Econometrics is concerned with the tasks of developing and applying quantitative or statistical methods to the study and elucidation of economic principles.[1] Econometrics combines economic theory with statistics to analyze and test economic relationships. Theoretical econometrics considers questions about the statistical properties of estimators and tests, while applied econometrics is concerned with the application of econometric methods to assess economic theories. Although the first known use of the term "econometrics" was by Paweł Ciompa in 1910, Ragnar Frisch is given credit for coining the term in the sense that it is used today.[2]
Although many econometric methods represent applications of standard statistical models, there are some special features of economic data that distinguish econometrics from other branches of statistics. Economic data are generally observational, rather than being derived from controlled experiments. Because the individual units in an economy interact with each other, the observed data tend to reflect complex economic equilibrium conditions rather than simple behavioral relationships based on preferences or technology. Consequently, the field of econometrics has developed methods for identification and estimation of simultaneous equation models. These methods allow researchers to make causal inferences in the absence of controlled experiments.
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The two main purposes of econometrics are to give empirical content to economic theory and to subject economic theory to potentially falsifying tests.[2]
For example, consider one of the basic relationships in economics: the relationship between the price of a commodity and the quantities of that commodity that people wish to purchase at each price (the demand relationship). According to economic theory, an increase in the price would lead to a decrease in the quantity demanded, holding other relevant variables constant to isolate the relationship of interest. A mathematical equation can be written that describes the relationship between quantity, price, other demand variables like income, and a random term ε to reflect simplification and imprecision of the theoretical model:
Regression analysis could be used to estimate the unknown parameters β0, β1, and β2 in the relationship, using data on price, income, and quantity. The model could then be tested for statistical significance as to whether an increase in price is associated with a decrease in the quantity, as hypothesized: β1 < 0.
There are complications even in this simple example, and it is often easy to mistake statistical significance with economic significance. Statistical significance is neither necessary nor sufficient for economic significance.[3] In order to estimate the theoretical demand relationship, the observations in the data set must be price and quantity pairs that are collected along a demand schedule that is stable. If those assumptions are not satisfied, a more sophisticated model or econometric method may be necessary to derive reliable estimates and tests.
One of the fundamental statistical methods used by econometricians is regression analysis. For an overview of a linear implementation of this framework, see linear regression. Regression methods are important in econometrics because economists typically cannot use controlled experiments. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. Observational data may be subject to omitted-variable bias and a list of other problems that must be addressed using causal analysis of simultaneous equation models.[4]
Data sets to which econometric analyses are applied can be classified as time-series data, cross-sectional data, panel data, and multidimensional panel data. Time-series data sets contain observations over time; for example, inflation over the course of several years. Cross-sectional data sets contain observations at a single point in time; for example, many individuals' incomes in a given year. Panel data sets contain both time-series and cross-sectional observations. Multi-dimensional panel data sets contain observations across time, cross-sectionally, and across some third dimension. For example, the Survey of Professional Forecasters contains forecasts for many forecasters (cross-sectional observations), at many points in time (time series observations), and at multiple forecast horizons (a third dimension).
Econometric analysis may also be classified on the basis of the number of relationships modeled. Single equation methods model a single variable (the dependent variable) as a function of one or more explanatory (or independent) variables. In many econometric contexts, such single equation methods may not recover the effect desired, or may produce estimates with poor statistical properties. Simultaneous equation methods have been developed as one means of addressing these problems. Many of these methods use variants of instrumental variable to make estimates.
Other important methods include Method of Moments, Generalized Method of Moments (GMM), Bayesian methods, Two Stage Least Squares (2SLS), and Three Stage Least Squares (3SLS).
A simple example of a relationship in econometrics from the field of labor economics is:
Economic theory says that the natural logarithm of a person's wage is a linear function of (among other things) the number of years of education that person has acquired. The parameter β1 measures the increase in the natural log of the wage attributable to one more year of education. The term ε is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, β0 and β1 under specific assumptions about the random variable ε. For example, if ε is uncorrelated with years of education, then the equation can be estimated with ordinary least squares.
If the researcher could randomly assign people to different levels of education, the data set thus generated would allow estimation of the effect of changes in years of education on wages. In reality, those experiments cannot be conducted. Instead, the econometrician observes the years of education of and the wages paid to people who differ along many dimensions. Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education. For example, people born in certain places may have higher wages and higher levels of education. Unless the econometrician controls for place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages.
The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above. Exclusion of birthplace, together with the assumption that ε is uncorrelated with education produces a misspecified model. A second technique for dealing with omitted variables is instrumental variables estimation. Still a third technique is to include in the equation additional set of measured covariates which are not instrumental variables, yet render β1 identifiable[5]. An overview of econometric methods used to study this problem can be found in Card (1999).[6]
The following are the Nobel Memorial Prize in Economic Sciences recipients in the field of econometrics:
The Econometric Author Links of the Econometrics Journal provides personal links to recent articles and working papers of econometric authors via the RePEc system in EconPapers.
The main journals which publish work in econometrics are Econometrica, the Journal of Econometrics, the Review of Economics and Statistics, the Econometric Theory, the Journal of Applied Econometrics, the Econometric Reviews, the Econometrics Journal, the Journal of Business and Economic Statistics and the *Journal of Economic and Social Measurement.
This is a graduate level course concerned with theory and application of linear regression methods. The classical regression model is discussed, and the statistical properties of the estimator are examined. The effect of violations of the classical assumptions are considered, and appropriate estimation methods are introduced. This course is the first of a two-course sequence. At course completion, a successful student will:
-Davidson and MacKinnon "Econometric Theory and Methods"
-DeGroot and Schervish "Probability and Statistics" 3rd edition
A review of matrix algebra is recommended. In econometrics, it is necessary to work with very large sets of data. In order to manipulate the data and follow the discussion, you must be familiar with matrices.
How do we handle random processes? We can define a random variable as a measurable function defined on a probability space. Bievens(2004)
See set theory. Kolmorgorov gives us the axioms of probability.
for A contained in the probability space S 
.
.
.For example, in a coin toss, the probability space is heads and tails. If x is a function over the probability space, we can say that x(heads) equals one and x(tails) equals zero. So the probability that x is one equals the probability of heads, and the probability that x is zero equals the probability of tails, and they are disjoint probabilities. So if the probability of heads is Ph, the probability of tails is 1-Ph. (Note that this example does not assume that you have a fair coin, though you could.)
Matrices: positive semidefinite (PSD), positive definite (PD), quadratic forms, symettric, idempotent, diagonal, block diagonal,
Matix derivatives
The Probability Distribution Function is 
where 
Description of linear regression:
By having a set of y's we are assuming are dependent on a set of
x's, we solve for some constant 
.
(y is a kx1 vector and x is a kxn matrix multiplied by an nx1
vector
which relates y and x, where k is the number of observations, and n
is the number of predictor or independent variables.)
To solve for ,
which will give us an expected value of
we will call beta hat 
we use this linear operation:
This gives us beta hat, .
Then 
or x times beta hat equals y hat, where y hat is our expected value
for y given x and our calculated value of beta, beta hat.
Now the difference between the predicted values of y and the
actual values of y are given by: 
where 
is residual values, sometimes called error.
Matrix algebra,
Properties of Ordinary Least Squares (OLS estimator beta hat is
unbiased for beta, and the Covariance Matrix for beta hat is 
),
Classical Normal, The Information Matrix, Chi Square Distribution,
The relationship between e and epsilon, The Maximum Likelihood
Estimator of the variance is biased, Distribution of the variance
under normality,
regression, principles of estimation and testing, stationary time
series models, limited dependent variable models, longitudinal
(panel) data models, generalized methods of moments, instrumental
variable models, non-stationarity, stochastic trends,
co-integration,
Econometrics is a branch of economics. It is the use of statistical and mathematical methods to describe the relation between economic forces such as capital (any of the tools, work, or other things needed to make something useful), interest rates (the price of borrowing money), and labor.
Much of econometrics is making models which are simple pictures of the real world. These models then can be used to predict what will happen in the real world.
An example of econometrics would be looking at the prices of houses in a town. An economist (someone who studies economics) can try to make a simple picture of the house prices in the town. This picture might show that houses close to the market are worth more. An economist could then say that if a new market is made in another part of the town, home prices there might go up. The economist also might say that the new market could make prices less than before near the old one, because the new market will make it so that more houses are near a market. This would make the people who sell houses near a market sell them for less, since there could be more sellers than buyers.
   | Econometric Author Links of the Econometrics Journal - Econometric Authors Articles and Papers Links Econometrics Journal |
| | RePEc - RePEc: Research Papers in Economics |
| | Econometric Links - Econometric Links Econometrics Journal |
| | Applied Econometric Association - Applied Econometrics Association - Welcome |
| | ''Handbook of Econometrics'' - ScienceDirect - Handbook of Econometrics, Volume 6, Part 2, Pages 4777-5752, I1-I52 (2007) |
| | Teaching Econometrics - Subject Index: Econometrics (Economics Network) |
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