Developing Econometrics - Assignment Example

Developing Econometrics Our study hypothesized that consumption is directly related to income but inversely related to unemployment and real interest rates. As such, we used mathematical reasoning, statistical inference, and economic theories to quantify the above hypothesis. In simple terms, we turned four theoretical economic models (starting with model 1) into meaningful and useful tools that can be adopted for economic policymaking. Our objective was to convert the qualitative statement (hypothesis) using data from Japan into quantitative statements. Model 1 was formulated as: ∆LCJAPt = β1 + β2∆LGJAPt + β3∆RIJAPt + β4∆UJAPt + Ut Where; the β,s were coefficients of estimation and were stochastic error terms; Subscript t represented the time period; ∆ was the change in parameters; LCJAPt represented in consumption in time t (dependent variable); LGJAPt represented income in time t; RIJAPt represented real interest rate in time t; ∆UJAPt represented the change in unemployment in time t; and Ut represented the error term in time t. Results and Discussion So as to explore the determinants of consumption in Japan, we estimated the nature of the relationship between consumption, interest rate, unemployment and disposable income. After subjecting the data set from 1957 to 1994 (using the Japan economy) to various statistical analyses, the results were displayed in Table 1 below: Model 1 Model 3 Intercept 1.258 (-3.55) 0.252 (-2.075) ∆LGJAPt 0.982 (17.298) 1.003 (6.940) ∆RIJAPt -0.015 (-2.733) ∆UJAPt 0.30 (5.519) LCJAPt -1 -0.250 (-2.210) LGJAPt -1 0.200 (2.278) Fit Measures R2 0.999 0.658 Adjusted R2 0.898 0.628 S 0.1330 0.017 F (R2 = 0) 228.53 21.851 (0.000) Misspecification tests DW 1.222 1.650 LMA1 4.039 [0.037] 0.963 (0.327) LMA2 0.016 [0.834] 1.031 (0.589) LRF1 1.346 [0.328] 0.112 (0.737) LMN2 5.876 [0.098] 0.103 (0.749) LMH 5.021 [0.012] 0.942 (0.815) LMARCH1 3.549 [0.027] 0.103 (0.749) FCHOW 1.252 [0.432] 3.351 (0.022) Notes: The dependent variable is LCt and figures in parentheses coefficients are estimated t-ratios. Adjusted R2 is the coefficient of determination adjusted for degrees of freedom, s is the regression standard error and F(R2=0) is the F-test for deleting all slope coefficients from the model. DW is the Durbin-Watson statistic, LMA1 is the lagrange multiplier (LM) test for first order autocorrelation and LMA2 is the LM test for second order autocorrelation. LRF1 is the LR-test for non-linear functional form, LMN2 is the LM test for departures from normality, LMH is the LM-test for heteroscedasticity, LMARCH1 is the LM-test for first-order ARCH effects and FCHOW is Chow’s first (F-) test for structural stability with a breakpoint in 1976. Probability values for selected tests are reported in squared brackets below the statistic to which they correspond. All the variables were significant at 1%. As expected, they had a positive influence on the consumption. Conversely, the effect of real interest rate was negative (-0.015) though statistically insignificant. This could be accredited to the reality that interest rates can have two sets of influences on consumption, a positive income effect and negative income effect, which may approximately cancel. The major determinant of consumption in the model was disposable income. A unit change in disposable income can cause a 0.982 increase in consumption. The resulting coefficient of determination R2, that reflected the quality of our estimation, was 0.999 in model 1. The model explained nearly 94 per cent of the variation in consumption. Furthermore, the autocorrelation test of the errors statistically showed the absence of such autocorrelation in the models. The economic implications of the results from model 1 were that consumption was influenced by current income, unemployment rate and real interest rate. The error term was applied to take care of any political and/or social uncertainty in Japan for the period of study. This variable was statistically significant for model 1 and thus, it was included in our reported results. The results specified that real interest rate had a negative coefficient, which was just significant at less than 10% in model 1. In model 1, the speed of adjustment was about 14% per year. The findings showed also that there is a short-run impact of disposable income, unemployment, and real interest rate on private consumption. Moreover, the alterations in both the first and second lag had a significant but negative impact of real interest rate on consumption. According to Baltagi (2011), such outcomes could replicate the losses concerning real liquid assets, may be, due to inflation. Nonetheless, the disposable income displayed a positive influence on consumption for similar lags in model 1. Group Report: Model 5 Word Count: 701 In parsimonious model 5, we had three regressors together with the intercept. The incorporated variables were LGJAPt , LCJAPt -1 and LGJAPt-. Not even the term of interest rate or unemployment rate was in our preferred model. The two were not significant. Therefore, in our investigation there were evidences proving that fluctuations in real consumption in Japan do not rely on the unemployment rate and interest rate. Such an outcome was not surprising especially in a welfare nation like Japan where uncertainty of income is low and the government has vast schemes for the future generations.  Each of the regressors, counting the intercept, in our preferred model was significant. Moreover, the F-statistic put forward that the regressors jointly have significant impact on ∆LCJAP. The R2 showed that the projected model explained 65.8 per cent of the variations as far as the ∆LCJAP are concerned. This was a moderate degree of explanatory power. Adjusted R2 can be utilized for comparison purpose. The preferred model 5 had the uppermost explanatory capacity compared with the four fitted models as shown by the adjusted R2. Standard error of the regression was also the smallest in model 5. The parsimonious model was not influenced by any misspecification because p-values regarding the test statistics of different misspecification tests stated in the table were higher than 0.01. Results and Discussion Our parsimonious model was represented in an equation as shown below: ∆LCJAPt = - 0.252(-2.075) + 1.003 (6.94)∆LGJAPt – 0.250 (-2.210)LCJAPt -1+ 0.200 (2.278)LGJAPt -1 Adjusted R2 = 0.628, R2 = 0.658 s = 0.017 F(R2 = 0) = 21.850 P(F) = 0.000 ∆LGJAPt had a coefficient with positive sign, implying that short run variations in real consumption are positively related with changes in real income. However, the negative coefficient on the LCJAPt -1, which was the adjustment coefficient, designated a valid error rectification mechanism in the estimated preferred model. A coefficient of -0.250 represented a 25 per cent error correction in every year than the preceding year irrespective of the current value of the LCJAPt ; whether below or above the long run equilibrium mark. We carried out a valid error correction test using F-test for our model since the model was not formulated at level terms as one variable. The alternate and the null hypotheses were: Ho: αLCJAP  = βLGJAP = 0 (There is no valid error correction) H1: αLCJAP  ≠ βLGJAP ≠ 0 (Valid error correction) A redundant variable test found the F-statistic to be 2.66 with 0.084 as the p-value. The critical F-value was F5%,38 ≅ F5%,50 = 6.08. Since the calculated F< critical F, we could not reject our null hypothesis and so our model did not meet one condition for valid error correction technique. With no valid error correction, any equilibrium association between real consumption and real income was nullified. This was not in line with economic theory. Derivation of long run static solution Since in equilibrium variables do not change, C = Ct = Ct -1 = Ct -2 and G = Gt = Gt-1 = Gt -2 and ∆Ct = ∆Gt. We applied these concepts in our parsimonious model and obtained that: 0 = (1.003 - 252 * 0) – 0.250LCJAPt + 0.200LGJAPt Implying 0.250LCJAP = -252 + 0.200LGJAP Thus, LCJAP = (-0252/0.250) + (0.200/0.250) LGJAP = -1.008 + 0.80LGJAP Since the coefficient of LGJAP (marginal propensity for consumption in long run) was less than one and positive (0.80), we affirmed that our results matched the economic theory. By finding that real interest rate did not show much impact on consumption level of Japanese in model 1 and 5, we affirmed previous studies like Baltagi (2011) who discovered, by investigating Argentine, statistically insignificant relationship between interest rate and consumption based on yearly data. Just as inflation rate is related inversely to consumption in the short run and directly in the long run, disposable income tends to behave the same. Tong, Kumar & Huang (2011) explain this paradox by showing that if prices upsurge faster than income, an individual increases the level of consumption. Similarly, if prices decrease faster than income, individuals increase their savings so as to preserve their own wealth to the preferred levels and hence, they lessen their consumption level. Reference List Tong, H., Kumar, T. K., & Huang, Y. X. 2011. Developing econometrics. Chichester, West Sussex: Wiley. Baltagi, B. H. 2011. Econometrics. Berlin: Springer. Read More