1 Econ 310 Professor Wallace September 3, 2012 Lecture: 1. Syllabus 2. Course Overview Course Overview The course can be broken up into 4 parts 1. Data and Descriptive and Statistics (Weeks 1-2) 2. Probability Theory (Weeks 3-6) 3. Basics of Estimation and Inference (Weeks 7-11) 4. Intro to Regression Analysis (Weeks 12-15) Data and Descriptive Statistics – methods of organizing, summarizing, describing, and presenting data • Methods of classifying variables and data • Graphical methods (bar graphs, frequency distributions, histograms, pie charts, stem and leaf displays, ogives, time series plots, scatter plots) • Numerical methods (measures of central location, measures of variability, relative standing and box plots, measures of linear relationships) Probability Theory – serves as a theoretical foundation for statistical inference • Properties of probability • Calculating probabilities • Expected value, variance, and properties thereof • Specific probability distributions (binomial, hypergeoretric, Poisson, normal, exponential, F, Chi-squared) Wax on Wax Off!2 Statistical Inference – statistical inference is the science of inferring something about a population parameter from sample statistics. Inferential statistics is nothing more than a framework for determining what conclusions can be drawn about population parameters from statistics obtained from a sample (sample statistics). • Population parameter – an underlying characteristic of the population. For our purposes it is usually the population mean ()µdifference of two population means ()12µµ− Example 1: We may be interested in mean weekly earnings among full-time, full year male workers. This would be a µ. Example 2: We may be interested in the difference in mean weekly earnings between black and white full-time, full-year male workers. This difference in population means would be a BWµµµ∆=−. Example 3: The populations might be hypothetical. For example, consider a social experiment where every family in a particular city that is living in public housing and on the very long waiting list for a Section 8 housing voucher is randomly assigned to one of three groups. The first group remains on in public housing, the second group receives a Section 8 voucher, and the third group receives a geographically targeted housing voucher that is can only be redeemed in for housing in a low poverty neighborhood. In this case population 1 represents the population under a public housing regime, population 2 represents a population under a Section 8 only regime, and population 3 represents a population under targeted housing voucher regime. In a pure sense these populations exist, but we might still be interested in the population parameters21µµ− or 31µµ− .1 1 This experiment, called Moving to Opportunity, was conducted in Baltimore, Boston, Chicago, Los Angeles, and New York. 3 • Sample Statistics – the sample statistics that we are going to use most often are the sample mean()x, the sample standard deviation()S, and the difference between two sample means()12xx−. • We will use the sample statistics pursue three objectives o Construct point estimates of the underlying population parameter. For example the sample mean xis an estimator of the population meanµ that has certain desirable properties. Example: An estimate of the difference in weekly earnings between black and white full-time, full-year workers is -$335 (the difference in sample mean earnings). o Construct confidence intervals – Example: We are 95 percent certain-confident that the true difference in weekly earnings between black and white full-time, full-year workers is between -$382 and -$288 o Hypothesis testing Example: Do we have strong evidence to suggest that the weekly earnings of black and while full-time, full year workers are not equal? It turns out we do.4 Regression Analysis • Bread and butter of quantitative tools used by economist and other social scientist • Concerned with estimating and making inferences about functional relationships • Allows us to talk about the effect of X (say being black) on Y (weekly earnings) holding Z (years of schooling) constant. 01 2()()iiiiearnings black ed eβββ=+⋅ +⋅ + In the context of this model 01 2, , and βββ are population parameters to be estimated and inferred about and ie is a disturbance term (because the relationship can’t hold exactly) ¾ 1β=the average impact of being black on earnings, holding education constant ¾ 2β=the average impact of an additional year of schooling on earnings, holding race constant ¾ Using regression analysis we can construct point estimates confidence intervals for, and evaluate hypotheses about, these population parameters. Example (hypothesis test): Do we have strong evidence that the weekly earnings of white and black full-time, full-year workers are different after accounting for the effect of education on
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