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The method of econometric research aims, essentially, at a conjunction of economic theory and actual measurements, using the theory and technique of statistical inference as a bridge pier. Econometrics is an amalgam of economic theory, mathematical economics, economic statistics, and mathematical statistics. Economic theory makes statements or hypotheses that are mostly qualitative in nature. For example, the microeconomic theory states that other things remaining the same, a reduction in the price of a commodity is expected to increase the quantity demanded of that commodity. But the theory itself does not provide any numerical measure of the relationship between the two.  It is the job of the econometrician to provide such numerical estimates. Stated differently, econometrics gives empirical content to most economic theories.
The main concern of mathematical economics is to express economic theory in mathematical form (equations) without regard to measurability or empirical verification of the theory. Econometrics, as noted previously, is mainly interested in the empirical verification of the economic theory. 

Economic statistics is mainly concerned with collecting, processing, and presenting economic data in the form of charts and tables. These are the jobs of the economic statistician. But the economic statistician does not go any further, not being concerned with using the collected data to test economic theories. Of course, one who does that becomes an econometrician.
Although mathematical statistics provides many tools used in the trade, the econometrician often needs special methods in view of the unique nature of most economic data, namely, that the data are not generated as the result of a controlled experiment. The econometrician, like the meteorologist, generally depends on data that cannot be controlled directly. 

In econometrics the modeler is often faced with observational as opposed to experimental data. This has two important implications for empirical modeling in econometrics. First, the modeler is required to master very different skills than those needed for analyzing experimental data. . . . Second, the separation of the data collector and the data analyst requires the modeler to familiarize himself/herself thoroughly with the nature and structure of data in question