# Quantitative Research Methods

**Topics:**Null hypothesis, Per capita income, Statistical hypothesis testing

**Pages:**8 (1968 words)

**Published:**April 14, 2009

Introduction

The annual data is from 1955 to 1994, it is the finnish aggregate and it has extracted logarithm of income as, natural logarithms of real per capita consumption(LCFI) and natural logarithm of real per capita income (LGFI), the real interest rate (RFI), and the rate of unemployment (UFI).here, income is positively related to consumption economics and unemployment and interest rate is negatively related. The real goal of mine is for understanding the above data with the help of e-views application considering it is really valid according to economics which shows that income is positively related to consumption economics and unemployment and interest rate is negatively related. . Here, the following variables are symbols of natural logarithm of real per-capita consumption (LCFI), the natural logarithm of real per-capita income (LGFI), the real interest rate (RFI) and the rate of unemployment (UFI). β1, β2, β3, β4, β11, β21, β31, β41 are coefficients to be estimated and ut is a stochastic error term. Subscripts t and t-1 refer to the time period and solve it with help of e-views application. There are two following models have to be tested for misspecification tests. (5% level of significance is applied for all the tests, except heteroscedasticity test in model 3 (1%).) to do that we need to Apply general-to-specific methodology to the 2nd model, parsimonious model has to be obtained, and tested. (a) LCFIt = β1+ β2LGFIt + β3RFIt + β4UFIt + ut

(b) LCFIt = β1+ β2LGFITt + β3RFIt + β4UFIt + β11LCFIt-1 + β21LGFIt-1 + β31RFIt-1 + β41UFIt-1 + ut

Misspecification tests applied in this Assignment coursework include: 1. 1st order autocorrelation: Durbin Watson (DW) test,

2. 1st order autocorrelation: Breusch-Godfrey test,

3. Non-linear functional form: Ramsey’s RESET test,

4. Non-normally distributed residuals: Jarque-Bera test,

5. Heteroscedasticity: White’s test without cross terms,

6. First order ARCH effect

ANALYSIS FOR THE DATA :

MODEL 1:

LCFIt = β1+ β2LGFIt + β3RFIt + β4UFIt + ut

Ln(LCFI) = -0.674520+ 0.988854 ln(LGFI) +-0.052366 RFI +0.003446 UFI R2 = 0.997255, Adjusted R2 = 0.997020, s = 0.019455, F =4238.637, URSS = 0.013247, Pr[F(R2)] = 0.000. β2 = 0.988854> 0, β3 = 0.052366 > 0, β4 = 0.003446 > 0.

β1, β3 and β4 are statistically insignificant at 5% level: -t = -2.000* < t(β1) = -21.190, t(β3) = -0.56435, t(β4) = 0.036035 > +t = +2.000* β2 is statistically significant at 5% level:

t(β2) = 93.468 > +t = +2.000

The model’s explanatory power is 99.70% - 99.72%. [R2 = 0.9972, Adjusted R2 = 0.9970] R2 indicates 99.72% explanatory power, which shows that the model could explain up to 99.70% of the variance in particular data. The model have significant explanatory power:

F = 4238.637 > F [5%] ≈ 2.88.

Pr[LMA(1)] = 0.0002

Pr[LRFF(1)] = 0.6267

Pr[LMN(2)] = 0.000

Pr[LMH] = O.9375

Pr[LMARCH(1)] = 0.1088

The probabilities test reflects evident autocorrelation, non-normality and non-linearity in the model, because their values are significant at 5% level (i.e:< 0.050). Misspecification tests: model 1

1. Durbin Watson test (DW)

DW = 0.723 < dL, 3,39 At 5% i.e:1.328 ' here,there is positive autocorrelation which indicates we can reject the null hypothesis i.e: HO 2. Breusch-Godfrey test

The probability value 0.0002 shows autocorrelation is insignificant upto 0.02% level. Hence, autocorrelation is significant at all the higher levels and 5% level, as 0.0002 < 0.05 or 0.02% x2 (1) 5% = 3.84 ' it shows evident in autocorrelation 3. Ramsey’s RESET test

LRFF (1) = 0.236 < χ2 (1) 5% = 3.84 ' here there is no non-linearity. Therefore probability value 0.627 defines that non-linearity is insignificant up to the 62.7% level. Since the Pr [LRFF (1)] = 0.627 > 0.05. non-linearity is insignificant at 5% level. Then the decision is that we do not reject null hypothesis. 4. Jarque Bera test

LMN (2) = 0.1105 < χ2(2)5% = 5.99 ' here there is evidence of no...

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