Home / Inflation

Unit Root Test Results According to Model 1 Method


Table 4.6 Unit root test results according to model 1 method



Variable

t statistic

Level I(0)

Level I(1)

No blocking factor

Has blocking factor

Has coefficient

Block and trend

No blocking factor

Has blocking factor

Has coefficient

Block and trend

CPI t

4.04

-0.59

-1.33

-2.22(**)

-3.43(**)

-

NFA *

t

-4.17(***)

-7.63(***)

-7.63(***)

-

-

-

NDA * t

-3.78(***)

-4.39(***)

-4.76(***)

-

-

-

MM t

3.12

-0.91

-3.26(*)

-8.67(***)

-12.32(***)

-

Y​

-3.65(***)

-3.59(***)

-3.56(**)

-

-

-

V t

-3.61(***)

-6.95(***)

-9.00(***)

-

-

-

DL t

-7.08(***)

-0.60

-3.16

-6.12(***)

-13.13(***)

-


Critical value

Significance level

1%

5%

10%

No blocking factor

-2.60

-1.94

-1.61

Has blocking factor

-3.56

-2.91

-2.59

Has blocking and trend coefficients

direction

-4.14

-3.49

-3.17

Maybe you are interested!

Unit Root Test Results According to Model 1 Method

Note: (***): Significance level 1% ; (**): Significance level 5% ; (*): Significance level 10%

Source: Author's calculation


Table 4.7 Unit root test results according to DFGLS model 1



Variable

t statistic

Level I(0)

Level I(1)

Has blocking factor

Has coefficient

Block and trend

Has blocking factor

With intercept and trend

CPI t

0.20

-1.91

-4.13(***)

-

NFA *

t

-1.53

-4.30(***)

-

-

NDA * t

-1.80(**)

-2.33

-

-

MM t

-0.25

-3.36(**)

-8.13(***)

-

Y​

-2.62(***)

-2.78(***)

-

-

V t

-2.80(***)

-2.92

-

-

DL t

-2.80(***)

-3.77(***)

-

-


Critical value

Significance level

1%

5%

10%

Has blocking factor

-2.61

-1.94

-1.61

Has blocking factor

and trends

-3.76

-3.18

-2.88

Note : Note: (***): Significance level 1%; (**): Significance level 5%; (*): Significance level 10%

Source: Author's calculation

The results show that according to the three testing methods, the variables NFA, NDA, Y and V all have cases of stopping at Level I(0) with significance levels of 1%, 5% or 10%. The variables CPI, MM stop at Level I(1); only the variable DL stops at Level I(1) with ADF and PP tests, stops at Level I(0) with DFGLS tests. Thus, the research data meets the conditions for using the ARDL Bounds Test model.


4.3.1.2. Cointegration test results

Running the ARDL model using Eviews 9 software, the results show that the optimal lag of the variables in the model according to the Schwarz Criterion (SC) is ARDL(2, 1, 2, 3, 4, 1, 2). The results are shown in Table 4.8

Table 4.8: Results of running the ARDL model




Variable


Coefficient

Standard error

t statistic


P value

CPI(-1)

1.147319

0.119327

9.614899

0.0000

CPI(-2)

-0.426621

0.110957

-3.844911

0.0006

NFA_AD

0.057566

0.020834

2.763019

0.0100

NFA_AD(-1)

0.048671

0.014965

3.252378

0.0030

NDA_AD

0.009273

0.026252

0.353232

0.7266

NDA_AD(-1)

0.070386

0.026058

2.701095

0.0116

NDA_AD(-2)

0.072564

0.022991

3.156203

0.0038

MM

0.014018

0.008315

1.685932

0.1029

MM(-1)

-0.002757

0.008214

-0.335599

0.7397

MM(-2)

0.019933

0.008018

2.486146

0.0191

MM(-3)

0.026536

0.007911

3.354158

0.0023

Y

-0.005037

0.002369

-2.126353

0.0424

Y(-1)

0.000372

0.002751

0.135292

0.8933

Y(-2)

-0.003849

0.003954

-0.973222

0.3388

Y(-3)

-0.008277

0.004467

-1.852788

0.0745

Y(-4)

0.022719

0.003513

6.466909

0.0000

V

0.057480

0.023917

2.403295

0.0231

V(-1)

0.055027

0.016340

3.367545

0.0022

DL

0.048147

0.024757

1.944779

0.0619

DL(-1)

0.012408

0.036795

0.337234

0.7385


DL(-2)

-0.167291

0.030499

-5.485137

0.0000

C

0.075434

0.079128

0.953317

0.3486

R-squared

0.999599

Mean dependent var

1.098350

Adjusted R-squared

0.999299

SD dependent var

0.331127

SE of regression

0.008767

Akaike info criterion

-6.335549

Sum squared residue

0.002152

Schwarz criterion

-5.494259

Log likelihood

180.3887

Hannan-Quinn critic.

-6.015181

F-statistic

3327.582

Durbin-Watson statistics

1.697823

Prob(F-statistic)

0.000000




Source: Author's calculation

The R-squared coefficient of the model is very high (R 2 = 0.999599), which shows that the model has multicollinearity. Furthermore, when reviewing the correlation coefficient matrix between the variables, there is a high correlation between the two variables MM and DL. The correlation coefficient matrix between the variables is shown in Table 4.9:


Table 4.9. Correlation coefficient matrix between variables


Correlation coefficient

P value

NDA_AD

NFA_AD

V

Y

DL

MM

NDA_AD

1.000000







-----






NFA_AD

-0.170348

1.000000






0.2181

-----





V

-0.275140

-0.696227

1.000000





0.0441

0.0000

-----




Y

-0.277079

-0.115108

0.044692

1.000000




0.0425

0.4072

0.7483

-----



DL

-0.138412

0.001826

0.408424

-0.057000

1.000000



0.3182

0.9895

0.0022

0.6822

-----


MM

0.335837

-0.160872

-0.398668

-0.006362

-0.922135

1.000000


0.0130

0.2452

0.0028

0.9636

0.0000

-----


Source: Author's calculation


According to table 4.9, the correlation coefficient between variables MM and DL is -0.92 (absolute value greater than 0.8), so there is multicollinearity between these two variables in the model.

According to Lawrence's rule of thumb (1962), this rule of thumb states that multicollinearity is a problem only if the R 2 obtained from an auxiliary regression function is larger than the R 2 of the main regression function. In other words, multicollinearity is ignored if the R 2 coefficient of the main regression model is larger than all the R 2 coefficients of the auxiliary regression models. Therefore, the author continues to conduct auxiliary regressions of the independent variables in the model to see whether the multicollinearity problem is ignored or not.


The ARDL(2, 1, 2, 3, 4, 1, 2) model with the variables is expressed as follows:

CPI = C + CPI(-1) + CPI(-2) + NFA_AD + NFA_AD(-1) + NDA_AD + NDA_AD(-1)

+ NDA_AD(-2) + MM + MM(-1) + MM(-2) + MM(-3) + Y + Y(-1) + Y(-2)+ Y(-3) +

Y(-4) + V + V(-1) + Dl + Dl(-1) + Dl(-2) + u t (4.1)


Conducting the auxiliary regression by regressing each independent variable in equation (4.1) on the remaining independent variables, the author obtained the R2 coefficients of the auxiliary regression functions as follows:

Table 4.10. R-squared coefficients of the auxiliary regression models


Variable

R2 model coefficient

auxiliary regression


Variable

R2 model coefficient

auxiliary regression

CPI(-1)

0.999009

Y

0.762435

CPI(-2)

0.998861

Y(-1)

0.817025

NFA_AD

0.969836

Y(-2)

0.909938

NFA_AD(-1)

0.942460

Y(-3)

0.916159

NDA_AD

0.885770

Y(-4)

0.853905

NDA_AD(-1)

0.883607

V

0.968959

NDA_AD(-2)

0.840942

V(-1)

0.943022

MM

0.977234

DL

0.986880

MM(-1)

0.977193

DL(-1)

0.994157

MM(-2)

0.976357

DL(-2)

0.991556

MM(-3)

0.976362



Source: Author's calculation

According to table 4.10, the coefficients R 2 of the secondary regression models are all smaller than the coefficients R 2 of the main regression model. Thus, the phenomenon of multicollinearity in the model is ignored. The author continues to perform the following tests.


Conducting the Bounds Test, the author obtained the following results:

Table 4.11. Bounds Test results


Number

step

Statistical value

F

Limit values ​​of the contours

K 6

F Statistic 10.51

1%

2.5%

5%

10%

I(0)

I(1)

I(0)

I(1)

I(0)

I(1)

I(0)

I(1)

2.88

3.99

2.55

3.61

2.27

3.28

1.99

2.94

Source: Author's calculation

Thus, the F statistic results are greater than the limit values ​​of the envelope curves at significance levels from 1% to 10%. This demonstrates that there is a long-run cointegration relationship between the variables in the model.

To determine the reliability of the model, the author continued the diagnostic tests including: Testing for heteroscedasticity, autocorrelation, normal distribution of residuals and checking the stability of the model by testing the cumulative sum of residuals (CUSUM test) and the adjusted cumulative sum of residuals (CUSUMSQ test) of the ECM equation (3.10). The results are shown in Table 4.12 and Figure 4.17.

Table 4.12. Results of diagnostic tests


STT

Inspection

Statistical value

1

Variance change

(Heteroskedasticity Test: ARCH)

Prob(F21,28) = 0.57

2

Autocorrelation

(Breusch-Godfrey Serial Correlation LM Test)

Prob(F4,24) = 0.49

3

Normal distribution of residuals

(Histogram Normality Test)

Jarque Bera = 2.13

Prob = 0.34

Source: Author's calculation


16


12


8


4


0


-4


-8


-12


-16


2010 2011 2012 2013 2014 2015 2016 2017

1.4


1.2


1.0


0.8


0.6


0.4


0.2


0.0


-0.2


-0.4


2010 2011 2012 2013 2014 2015 2016 2017


CUSUM 5% Significance


CUSUM of Squares 5% Significance


Figure 4.17. Results of testing the cumulative sum of residuals and the adjusted cumulative sum of residuals.

Source: Author's calculation

The results show that the model residuals have no autocorrelation, no heteroscedasticity, and are normally distributed. In addition, the cumulative sum of residuals and the adjusted cumulative sum of residuals are both within the standard range at the 5% significance level. This proves that the model used is reliable and stable.

After satisfying the diagnostic test conditions, the author continues to estimate the short-run adjustment coefficient of CPI to return to equilibrium and the coefficients of the long-run equation, the results obtained in Table 4.13 are as follows:


Table 4.13. Estimated results of long-run coefficients and adjustment coefficients


Variable

Coefficient

Standard error

t statistic

Prob.

NFA *

0.38 (***)

0.11

3.23

0.0031

NDA *

0.54(***)

0.15

3.43

0.0019

mm

0.20(***)

0.02

7.11

0.0000

Y

0.02(**)

0.00

2.15

0.0396

V

0.40(***)

0.12

3.33

0.0024

DL

-0.38(***)

0.05

-7.18

0.0000

Adjustment factor

EC t-1

-0.28 (***)

0.02

-10.25

0.0000

Source: Author's calculation

The adjustment coefficient EC t-1 = -0.28 shows that when inflation goes beyond the equilibrium level

, the negative adjustment coefficient will pull inflation back to the long-run equilibrium level with an adjustment speed of 28% and it takes 1/0.28 = 3.6 periods (about one year) to restore equilibrium under the condition that other factors remain unchanged. The results also show that in the long run , NFA * t , NDA * t , mm, Y, V have a positive impact on CPI, while DL has a negative impact on CPI during the research period.

In addition, to assess the short-term impact of foreign exchange reserve accumulation and dollarization on inflation, the author continues to conduct Wald tests of the coefficients of the variables NFA* and DL in the difference equation (3.8), the results obtained are as follows:


Table 4.14. Wald test results of the coefficients of the difference equation



Variable

Wald test

t statistic

Prob

NFA *

5.49

0.000

DL

8.08

0.000

Source: Author's calculation Thus, the results all show that the hypothesis H0 is rejected , that the coefficients of the variables NFA* and DL in the difference equation (3.8) are equal to 0. This proves that these coefficients are different from zero. Therefore, in the short run, both NFA* and DL have an impact on CPI.

4.3.1.3. Testing the stability of the estimated results

To test the stability of the model and the estimation results (Robustness Test), the author re-estimates the model with the period from the second quarter of 2007 to the second quarter of 2017 (3 years shorter than the initial estimate of the thesis). The results show that the optimal lag of the variables in the ARDL model is ARDL(2, 1, 2, 3, 4, 1, 2). The variables in the model still have a cointegration relationship after the Bounds Test. Estimating the long-term coefficients shows that NFA still has a positive impact on CPI (Coefficient is 0.47) and DL has a negative impact on CPI (Coefficient is -0.33). The EC t-1 adjustment coefficient is -0.24 and is statistically significant . Continuing the Wald test to test the coefficients of NFA * and DL to determine the short-term impact of NFA * and DL on CPI, the results all show rejection of the hypothesis H 0 that these coefficients are 0. Thus, similar to the initial study, NFA * and DL both have short-term impacts on CPI. This shows that the ARDL Bounds Test model is used and the results of the short-term and long-term impacts of foreign exchange reserve accumulation and dollarization on inflation are reliable.


4.3.1.4. Discussion of research results

Thus, in the short term, the accumulation of foreign exchange reserves has an impact on inflation. In addition, the accumulation of foreign exchange reserves has a positive impact on inflation in the long term, which proves that the accumulation of foreign exchange reserves will increase inflation. This result is similar to empirical studies in other countries and in the world such as Heller (1976), Steiner (2009), Lin & Wang (2005), Chen & Huang (2012). These empirical studies all mentioned that the cause of the accumulation of foreign exchange reserves causing inflation is due to the increase in money supply as the mechanism mentioned in section 2.2.1.1. In Vietnam, it is similar, from 2000 to now, money supply has always been one of the causes mentioned for increasing inflation. Especially in 2007, when the State Bank accumulated a large amount of foreign exchange reserves (10 billion USD) but did not withdraw VND, it caused the money supply in the economy to increase, causing inflation in 2008 to reach 23%.

The results of the study are contrary to the results of Chaudhry & ctg (2011) with the conclusion that foreign exchange reserve accumulation is negatively related to inflation in Pakistan. Because the case of Pakistan is different from developing countries including Vietnam. According to Chaudhry & ctg (2011), developing countries have higher income and more elastic imports. Pakistan's imports are based on food, crude oil, agricultural raw materials, machinery and medicines ... and all imports are more or less based on foreign exchange reserves. The decline in foreign exchange reserves in turn immediately reduces imports of industrial and agricultural raw materials and creates a shock that raises the price level.

Empirical research in Vietnam, by approaching the Var model, Pham Thi Tuyet Trinh (2015) showed that the accumulation of foreign exchange reserves caused inflation to start increasing from the 3rd quarter and reach a new equilibrium from the 7th quarter at 1.1% units. Compared to this study, the research results of the thesis clearly indicate the short-term and long-term impacts of foreign exchange reserve accumulation on inflation in Vietnam. This may be due to the difference in research period and estimation method. Pham Thi Tuyet Trinh (2015) studied the impact of foreign exchange reserves on inflation.


The thesis studies the impact of foreign exchange reserve accumulation on inflation in Vietnam from the first quarter of 2000 to the second quarter of 2014, while the thesis studies the period from the first quarter of 2004 to the second quarter of 2017. With different time periods, the impact level will be different. From 2000 to 2004, in general, foreign exchange reserves in Vietnam did not fluctuate much, and foreign exchange reserve accumulation was slow. On the contrary, in the period from the second quarter of 2014 to the second quarter of 2017, in general, foreign exchange reserves continuously tended to accumulate, except for the period of 2015. Therefore, the impact of foreign exchange reserve accumulation on inflation in the thesis is more clearly demonstrated than in the study of Pham Thi Tuyet Trinh (2015). Furthermore, when approaching with the VAR model, the study cannot evaluate the short-term and long-term effects between the independent variables and the dependent variables in the model like the ARDL Bounds Test model that the thesis used.

The research results show that the variables NDA * and mm have a positive impact on inflation in the long run. This is also consistent with the research hypothesis and the development of the Vietnamese economy. The change in NDA * and mm affects the money supply in the economy. When the State Bank implements an expansionary monetary policy, NDA * and MM increase, leading to an increase in money supply and affecting inflation. The development of money and inflation in the economy in the period 2010 - 2011 clearly shows the above relationship. Inflation at the end of 2011 increased by 18.13%, higher than the 11.75% of 2010, while the average inflation reached 18.58% compared to the corresponding level of 9.19% in 2010. 13 Inflation in 2011 increased higher than in 2011 due to the simultaneous impact of supply and demand factors. Among the causes of the increase in inflation in 2011, there was a cause originating from the delayed impact of the loose monetary policy in 2010. From the second quarter of 2010 to the fourth quarter of 2011, the amount of loans to credit institutions of the State Bank continuously increased compared to before (increased from 95,730,973 million VND in the second quarter of 2010 to 152,361,790 million VND in the fourth quarter of 2011 14 ), causing the NDA of the State Bank to increase. At the same time, in 2010, the State Bank maintained the required reserve ratios for


13 According to the 2011 annual report of the State Bank.

14 According to IFS (2018)

Comment


Agree Privacy Policy *