Vector Error Correction Model (VECM)

Chapter 5: Evaluation of significant fundamental determinants of the NZX 50 Index 67

5.4 Results and discussion

5.4.4 Vector Error Correction Model (VECM)

results are broadly similar for different dependent variables, with the tau-statistic consistently failing to reject the null of no cointegration at conventional levels. The results for the Z- statistics are mixed, with the residuals from the NZX 50 equation rejecting the unit root null at the 5% level. These test statistics confirm that the null hypothesis of no cointegration cannot be rejected.

Table 5.1: Vector Error Correction Model (VECM)

The table below shows the VECM results using the following equation.

Δ ln 𝑁𝑍𝑋 50_𝑡= 𝜇₁+ ∑ 𝛽_11,𝑖

𝑝

𝑖=1

Δ 𝑙𝑛 𝑁𝑍𝑋 50_𝑡−𝑖+ ∑ 𝛽_12,𝑖

𝑝

𝑖=1

Δ ln 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛_𝑡−𝑖

+ ∑ 𝛽_13,𝑖

𝑝

𝑖=1

Δ 𝑙𝑛 𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒_𝑡−𝑖+ ∑ 𝛽_14,𝑖

𝑝

𝑖=1

Δ ln 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡_𝑡−𝑖 + ∑ 𝛽_15,𝑖

𝑝

𝑖=1

Δ ln 𝑆&𝑃_𝑡−𝑖+ 𝜓₁𝐸𝑇𝐶_𝑡−1+ 𝜀

𝑡 𝑁𝑍𝑋

∆ (ln NZX 50) = C(1) * [ln NZX 50(-1)+16.9219052098 * ln Inflation(-1) - 0.850135710618 * ln Exchange(-1) + 0.650108905806 * ln Interest(-1) - 1.40108000703 * ln S&P 500(-1) - 118.287078688] + C(2) * ∆ [ln NZX 50*(-1)] + C(3) *

∆ [ln NZX 50(-2)] + C(4) * ∆ [ln Inflation(-1)] + C(5) * ∆ [ln Inflation(-2)] + C(6) * ∆ [ln Exchange(-1)] + C(7) * ∆ [ln Exchange(-2)] + C(8) * ∆ [ln Interest(-1)] + C(9) * ∆ [ln Interest(-2)] + C(10) * ∆ [ln S&P 500(-1)] + C(11) * ∆ [ln S&P 500(- 2)] + C(12)

Coefficient Std. Error t-Statistic Probability

C(1) -0.0023 0.0020 -1.1264 0.2604

C(2) 0.0539 0.0380 1.4167 0.157

C(3) 0.0323 0.0345 0.9367 0.3492

C(4) 0.0632 0.4767 0.1325 0.8946

C(5) -0.2012 0.4755 -0.4233 0.6722

C(6) -0.0172 0.0246 -0.6989 0.4848

C(7) 0.0038 0.0242 0.1584 0.8742

C(8) 0.0378 0.0278 1.3589 0.1746

C(9) -0.0202 0.0277 -0.7304 0.4654

C(10) 0.2483 0.0211 11.7979 0.0000

C(11) 0.0433 0.0235 1.8423 0.0659

C(12) 0.0003 0.0002 1.8983 0.0581

R-squared 0.19259 Mean dependent var 0.00044

Adjusted R-squared 0.17981 S.D. dependent var 0.00522 S.E. of regression 0.00473 Akaike info criterion -7.85487 Sum squared residuals 0.01552 Schwarz criterion -7.77745 Log-likelihood 2788.695 Hannan-Quinn criterion -7.82496

F-statistic 15.07032 Durbin-Watson stat 2.01246

Prob(F-statistic) 0.00000

The coefficient C1 in Table 5.1 is the error correction term of the cointegrated model. C1

is -0.0023, suggesting that 0.23% of disequilibrium is corrected daily as the data frequency used in this analysis is daily. For the long-run causality to be present in the VECM, the Error Correction Term (C1) must be negative and statistically significant. Although the sign and the size of the coefficient (C1)are acceptable, it is not statistically significant. The findings confirm the nonexistence of long-run causality from the inflation rate, exchange rate, interest rate, and S&P 500 Index on the NZX 50 Index.

Wald test [294] is conducted to evaluate whether each of the individual explanatory variables (inflation rate, exchange rate, interest rate, S&P 500 Index) has a short-run joint causality on the NZX 50 Index or not. The short-run causality can be observed from C2 to C11 coefficients in Table 5.1. A null hypothesis of no short-run joint causality from each independent variable to the 50NZX Index is tested, and the results are presented in Table A.9 in Appendix A. For example, a “null hypothesis of C (4) = C (5) = 0” refers to the inflation rate (lag 1) and inflation rate (lag 2) having no short-run combined influence on the NZX 50 Index.

A “null hypothesis of C (10) = C (11) = 0”, which refers to having no short-run joint influence from the S&P 500 Index (lag 1) and the S&P 500 Index (lag 2) to the NZX 50 Index, is tested.

The Chi-square value of 140.46 with a Chi-square P-value of 0.0000 confirms the result is statistically significant, and therefore the null hypothesis “C (10) = C (11)” is rejected. This finding confirms that the S&P 500 Index has a strong significant short-run Granger Causality (GC) to the NZX 50 Index. However, none of the other tested variables shows any short-run GC to the NZX 50 Index as their Chi-square P-values are statistically insignificant.

It is imperative to examine the statistical and econometrical validity of the VECM presented in Table 5.1. The Coefficient of Determination (R² = 0.1926) and the Adjusted Coefficient of Determination (Adj-R² = 0.1798) are low. When the statistical significance of the explanatory variables is individually evaluated, only S&P 500 Index is statistically

significant at 10%. However, the F-statistic that assesses the multiple regression's joint significance is statistically significant as the probability of the F-statistic is 0.0000. The evidence suggests that all the explanatory variables (inflation rate, exchange rate, interest rate and S&P 500 Index) in the VECM jointly influence the dependant variable (NZX 50 Index).

VECM validation diagnostic plots and numerical diagnostic summaries are presented in Table A.10 in Appendix A, which evaluates the robustness of my estimated model. VECM residuals are tested for heteroskedasticity, serial correlation, and normality.

To detect the presence or absence of heteroskedasticity in the VECM, I employed the White test (see [295]) and Breusch-Pagan-Godfrey test (see [296]–[298]). For both tests, a null hypothesis of homoskedasticity is tested. The White test statistic has a p-value greater than an appropriate threshold (P > 1%). Additionally, the p-value for the Breusch-Pagan-Godfrey statistic is greater than the 1% threshold. Both test results validate the presence of homoscedastic errors in the VECM in Table 5.1.

Breusch-Godfrey LM test (see Breusch [297] and Godfrey [298]) and Q Statistics (see Ljung & Box [299]) are used to detect the absence or the presence of serial correlation issues.

For both tests, a null hypothesis of no serial correlation is examined. Autocorrelations (AC) and Partial Autocorrelations (PAC) at all lags are nearly zero, and all Q-statistics are insignificant with large p-values. Similarly, the Breusch-Godfrey LM test statistic has a p-value greater than an appropriate threshold (P > 1%). Both test results confirm the VECM presented in Table 5.1 is free of serial correlation.

Jarque-Bera test is a test statistic for assessing whether the series is normally distributed (see Jarque-Bera [300] and Godfrey [301]). Jarque-Bera test is carried out to examine the normality of the residuals in the VECM. A null hypothesis of the residuals is normally distributed is evaluated. The p-value for the Jarque-Bera test is smaller than an appropriate

threshold (P < 1%), suggesting the residuals are not normal at 1%. The comparative chart of actual, fitted and residuals of the VECM model presented in Table A.10 shows the presence of a few outliers that might be causing the normality test to fail. However, this will not be a significant issue as the sample used to estimate the VECM model is large (n=710), and the mean value of the residuals of the VECM is almost zero (-5.44E-18).

Additionally, the Augmented Dickey-Fuller unit root test (ADF) ([248], [249]) and the Phillips-Perron (PP) unit root test [250] are applied to the VECM residuals. Both ADF and PP tests confirm that the residuals of the VECM possess stationarity property as the p-values of both test statistics are less than an appropriate threshold (P<1%). These results confirm the VECM is a robust model with white noise residuals.

The findings of my study are compared with similar prior studies. For example, [78]

examined the relationship between the NZSE 40 Index and selected macroeconomic variables in the New Zealand financial market. Using data from 1990 to 2003, they examined the association between NZSE 40 Index and some macroeconomic variables, while I evaluated the relationship between the NZX 50 Index and selected macroeconomic variables. Note that NZSE 40 Index was replaced as the headline index by the NZX 50 Index in 2005 [302]. The test results of [78] revealed that the NZSE 40 Index did not Granger cause any of the selected macroeconomic variables during the period under investigation. [78] pointed out that this is because the New Zealand stock market is relatively small compared to other developed nations’

stock markets. [72] evaluate the Korean stock market as somewhat smaller than the US and Japan stock markets. [72] found that Korea Composite Stock Price Index (KOSPI) and Small- size Stock Price Index (SMLS) did not Granger cause the tested macroeconomic variables.

These findings contradict the findings of [39] and [279], where they evaluated larger stock markets such as the US and Japan and found stock market indices Granger caused macroeconomic variables used in their studies. Additionally, [78] recommended incorporating

global macroeconomic factors since New Zealand is a small open economy, and the economy may well be susceptible to global economic and financial factors. Adopting [78]’s proposal, I have used the S&P 500 Index and found the error correction term is statistically insignificant, which is consistent with [78] and [72]. Adopting [78]’s direction, I have used the S&P 500 Index as a leading macroeconomic variable and found that the error correction term is statistically insignificant, confirming the absence of long-run causality originating from the inflation rate, exchange rate, interest rate, and S&P 500 Index on the NZX 50 Index. However, out of all the variables evaluated in this analysis, only the S&P 500 Index has a solid short-run Granger Causality (GC) to the NZX 50 Index. This is more explicit evidence of how an extensive and substantial stock market like the US could influence a smaller open economy like New Zealand.