Econometrics is a branch of economics that applies statistical methods to the empirical study of economic theories and relationships. It is as a form of mathematical economics. By being able to translate qualitative statements in quantitative measurements, statements can at least in principle be objectively proven, disproven, measured, and compared. Econometrics differs from statistics done in other fields since controlled experiments are often impractical, so econometics has to frequently deal with data as is.
Arguably the most important tool of econometrics is regression analysis (for an overview of a linear implementation of this framework, see linear regression).
Econometric analysis can often be divided into time-series analysis and cross-sectional analysis. Time-series analysis examines variables over time, such as the effect of interest rates on national expenditure. Cross-sectional analysis studies relationship between different variables at a point in time. For instance, the relationship between income, locality, and personal expenditure. When time-series analysis and cross-sectional analysis are conducted simultaneously on the same sample, it is called panel analysis. If the sample is different each time, it is called pooled cross section data.
A simple example of a relationship in econometrics is:
The above example can also be used to illustrate the many difficulties facing the applied econometrician. For instance, do we really know that the above relationship is correct? Perhaps the true relationship between personal expenditure and income is non-linear (that is, curved). Even if we know the correct theory, it is not certain we can meaure personal expenditure and income correctly. For instance, the value of work by e.g. housewifes is not recorded although it contributes to income. There are also a variety of statistical pitfalls that potentially lead to incorrect conclusions. Econometrics has dealt extensively with such issues. Often it turns out to be difficult to fully implement the resulting methods in practice.
Robert Engle and Clive Granger were awarded the Nobel Prize for Economic Sciences in 2003 for work on analysing economic time series. Engle pioneered the method of Autoregressive Conditional Heteroskedasticity (ARCH) and Granger the method of cointegration.