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Econometrics For Dummies Cheat Sheet
Economics
University of Calcutta
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From Econometrics For Dummies By Roberto Pedace
You can use the statistical tools of econometrics along with economic theory to test hypotheses of economic theories, explain economic phenomena, and derive precise quantitative estimates of the relationship between economic variables. To accurately perform these tasks, you need econometric model-building skills, quality data, and appropriate estimation strategies. And both economic and statistical assumptions are important when using econometrics to estimate models.
Econometric Estimation and the CLRM Assumptions
Econometric techniques are used to estimate economic models, which ultimately allow you to explain how various factors affect some outcome of interest or to forecast future events. The ordinary least squares (OLS) technique is the most popular method of performing regression analysis and estimating econometric models, because in standard situations (meaning the model satisfies a series of statistical assumptions) it produces optimal (the best possible) results.
The proof that OLS generates the best results is known as the Gauss-Markov theorem, but the proof requires several assumptions. These assumptions, known as the classical linear regression model (CLRM) assumptions, are the following:
Cheat Sheet
Econometrics For Dummies Cheat Sheet
The model parameters are linear, meaning the regression coefficients don’t enter the function being estimated as exponents (although the variables can have exponents).
Useful Formulas in Econometrics
After you acquire data and choose the best econometric model for the question you want to answer, use formulas to produce the estimated output. In some cases, you have to perform these calculations by hand (sorry). However, even if your problem allows you to use econometric software such as STATA to generate results, it’s nice to know what the computer is doing.
The values for the independent variables are derived from a random sample of the population, and they contain variability.
The explanatory variables don’t have perfect collinearity (that is, no independent variable can be expressed as a linear function of any other independent variables).
The error term has zero conditional mean, meaning that the average error is zero at any specific value of the independent variable(s).
The model has no heteroskedasticity (meaning the variance of the error is the same regardless of the independent variable’s value).
The model has no autocorrelation (the error term doesn’t exhibit a systematic relationship over time).
If one (or more) of the CLRM assumptions isn’t met (which econometricians call failing), then OLS may not be the best estimation technique. Fortunately, econometric tools allow you to modify the OLS technique or use a completely different estimation method if the CLRM assumptions don’t hold.
constant (linear).
The precise functional form depends on your specific application, but the most common are as follows:
Typical Problems Estimating Econometric Models
If the classical linear regression model (CLRM) doesn’t work for your data because one of its assumptions doesn’t hold, then you have to address the problem before you can finalize your analysis. Fortunately, one of the primary contributions of econometrics is the development of techniques to address such problems or other complications with the data that make standard model estimation difficult or unreliable.
The following table lists the names of the most common estimation issues, a brief definition of each one, their consequences, typical tools used to detect them, and commonly accepted methods for resolving each problem.
Problem Definition Consequences Detection Solution High multicollinearity
Two or more independent variables in a regression model exhibit a close linear relationship.
Large standard errors and insignificant t-statistics Coefficient estimates sensitive to minor changes in model specification Nonsensical coefficient signs and magnitudes
Pairwise correlation coefficients Variance inflation factor (VIF)
- Collect additional data.
- Re-specify the model.
- Drop redundant variables.
Heteroskedasticity The variance of the error term changes in response to a change
Inefficient coefficient estimates Biased standard errors
Park test Goldfeld- Quandt test
- Weighted least squares (WLS)
in the value of the independent variables.
Unreliable hypothesis tests
Breusch- Pagan test White test
- Robust standard errors
Autocorrelation An identifiable relationship (positive or negative) exists between the values of the error in one period and the values of the error in another period.
Inefficient coefficient estimates Biased standard errors Unreliable hypothesis tests
Geary or runs test Durbin- Watson test Breusch- Godfrey test
- Cochrane- Orcutt transformation
- Prais- Winsten transformation
- Newey-West robust standard errors
A distinctive feature of a normal distribution is the probability (or density) associated with specific segments of the distribution. The normal distribution in the figure is divided into the most common intervals (or segments): one, two, and three standard deviations from the mean.
With a normally distributed random variable, approximately 68 percent of the measurements are within one standard deviation of the mean, 95 percent are within two standard deviations, and 99 percent are within three standard deviations.
Suppose you have data for the entire population of individuals living in retirement homes. You discover that the average age of these individuals is 70, the variance is 9
and the distribution of their age is normal. Using shorthand, you could simply write this information as
If you randomly select one person from this population, what are the chances that he or she is more than 76 years of age?
Using the density from a normal distribution, you know that approximately 95 percent of the measurements are between 64 and 76
A shorthand way of indicating that a random variable, X, has a normal distribution is to write
(notice that 6 is equal to two standard deviations). The remaining 5 percent are individuals who are less than 64 years of age or more than 76. Because a normal distribution is symmetrical, you can conclude that you have about a 2 percent (5% / 2 = 2%) chance that you randomly select somebody who is more than 76 years of age.
If a random variable is a linear combination of another normally distributed random variable(s), it also has a normal distribution.
Suppose you have two random variables described by these terms:
In other words, random variable X has a normal distribution with a mean of
and variance of
and random variable Y has a normal distribution with a mean of
and a variance of
If you create a new random variable, W, as the following linear combination of X and Y, W = aX + bY, then W also has a normal distribution. Additionally, using expected value and variance properties, you can describe the new random variable with this shorthand notation:
Econometrics For Dummies Cheat Sheet
Course: Economics
University: University of Calcutta
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