Introduction to Econometrics
- 2. WHAT IS ECONOMETRICS….? Literally econometrics means ‘economic measurement’. Econometrics, the result of a certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results Econometrics is concerned with the empirical determination of economic laws. Econometrics is an amalgam of economic theory, mathematical economics ,economic statistics and mathematical statistics
- 3. WHY A SEPARATE DISCIPLINE….? Economic theory - makes statements or hypotheses that are mostly in qualitative in nature like demand and price thus economic theory postulates a inverse relationship but the theory itself does not provide any numerical measure of the relationship. it is the job econometrician to provide numerical estimates. Mathematical economics-is to express economic theory in mathematical form without regard of measurability or empirical verification of the theory . Econometrician uses mathematical equations proposed by mathematical economist .this conversion requires a great deal of ingenuity and practical skill
- 4. Economic statistics- this is mainly concerned with collecting ,processing and presenting economic data in the form of charts and tables. this is the job of an economic statistician .he is not concerned about testing the economic theories Mathematical statistics- provides many tools used in trade, the econometrician often needs special methods in view of the unique nature of most economic data the data are not generated as the result of a controlled experiment.
- 5. METHODOLOGY OF ECONOMETRICS Statement of Economic theory Specification of the Mathematical model Specification of the Econometric model Obtaining Data Estimation of econometric model Hypothesis testing Forecasting or prediction Use of the model for policy purposes
- 6. Statement of Economic theory- Keynes postulated that the Marginal propensity to consume ,the rate of change of consumption for a unit ,change in income is greater than zero but less than 1. Specification of the Mathematical model-keynes postulated a positive relationship between consumption and income ,he did not specify the precise form of the functional relationship between the two Y=ß1+ß2X 0<ß2<1 Where Y=consumption expenditure and X=income, ß1 and ß2 known as parameters as well as intercept and slope respectively .
- 7. The ß2 measures the MPC. Consumption is linearly related to income .the relationship between consumption and income is consumption function.the variable appearing on left side i.e consumption is dependent variable and on right side i.e income is called explanatory variable. A model having one equation is single equation model and more than one is multiple equation model. CONSUMPTIONEXPENDITURE INCOME ß2=MPC ß1
- 8. Specification of the econometric model of consumption- it assumes that there is an exact or deterministic relationship between consumption and income. But relationships between economic variables are generally inexact .for example 500 families, we would not expect all 500 observations to lie exactly on the straight line because in addition to income, others variables affect consumption expenditure like size of family, age of members ,religion etc.the econometrician would modify the deterministic consumption function . Y=ß1+ß2X+u where u is known as the disturbance or error terms a random (stochastic)variable that has well defined probabilistic properties
- 9. Obtaining of data-to estimate the econometric model ,to obtain the numerical values of ß1 and ß2 we need data . Estimation of econometric model -now that we data ,our next task is to estimate the parameters of the consumption function .the numerical estimates of the parameters give empirical content to the consumption function. the statistical techniques of regression analysis is the main tool used to obtain the estimates. Hypothesis testing-assuming that the fitted model is reasonably good approximation of reality, we have to develop suitable criteria to find out whether the estimates obtained are in accord with the expectations of the theory that is being tested
- 10. Forecasting or prediction- if the chosen model does not refute the hypothesis or theory under consideration, we may use it to predict the future value of the dependent or forecast variable y on the basis of the known or expected future value of the explanatory or predictor, variable X. Use of models for control or policy purpose- as the estimated model is used to make policies by appropriate mix of fiscal and monetary the government can manipulate the control variable X to produce a desired level of the target variable Y.
- 11. RELATIONSHIPS Statistical versus deterministic- In statistical relationships among variables we essentially deal with random variables ,in deterministic relationships it also deals with variables Regression versus causation- there is no statistical reason to assume that rainfall doesn’t depend on crop yield. commonsense says that inverse relationship in itself cannot logically imply causation.
- 12. Regression versus correlation- the strength of association between two variables is correlation ,it is measured by correlation coefficient .to estimate or predict the average value of one variable on the basis of the fixed variable .in regression analysis there is an symmetry in the way the dependent and explanatory variables are treated. in correlation ,variables are symmetrically.
- 13. Explained variable Predictand Regressand Response Endogenous Outcome Controlled variable Independent variable Predictor Regressor Stimulus Exogenous Covariate Control variable Dependent variable Explanatory variable
- 14. TYPES OF DATA Time series data- it is a set of observations on the values that a variable takes at different times.such data may be collected at regular intervals like daily ,weekly, quarterly,annually etc.time series data is stationary it means that mean and variance not vary systematically over the time Cross section data- data collected at the same point of time
- 15. Pooled data –it is combined ,data are elements of both time series and cross section data Panel ,longitudinal or Micropanel data- it is a special type of pooled data in which the same cross sectional unit is surveyed over time
- 16. THE MEANING OF LINEAR Linearity in variables – the regression curve of above equation is linear or straight line .if E(Y/Xi)= ß1+ß2Xi2 is the equation, as the power of the variable Xi is 2 ,this cannot be a linear equation. Linearity in parameters- the regression equation is E(Y/Xi)= ß1+ß2 2Xi ,this is an example of non linear regression model
- 17. THE CONCEPT OF POPULATION REGRESSION The conditional mean E(Y/Xi) is a function of Xi ,where Xi is a given value of x E(Y/Xi)=f(Xi) Where f(Xi) denotes some function of the explanatory variable Xi. E(Y/Xi) is a linear function of Xi this is conditional expectation function (CEF) or population regression function. E(Y/Xi)=ß1+ß2Xi This is a linear population regression function
- 18. SAMPLE REGRESSION FUNCTION Yˆi= ߈1+߈2Xi+uˆi Yˆi = estimator of E(Y/Xi) ߈1 = estimator of ß1 ߈2 = estimator of ß2 uˆi= estimator of PRF
- 19. STOCHASTIC SPECIFICATION OF PRF E(Y/Xi)=ß1+ß2Xi Yi= ß1+ß2Xi+ui Yi= E(Y/Xi) +ui ui=Yi- E(Y/Xi) Ui is a non systematic ,random ,stochastic term.it is an unobseverable random variable taking positive or negative values Yi= E(Y/Xi) +ui now if we take the expected value on both the sides E(Y/Xi)= E(E(Y/Xi) )+E(ui/Xi)
- 20. E(Y/Xi)= E(Y/Xi) )+E(ui/Xi) Expected value of a constant is that of constant itself.this implies E(ui/Xi)= 0 Thus the assumption that the regression line passes through the conditional means of Y implies that the conditional means of ui are zero.
- 21. SIGNIFICANCE OF STOCHASTIC TERM Vagueness of theory- in the given theory ,we might be ignorant about or unsure about the other variables affecting the dependent variables (Y).therefore ‘ui’ may be used as a substitute for all excluded or omitted variables of model. Unavailability of data-even if we know some excluded variables ,we may not have the quantitative information about those variables example family wealth
- 22. Core variables versus peripheral variables- considering the variables it is quite possible that the joint influence of all may be more or less. one hopes that their combined effect can be treated as random variable Intrinsic randomness of behavior- this random variables may very well reflect this intrinsic randomness Poor proxy variables-there may be errors of measurement for example Milton’s friedman, regards permanent consumption as function of permanent income .since data on these variables are not directly observable, we use proxy variable current consumption and current income. since they are not equal
- 23. Principle of parsimony –if the theory is not strong enough to suggest what other variables might be included so why to introduce more variabled,instead add a random variable (ui) just to keep the model simple Wrong functional form- there may be wrong formation of the relationship between X and Y variables. For two variable models it is easy by scatter diagram but in mutiple regression model it is not possible to visualise,