History Of Econometrics
The first known use of the term "econometrics" (in cognate form) was by Polish economist PaweĊ‚ Ciompa in 1910. Jan Tinbergen is considered by many to be one of the founding fathers of econometrics. More so, Econometrics was pioneered by Lawrence Klein, Ragnar Frisch and Simon Kuznets. All three won the Nobel Prize in economics for their contributions in 1971. Econometrics is used regularly among academics as well as practitioners such as Wall Street traders and analysts. Ragnar Frisch is credited with coining the term in the sense in which it is used today. The basic tool for econometrics is the multiple linear regression model.

Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analysing economic history, and forecasting.

Today,  econometrics is conducted using statistical analysis software packages designed for these purposes, such as STATA, SPSS, or R. These software packages can also easily test for statistical significance to provide support that the empirical results produced by these models are not merely the result of chance. R-squared, t-tests,  p-values, and null-hypothesis testing are all methods used by econometricians to evaluate the validity of their model results.

Meaning of Econometrics
Econometrics is the application of statistical methods to economic data and is described as the branch of economics that aims to give empirical content to economic relations. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships".
Further more, Econometrics is the quantitative application of statistical and mathematical models using data to develop theories or test existing hypotheses in economics, and for forecasting future trends from historical data. It subjects real-world data to statistical trials and then compares and contrasts the results against the theory or theories being tested. Depending on if you are interested in testing an existing theory or using existing data to develop a new hypothesis based on those observations, econometrics can be subdivided into two major categories: theoretical and applied. Those who routinely engage in this practice are commonly known as econometricians.

Econometrics analyzes data using statistical methods in order to test or develop economic theory. These methods rely on statistical inferences to quantify and analyze economic theories by leveraging tools such as frequency distributions, probability and probability distributions, statistical inference, correlation analysis, simple and multiple regression analysis, simultaneous equations models and time series methods.

An example of the application of econometrics is to study the income effect using observable data. An economist may hypothesize that as a person increases his income, his spending will also increase. If the data show that such an association is present, a regression analysis can then be conducted to understand the strength of the relationship between income and consumption and whether or not that relationship is statistically significant - that is, it appears to be unlikely that it is due to chance alone.

Methodology of Econometrics
The first step to econometric methodology is to obtain and analyze a set of data and define a specific hypothesis that explains the nature and shape of the set. This data may be, for example, the historical prices for a stock index, observations collected from a survey of consumer finances, or unemployment and inflation rates in different countries. If you are interested in the relationship between the annual price change of the S&P 500 and the unemployment rate, you'd collect both sets of data. Here, you want to test the idea that higher unemployment leads to lower stock market prices. Stock market price is therefore your dependent variable and the unemployment rate is the independent or explanatory variable.

The most common relationship is linear, meaning that any change in the explanatory variable will have a positive correlated with the dependent variable, in which case a simple regression model is often used to explore this relationship, which amounts to generating a best fit line between the two sets of data and then testing to see how far each data point is, on average, from that line. Note that you can have several explanatory variables in your analysis, for example changes to GDP and inflation in addition to unemployment in explaining stock market prices. When more than one explanatory variable is used, it is referred to as multiple linear regression model - which is the most commonly used tool in econometrics.

Several different regression models exist that are optimized depending on the nature of the data being analyzed and the type of question being asked. The most common example is the ordinary least-squares (OLS) regression, which can be conducted on several types of cross-sectional or time-series data. If you're interested in a binary (yes-no) outcome, for instance how likely you are to be fired from a job (yes you get fired or no you do not) based on your productivity, you can use a logistic regression or a probit model. Today, there are hundreds of models that an econometrician has at his disposal.

Econometrics is sometimes criticized for relying too heavily on the interpretation of data without linking it to established economic theory. It is crucial that the findings revealed in the data are able to be adequately explained by a theory, even if that means developing your own theory of the underlying processes. Regression analysis also does not prove causation, and just because two data sets show an association, it may be spurious: for example drowning deaths in swimming pools increase with GDP. Does a growing economy cause people to drown? Of course not, but perhaps more people buy pools when the economy is booming.

Stages of Applied Econometric Research
In econometric research there are four main stages. These stages follow a chronological order, a good knowledge of economic theory will assist in identifying the econometric research structure and the characteristics associated with it, some of these basic stages of
applied econometric research include:
(i) Model Formulation: This stage involves expressing economic relationships between the given variables in mathematical form. Here, one needs to determine the dependent variable as well as the explanatory variable(s) which will be included in the model. Also expressed here is a prior theoretical expectation regarding the sign and size of the parameters of the function, as well as the nature of the mathematical form the model will take such that the model is theoretically meaningful and mathematically useful. Model specification or formulation therefore, presupposes knowledge of economic theory and the familiarity with the particular phenomenon under investigation, the theoretical knowledge allows the researcher to have an idea of the interdependence of the variables under study.
(ii) Model Estimation: Model estimation entails obtaining numerical estimates (values) of the coefficients of the specified model by means of appropriate econometrics techniques. This gives the model a precise form with appropriate signs of the parameters for easy analysis. In estimating the specified model, the following steps are important.
  • Data collection based on the variables included in the model.
  • Examining the identification conditions of the model to eensure that function that is being estimated is the real function in question.
  • Examining aggregation problems of the function to avoid biased estimates.
  • Ensuring that the explanatory variables are not collinear, the situation which always results in misleading results.
  • Appropriate methods should be adopted on the basis of the specified model.

(iii). Evaluation of Model Estimates:
Evaluation entails assessing the results of the calculation in order to test their reliability. The results from the evaluation enable us to judge whether the estimates of the parameters are theoretically meaningful and statistically satisfactory for the econometric research.
(iv). Testing the Forecasting Power of the Estimated Model :Before the estimated model can be put to use, it is necessary to test its forecasting power. This will enable one to be assured on the stability of the estimates in term of their sensitivity to changes in the size of the model even outside the given sample data within the period.

Concepts of Economic and Econometric Model
A model is a simplified representation of a real world process. That is, it is a prototype of reality, and so describes the way in which variables are interrelated. These models exhibit the power of deductive reasoning in drawing conclusions relevant to economic policy. Economic model describes the way in which economic variables are interrelated. Such model is built from the various relationships between the given variables. In examining these concepts Bergstron (1966) defined model as any set of assumption and relationships which approximately describe the behaviour of an economy or a sector of an economy. In this way, an economic model guides economic analysis.

Econometric model on the other hand, consists of a system of equations which relate observable variables and unobservable random variables using a set of assumptions about the statistical properties of the random variables. In this respect, econometric model is built on the basis of economic theory. Econometric model differs from economic model in the following ways:
  • For an econometric model, its parameters can be estimated using appropriate econometric techniques.
  • In formulating econometric model, it is usually necessary to decide the variables to be included or not. Thus, the variables here are selective, depending on the available statistical data.
  • The specific nature of econometric model, it allows fitting in line of best fit, and this is not possible with economic model.
  • The formulation of an econometric model involves the introduction of random disturbance term. This will enable random element that are not accounted for to be taken care of in the sample.