Econometrics literally means 'economic measurement'. It is a combination of mathematical economics, statistics, economic statistics and economic theory.
The two main purposes of econometrics are to give empirical content to economic theory and also to empirically verify economic theory. For example, econometrics could empirically verify if indeed a given demand curve slopes downward as economic theory would suggest. Empirical content is also given in that a numerical value would be given to this slope, while economic theory alone is usually mute on actual specific values.
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. Multi-dimensional panel data analysis is conducted on data sets that have more than two dimensions. For example, some forecast data sets provide forecasts for multiple target periods, conducted by multiple forecasters, and made at multiple horizons. The three dimensions provide more information than can be gleaned from two dimensional panel data sets.
A simple example of a relationship in econometrics is:
Personal Expenditure = Propensity to Spend * Income + random error
This statement asserts that the amount a person spends is dependent on his or her income and his or her willingness to spend money. If we can observe personal expenditure and income, techniques such as regression analysis can then be applied to find the value of the coefficients, here just the propensity to spend. The estimated coefficient can then be compared across samples (such as different countries or income brackets) and conclusions made.
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 measure personal expenditure and income correctly. For instance, the value of work by homemakers 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.