Economía

Introduction to Econometrics

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Review: Random variables and sampling theory Chapter 1: Covariance, variance, and correlation Chapter 2: Simple regression analysis Chapter 3: Properties of the regression coefficients and hypothesis testing Chapter 4: Multiple regression analysis Chapter 5: Transformations of variables Chapter 6: Dummy variables Chapter 7:Specification of regression variables: A preliminary skirmish Chapter 8: Heteroscedasticity Chapter 9: Stochastic regressors and measurement errors Chapter 10: Simultaneous equations estimation Chapter 11: Binary choice and limited dependent models and maximum likelihood estimation Chapter 12: Models using time series data Chapter 13: Autocorrelation

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REVIEW: RANDOM VARIABLES AND SAMPLING THEORY
In the discussion of estimation techniques in this text, much attention is given to the following properties of estimators: unbiasedness, consistency, and efficiency. It is essential that you have a secure understanding of these concepts, and the text assumes that you have taken an introductory statistics course that has treated themin some depth. This chapter offers a brief review.

Discrete Random Variables Your intuitive notion of probability is almost certainly perfectly adequate for the purposes of this text, and so we shall skip the traditional section on pure probability theory, fascinating subject though it may be. Many people have direct experience of probability through games of chance and gambling, and theirinterest in what they are doing results in an amazingly high level of technical competence, usually with no formal training. We shall begin straight away with discrete random variables. A random variable is any variable whose value cannot be predicted exactly. A discrete random variable is one that has a specific set of possible values. An example is the total score when two dice are thrown. Anexample of a random variable that is not discrete is the temperature in a room. It can take any one of a continuing range of values and is an example of a continuous random variable. We shall come to these later in this review. Continuing with the example of the two dice, suppose that one of them is green and the other red. When they are thrown, there are 36 possible experimental outcomes, since thegreen one can be any of the numbers from 1 to 6 and the red one likewise. The random variable defined as their sum, which we will denote X, can taken only one of 11 values – the numbers from 2 to 12. The relationship between the experimental outcomes and the values of this random variable is illustrated in Figure R.1.

red green
1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 56 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

Figure R.1. Outcomes in the example with two dice

 C. Dougherty 2001. All rights reserved. Copies may be made for personal use. Version of 19.04.01.

REVIEW: RANDOM NUMBERS AND SAMPLING THEORY

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TABLE R.1 Value of X Frequency Probability 2 1 1/36 3 2 2/36 4 3 3/36 5 4 4/36 6 5 5/36 7 6 6/36 8 5 5/36 9 4 4/36 10 3 3/36 11 2 2/36 121 1/36

Assuming that the dice are fair, we can use Figure R.1 to work out the probability of the occurrence of each value of X. Since there are 36 different combinations of the dice, each outcome has probability 1/36. {Green = 1, red = 1} is the only combination that gives a total of 2, so the probability of X = 2 is 1/36. To obtain X = 7, we would need {green = 1, red = 6} or {green = 2, red =5} or {green = 3, red = 4} or {green = 4, red = 3} or {green = 5, red = 2} or {green = 6, red = 1}. In this case six of the possible outcomes would do, so the probability of throwing 7 is 6/36. All the probabilities are given in Table R.1. If you add all the probabilities together, you get exactly 1. This is because it is 100 percent certain that the value must be one of the numbers from 2 to...