In this article we will discuss about the Application of Econometric Methods to Various Economic Problems.

It is well known that the quantitative methods in the discipline of Economics are being extensively used to examine the economic relationships among variables [Functional Relationships]. The combination of the theory of Economics, Methods of Statistics and Mathematics is referred to as Econometrics [Measurement in Economics]. Application of Econometric Methods to various economic problems is known as Applied Econometrics.

This provides an empirical content [numerical estimates] to various economic relationships. Estimates of these economic relationships help in understanding whether the sign and size of the estimates of parameters are in line with the economic theory or not.

**Economic relationships such as: **

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1. Marginal propensity to consume,

2. Elasticity [powerful unit-free concept] of consumption expenditure with respect to disposable income,

3. Own price, cross price and Income elasticities of demand for commodities,

4. Income and price elasticities of demand for exports,

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5. Income and interest elasticities of demand for money,

6. Marginal productivity of different inputs, Elasticities of output with respect to different inputs,

7. Returns to scale and Returns to variable,

8. Constant and Variable Elasticities of substitution between inputs [factors of production],

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9. Engel elasticities for different food and non-food items and Economies of scale in consumption expenditure,

10. Tax buoyancy,

11. Validity of laffer curve,

12. Output and wage rate elasticities of employment,

13. Income elasticity of public expenditure,

14. Output elasticity of marketed surplus of food grains,

15. Price elasticity of market arrivals of agricultural commodities,

16. Short-run [The period of time during which it is not possible for consumers or producers to adjust completely to the changes in independent variables] and long-run [The period of time during which it is possible for consumers or producers to adjust to the changes in independent variables] price elasticities of acreage [Supply response function in agriculture],

17. Economies and diseconomies of scale in cost of production,

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18. Long run equilibrium relationship between non- stationary time series variables, Degree of disequilibrium between short run and long run values etc., have to be empirically measured using relevant data points to scan the sign and size.

The empirical information on the size and sign of the estimates helps in understanding the nature of relationship between the economic variables. The estimation of these economic relationships with cross-section data/time series data/pooling of cross-section and time series data/panel data is concerned with the empirical research. The development of econometric methods [mainly regression analysis] would help to estimate the above mentioned economic relationships.

In most empirical studies, both correlation and regression techniques are being widely used to estimate the economic relationships. The use of correlation to examine the degree of relationship between economic variables [Y, X_{1}, X_{2},..X_{n}] has certain limitations. One among them is that the classification of independent variable and dependent variable is irrelevant.

In a way there will be a symmetrical relationship between two variables, X and Y and Y and X i.e., the numerical value of correlation coefficient remains the same irrespective of the classification of the variables. Then it will be very difficult to examine the nature of relationship between economic variables. Therefore, the nature of relationship between independent and dependent variables can be examined by the regression analysis.

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**The regression analysis [various forms of regression equations such as: **

[1] linear

[Y = b_{0}+ b_{1} X_{1}+ b_{2} X_{2}………. + b_{n}X_{n}]

[2] Quadratic

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[Y = b_{0 }± b_{1}X_{1}_{ }± b_{2}X_{2}^{2}]

[3] Logarithmic linear

[log Y = log b_{0} + b_{1} log X_{1} + b_{2} log X_{2} +……………. + b_{n} log X_{n}]

etc., (where b_{0}, b_{1}, b_{2}..b_{n} are the estimates of the parameters to be estimated by the econometric methods to know the sign and size of economic relationships) based on the functional relationship between the variables i.e., Y = *f* [X_{1}, X_{2}, X_{3}…. X_{n}], is mainly based on the Ordinary Least Squares Method [OLSM]. The OLSM is in turn based on various assumptions.

**Some of them are: **

1. The random variable [Known as error term/stochastic term (Difference between actual/observed value of dependent variable and estimated value [Trend Value] of the dependent variable for a given value of independent variable] must have zero mean.

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2. The random variable must be followed by normal distribution [Symmetrical distribution] around the zero mean.

3. The co-variance between the successive values of the random variable must be zero i.e., the value of the random variable in any, period does not depend on its previous values [Absence of autocorrelation]

4. The co-variance between the two independent variables must be zero i.e., one of the independent variables is independent of other independent variable(s) [Absence of multicollinearity]

5. The co-variance between the independent variable and random variable must be zero. This would be possible only if there is one way causation between X and Y [Absence of errors in variables]

6. The variance of random variable must be constant i.e., the distribution of the various values of random variable around the trend line [regression line] in relation to different values of the independent variable [s] must be within two boundary [upper and lower] lines [Presence of homoscedasticity]

7. The variable to be used in the model must be in line with the definition given by the theory of Economics.

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8. The macro-variables to be used in the model must be error free.

9. The function of the model to be estimated must be identified.