## 2010 Census Short-form

If you think creating a survey which will compel respondents to answer in an unbiased manner is easy, check out this article originally published in the Wall Street Journal in February (“Census 2010 plays six not-so-easy questions“). The six questions proposed to be asked in 2010 Census short-form questionnaire are as follows: Name of person…

## Bayesian Inference III

Today we will look at some common distributions used for Bayesian inference. Beta The first distribution we will look at is the Beta distribution. The beta distribution is equal to: [B(a,b)]-1πa-1(1-π)b-1. We can show that: If the prior ~ πa(1-π)b And likelihood ~ πS(1-π)F Then the posterior ~ πa+S(1-π)b+F Where ‘~’ denotes equal except for…

## Bayesian Inference II

Now we will give an example of Bayesian inference in a more complicating setting. This example is based on a problem from pp. 588-591 of Introductory Statistics for Business and Economics by Wonnacott and Wonnacott. Let us assume that there is a consumer electronics company named Banana, inc.. Banana sells iPood mp3 players. Banana, inc.,…

## Bayesian Inference I

Bayesian Inference is an important econometric tool. Over the next few days, we will review some of the basic Bayesian inference methods. Economicitis occurs in 300 out of every 100,000 adults. Recently, however, a test has been developed to screen for the disease. Of 1000 individuals with economicitis who were tested, only 40 had an…

## Basic Econometric Concepts: Time Series

Today I will review a few basic concepts of time series econometrics. A time series is a stochastic process where observations appear in different time periods. For instance, {zi} (i=1,2,3,…) is a stochastic process with zi representing the GDP each quarter. Below are a few important definitions which are important to econometric estimation using time…

## Type I vs. Type II errors

One of the basic concepts in statistics is the use mathematically rigorous tests to determine whether or not a researcher can reject their null hypothesis. The null hypothesis is the state of the world the researcher assumes exists. The alternative hypothesis is—as the name suggests—an alternative to the null hypothesis. Through these statistical tests, researchers…

## Hausman Endogeneity Test

OrdinaryÂ Least SquaresÂ  If you have studied basic statistics, its likely that you have come across the ordinary least squares (OLS) estimation technique.Â  OLS attempts to minimize the squared distance between dependent variables (‘y‘) and the a linear prediction of yÂ (y_hat=xÎ²).Â  The parameter vector ‘Î²_ols‘ minimizes this distance.Â Â The most important assumptionÂ in order for Î² toÂ reflect toÂ true…

## Ordered Probit (or Logit) Estimation

What is one to do when the dependent variable under investigation is categorical?  Well if these categories are ordered, then an ordered probit (or logit) estimation technique is a sensible means for estimation.  An example where ordered probit estimation should be used is for an integer index ranking of physician quality between one and five.    On…

## Disproportionate Stratified Sampling

Many data sets that social scientists come across use disproportionate stratified sampling. If a subpopulation is small, the survey designers may want to oversample this group. For example, in the Survey of Income and Program Participation (SIPP) poor individuals are oversampled and in the Community Tracking Study (CTS) uninsured individuals are oversampled in order to…

## Poisson Distribution Estimation

The Poisson distribution is one that is often used in health economics.  Wikipedia has a nice basic summary of the Poisson distribution; Wolfram MathWorld gives a more sophisticated analysis.  The distribution is where ‘λ‘ is equal to the number of expected occurrences in a period.  The distribution expresses the probability of a number of events…