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05.stats-review4-sampling

05.stats-review4-sampling - Lecture 5 Review of...

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    Lecture 5:  Review of Statistics (Part 4) Sampling and Estimation BUEC 333  Summer 2009 Simon Woodcock
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    The Goal: Learn Something About A  Population of Interest Our objective as econometricians is to learn something about a population of interest. This is called inference. The population can be almost any group of people, businesses, etc. that we are interested in, e.g., all Canadian adults all firms (businesses) all publicly-traded firms the thirty largest firms traded on the New York Stock Exchange (i.e.,the DJIA) Exactly what we hope to learn depends on the specific question we hope to answer. what is the average labour income in Canada? What is its variance? What proportion of Canadian adults earn over $100,000 per year? what is the relationship between educational attainment and income? what is the elasticity of demand for product X? what is the probability that the price of stock X will increase in the next year? what is the expected change in the price stock X over the next year? what is the expected price of stock X one year from now if the price of oil increases to $75/barrel? In general, we want to learn something about the probability distribution of a variable of interest , or about the joint distribution of a group of variables .
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    Sampling In theory, we could measure the quantity we care about using the whole population. But we almost never do, because it’s expensive ($, time, etc.) e.g., a VERY expensive way to measure the average income of Canadians is to contact every one of them and ask them how much they earn. StatCan almost does this in the Census of Population Every household gets a census form to complete 4/5 get “short forms” – these only record who lives at that address, their age, sex, marital status, and first language 1/5 get “long forms” – in addition, these ask how much you earn, what industry you work in, etc. Collecting this information from 1/5 of the population is so expensive we only do it every 5 years But this illustrates the basic idea: rather than contacting everyone in the population, a cheaper alternative is to contact a small , representative group of individuals and ask them how much they earn this group is called a SAMPLE
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    Populations and Samples ECONOMETRIC INFERENCE ABOUT A POPULATION IS ALMOST ALWAYS BASED ON A SAMPLE! How do we choose which population members to sample? In a nutshell: choose them randomly . Example: Suppose I’m interested in the probability distribution of my commuting time to campus. Rather than recording my commuting time every day , I could randomly select five days each month to record my commuting time.
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