Question A:
This report will choose the USA economic statistical data as the sample. It will be based on a classic economic growth model-Augmented Solo Growth Model and develop new models to analyze the impact of labor, capital and FDI on the GDP growth in the USA.
Model:
When studying the relation between inputs and economy growth, the Augmented solo model is a common method. This report will use the augmented solo model as a basic model and take labor and capital as core variables. FDI will be put into an expended function as an independent input factor. Finally I will use estimations to examine the relation between FDI and GDP growth.
The production function of Augmented Solo Model is below:
Y =AF(K, L )t= (1……n)
When studying the relation between inputs and economy growth, the Augmented solo model is a common method. This report will use the augmented solo model as a basic model and take labor and capital as core variables. FDI will be put into an expended function as an independent input factor. Finally I will use estimations to examine the relation between FDI and GDP growth.
The production function of Augmented Solo Model is below:
Y =AF(K, L )t= (1……n)
Y = AKaLß 0 < a < 1, ß=1- a
Where: A is Technology,Y is output; L is human capital; K is physical capital;t is time series; ß,a, X is coefficient.(Verbeek, M. 2008)?
The two core variables are: capital selected as Gross Fixed Capital Formation, labor as Labor Force Total. The other non-variable is selected FDI. Therefore, the economic model is expanded as below:
The two core variables are: capital selected as Gross Fixed Capital Formation, labor as Labor Force Total. The other non-variable is selected FDI. Therefore, the economic model is expanded as below:
Y =AF(K, L,F )t= (1……n)
Y = AKaLß F? 1=ß+a+?
Y = AKaLß F? 1=ß+a+?
Using log function on both sides, we can get the linear function for this statistical model.
LnY = LnA+aLnK+ßLnL+?LnF
= X+aLnK+ßLnL+?LnF
LnY = LnA+aLnK+ßLnL+?LnF
= X+aLnK+ßLnL+?LnF
Where: (X = LnA),Y is GDP; K is gross fixed capital formation; L is Labor Force Total; F is FDI; t is time series; ß,a,?, X is coefficient respectively.Click Here To Get More On This Paper!!!!
Question B:
All the data in this report comes from the World Bank World Development Indicators. Based on time series, the data from 1990 to 2010 are chosen, which includes GDP(billion US$), gross fixed capital formation(billion US$), labor force total(million), FDI(billion US$)
All the data in this report comes from the World Bank World Development Indicators. Based on time series, the data from 1990 to 2010 are chosen, which includes GDP(billion US$), gross fixed capital formation(billion US$), labor force total(million), FDI(billion US$)
Figure 1: USA Economic Statistics Data from 1991 to 2010
(Resource: World Bank World Development Indicators,2013)
(Resource: World Bank World Development Indicators,2013)
The analysis of the data central tendency: we can calculate each variable of the mean value and median. Mean value can reflect the average level. The median can reflect the intermediate position of one level from a set of data.
The analysis of dispersion: The degree of dispersion is usually reflected by variance and standard deviation. For standard deviation, the higher it is, the higher the dispersion of data is
The distribution of data: If the sample’s skewness is close to 0 and its kurtosis is close to 3, this sample can be seen as normal distributed.Click Here To Get More On This Paper!!!!
The first chart shows the GDP data in the USA between 1991 and 2010. We can see a tremendous increase in GDP, from $5930 billion in 1991, to $14419 billion in 2010. The total labor force also increases from 1288 million in 1991, to 1579 million in 2010. Gross capital formation and FDI have both increase from 3-digits(966 billion, 231 billion respectively) to 4-digits(2140 billion, 2709 billion respectively) in these two decades.
The mean values of log of GDP, labor force, gross fixed capital formation and FDI are 9.5793, 7.4815, 7.2826 and 7.2819 respectively. It represents the average level of a set of data. The Standard-deviations are: GDP(LG) is 0.28965, labor force(LC): 7.4815, gross fixed capital formation(LL)0.066527 and FDI(LF) is 0.83087. The std.dev measures the spread of a set of data.
The kurtosis: LG(GDP) is -1.1543, LC(Labor force) is -0.80717, LL(Gross fixed capital formation is -1.0823 and LF(FDI) is -0.64429
The skewness: LG(GDP) is -0.20561, LC(Labor force) is -0.53227, LL(gross fixed capital formation) is -0.38350 and LF(FDI) is -0.81276
Note: If the sample’s skewness is closed to 0 and the kurtosis is closed to 3, it can judge the overall distribution close to normal distribution. So the data do not fit the normal distribution (Breedon et al, 2012).Click Here To Get More On This Paper!!!!
The skewness: LG(GDP) is -0.20561, LC(Labor force) is -0.53227, LL(gross fixed capital formation) is -0.38350 and LF(FDI) is -0.81276
Note: If the sample’s skewness is closed to 0 and the kurtosis is closed to 3, it can judge the overall distribution close to normal distribution. So the data do not fit the normal distribution (Breedon et al, 2012).Click Here To Get More On This Paper!!!!
Question C:
The chart above illustrates the trends of each variables and total GDP growth over the 20 years. Except the period 1993-1995(which shows a rapid increase then sharp decrease), the growth is steady and after 2008, the growth rate is decreasing as the line is approaching to flat.
For the variables: the total labor force has not increased a lot compared to other variables as the line is more flat. The gross capital formation has increased until 2006 then decreased gradually after 2006 until 2008. From 2008 to 2010, it shows an increase back. The number of FDI has rised in a “stair-case” shape. There are two sharp increase period which are 1998-2000 and 2006-2008.
In this model, LG represents GDP, LL represents labor force total(million), FDI(billion US$). LC is gross fixed capital formation and LF is FDI. The results indicates that significant coefficient exists, as the p-value is close to 0. R square is 0.98, which means small errors in this model.
LG’s coefficient means that if other conditions remain unchanged, Gross fixed capital formation increased 1%, GDP rose 0.06%.
These coefficients indicate that all the independent variables have a positive impact on GDP. the 0. 6 +5.8 +0.15> 1, so that a = 0.406, ß = 2.005 and ? = 0.291. This explains that it is a scale increasing function and these data can effectively influence growth of GDP.Click Here To Get More On This Paper!!!!
LG’s coefficient means that if other conditions remain unchanged, Gross fixed capital formation increased 1%, GDP rose 0.06%.
These coefficients indicate that all the independent variables have a positive impact on GDP. the 0. 6 +5.8 +0.15> 1, so that a = 0.406, ß = 2.005 and ? = 0.291. This explains that it is a scale increasing function and these data can effectively influence growth of GDP.Click Here To Get More On This Paper!!!!
Question D:
When testing the OLS, the regression is often affected by Multicollinearity. Multicollinearity refers to those highly correlated variables existing in the linear regression, which leads to the inaccuracy in the model or causes difficulties in the estimation process (Gujarati and Porter, 2009). Gujarati and Porter explain that the multicollinearity often happens to some degree, and the completely Multicollinearity situation is rare. The multicollinearity often happens in three ways: all variables have a common trend in growth or decline, the introduction of lagged variables, sample data restrictions. When it comes to the statistical calculations, when OLS encountered Multicollinearity, although the R-squared OLS high (close to 0.9), but its T-value is less than 2. In other words, T-value is not statistically significant. Therefore, when the OLS encounter Multicollinearity, OLS estimators are still linear and so good statistical properties. However, every variable’s contribution to R-square can not be explained (Gujarati and Porter, 2009).
In the model set for this paper, we can find that the regression of labor, the regression of capital, the regression of FDI, and the regression of GDP have similar growth trend. In order to be more accurate in analyzing whether the OLS is encourtered Multicollinearity, we can use Bibvariate Correlation between independent variables method, Variance Inflating Factor (VIF) and Tolerance (TOL) method to test.
1.Bibvariate Correlation between independent variables:Click Here To Get More On This Paper!!!!
In the model set for this paper, we can find that the regression of labor, the regression of capital, the regression of FDI, and the regression of GDP have similar growth trend. In order to be more accurate in analyzing whether the OLS is encourtered Multicollinearity, we can use Bibvariate Correlation between independent variables method, Variance Inflating Factor (VIF) and Tolerance (TOL) method to test.
1.Bibvariate Correlation between independent variables:Click Here To Get More On This Paper!!!!
If each individual R-square between variables are close to 1, it means this OLS has Multicollinearity issue.
Through the above chart, the R-square of LC and LF equals 0.957. The R-square of LL and LC equals 0.950. The R-square of LL and LF is 0.977. Since all the r-square existing within each pair of independent variables, significant statistical relationship exists between each of the independent variables. Therefore, multicollinearity issue exists in this OLS.
2.Variance Inflating Factor (VIF) and Tolerance (TOL)
if the VIF> 10 and the TOL is close to zero, the multicollinearity problem exists in the OLS. In the model within the context, we found that when the r-square = 0.981,
VIF = 1 / (1-R2) = 18 TOL = (1-R2) = 0.18
Therefore, multicollinearity exists in this OLS.
VIF = 1 / (1-R2) = 18 TOL = (1-R2) = 0.18
Therefore, multicollinearity exists in this OLS.
Heteroscedasticity
This article will use Glejser test method to test the heteroscedasticity which existing in the relationship between LF (FDI) and LG (LGDP).
First, we create a new model based on the original model:
LnGDP =a+ßLnFID+U
First, we create a new model based on the original model:
LnGDP =a+ßLnFID+U
where:U is proxy and residual obtained from the OLS regression?
Secondly, we establish a linear relationship about the absolute of value U on variable FDI.
Finally, we use statistical software to test the linear absolute of value U on FDI, linear absolute of value U on the reciprocal of FDI (Finv), linear absolute of value U on the square root of the FDI (Fsqt).
We need to use t-value < 2, while p-value is relatively high, to verify the existence of heteroscedasticity in OLS. Throgh the above diagram, we can see that FINV’s t-value equals 0.9 and p-value is 0.3. FQST’s t-value is 0 .54007 but p-value is 0.596. LF’s t- value is 0. 07 but p-value is 0.9. Their t-values are all less than 2, but the p-values are all relatively high. By analysing the above data, we can determine that heteroscedasticity exists in this OLS linear model.
Test spurious regression
Test spurious regression
In time series regression, OLS regression often suffers from the spurious regression phenomena (Gujarati and Porter, 2009). Spurious regression phenomena lead to a false relationship between LGDP and the variables. Gujarati, D.N. and D.C. Porter (2009)) believe that if the r-squared value is far greater than the DW-statistic, the OLS linear complies with rule of thumb, which means the model exists spurious regression. Therefore, we need to compare each of the variables’ impact on GDP. We will establish OLS linear model of LGDP on LL, LGDP on LC and LGDP on LF separately.
From the above chart we can see that the r-square value of the first set of data is 0.96 and the DW value is 0.52. R-square is greater than DW value. As for the second set of data, r-square value is 0.97 and the DW value is 1.38. R-square is larger than DW value. In The third group of data, r-square value is 0.99 and the DW value is 0.6. R-square is larger than DW value. For all these three sets of data, r-square value is much larger than the DW value. Therefore, spurious regression exists in this OLS linear models.
Question E:
When dealing with the problems about time series, we need to verify the series stationary of a certain variable. In this article, we will use the Dickey-Fuller unit root test to verify if stationary exists in this OLS linear model.
There are 21 time periods in this sample. Therefore, the sample size we selected for the test is 25 and the critical value we choose is 5%
Hypothesis:
? Null hypothesis: H0: d = 0; X is a non-stationary
Alternative hypothesis: H1: d<0, X is stationary
If the absolute T value less than critical value of Dickey-Fuller (t), null hypothesis is rejected(Gujarati and Porter, 2009).
Question E:
When dealing with the problems about time series, we need to verify the series stationary of a certain variable. In this article, we will use the Dickey-Fuller unit root test to verify if stationary exists in this OLS linear model.
There are 21 time periods in this sample. Therefore, the sample size we selected for the test is 25 and the critical value we choose is 5%
Hypothesis:
? Null hypothesis: H0: d = 0; X is a non-stationary
Alternative hypothesis: H1: d<0, X is stationary
If the absolute T value less than critical value of Dickey-Fuller (t), null hypothesis is rejected(Gujarati and Porter, 2009).
The Analysis of LG
Through the figure above, we can see that the t-value is 3.32. The augmented Dickey-Fulle’s critical value is -1.95. By comparison, the critical value -1.95 is less than 3.32. Therefore, stationary exists in this OLS linear model.
Through the figure above, we can see that the t-value is -1.294. The augmented Dickey-Fulle’s critical value is -3.0. By comparison, the critical value -3.0 is less than -1/294. Therefore, stationary does not exist in this OLS linear model.
Through the figure above, we can see that the t-value is -3.52. The augmented Dickey-Fulle’s critical value is -3.6. By comparison, the critical value -3.6 is less than -3.52. Therefore, stationary does not exist in this OLS linear model.
Through the above three results we can conclude that the LG-OLS is non-stationary linear
The analysis of LL
Through the figure above, we can see that the t-value is 0.22. The augmented Dickey-Fulle’s critical value
is -3.6. By comparison, the critical value -3.6 is less than 0.22. Therefore, stationary does not exist in this OLS linear model.
is -3.6. By comparison, the critical value -3.6 is less than 0.22. Therefore, stationary does not exist in this OLS linear model.
Through the figure above, we can see that the t-value is -3.98. The augmented Dickey-Fulle’s critical value is -3.0. By comparison, the critical value -3.0 is larger than -3.98. Therefore, stationary exists in this OLS linear model.
Through the figure above, we can see that the t-value is -3.52. The augmented Dickey-Fulle’s critical value is -1.59. By comparison, the critical value -1.59 is larger than -3.52. Therefore, stationary exists in this OLS linear model.
Through the above three results we can conclude that the LG-OLS is stationary linear
The analysis of LC:
The analysis of LC:
Through the figure above, we can see that the t-value is 2.0. The augmented Dickey-Fulle’s critical value is -1.59. By comparison, the critical value -1.59 is less than 2. Therefore, stationary exists in this OLS linear model.
Through the figure above, we can see that the t-value is -2.33. The augmented Dickey-Fulle’s critical value is -3.0. By comparison, the critical value -3.0 is less than -2.33. Therefore, stationary exists in this OLS linear model.
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Through the figure above, we can see that the t-value is -0.55. The augmented Dickey-Fulle’s critical value is -3.6. By comparison, the critical value -0.55 is larger than -3.6. Therefore, stationary exists in this OLS linear model.
Therefore, the OLS is stationary.
Therefore, the OLS is stationary.
The analysis of LF
Through the figure above, we can see that the t-value is -1.77. The augmented Dickey-Fulle’s critical value is -3.6. By comparison, the critical value -3.6 is less than -1.77. Therefore, stationary exists in this OLS linear model.
Through the figure above, we can see that the t-value is -3.53. The augmented Dickey-Fulle’s critical value is -1.59. By comparison, the critical value -1.59 is larger than -3.53. Therefore, stationary does not exist in this OLS linear model.Click Here To Get More On This Paper!!!!
Through the figure above, we can see that the t-value is 3. The augmented Dickey-Fulle’s critical value is -1.59. By comparison, the critical value -1.59 is less than 3. Therefore, stationary does not exist in this OLS linear model.
Through the above three results we can conclude that the LF-OLS is non-stationary linear
Question F:
By testing the model stationary, we find that LG-OLS is non-stationary linear, LF-OLS is non-stationary linear. Therefore, we can use the Augmented Engle-Granger to fix these two non-stationary linear. We have established Cointergration Regression about LG on LF.
By testing the model stationary, we find that LG-OLS is non-stationary linear, LF-OLS is non-stationary linear. Therefore, we can use the Augmented Engle-Granger to fix these two non-stationary linear. We have established Cointergration Regression about LG on LF.
According to the test, the result showed that DRESTT-value’s T is -4., and its absolute–value is larger. The absolute–value of 5% of EG asymptotic critical value -3.34, so it is stationary.
Question G
References:
D N.Guarati and D C.Porter (2009) .Basic Econometrics.Fifthedition
r />Walter N and Patrick V. (1996 ) .A Further Augmentation of the Solow Model and the Empirics of Economic Growth for OECDCountries. The Quarterly Journal of Economics, Vol. 111, No. 3 (Aug., 1996), pp. 943-953
World Bank World DevelopmentIndicators(2013) World bank 2013
Verbeek, M. (2008): A Guide to Modern Econometrics, 3rd. edition. Wiley.
D N.Guarati and D C.Porter (2009) .Basic Econometrics.Fifthedition
r />Walter N and Patrick V. (1996 ) .A Further Augmentation of the Solow Model and the Empirics of Economic Growth for OECDCountries. The Quarterly Journal of Economics, Vol. 111, No. 3 (Aug., 1996), pp. 943-953
World Bank World DevelopmentIndicators(2013) World bank 2013
Verbeek, M. (2008): A Guide to Modern Econometrics, 3rd. edition. Wiley.
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