The Solow Growth model

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Empirical analysis

 Data collection

The data is collected from World Bank statistics and statistics from the International Tele-communications Union (ITU), where the latter is an agency in the United Nations which surveys all forms of telecommunication in the world. Based on the availability of data re-garding specifically broadband, the data submitted for a regression will most likely be from 2001 until 2009 as prior to 2001 there were very few countries with broadband at all which will lead to a biased regression. The data for ICT will be collected from the ITU and data for economic growth, education and other data that is not directly ICT related is collected from the World Bank.

Methodology

As a large numbers of the countries in the world do not have access to broadband technol-ogy, it would be a technical fallacy to include these countries into the model as the risk for bias in the regression from missing values would affect it to a large extent. Therefore, any country with lack of data on broadband spread for more than 6 years is excluded from the data set. In addition to this reduction of the dataset also the variables for human capital have been counted per country as to minimize the effect of missing values in the regres-sions. The dataset is thus unbalanced, since some countries lack input for other variables than fixed broadband subscription for the full period of time as shown in the descriptive statistics and in the appendix regarding missing values

Defining variables and motivation for usage.

GDP per capita – the annual GDP in a country, with aggregates based on year of 2000’s value divided by the population at the time.
Education – education is counted as percentage of gdp per capita spent per student in three sectors of the educational program, primary, secondary and tertiary. Where primary is elementary school, secondary high school and tertiary university or college. It also includes the expenditure to both public and private education. As this is given in percentages of GDP per capita initially, it was necessary to multiply it by the GDP per capita values giving a monetary input to education. In the empirical study the different types of education will be stated as Edu1, Edu2 and Edu3 to point out the different types of education. The moti-vation for using the three stages of education is based on the argument presented at the end of page 8 regarding that higher education creates more refined skillsets and should thus affect the economy slightly differently.
Capital – annual addition of capital in the economy in terms of additions to tangible assets as well as inventories in the economy. The capital formation is based on US dollars fixed at year 2000’s value. In order to retrieve a good measurement against the other variables this variable has been divided by the population of the country at t to render capital per capita.
Spread of Broadband – counted as fixed broadband-subscriptions per 100 people. What should be noted is that it is subscriptions and not total sum of users, which changes the de-sired interpretation of the result compared to a “real individual spread”. But as the real spread is impossible to discover and only possible to estimate by an amount of hidden numbers, the subscription spread is the most easily attainable at the moment and to some extent the most realistic data on spread. Furthermore, it should be noted that this variable may have population overlaps since both individuals and institutions in society have sub-scriptions to broadband, by institutions it is meant companies, schools and government agencies may have broadband in many countries. Thus, some individuals may be subject to taking a share in several broadband subscriptions as they may receive it both at home and at work or similar occupation. This fact creates a standard deviation around the true mean of spread, whereas in some countries it could mean that the a person who has access at both home and at work due to education and wealth whilst being an exception to society regarding this status, can in fact create a bias in the data. The term fixed broadband refers to the type of broadband measured, that it is spread by wires in contrast to mobile broad-band which is spread by antennas.

Descriptive statistics

By investigating the descriptive statistics given in the appendix, one may see several differ-ences and noteworthy facts regarding the statistics. To comment the distribution of the variables one may see that there is excess kurtosis in several of the variables and the skew-ness of the distribution shows that the distribution within the variables tend to not be in the shape of a normal distribution. In all of the variables presented there is skewness and kurtosis, specifically almost all the variables as one may see from figure 12 to 17 in the ap-pendix are leptokurtic and are positively skewed when comparing them to the normal curve in the histograms. This may affect the results as the variables used tend to not follow the normal curve, therefore test-statistics using normality assumptions could be affected. As a result of this the statistics used may not be seen as reliable as if the variables had followed a normal distribution. Also, a further notice to compliment the skewness and kurtosis, one may see that the medians and means for the variables differ from each other where the median is lower than the mean for all variables.
As if one would look at the count of the missing values in table 8 in the appendix, one may see that for the case of GDP per capita and Fixed broadband, the count of valid values is high enough to doubtly affect the regression statistics. While on the other hand, the Capital variable, Edu1 and Edu2 do have higher grade of missing values, where as count of ,missing values are at 31, 30 and 32 respectively and in the case of Edu3 the count of miss-ing values is at 64 out of totally 322 observations. This accounts for that there is an imbal-ance in the dataset.

Model specification

Based on the theory presented, the regression would have components from each part of the theory. The overall construction is based on the classical Solow growth theory, using output and capital as stated in Solow’ s equation, but the labor is here changed to the hu-man capital model and the broadband is included similarily as the technological difference. From the human capital model, investment into education per capita is added at three steps, primary, secondary and tertiary education.
The theory has thus given the basic production function with inclusion of broadband Where subscript i and t denotes country and year in the equation.
By taking the logarithm of each variable the production function becomes the growth equation of GDP, which gives:
One of the implications of using panel data is that the pooled Ordinary Least Squares (OLS) model may not be consistent or it may be biased as the heterogeneity may likely be present within the dataset. Therefore were all three models run firstly with pooled OLS in order to run a panel diagnostics test to confirm an appropriate coefficient estimation model choosing between pooled OLS, the fixed effects model [the fixed effects in this case(the case of the test) is only pertinent to the one way groups fixed effects, not the two way group and time effects] and the random effects model. The panel diagnostics consist of three tests; test for differing group intercepts for distinguishing between OLS and fixed ef-fects, Breusch -Pagan test for distinguishing between OLS and random effects and at last a Hausman test for distinguishing between random effects and fixed effects. Strictly through all the three models the panel diagnostics showed a favour of the fixed effects model since, the test for differing group intercepts gave a very low p-value in all models pointing to use fixed effects, the Breusch-Pagan test had as well very low p-values directing to use random effects. At last the Hausman test distinguished between using random effects or fixed, pointing to that fixed effects were to be used as the p-value was very low counting against the null hypothesis that the random effects would be correct. These tests are included in the secondary appendix labelled panel diagnostics for each regression. Based on the tests made the estimation has been done with fixed effects. Moreover, to control for time im-pacts between the years, time dummy varibables have been used, therefore modifying the fixed effects model to a two way fixed effects model. The significance of this has also been tested for as the joint significance test for the time dummy variables show that the null hy-pothesis of all dummy variables are equal to 0 is rejected.
Thus the change to the original model is as one adds α_it to the original model which is the capturing of omitted effects correcting, “the assumption that the omitted effects in the model are correlated with the included variables” (Greene, 2008, p193) . What would hap-pen if this was not done is that the error term would correlate with the variables, resulting in that the error term would not be indepent and identically distributed (IID) as the variance would else consist of where u_i is the individual unobserved effects and v_it is the remaining disturbance
What should be noted is that the fixed effects do not fix any specific variable in anyway, it does only correct for differences between groups by capturing it in the alpha parameter, which is estimated in each regression. In the context of this thesis, groups are defined as countries

Results from investigating broadband effects.

Regression 1 uses primary education labelled Edu1
In the first regression an one percent increase in; capital would increase growth in GDP by 0.185%, broadband would increase growth in GDP by 0.017%, primary education would increase growth in GDP by 0.141%. Regarding significance, all of the explanatory variables are significant. The fit of the variables to the model show that in explaining variance, it ex-plains 99% of the variance in growth in GDP.
In similarity to regression 1, the capital and broadband variable are significant, while the secondary education variable is not. If one would make an increase by 1%; in capital, growth in GDP would increase by 0.213%, in broadband growth in GDP would increase by 0.018% and in secondary education it would have been an increase by 0.087%. Regard-ing the models power to explain variance it is at 99% , similarily to regression 1.
As in regression 2, only capital and broadband were significant while tertiary education was insignificant. The effect of an 1% increase in; capital gives a 0.256 % increase in growth of GDP, broadband gives a 0.020% increase in growth of GDP, tertiary education would have increased growth in GDP by 0.060%. In the third regression the explanatory power of the model is at 99% explanation of variance in growth of GDP.
Regarding the test statistics run in each regression for each of the fixed effects, group and time, they showed that fixing the effects did have a significance in the regressions. The test for differing alphas rejected the null hypothesis in each regression regarding if the alphas were significantly different from each other or not. Also the joint significance test for the time dummies proofed that at least one was significantly different from 0 which can also be seen in the coefficient statistics. Thus the two-way fixed effects model could be seen as a true model of estimation and an pooled OLS would have been inconsistent and along with a one way fixed effects it would also suffer from omission bias (Baltagi, 2008 , p 36).
By inspecting the qq-plots of the residuals in the appendix one may see some similar fea-tures of the residuals in the regression that over all the residuals fit closely to the 45-degree line except for in the first percentiles of the plots where the residuals seem to be fitting be-low what is to be expected from the residuals. There are also streaks of a likely secondary function closely to the median of the qq-plots, though the streaks are fitting closely to the 45-degree line. Therefore the residuals seem to be well fitted overall in all three regressions. Though, as a limitation to the examination of the residuals, no histograms have been avail-able after using fixed effects as a model of estimation, which could have been more usefull than qq-plots in the regressionwise examination of the residuals

1 Introduction 
1.1 Purpose and research question
1.2 Literature review
2 Theory
2.1 The Solow Growth model
2.2 Representation of technology
2.3 Importance of education in the use of technology
2.4 Spread of broadband
2.5 Summation of theory
3 Empirical analysis 
3.1 Data collection
3.2 Methodology
3.3 Defining variables and motivation for usage.
3.4 Descriptive statistics
3.5 Model specification
3.6 Results from investigating broadband effects
3.7 Limitations in the results and in dataset
4 Analysis 
5 Conclusion 
6 Appendix
6.1 Graphs
6.2 Statistical tables
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