Major Econometrics Issues and Multicolinarity - Essay Example

?Your Full Topic: Econometrics, Essay Question log(Urea Amount) = 9.760-0.182 log(Previous years application)-0.0561 log (Urea Price)+0.459 log(Open Market Price of Paddy)- 0.261log(Wages)-0.145log(Oil Price) Table 1: Econometrics Estimates (1) (2) Urea Amount(Mt) Log Urea amount Lag dependent -0.137 (0.305) Urea Price (Rs/Kg) -0.00218 (0.0125) Open Market Price of Paddy (Rs/Mt) -91.73* (32.53) Wages (Rs/Day) 44.99 (67.63) Oil Price(Rs/Bbl) 4.822* (2.117) Log- Lag dependent -0.182 (0.320) Log-Urea Price (Rs/Kg) -0.0561** (0.0621) Log- Open Market Price of Paddy (Rs/Mt) 0.459** (0.131) Log- Wages (Rs/Day) -0.261 (0.188) Log- Oil Price(Rs/Bbl) -0.145* (0.0628) Constant 3333.0** 9.760*** (918.1) (2.342) N 23 23 R2 0.641 0.626 adj. R2 0.535 0.516 F 14.82 15.94 Standard errors in parentheses + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.001 Two econometrics models were estimated for predicting the demand for urea fertilizer by the paddy producers in India. Accordingly the log-log model was found consistent with the economic theory. For example, the coefficient of own price was not significant while the coefficient of output price was negatively correlated in the linear-linear model. Cost minimizing farmers’ input demand however, should be positively correlated to the output price i.e. with increasing output price which in turn increase farmer’s profit the demand for inputs also should increase. Therefore, in the urea fertilizer demand model the paddy price should be positively correlated with the fertilizer demand. And also the price of urea should be negatively and significantly correlated to the demand for urea. Hence the log-log model is consistent with the economics theory. Therefore, it was used for interpretation as follows. Table2: Test for Autocorrelation Breusch-Godfrey LM test for autocorrelation lags(p) chi2 df Prob > chi2 1 0.520 1 0.4709 H0: no serial correlation N*R2 = 23*0.516 = 11.868 N*R2 > chi2 Therefore reject H0. There is auto correlation in the model. Thus the robust estimates were taken. Table3: Test for Multicolinarity Variable VIF 1/VIF Log-Urea Price (Rs/Kg) 2.67 0.37453 Log- Open Market Price of Paddy (Rs/Mt) 2.42 0.41322 Log- Wages (Rs/Day) 2.08 0.48072 Log- Lag dependent 1.58 0.63344 Mean VIF 2.19 ii) In log-log equations the coefficients reflects the price elasticity of the respective variables. For example in the above model the own price elasticity of urea demand is -0.0561 i.e. with 1 percentage proportion decrease in urea price the increase the demand for urea by 5.6 percentage proportion. Similarly, the elasticity of urea demand for paddy price is 0.459 i.e. 1 percentage proportion increase in open market price of paddy can increase the demand for urea fertilizer by 45.9 percentage proportion. In the model the largest, significant coefficient was associated with the open market price of paddy. This shows that paddy farmers production decisions are influenced highly by the output price compared to the price of other factors of production such as fertilizer, labor and crude oil. However both own price elasticity and output price elasticitys are less than one and hence are inelastic. The demand for fertilizer is negatively correlated to the wage rates and crude oil prices. With increasing wage rates and oil prices the cost of production increase and hence these variables are negatively correlated in the demand model. The elasticity of demand with respect to wage rates is -0.261 while the elasticity of demand with respect to crude oil price is -0.145. therefore the demand for urea fertilizer decrease by 26.1 and 14.5 percentage proportions with respect to 1 percentage proportion increase in wage rates and crude oil prices respectively. Crude oil price represent the transport cost and also paddy processing costs. The goodness of fit as denoted by the adjusted R2 value of the above model is 51.6 percentage proportion and the probability value of the f statistic was 0.00. Therefore the model is statistically significant and powerful in predicting ability. b) (1) Log-Urea amount Log- Lag dependent 0.0145 (0.276) Log-Urea Price (Rs/Kg) -0.0210 (0.0652) Log- Open Market Price of Paddy (Rs/Mt) -0.423** (0.146) Log- Wages (Rs/Day) 0.0398 (0.171) Constant 8.883*** (2.160) N 23 R2 0.456 adj. R2 0.437 F 7.618 In the above model the adjusted R2 value is lower compared to the full model. Therefore, the predictive power of the model has been reduced. And also the own price elasticity is not statistically significant in the above model. Therefore the model is not statistically significant for predicting the demand for urea by the paddy producers. Question 2 (20 marks). a) Classical Linear Regression assumptions state that explanatory variables are independently distributed. Therefore, the error is normally distributed, mean is zero and variance is constant. According to the Gauss–Markov theorem, a linear regression model in which the expected values of error terms are zero, are uncorrelated and have equal variances OLS yield the best linear unbiased estimators (BLUE). “Best” attributes to the lowest variance of the estimate, compared to the other unbiased, linear estimates. Multicollinearity and heteroscedasticity violates the assumptions of CLR. In the presence of perfect multicollinearity the correlation between the explanatory variables equals to 1. In the presence of heteroscedasticity the variance of error is not constant. b) The estimates of OLS no longer associate with minimum variance in the presence of ‘multicollinearity’ and ‘heteroscedasticity’. It can be shown that OLS estimates are linear and unbiased in the presence of multicollinearity’ and ‘heteroscedasticity’ however are not efficient. Moreover, the values of Standard Error terms are biased and t statistics are erroneous. Therefore, the confidence interval of the statistical estimates increase which in turn increase the probability of accepting the null hypothesis. c) Coefficient between explanatory variables can be examined to understand whether multicollinearity presents in the data set. Moreover, OLS estimates show high R2 values with statistically insignificant coefficients in the presence of multicollinearity. To detect multicollinearity the variance inflation factor (VIF) can be estimated. Sometimes multicollinearity can be the nature of the economic data. However, if the degree of multicollinearity is not tolerable according to the statistics one of the correlated explanatory variables can be dropped based on priori information. Heteroscedasticity can be detected by Breusch–Pagan test and White’s test. Heteroscedasticity can arise due to specification errors in the model such as omitted variables. To correct heteroscedasticity problem changing the functional can be useful. Question 3 (20 marks). a) The above estimates show that the salary of the employees in British academia is statistically correlated with the gender, the subject and number of years of experiences. Accordingly males obtain a higher salary compared to the females with the same conditions (the positive margin of being males in the salary model is 0.077). The males who are working in social sciences and have more working experiences obtain a higher salary compared to otherwise. Female workers, who are working in social sciences and having a higher number of years of working experiences, obtain a higher salary compared to the other female workers. The above model is capable of describing 60 percentage proportion of the variability in the dependent variable i.e. sums of squares regression divided by the sums of squares total equals to 60. Therefore, the predictive ability of the model is strong and statistically significant. c) Autocorrelation is the presence of correlations in the error terms across a time period. Accordingly, autocorrelation violates the assumptions of CLR and results in inefficient estimates under OLS. It is a phenomenon observed in time series data. In the above model cross section data has been used. Therefore, the estimation cannot be affected by autocorrelation. Read More