confident 53 Decision rule Common decision rule is to use a 95 confidence level 90 and 99 also common ttest Used for hypothesis testing of individual regression coefficients Standardize the hat to use a common distribution the tdistribution In the CLM hat N var hat t hat ose hat t NO s2 This is why the assumptions of the CLM are so important If we violate any of the assumptions like normality no autocorrelation no heteroskedasiticity then the se hat are incorrectly estimated using OLS and all of our statistical inference is incorrect Ftest Used for hypothesis testing of multiple regression coefficients at once