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AFE6019-B - Econometrics

AFE6019-B - Econometrics

 

 

 

Econometrics 2

AFE6019-B

Word Count: 1886 (Excluding titles, questions and references)

 

 

Econometrics 2

 

  1. The data I managed to collect through intensive research has come from a reliable source in the World Bank Data. The reason I have used this source is due to the fact that they are well respected and hold information which is very accurate. So, the time series I have collected include data from 30 years of 1988 to 2018 in Canada. The 2 independent variables which have been examined are exports (% of GDP) and FDI (% of GDP). These variables affect the dependent variable examined which is, GDP (Annual %). The reason for choosing Canada is due to the fact that they are a developed economy from many years of trade, reinvestment and development.

 

The required data is managed from most reliable source which is the World Bank data. The World Bank site provides most reliable data sets for economic parameters. I have chosen Canada as my country , and I have collected data starting from 1988 up to 2018. The independent variable for my study are foreigh Direct Investment (FDI) in % if Gross Domestic Product (GDP) and exports as % of GDP. The annual GDP is is final variable which gets effected due to changes in the independent variables namely FDI. I have chosen a developed economy like Canada for my study.

 

Gross domestic product is in essence a measure of an economy’s performance (Garciga, C and Knotek, E.S. 2019). GDP can be summed up by its components which include investment, consumption, government intervention and net exports (Landfield, J.S. et al. 2008). The components can be further derived into sub-components. However, as these are the specific components of GDP, FDI can also contribute to the growth of an economy.

 

Any country total measure of all economic activities is captured in this parameter called GDP (Garciga, C and Knotek, E.S. 2019). The GDP comprises of consumption, investment, government intervention, along with total exports of goods and services (Landfield, J.S. et al. 2008). There can be further subdivions of GDP, and FDI too contributes to the growth of the economy thus that also may affect the GDP.

 

Foreign direct investment can be defined as ‘investment made to acquire lasting interest in enterprises operating outside of the economy of the investor’ (Larimore, H.E. 2008). FDI increases economic growth (GDP) as it promotes more investment within a country as well as creating jobs and causing people to consume more. However, (Li, X. 2005) claims that FDI and economic growth can have a negative relationship as well as a positive relationship due to the lack of time-series and cross-country studies. Net exports are the total exports minus the total imports for a chosen country. Exports affect economic growth directly as the it contributes to money entering an economy in the trade of goods and services. Trade is said to improve the level of productivity of an economy and is a strong factor in GDP growth and the ‘real openness’ to trade (Mo, P.H. 2010). One componenet of FDI is the companies which are acquired the companies which are operating outside the contry but are part of FDI ((Larimore, H.E. 2008).

 

 

 

 

F D I is defines as ‘investment made for acquiring lasting interest in enterprises operating outside of the economy of the investor’ (Larimore, H.E. 2008). The economic growth gets increased with increase in F D I. The reason for growth is increase in investment from investers of ones own contry, thus this investment is from within the contry. This investment creates more job apportunities for ones own contry. The consumption of the people also gets increased as earning increases. However, (Li, X. 2005) has claimed just the oppsite, he said that that “economic growth can have a negative relationship “ in some cases , while FDI may have positive relationship. This he attributed to the deficiency in the data of investments done across contries. Exports causes more fund to inter the economy thus has a posive effect on the economy, as it boosts investment. It causes services and goods consumption to get improved. As money increases due to exports trades of goods and services increases. Increase in trade causes improvement in the level of productivity. All these parameters has positive parameter to create growth in GDP( Mo, P.H. 2010). One FDI componenet is acquired companies which are operating outside the country ((Larimore, H.E. 2008).

  •  

Canada’s outward direct stock investment initially grew at a much faster rate than that of the inward direct investment. It wasn’t until the mid-1990s that Canada became a major net exporter. Over the past 20 years from 2000-2018, the difference between the outward and inward FDI stocks grew from $118 billion to $402 billion (Rao, S and Zhang, Q. 2019), which shows how much of an affect FDI has had on the Canadian GDP growth.

 

For the Canada it is seen that initially growth in direct stock investment took place at heigher rate compared to inward direct investment. Only after 1990 Canada could become net exporter. From the data we can see that in past 20 years strting from 2000, the ouward FDI and inward FDI grew to USD$402 from USD$118((Rao, S and Zhang, Q. 2019), This proved the point that increase in FDI causes growth in GDP.

 

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(Table 1: Canada’s Inward and Outward FDI stocks (US$ Billions) from the years 1990 to 2017. (Rao, S and Zhang, Q. 2019))

Table 1 : This table shows the change in outward and inward FDI growth of stocks in USA$ in unit of billions during 1900 to 2017 (Rao, S and Zhang, Q. 2019))

 

 

As it is visible from table 1, from 1990 we can see that inward FDI stock was higher by almost $30 billion. However, from the 2000s outward FDI stock has continued to be higher than inward FDI stock which shows that it has become a net exporter.

 From the table we can see that in 1990 outward stock – Inward stock is negative 28M$ and from year 2000 onward it becomes Positive and peaks in the year 2017. This has happned due to ouward FDI becoming more then Inward FDI., confirming that Canada became net exporter from year 2000 onward.

Net exports affect GDP growth as it has a direct effect on the Canadian dollar. For example, if Canada’s net exports outweigh net imports, more money would be leaving the Canadian economy and this in theory would cause the value of the dollar to depreciate. In addition to this, exports require the exchange of one currency to another currency, this would affect the exchange rates within Canada and its trading partners (Dion, R. etal. 2005).

 

The GDP is affected by net exports as this alters the value of the Canadian dollar. If the exports are greater than the imports, the CAD would appreciate in value as money flows into the economy from abroad. Also, imports and exports require an exchange between currencies, this alters the exchange rate of the CAD and the currencies of its trading partners. (Dion, R. etal. 2005).

 

  1.  

 

(Figure 1: shows is stationary trend as there isn’t any obvious or significant drift in the past 30 years)

Figure 1 : Here only stationery trends are plotted, no significant drift is noticed within past 30 years

 

(Figure 2: shows an upwards drift, as Canada became a more net exporting country than a net importing country)

Figure 2 : The exports show upward movement after 1991 as Canada exports increases compared to imports

 

(Figure 3: shows a random walk with a stationary model)

Figure 3 : GDP growth shows random walk superimposed on stationary mean

 

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(Figure 4: shows a stationary model in first differences in FDI overall)

Figure 4: Plot of Diff( LN_FDI) , shows first difference in overall FDI

 

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(Figure 5: shows a random walk model in first differences of exports as values are changing each year and there is no consistent drift. Therefore, shows stationary model)

Figure 5: Plot of Diff( LN_Exports) ,shows a random walk model in first differences of exports as values are changing each year and there is no consistent drift.

 

 

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(Figure 6: shows a stationary model in first differences for GDP growth)

Figure 6 : Plot of Diff( Ln_GDP_Growth) shows first differences for GDP growth super imposed on stationary trend

 

 

  1. In order to calculate the aggregate production function for the dependent variable I am assessing, we would present it in the following equation;

 

GDP= f (FDI, EXP)

 

KEY

           

            GDP is Growth Domestic Product

            FDI is Foreign Direct Investment

            EXP is Exports

           

An estimating equation which represents the economic model is given in the form of logs. The equation can be seen below:

 

LnGDP = b0 + b1LnFDIt + b2LnEXPt + ut

 

KEY

 

Each of b0, b1, and b2 are constant within the equation

ut is the error term

 

The aggregate production function can be determined using the following equation;

 

GDP= f (FDI, EXP)

 

where

           

            GDP represents Growth Domestic Product

            FDI represents Foreign Direct Investment

            EXP represents Exports

           

The economic model in the form of a logarithmic equation is given below:

 

LnGDP = b0 + b1LnFDIt + b2LnEXPt + ut

 

where b0, b1, and b2 are constants and ut is the error term

 

 

  1. Three time series data was examined for the existence of unit root, the augmented Dickie Fuller unit test root will be exploited. The decision behind using this test was the fact that there is an involvement of stochastics which are error terms. Furthermore, the Dickie Fuller test is used when the time series data produced shows signs of stationary. There are three tests which can be used, for two out of my three variables the DF test 1 will be utilised as the time series fluctuates around the average of 0. So, lagged variables of FDI and GDP growth will be used for this test. Whereas, the DF test 2 will be used for the lagged variable of exports as the data fluctuates around a mean which is not 0 but shows an upwards drift. The significance level which will be used is the 5% figure and the sample size being used is 25 as the sample size of the data collected is for 30 different years.

 

After carrying out the Dickie Fuller tests for the three lagged variables, the results showed that they were non-stationary.

 

The augmented Dickie Fuller unit test root is determined using three time series data. The presence of error values requires the use of this test. As the time series data is stationary, the Dickie Fuller test is appropriate to use here. It is possible to use three tests but the DF test is best suited for one of the variables as it averages to 0. For FDI and GDP growth, the lagged time series data is used. It is seen that the lagged exports do not average to 0, so the DF test 2 is ideal in this case. Here, a 5% significance level is used and a sample size of 25 is used that has been collected over 30 years.

 

The results of the Dickie Fuller tests for the lagged variables, is found to be non-stationary.

 

 

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-37.133

33.233

 

-1.117

.274

Year

.019

.017

.201

1.128

.269

LAGFDI

-.537

.171

-.561

-3.139

.004

  1. Dependent variable: DIFF(Ln_FDI,1)

(Table 2: shows the data collected for lagged variable FDI)

 

The results for the ADF unit root test 1 for FDI show that stationarity exists. The test statistics gained is -3.139 which is smaller than the 5% critical value of -1.95. Therefore, we do reject the null hypothesis of a unit root and conclude the variable is stationary.

 

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

3.273

2.483

 

1.318

.199

Year

-.001

.001

-.216

-1.179

.249

LAGEXP

-.087

.067

-.238

-1.302

.204

  1. Dependent Variable: DIFF(Ln_Exports,1)

(Table 3: shows the data collected for lagged variable exports)

 

The results of the ADF unit root test 2 for exports show that the test statistics obtained a value which is -1.302. This variable (exports) had a t statistic which is greater than the 5% significant level and critical value of -3.00. So, we do not reject the null hypothesis of a unit root as the results show non-stationarity.

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-4.677

37.629

 

-.124

.902

Year

.003

.019

.026

.144

.887

LAGGDP

-.849

.291

-.524

-2.913

.008

  1. Dependent Variable: DIFF(Ln_GDP_Growth,1)

(Table 4: shows the data collected for lagged variable GDP growth)

 

The results of the ADF unit root test 1 for GDP growth show the t statistic has a value of -2.913. The value for this variable is smaller than the 5% significance level and critical value of -1.95. Therefore, we reject the null hypothesis of a unit root, and conclude that the variable is stationary as presumed in the graph above (Figure 3).

ADF unit root 1 test results done on GDP growth, has t statists of -2.9, which is lower than 5% significance level value od -1.95. Thus null hypothesis gets rejected. The final conclusion is that the variables show up stationary trend which are shown in Figure 3.

 

  1. The results gained from question 4 proved that FDI and GDP growth showed stationarity. However, as predicted, exports produced non-stationarity. This suggests one of the variables consist of a unit root. In order to see if there is a possibility of combinations of non-stationary variables being stationary together, we carry out the cointegration analysis. However, as two out of the three variables are stationary, then it is possible to avoid spurious regressions (Studenmund, A.H. 2011).

The FDI and GDP growth calculated in Q4 is found to be stationarity. But the prediction of exports is found to be non-stationarity. One of the variables has a unit root. A cointegration analysis is carried out to determine if the combination of non-stationary is stationary. Spurious regressions are avoided as 2 variables of the 3 are found to be stationary. (Studenmund, A.H. 2011).

 

 

First in order to perform a test for co-integration, OLS regression had to be undertaken. The results from the tests are shown below;

First estimated equation:

Co-integration testing requires co-integration, we get results as given in table 5 shown  below

LnGDPGrowtht = b0 + b1LnFDIt + b2LnExpt + ut

 

Variable

Coefficient

T-Statistic

P Value

Constant

3.172

-2.178

0.039

LnFDI

0.173

-0.393

0.697

LnExports

0.915

2.439

0.022

R Squared

0.191

 

 

Adjusted R Squared

0.129

 

 

Durbin Watson

1.923

 

 

(Table 5: shows the results of model 1 OLS regression)

Table 5 : Here OLS regression results are tabulated

Using the data from the table above, the following estimated equation is shown as:

 

LnGDPGrowtht = 3.172 + 0.173LnFDIt + 0.915LnExpt

 

The following graph shows the time series of residuals:

 

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            (Figure 7: shows time series of residuals from 1988-2018)

            Figure 7: Plot of standardised Residulas for the time period 1988 to 2018

To enable us to identify if there was a unit root for the residuals, a further Augmented Dickie Fuller test unit root had to be undertaken. For the Augmented Dickie Fuller test to work for the residuals, the equation has to be rearranged to make the residual the subject. Consequently, the equation is displayed in the following:

 

ut = LnGDPt – b0 + b1LnFDIt + b2LnExpt

 

so, residuals are shown as the subject of the formula.

 

Using a Augmented Dickie Fuller test  allows the identification of unit roots for the residuals. This requires the Augmented Dickie Fuller test to be used on residuals, a further rearrangement of the equation has to be done so that the subject is the residual. The new altered equation is :

 

ut = LnGDPt – b0 + b1LnFDIt + b2LnExpt

 

so, residuals are shown as the subject of the formula.

 

 

Figure 7 shows results of the data fluctuating around a linear trend. Therefore, DF test 3 was carried out. From carrying this test out, the results created show that the residual’s t-statistic 6.177 is smaller with the 5% level and critical value of -3.60. This means that we do not reject the null hypothesis as non-stationarity exists. Results are shown below:

 

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-20.238

26.438

 

-.765

.452

Year

.010

.013

.097

.761

.454

Unstandardized Residual

1.041

.170

.780

6.117

.000

a. Dependent Variable: DIFF(RES_1,1)

(Table 6: shows data collected for residuals)

 

  1. For the first differences in each time series of data, the Dickie Fuller test will again be used to check for stationarity and unit root of the model:

 

Variable

T-Statistic

DIFF_FDI

3.162

DIFF_EXP

0.608

DIFF_GDP

6.259

(Table 7: shows the t-statistics for the first differences of each time series data)

 

Both first differences for FDI and GDP are greater than the 5% significance level and critical value of -1.95 which show they are non-stationary. Also, the first difference for the EXP is greater than the 5% significance and critical value -3.00 which also means non-stationarity is existent. In, conclusion each first difference for each variable show non-stationarity. Each of these variables also show unit root.

 

Variable

Coefficient

T-Statistic

P Value

Constant

0.188

-0.985

0.335

DIFF_FDI

0.232

0.334

0.741

DIFF_Exports

3.844

0.778

0.445

R Squared

0.037

 

 

Adjusted R Squared

-0.047

 

 

Durbin Watson

2.439

 

 

(Table 8: shows the results of OLS in first difference in model 2)

 

The estimating equation can be represented as:

 

DLnGDPGrowtht = b0 + Db1LnFDIt + Db2LnExpt + ut

 

Using the data from the table the equation would be shown as;

 

DLnGDPGrowtht = 0.188 + 0.232DLnFDIt + 3.844DLnExpt

The equations for estimating are given below:

DLnGDPGrowtht = b0 + Db1LnFDIt + Db2LnExpt + ut

 

Utilizing the  data from the table the final equation becomes as shown;

 

DLnGDPGrowtht = 0.188 + 0.232DLnFDIt + 3.844DLnExpt

 

 

 

 

 

  1. From looking at the results from model 1 and model 2 it would be clear to say that model 1 is more accurate and reliable as the r squared value and the adjusted r squared value is higher than the r squared and adjusted r squared value of model 2. However, the Durbin Watson value for model 2 is higher than that of model 1, but not by a lot. Table 4 shows for model 1 that the Durbin Watson value for model 1 is 1.923 whereas if we look at table 7 for model 2, the value is 2.439. As the value is above 1 for both the models, this shows that there is not much positive autocorrelation. The lesser the positive autocorrelation the better.

 

Furthermore, according to the meaning of the r-squared value, this value analyses the variability around the average/mean. The higher the value, the more variability the model accounts for. From looking at each data set, model 1 r squared value is 0.191 whereas for model 2 the value for r squared is 0.037 shows less variability around the mean. This means model 1 is better as it accounts for more variability than model 2. The adjusted r squared value for model 1 is 0.129 and for model 2 the adjusted -0.047 which means that the variability fits better around the mean in model 1 than it does in model 2. In addition, for model 2 has a negative adjusted r squared value which implies the variability around the mean isn’t very significant and it would be pointless using the data received from this model 2 to check the variability.

 

Also, the t-statistic for model 2 both have positive values for the first difference of FDI and exports, which show cointegration as they both have a greater value than the critical value. But, model 1 shows more detailed results as it shows that the log variables of FDI has a smaller value than the critical value of -3.60, this shows non-stationarity and allows us to test for cointegration.

 

In conclusion, model 1 would be the more trustworthy model to use in this case for the country Canada, as it provides results which can be used to carry out further tests to increase the accuracy of its results. Whereas, for model 2 the data is less reliable than that of model 1 so for this reason we avoid model 2. However, results for both models could be inaccurate and therefore to overcome this, we would repeat the tests with data from different countries and conclude whether model 1 is still the most conclusive or if model 2 becomes more consistent to use.

 

An analysis of results obtained from the two models shows that accuracy and reliability is greater with model 1 which follows from the fact that r squared and the adjusted r squared of model 1 are greater than that of model 2. The Durbin Watson value of model 2 is slightly higher than that of model 1. Table 4 and Table 7 shows that the Durbin Watson value of model 1 and model 2 is 1.923 and 2.439 respectively. A value greater than 1 indicates the lack of positive autocorrelation. A smaller positive autocorrelation is better.

 

The r-squared value, is a measure of variability around the mean. If this is higher, so is the variability of the model. The r squared values obtained for model 1 and model 2 are 0.191 and 0.037 respectively. The smaller value indicated a lower variability around the mean. Therefore model 1 is better than model 2. Looking at the adjusted r squared values of model 1 and model 2 at 0.129 and -0.047, the variability fit is better for model 1 compared to model 2. Also, model 2 has a negative adjusted r squared value which implies the variability around the mean isn’t ver

y significant and it would be pointless using the data received from this model 2 to check the variability.

 

Also, the t-statistic for model 2 both have positive values for the first difference of FDI and exports, which show cointegration as they both have a greater value than the critical value. But, model 1 shows more detailed results as it shows that the log variables of FDI has a smaller value than the critical value of -3.60, this shows non-stationarity and allows us to test for cointegration.

 

In conclusion, model 1 would be the more trustworthy model to use in this case for the country Canada, as it provides results which can be used to carry out further tests to increase the accuracy of its results. Whereas, for model 2 the data is less reliable than that of model 1 so for this reason we avoid model 2. However, results for both models could be inaccurate and therefore to overcome this, we would repeat the tests with data from different countries and conclude whether model 1 is still the most conclusive or if model 2 becomes more consistent to use.

 

 

 

References:

 

Larimore, H.E (2008) Foreign Direct Investment. Nova Science Publishers, Incorporated.

 

Li, X and Liu, X (2005) Foreign Direct Investment and Economic Growth: An increasingly Endogenous Relationship. World Development. Vol 33, Iss 3. pp. 393-407.

 

Mo, P.H (2010) Trade Intensity, Net Export and Economic Growth. Review of Development Economics. Vol 14, Iss3. pp. 563-576.

 

Rao, S and Zhang, Q (2019) Macro-Economic Effects of Inward and Outward FDI in Canada. Transnational Corporations Review. Vol 11, Iss 1.

 

Dion, R. et al (2005) Exports, Imports, and the Appreciation of the Canadian Dollar. Bank of Canada Review. Ottawa.

 

Landfield, J.S. et al (2008) Taking the Pulse of the Economy: Measuring GDP. Journal of Economic Perspectives. Vol 22, Iss 2. Pp. 193-216.

 

Garciga, C and Knotek, E.S (2019) Forecasting GDP growth with NIPA Aggregates: In search of core GDP. International Journal of Forecasting. Vol 35, Iss 4.

 

Studenmund, A.H (2011) Using Econometrics: a practical guide. The Pearson Series in Economics. 6th edition

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