ABSTRACT
Econometrics has come a long way over a relatively short period. Important advances have been made in the compilation of economic data and in the development of concepts, theories and tools for the construction and evaluation of a wide variety of econometric models. Applications of econometric methods can be found in almost every field of economics. For conducting econometric research, it has to pass through four phases viz.,
Specification of the model:
Estimation of the model by employing an appropriate econometric method
Evaluation of the estimates
Forecasting the findings of econometric model
Specification of the model: The success of econometric research mainly depends upon the correct specification or formulation of the econometric model. Usually economic theory is considered as a base for the specification of the econometric model. The specified econometric model is employed to measure the phenomenon under consideration through conducting appropriate analysis. This phase is, otherwise, called as Formulation of maintained hypothesis. In the specified model, the researcher has to select or identify the variables and these variables are expressed in an econometric form. We already know, in the formulation of an econometric model, error term ‘μ’ (PRF) or ‘e’ (SRF) is also included to indicate the unexplained variation of the dependent variable. The following are the important aspects to be considered for the specification of the econometric model:
Variables that are to be included in the model
Size (Magnitude) and signs of the estimates
Formulation of the econometric model.
224Variables that are to be included in the model: Based on the economic theory, the researcher has to be identify the variables that are to be included in the econometric model. The economic theory also guides the researcher, which is/are the independent variable(s) and which is the dependent variable. For example, as per the demand function: Qp=f(Pp, I, Pw)https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1300.tif"/>
where, Qp= Quantity demanded of paddy
Pp = Price of paddy
I = Income of the consumer
Pw = Price of wheat (substitute)
In the above model, three independent variables (R.H.S) and one dependent variable (L.H.S) are included. Besides these independent variables, the researcher can also include some more variables after thorough verification of published research reports. In general, among several independent variables that influence the dependent variable, usually 4 to 5 variables will be considered for the study based on the scattergram analysis. Since, some of the variables are not captured in the model, an error term ‘μ’ (population data) or ‘e’ (sample data) will be included in the econometric model. We have already discussed the assumptions regarding independent variables, error term and dependent variable of CLRM in the earlier Chapter 5.
Size (Magnitude) and signs of the estimates: Prior economic research conducted and background economic theory guides the researcher in judging both magnitudes and signs of the estimates of the econometric model. With reference to Table 1.4 of Chapter 1, the estimated regression equation for consumption function is given below. Y^i=a^+b^Xihttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1301.tif"/> Y^i=0.9645+0.6699X1https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1302.tif"/>
With reference to the above Equations 1.6 and 1.9, the estimated b^https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1303.tif"/> value (MPC) is 0.6699 and this infers that, on an average, with increase in income, the consumption expenditure also increases, but less than proportionately. So, the value of b^https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1304.tif"/> is less than one, but positive and this is in accordance with the Keynes Psychological Law of Consumption. This law states that, ‘the rate of change of consumption for a unit (say a rupee) change in income is greater than zero but less than one’. So, the magnitude of the estimate derived above is in accordance with the Keynes Psychological Law of Consumption. Further, the sign of the estimate is also in conformity with the above Law, as the value of b^https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1305.tif"/> 225(slope i.e., MPC) is positive and less than one. In the above estimated consumption function, the intercept is also positive and this infers that, even when the income of the consumer is zero, consumption expenditure will assume a positive value implying that, the consumer may still borrow the money and spend on consumer goods.
Let us take another example discussed earlier with reference to demand function: Qp= f(Pp, I, Pw)https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1306.tif"/>
The above function can be expressed as: Y=a+b1X1+b2X2+b3X3+ehttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1307.tif"/>
where, Y = Quantity demanded of paddy; X1 = Price of paddy; X2 = Income of the consumer and X3 = Price of the substitute, wheat.
Regarding size or magnitude of the parameters, since the commodity considered is a necessary good (paddy), both price and income elasticities are small (i.e., b^1https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1308.tif"/> and b^2https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1309.tif"/>). Similarly, the substitute commodity, wheat which is a very close substitute of paddy, the cross elasticity of demand i.e., b^3https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1310.tif"/> will be high. So, the size of the estimates (both price and income elasticities) in the demand function is mainly related to the nature of the commodity under consideration i.e., necessary or luxury. Similarly, the estimate regarding cross elasticity of demand depends upon how close the two commodities are?
Regarding the signs of estimates, b^1https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1311.tif"/> is with negative sign in accordance with the law of demand i.e., quantity demanded of a commodity varies inversely with its price. The second estimate b^2https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1312.tif"/> (income elasticity of demand) will have a positive sign because, the commodity under consideration i.e., paddy is a normal good and not an inferior good. The third estimate b^3https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1313.tif"/> will have positive sign because, both paddy and wheat are good substitutes. This infers that, regarding both magnitude and signs of the estimates, economic theory forms base for the researcher and also to judge the reliability of the estimates. The scattergram is to be fitted earlier, before actually analyzing the regression model and this will throw some light regarding the signs of the estimates in the function.
Formulation of econometric model: We already discussed the differences between the mathematical model and an econometric model, as in the latter, error term ‘μ’ (PRF) or ‘e’ (SRF) is included that accounts for unexplained variation in the dependent variable. In fact, economic theory will not suggest the researcher about the econometric model to be formulated for analyzing the relationship between the selected variables. For example, in analyzing the cost function, 226instead of linear and quadratic cost functions, cubic cost function best fits the data (Figure 5.3) to draw the relationship between output (X) and per unit cost say, MC (Y). Further, economic theory will not indicate the number of equations to be formulated to analyze the relationship between the variables. For example in analyzing the law of demand, the demand theory will not suggest, whether the researcher has to propose Single equation model or Simultaneous equations models. Further, the theory of demand does not indicate, whether the relationship between quantity demanded and price is linear or non linear.
Considering the above limitations of economic theory regarding the formulation of econometric model and number of equations to be formulated, it is important for the researcher to plot the actual data of the considered variables (say, in analyzing cost function, the two variables under consideration are output and MC of the firm) in a two dimensional diagram. Say, in analyzing cost function, we may consider output as dependent variable and MC of firm as independent variable as one case, and considering the MC of the firm as dependent variable and output as the independent variable as another case. Based on the scattergram analysis with the background of economic theory, now the researcher can draw meaningful relationships between the variables (ie., by considering MC of the firm as dependent variable and output as the independent variable) and this guides him to formulate an econometric model.
Note that, the specification of an econometric model is one of the most important and difficult phases in conducting econometric research. Hence, the researcher must be very careful in understanding the economic theory and also the scattergram analysis to formulate a reliable econometric model for the study. Some of the reasons for specification errors of the econometric model may be related to:
Imperfect understanding of economic theory.
Omission of relevant variables from the function.
Lack of knowledge on the part of the researcher regarding the variables that significantly influence the outcome.
Non availability of data for relevant variables.
Improper understanding of scattergram analysis.
Estimation of the model by employing an appropriate econometric method:
After specifying the econometric model, now the researcher has to proceed to obtain the parameters (PRF) or sample estimates (SRF) of the model. This stage of econometric analysis demands more technicality on the part of researcher. That is, the researcher should have thorough knowledge about various econometric methods, assumptions about the variables included in the model and interpretations of the findings. This stage involves the following steps:
227Collection, compilation and tabulation of data (cross-section data, time-series data, panel data etc).
Examine the multicollinearity, heteroscedasticity, autocorrelation etc., problems if any, in the data.
Choice making regarding the selection of an appropriate econometric technique (say, OLS estimator, Single equation model or Simultaneous equations model) to analyze the model.
Interpretation of the findings and drawing the economic implications of the estimates.
Evaluation of the estimates: After obtaining the sample estimates from the econometric model, we have to evaluate them to know, whether they are theoretically meaningful, statistically significant and free from econometric problems like multicollinearity, heteroscedasticity, autocorrelation etc.? So, three criteria are to be employed to judge the findings of econometric research and they include viz., Economic ‘apriori’ criteria, Statistical criteria and Econometric criteria and these are discussed here under.
i. Economic ‘a priori’ criteria or Theoretical criteria: These criteria deal with the principles of economic theory, size and sign of the sample estimates explaining the economic relationship. As explained earlier with reference to Equation 6.1, economic theory guides the relationship between price of paddy and quantity demanded of paddy; income of the consumer and quantity demanded of paddy; and price of wheat and quantity demanded of paddy. Further, the economic theory also guides the size and sign of the estimates depending upon the nature of good (dependent variable) and nature of relationship between two goods. These ‘a priori’ criteria will be used to predict and infer the sample estimates of the demand function. However, not much information can be generated from the above a priori criteria regarding the magnitudes of b^1,b^2https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1314.tif"/> and b^3https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1315.tif"/>. If the researcher is having good experience in this analysis, it may help him to judge limits of b^1,b^2https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1316.tif"/> and b^3https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1317.tif"/>. If the size and sign of the sample estimates were not in confirmation with the economic theory, then the researcher has to reject the formulated econometric model otherwise, a valid reason is to be given to explain for the violation. In most cases, the wrong sign and magnitude of the sample estimates may occur due to improper sampling, deficiencies of the empirical data, non-reliable data etc.
Statistical criteria or First order tests: In these tests, we use the statistical tools to evaluate the reliability of the sample estimates of the econometric model. The most widely used statistical tools include: correlation coefficient, r2, regression coefficient, SE of the estimates etc. For example, the sample estimates should be rejected, if they have wrong sign and magnitude, even though r2 is high and 228SE is low. This is because, though the estimates are statistically significant, but theoretically they make up no sense in explaining the economic theory. Hence, statistical criteria or first order tests are secondary to ‘a priori’ or theoretical criteria. So, the sample estimates should be rejected, if they use wrong sign, wrong size or magnitude (a priori or theoretical criteria), low r2, high SE (statistical criteria or first order tests).
Econometric criteria or Second order tests: These are the criteria or tests developed by the econometricians, mainly to test, whether the assumptions of a formulated econometric model are satisfied or not. They also serve the purpose of determining the reliability of the statistical tests and in particular, SEs of the sample estimates. They further help the researcher to study, whether the sample estimates have the desirable properties like unbiasedness, consistency, efficiency etc. For example, in fitting a regression model, we generally assume that, there is no autocorrection. If this assumption is violated, it leads to autocorrection problem. To test, whether there is autocorrection problem or not, we have to go for Durbin-Watson’s ‘d’ statistic. This ‘d’ statistic is an econometric criterion used in studying the reliability of the estimates. If the econometric criteria or second order tests indicate violation of the assumptions of econometric model, it is customary to re-specify the model again by introducing the new variables or dropping some variables or collecting more data or transformation of the data etc., so as to meet the assumptions of the econometric model. We again run the model, till the sample estimates pass all the a priori, statistical and econometric criteria.
Forecasting the findings of econometric model: After judging the sample estimates from the econometric model and if they found relevant to economic theory, statistically significant and econometrically valid, it is the prime duty of econometrician to forecast the findings. For example, with reference to Equation 1.9 of Chapter 1, the estimated regression (consumption) function is given by: Y^i=0.9645+0.6699Xihttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1318.tif"/>
The above regression equation is with reference to Table 1.5 of Chapter 1. For instance, if we forecast the data on the aggregate income for 2016 as Rs.5.2 thousand crore, we can put this value in Equation 1.9, and obtain Rs.4.4 thousand crore as the predicted value of Yi^https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003079651/c17992fb-0a05-4de9-bb21-678306ddd8f0/content/eq1319.tif"/> for 2016 (ie., forecasted consumption expenditure). That is, if the forecasted aggregate income is Rs.5.2 thousand crore in 2016, the estimated (forecast) value of aggregate consumption expenditure would be Rs. 4.4 thousand crore in that year. Of course, when actual data on aggregate consumption expenditure for 2016 become available, we can compare the estimated (predicted) value with the actual value.
