March 2014
Why some countries are
poor and others rich
An extension of the Solow Growth Model
Paulien Janse
10003570
Abstract
This paper examines whether the predictions made by Solow still hold two decades later and whether the model improves by including more relevant variables. The additional variables are government consumption, depreciation, inflation, initial human capital, crime, corruption and tax evasion. Cross-sectional data is used from 1996 to 2010. This paper finds that there is an intermediate conditional convergence for the OECD and the OECD+ sample groups. Also, there is a strong unconditional convergence for the OECD and the OECD+ sample groups, whereas the effect is less strong for the N and I sample groups. Overall, the model developed in this paper is an improvement on the existing models on economic growth.
Index
1. Introduction ……….. 3
2. Literature Review ……….. 4
2.1 Solow ……… 4
2.2 Barro I ……….. 4
2.3 Mankiw, Romer and Weil ……….. 5
2.4 Durlauf and Johnson ………. 5
2.5 Mo ……….. 5
2.6 Detotto and Otranto ………. 6
2.7 Ho and Yang ………. 7
2.8 Barro II ………. 8
2.9 Motley ………. 8
2.10 Conclusion ………. 10
3. Theory - the Solow Growth model and the Augmented Solow Growth Model ……… 11
3.1 The Solow Model ………. 11
3.2 The Augmented Solow Growth Model ………. 13
3.2.1 The Regression Equation ……… 13
3.2.2 Speed of Convergence ………. 14
3.2.3 Parameter Values ……… 15
3.3 Conclusion ……… 16
4. Data and Methodology ………... 17
4.1 Methodology ……….. 17
4.2.1 Data ……….. 17
4.2.2 Sample ……… 19
5. Empirical Results ……… 22
5.1 Results and Data Analysis ……….. 22
5.1.1 Results and Data Analysis on Unconditional Convergence ………. 23
5.1.2 Results and Data Analysis on Conditional Convergence ………..……… 25
5.2 Comparisons ………..……… 26
5.2.1 Comparison of Conditional and Unconditional Convergence ……….. 26
5.2.2 Comparison of Unconditional Convergence with Mankiw, Romer and Weil ……… 27
5.2.3 Comparison of Conditional Convergence with Mankiw, Romer and Weil ……….. 27
5.4 Conclusion ……… 28
6. Conclusion ……….. 29
6.1 Literature Review ……….… 29
6.2 The Augmented Solow Model ……… 30
6.3 Results ………. 30
6.4 Conclusion ……… 31
7. Further Research ……… 32
7. Bibliography ……….. 33
1. Introduction
Economic growth is something that many people care about, economists, politicians and Joe the Plumber. Economic growth determines households’ purchasing power and it reduces unemployment. It enables an increase in social spending without raising taxes, it promotes innovation and research, it shifts people to higher indifference curves and promotes an increase in welfare.
In 1956 the economist Robert Solow built a model predicting long-run economic growth. Many study books and papers use this model to explain theorems, test the model on particular sets of data and do research on its extensions. For example, Robert Barro (1991) tested the existence of relations between the growth rate of real per capita GDP and initial human capital, the initial level of real per capita GDP, the share of government consumption in GDP, the share of public investment and political stability. Another example is that Steven Durlauf and Paul Johnson examined multiple regimes and cross-country growth behaviour in 1991 and found that economic development varies with the marginal product of capital. The paper questions inferences made by the convergence hypothesis, the latter comes down to the question whether poorer countries will catch up to the richer countries in terms of real GDP per capita over time. Another very interesting paper on this topic is written by Mankiw, Romer and Weil in 1992. In this paper they test the Solow model, using variables such as labour force growth, the depreciation rate, the savings rate, and human capital accumulation to find that differences in savings, education and population growth explain cross-country differences in income per capita. It would be interesting to analyze whether economic variables such as tax evasion and possibly inflation, or more socioeconomic variables such as corruption and crime have an influence on economic growth.
However, all these papers analyzed data on the period from 1960 to 1985. Therefore, the aim of this paper is to see if all the results concluded previously still hold. This leads to this paper’s research question: ‘Does Solow’s prediction still hold two decades after the researches by Barro (1991), Durlauf
and Johnson (1991) and Mankiw, Romer and Weil (1992) were conducted and if additional relevant variables are included in the analysis?’ The expectation of this paper is that the research done in this
paper will have a higher explanatory power. Hence, Solow’s prediction still holds and the additional relevant variables help explain more of the variation in economic growth.
2. Literature Review
The base of this research paper consists of the papers A Contribution to the Theory of Economic Growth written by Solow (Solow, 1956) and A Contribution to the Empirics of Economic Growth written by Mankiw, Romer and Weil (Mankiw, Romer & Weil, 1992). Solow provides a theoretical model about long-run economic growth and the convergence theory. Section 3 discusses the model in detail. In the nineties, many researchers examined his model by adding more extensions, such as Durlauf and Johnson (1991), Barro (1991) and Mankiw, Romer and Weil (1992).
A Contribution to the Theory of Economic Growth describes a model about long-run economic growth
which is better known as the Solow Growth Model. The model is included in many study books on macroeconomics, for example Macroeconomics by Mankiw (2006). The Solow Growth Model is a theoretical framework. Durlauf and Johnson (1995), Barro (1991) and Mankiw, Romer and Weil (1992) examined whether the model held by testing it on empirics. According to the Solow model, countries reach different steady states. The model predicts conditional convergence, that is, the income per capita of a country converges to the steady stage holding constant other determinants of the steady state.
2.1 Solow
Solow finds that a country’s steady state depends on its levels of the saving rate, the investment rate, the depreciation rate, the population growth rate, capital and labour. The full design and characteristics of the model are discussed in section 3.
2.2 Barro I
In 1991, Barro tested the existence of relations between the growth rate of real per capita GDP and initial human capital, the initial level of real per capita GDP, the share of government consumption in GDP, the share of public investment and political stability. According to Barro (1991), poor countries have a tendency to converge to the level of income of rich countries if, and only if, they have a high level of human capital per person relative to their level of GDP per capita (Barro 1991 p. 437). He also argues that “government consumption introduces distortions, such as high tax rates, but does not provide an offsetting stimulus to investment and growth” (Barro 1991 p. 437). Furthermore he states that distortions in price, such as inflation, have a negative relationship with real per capita GDP growth.
2.3 Mankiw, Romer and Weil
One year after, in 1992, Mankiw, Romer and Weil came up with the idea to augment the Solow model with human capital. They divided countries into three subgroups and tested for convergence between the three groups. They found that in the augmented Solow model, differences in education, savings and population growth rate explain a large part of international variation in cross-country income per capita levels (Mankiw Romer and Weil 1992 p. 433). The augmented model is in detail discussed in section 3.
2.4 Durlauf and Johnson
Then, in 1995, Durlauf and Johnson examined multiple regimes and cross-country growth behaviour. In their analysis they followed Mankiw, Romer and Weil (1992). They found that not all countries have linear growth models. Furthermore, they found that for countries that do have linear growth models, some have very different production functions. This suggests that the output-labour ratios of more developed countries are actually higher than suggested by their capital-labour ratios (Durlauf and Johnson 1995 p. 366). To reach the latter conclusion, Durlauf and Johnson divided countries into four subsamples based on their output rate and literacy rate, both of which were either low or high. The outcome was that for each separate group there is an improved overall fit of growth variation compared to the analysis of Mankiw, Romer and Weil (Mankiw Romer and Weil 1992 p. 373-74). Hence, is it possible that different economies follow different linear models “when grouped according to initial conditions” (Durlauf and Johnson 1995 p.366). As a result, growth rate behaviour can go in harmony with multiple steady-states (Durlauf and Johnson 1995 p. 378).
More recently, some research was done to examine what other variables could influence economic growth. In 2001, Pak Hung Mo examined whether corruption is correlated to economic growth. Also, in 2002, Detotto and Otranto analyzed whether crime is a determinant of economic growth. A more detailed description of the two researches follows here.
2.5 Mo
According to Mo (2001), at first sight corruption has a two-sided effect. On the one hand, it is desirable, because “it works as a piece-rate pay for bureaucrats, which induces a more efficient provision of government services, and it provides a leeway for entrepreneurs to bypass inefficient regulations” (Mo 2001 p. 66). In this sense, corruption increases efficiency. On the other hand, corruption is harming for the economy, because it decreases the amount of innovation. The main reason is that “innovators need government-supplied goods more than established producers do. Demand for these goods is high and inelastic; hence, they become primary targets of corruption” (Mo 2001 p. 66). But there are more reasons. Settled producers are not as much credit-constrained
as innovators; hence for the latter it is much harder to pay back bribes. In turn, investment will be reduced, with a smaller stock of goods in the long run as a consequence. Moreover, corruption is the creator is inequality of opportunities, partly due to the slowdown of production, and leads to “income and wealth inequality, and frustration and sociopolitical instability”. When corruption is present, there is a large tendency for people to look for rent-seeking activities and neglect investments that would be much more productive. Empirically, some studies found that the level of corruption is inhibiting development (Mo 2001 p. 67). Mauro (1995) has found that corruption negatively affects investment. In turn, a decrease in investment means a decrease in economic growth. Mo (2001) investigates in what ways corruption influences economic growth; through investment, political stability and human capital.
Additionally, Mo finds that income inequality and sociopolitical instability have a positive correlation. In case of a large income inequality, the most disadvantaged group will find it profitable to practice illegal or violent activities in order to get “material benefits” (Mo 2001 p. 74). The effect is a decrease in confidence about the guarding of property rights, hence, productivity and investment will decrease. As a result, income inequality is negatively correlated with economic growth. This conclusion is also found by Perotti (1994), Alesina and Perotti (1996) and Mo (2000). An increase in income inequality creates “psychological frustration to the underprivileged but also reduces productivity growth, investment, and job opportunities (Murphy, Shleifer and Vishny, 1993)” (Mo 2001 p. 73). Taken together, sociopolitical instability arises. The conclusion is that an increase in the corruption index by one unit cuts economic growth by 0.545 percentage points (Mo 2001 p. 76). The main channel through which this effect occurs is political instability, which makes up 53 per cent of the overall effect. Other channels are private investment and human capital.
2.6 Detotto and Otranto
Furthermore, Detotto and Otranto (2010) found that crime negatively affects economic growth. There are multiple means by which the effect takes place, namely discouragement of investment, a reduction in the competitiveness of firms, and the reallocation of resources which generates uncertainty and inefficiency (Detotto and Otranto 2010 p. 340). The overall relation between crime and economic growth is as follows, a one per cent increase in the crime rate contracts real economic growth by 0.0004% per month, or 0.00481% per year1 (Detotto and Otranto 2010 p. 340). However, it needs to be mentioned that this research was a case study of Italy only. The authors do not mention anything about external validity, in other words they do not mention whether their findings can be generalized to other countries.
1
Besides analyzing crime and corruption as determinants of (negative) economic growth, this paper also wants to examine the effect of tax evasion on the real GDP growth. As will be mentioned in section 4, unfortunately there is only data available on tax evasion for OECD countries. However, excluding this data, although it has an influence on economic growth, is inferior than including it in the analysis with no significant effect, even though data exists only for part of the countries examined. Ho and Yang wrote an interesting paper on this topic, which is being discussed below.
2.7 Ho and Yang
The main argument by Ho and Yang (2002) is that the existence of tax evasion leads to a higher economic growth (Ho and Yang 2002 p. 1). In their reasoning they follow the Persson-Tabellini model and their argument is as follows. There exists a tradeoff caused by a tax rate, between the gains from income redistribution and the cost of tax distortion. The higher is the tax rate, the greater is the former and the higher the latter. The higher the cost of tax distortion, the smaller will be total income available for income redistribution. With the existence of tax evasion, the tradeoff is changed with both smaller gains from redistribution and larger distortionary costs. This causes the equilibrium redistribution level to be lower, resulting in a higher economic growth (Ho and Yang 2002 p.1).b Ho and Yang base their argument on empirical findings of other researches.
For example, Roubini and Sala-i-Martin (1995) found that when tax evasion was present and of considerable amount, government policy would be to enlarge seigniorage, which would be “repressing the financial sector and increasing inflation rates” (Ho and Yang 2002 p. 2). Then, the financial sector would serve the economy to a lesser extent, which results in lower economic growth (Ho and Yang 2002 p.2).
In addition, Caballe and Panades (1997) also analyzed the effect of changing the abidance of tax policies on economic growth, with focus on penalty fees and the audit probability. Their finding was that “the growth effects of greater enforcement depend on the relative productivity of private and public capital” (Ho and Yang 2002 p.2)
Furthermore, Lin and Yang (2001) examined what they called “a dynamic portfolio choice model of tax evasion” (Ho and Yang 2002 p. 2). In their research, they used tax revenue to supply public goods that were “nonproductive, though possibly utility-enhancing”. Following their argument, in this way tax evasion is a means to transfer “resources from the nonproductive public sector to the productive private sector” and this transfer “would be beneficial to growth” (Ho and Yang 2002 p.2). The empirics of the paper point out that “as tax rates progressively increase, the positive growth effect of the resource diversion through evasion would eventually dominate the negative growth effect of tax distortion” (Ho and Yang 2002 p. 2). Also, “the presence of tax evasion
will, all else equal, result in a lower equilibrium level of redistribution from political institutions” (Ho and Yang 2002 p. 15).
Overall, Ho and Yang, and Lin and Yang argue that the presence of tax evasion will result in a lower equilibrium redistribution level causing economic growth to be higher, while Sala-i-Martin argue the opposite; Caballe and Panades argue that the effect is ambiguous.
2.8 Barro II
Also, Barro (1991) finds that political instability has a negative influence on growth and investment. However, as he argues, this link could also represent “a political response to bad economic outcomes’’ (Barro 1991 p. 437). He uses revolutions, coups and political assassinations to measure political instability. The main channels he finds are from political instability to property rights and from property rights to private investment (Barro 1991 p. 437).
2.9 Motley
In 1998, Motley wrote a paper for the Federal Reserve Bank of San Francisco about a cross-country study on the relation between growth and inflation. He argues that “persistent inflation leads to a reduced growth rate of real GDP in the long run. Since a policy to reduce inflation is likely to slow economic activity in the short run, it is useful to estimate its benefits through higher long-run output growth.” (Motley 1998 p. 15). In his paper, Motley extends the augmented model by Mankiw, Romer and Weil by adding inflation and allowing it to affect the technological rate of change in a negative manner. The reason is as follows: at the point where the economy is in its long-run equilibrium as predicted by the Solow model, both capital stock and the level of output per effective worker will be constant. Therefore, “the equilibrium growth rate of GDP per actual worker depends only on the rate of technological change. Hence, any effect of inflation on steady state growth must occur through influencing the pace of technical change” (Motley 1998 p. 17). Motley uses the three groups created by Mankiw, Romer and Weil, and in addition he creates a fourth and a fifth group. Section 4discusses the sample groups in more details.
Motley argues as follows. If aggregate demand increases, real output rises and the latter goes hand-in-hand with rising prices. However, this is a short-run effect. He reasons that the long-run effect of inflation on real economic growth will be affecting aggregate supply instead of aggregate demand (Motley 1998 p.15). Inflation affects the aggregate supply via households, pecuniary and social costs, and investment and savings (Motley 1998 p. 16).
Additionally, inflation can impede market efficiency because it reduces the growth of the effective labour force. In this case, the growth of the effective output will be lower both in the convergence stage and in equilibrium. Also, inflation creates uncertainty amongst investors and
savers, therefore it increases the interest rates of long-term investments, hence it lowers the rates of investment in tangible and human capital (sK and sH). In turn, this will lower the long-run steady state
level of output. This means that the output growth rate will be affected when the economy is in convergence, but not once the economy reached its steady state (Motley 1998 p. 18). However, Mankiw, Romer and Weil state that it may take about several decades to move the economy only halfway to its steady state (Mankiw Romer and Weil 1992 p. 423). Therefore, the economy would grow slower during the convergence period. In conclusion, inflation can affect the growth rate of real output via effective labour force growth or via tangible or human capital (Motley 1998 p. 18).
To conclude, Motley finds that the ‘average annual real growth’ can be increased by 0.1 to 0.5 per cent by decreasing inflation by 5 per cent (Motley 1998 p. 16). Motley concludes as follows:
“I find a systematic tendency for higher rates of inflation to be associated with slower real growth. Thus, although one cannot claim that inflation is a major source of differences in rates of growth between countries, it does appear to be a systematic factor explaining at least part of these differences. Moreover, the results imply that it is a factor influencing growth in both advanced and less developed countries” (Motley 1998 p. 13).
This research is being taken seriously; however, one could argue that Motley is biased. The reason for this is that he wrote the paper whilst being a research officer for the Federal Reserve Bank of San Francisco. The outcome of his research is that a decrease in inflation can stimulate annual economic growth. Now low inflation has a positive effect on central banks because it encourages people to borrow money since interest rate are often low when inflation is low (Mishkin 2009 p. 351). The fact that low inflation goes hand in hand with high economic growth, is something a central bank would like to hear, since the primary goal of the European Central Bank is a stable price level (Mishkin 2009 p. 360) and the dual mandate of the Federal Reserve Bank consists of a stable price level and low unemployment2. On the other hand, “Barro (1991), Cozier and Selody (1992), and Fischer (1993) also conclude that countries with higher rates of inflation tend to have lower rates of real growth in the long run.” (Motley 1998 p. 16). So the results produced by Motley are still useful. As Ragan (2000) points out, negative relations between inflation and economic growth can be found, but they are fragile relation. The same is found by Levine and Renelt (1992) and Levine and Zervos (1993). Fischer argues that inflation is negatively correlated with growth (Fischer 1993). Barro (1991) argues that there exists a negative relation between a proxy for price distortions such as inflation, and growth. “These results are preliminary but do suggest a payoff to further research on the interplay between economic growth and government-induced distortions of markets” (Barro 1991 p. 437). Hence,
sufficient evidence suggests it is worthwhile to take inflation into account as a determinant of long-run economic growth via the channel of technology.
2.10 Conclusion
To conclude this section with, a small summary follows here of all the literature discussed above. First, Solow finds that a country’s steady state depends on its levels of the saving rate, the investment rate, the depreciation rate, the population growth rate, capital and labour. According to Barro (1991), poor countries have a tendency to converge to the level of income of rich countries if, and only if, they have a high level of human capital per person relative to their level of GDP per capita. Subsequently, Mankiw, Romer and Weil find that in the augmented Solow model, differences in education, savings and population growth rate explain a large part of international variation in cross-country income per capita levels. The conclusion by Durlauf and Johnson was that growth rate behaviour can go in harmony with multiple steady-states. Mo (2001) states that corruption decreases economic growth, mainly through political instability. Also, Detotto and Otranto (2010) found that crime negatively affects economic growth. The main argument by Ho and Yang (2002) is that the existence of tax evasion leads to a higher economic growth. Furthermore, Barro (1991) finds that economic growth is negatively correlated with political instability. Finally, Motley (1998) states that inflation lowers economic growth in the long run.
3. Theory - the Solow growth model
and the augmented Solow growth
model
This section discusses the Solow growth model and the augmented Solow growth model. First, the Solow growth model is explained. Solow describes multiple extensions to his model (neutral technological change, the supply of labor, variable saving ratio, taxation and variable population growth); however, Mankiw, Romer and Weil take technology growth and tangible and human capital as exogenous constant variables (Mankiw Romer and Weil 1992 p. 413). Therefore, only the extension on neutral technological change is being explained here. A side note needs to be placed here, namely that in the econometrics part of the research of this paper, technological growth will be analyzed separately to see whether it was correctly assumed to be 0.03, and the same goes for δ to test whether is equals 0.02 (Mankiw Romer and Weil 1992 p. 413). Second, the augmented Solow growth model is being described, it will be specified which extensions are added to the initial model and how its explanatory power changes.
3.1 The Solow Growth Model
Recall that the change in the community’s stock of capital with respect to time is equal to the savings rate times national income. Or, in formula form, (1). National income is an economy’s net output adjusted for depreciation, ) (2). It is assumed that the production function has constant returns to scale, and that the marginal product of capital exhibits diminishing returns to scale (Solow 1956 p. 66). In other words, the production function is convex and sloping upwards (the more capital and labour are used, the higher is production). Substituting the second equation into the first gives ) (3). It is also assumed that the labour force increases at a constant rate because of exogenous population growth, this is called n. In the initial model, Solow follows Harrod his reasoning, that there is absence of technological change. The supply of labour is given by the equation ) (4). Substituting equation (4) into (3) gives ) (5). According to Solow, this equation explains how capital accumulation evolves over time provided all labour is employed (Solow 1956 p. 67). It needs to be mentioned that Solow assumes that the level of accumulated capital is supplied inelastically. The process to reach equilibrium is described by Solow as follows:
“The process can be viewed in this way: at any moment of time the available labor supply is given by (4) and the available stock of capital is also a datum. Since the real return of factors will adjust to bring about full employment of labor and capital we can use the production function to find the current rate of output. Then the propensity to save tells us how much of net output will be saved and invested. Hence we know the net accumulation of capital during the current period. Added to the already accumulated stock this gives the capital available for the next period, and the whole process can be repeated.” (p. 68).
An explanation follows here about possible growth patterns. Suppose (6), then
(7). Then, (8) and ) (9). Substituting (8) and (9) into (7) gives ) . When one divides out L of F, one gets ) for .
When is zero, the ratio of capital to labour will be constant, and both will growth at the same
rate of n, see Solow (1956) for the full details. Since the production function is sloping upward and convex, if
i) r > r*, then r will decrease. If the initial capital stock is below the equilibrium ratio, capital and output will grow at a faster pace than the labour force until the equilibrium ratio is approached.
ii) r < r*, then r will increase. If the initial capital stock below the equilibrium ratio, capital and output will grow at a slower pace than the labour force until the equilibrium ratio is approached.
iii) Hence, r* is a stable equilibrium.
What follows from this reasoning is that the economy “will develop toward a state of balanced growth at the natural rate” (Solow 1956 p. 70), independent of the initial value of r, the capital-to-labour ratio.
However, there also exists the possibility that the sF curve does not intersect with the nr curve, because it lies either above or below the sF curve. In that case there will be no steady state. On the contrary, as Solow argues, “if neoclassical assumptions of variable production and constant returns to scale are present, the natural rate of growth is the same as the warranted rate of growth”, where
the warranted rate of growth is a function of savings and investment (Solow 1956 p. 65). He continues to argue that even though there does not have to be a narrow boundary, still the economy can , There may not be any knife-edge (narrow boundary), and the system can adjust to any given rate of growth of the labour force, and eventually approach a state of steady proportional expansion.
3.2 The Augmented Solow Growth Model
The reason this paper focuses on the augmented version of the Solow growth model is because the augmented model is being considered better than the original model: it includes more variables and it can explain more of the variance in economic growth than the original model.
Mankiw, Romer and Weil state that the Solow model correctly predicts the directions of the effects of savings and population growth, but they criticize the model for the predicted magnitudes of the effects. In the augmented model, human capital accumulation is also included. In this augmented model, 80 per cent of cross-country variation in economic growth is being explained (Mankiw Romer Weil 1992 p. 408). The prediction of both the original model and the augmented model is that there is a conditional convergence. That is, different countries reach different steady states. However, once differences in savings and growth are accounted for, there is a convergence at about the rate that the model predicts.
The way to measure human capital is to use the percentage of the labour force that is in secondary school, there is no attention paid to investment in health.
The inclusion of human capital in the model increases the effect of the accumulation of physical capital on income, because an increase in savings leads to an increase in income, which leads to an increased value of human capital in the steady state, although there is no change necessary in the part of income that is focused on human capital (Mankiw Romer Weil 1992 p. 417).
3.2.1 The Regression Equation
Where Solow states there was absence of technological progress, Mankiw Romer and Weil consider it exogenous, and it grows at g, so the number of effective units of labour grows at (n+g). They argue as follows: “g reflects primarily the advancement of knowledge, which is not country specific. And there is neither any strong reason to expect depreciation rates to vary greatly across countries, nor are there any data that would allow us to estimate country-specific depreciation rates” (Mankiw Romer Weil 1992 p. 410). Furthermore, A(0) reflects both technology and resource endowment, climate, institutions and so on; therefore, it might be different across countries. Following the same
reasoning: ln[A(0)] = a + ε, that is, technological growth consists of a constant and a country-specific shock (Mankiw Romer Weil 1992 p. 411).
It is also assumed that there is no cost of changing one unit of consumption into one unit of physical or human capital. Furthermore, the depreciation rate for physical and human capital is the same. Finally, decreasing returns to scale are assumed.
The regression equation (6), taken from Mankiw, Romer and Weil (p.417) becomes:
[ ] ) [
] ) [ ] ) [ ] ) In words, growth of real capita per GDP equals a constant plus technological growth minus a parameter times growth of the effective units of labour (n + g) and depreciation plus a parameter times the fraction of income invested in physical capita plus a parameter times the fraction of income invested in human capital.
A large part of cross-country differences can be attributed to the different determinants of the steady state; those are the population growth and physical and human capital accumulation. The prediction of the Solow growth model is not convergence, “it predicts only that income per capita in a given country converges to that country’s steady-state value. It is convergence “only after controlling for the determinants of the steady state, a phenomenon that might be called conditional convergence” (Mankiw Romer Weil 1992 p. 422). The overall conclusion is that by including human capital in the model, the overall fit of the Solow Growth model improves compared to the original model.
3.2.2 Speed of Convergence
The previous analysis has been assuming that countries already were in their steady states in 1996, or that the deviations from their steady state were random. However, this may not be true. Therefore, what follows is an analysis of how countries behave outside their steady states.
What is interesting to analyze is the speed at which countries move towards their steady states, called the convergence parameter. The prediction by the Solow model is as follows: y* is the steady-state level of income per effective worker as can be seen by equation (6). Then, y(t) is the actual value of income at time t. The speed of convergence is given by ( )) ) ) for
Following some algebra (see Mankiw, Romer and Weil for the full details) “the growth of income is a function of the determinants of the ultimate steady state and the initial level of income”, as can be seen below (Mankiw Romer Weil 1992 p. 423).
Substituting the value for into equation (6) and applying the equation to the model used in this paper, results in equation (7):
( )) ( )) ( ) ( ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ) ) ) ))
For ; GC is government consumption, ihc is initial human capital, I is investment, τ is tax evasion, π is inflation, cri is crime, cor is corruption, and the rest of the symbols are used as before.
The estimation results are that there is a significant tendency towards convergence for OECD countries (Mankiw Romer Weil 1992 p. 425). As previously mentioned, the convergence effect was strongest when conditional on saving, population growth and human capital, and, importantly, the speed of convergence is at about the rate that is predicted by the augmented model (Mankiw Romer Weil 1992 p. 429).
3.2.3 Parameter values
Mankiw Romer and Weil argue that g and δ are assumed to be constant and jointly equal to 0.05, because “there is no strong reason to expect them to vary greatly across countries” (p. 410). Furthermore they argue that “changes in this assumption have little effect on the estimates” (p. 413). Suppose that , then the parameter on ) will be -2. Therefore in the augmented model, “high population growth lowers income per capita because the amounts of both physical and human capital must be spread more thinly over the population” (Mankiw Romer and Weil 1992 p. 418). Concerning the convergence parameter, when , given , then . This means that the economy moves halfway to its steady state in approximately thirty-five years. It is interesting to note that in the textbook Solow model, human capital is not included in the model and this causes the convergence to be much faster. Since ,
, and the economy will come to halfway its steady state in approximately only seventeen years (Mankiw, Romer and Weil, p. 423).
3.3 Conclusion
According to the Solow model, the economy “will develop toward a state of balanced growth at the natural rate” (Solow 1956 p. 70), independent of the initial value of r, the capital-to-labour ratio. Both the Solow model and the augmented Solow model predict a conditional convergence. That is, countries reach different steady states but once differences in savings and growth are accounted for, there is convergence at about the rate predicted by the model. More precisely, income per capita converges to a country’s steady state value after controlling for the determinants of that steady state. By including human capital in the model, the fit of the model is better. Mankiw, Romer and Weil found that the speed of convergence is at about the rate predicted by their model, and the convergence effect was most significant when conditional on saving, population growth and human capital. In the textbook Solow model, given , and the economy will reach its steady state in about approximately seventeen years. However, when human capital is included in the model, the economy will move to halfway its steady state in thirty five years.
4. Data and Methodology
In this section, an explanation is given on the methodology conducted in the research of this paper. Afterwards, a description of the sample is given, specifically detailed about how the variables in this research were measured. Furthermore, information is provided on the sample groups on how they are composed. Finally, it is explained why or why not this paper wants to analyze some additional groups.
4.1 Methodology
The research this paper conducts is based on the augmented Solow growth model by Mankiw, Romer and Weil (1992), including the following variables: labour force growth, marginal product of capital, technological growth, depreciation rate, saving rate, population growth and human capital accumulation. Moreover, the research by Barro (1991) is also taken into account here. The variables used from his research are initial human capital, the initial level of real per capital GDP, the share of government consumption in GDP, the share of public investment in GDP and political stability. Thirdly, research by Motley (1998) points out that inflation also has a significant effect on economic growth. In addition, empirical evidence is found that crime and corruption also are determinants of long-run economic growth. Therefore, this paper takes all variables into account to examine whether there exists an overall improved fit of the model. However, the likelihood of multicollinearity between on the one hand political stability and on the other hand crime and corruption is high. To avoid the latter, the variable political stability is left out of the analysis and the variables crime and corruption are included, in order to determine their separate effects on long-run economic growth.
The methodology of the research is as follows. First, data was collected for all variables from 1996 until 2010. The reason for this time period is that for these sequential years, a reasonable amount of data is available for all variables. Unfortunately there was no possibility to find data that was consecutive to the data used by Mankiw Romer and Weil, which used a time period from 1960 until 1985. All data was measured in current US dollars. Second, all the data was put into an excel file where the log function of the averages over the years was taken for every variable. Then, a simple regression was done in excel. Here follows a description of how the variables were measured and how data was obtained. Since a substantial part of the data were collected from the World Databank, the data are likely to be consistently measured.
4.2.1 Data
Data for the variable labour force growth was deducted from data for the labour force by taking the natural logarithm, including for the year 1995 to calculate the annual growth.
The marginal product of capital (MPK) was measured by the real interest rate (r). Metzler (1950) argues as follows, if MPK < r then capital is accumulated too quickly, whereas if MPK > r then “the rate of economic growth is less than the socially desirable rate”. Therefore, MPK equals r in the steady state (Metzler 1950 p. 305). Since Mankiw Romer and Weil assume that countries are in their steady states in 1985 (Mankiw Romer Weil p. 422), this paper argues in the same way, concluding that countries are in their steady states in 2010. The marginal product of capital measures the rate of investment in tangible capital, or in symbols .
When looking for data for the savings rate, data for the net savings rate was chosen over the gross savings rate because the gross savings rate includes the consumption of fixed capital3, in which case depreciation would be measured double. The savings rate is measured as a percentage of Gross National Income (GNI).
Data for the variable GDP/capita was obtained in data measured in current United States (US) dollars.4
The variable government consumption is measured by the General Government Final Consumption Expenditure measured in current US dollars5.
Investment is measured as the share of investment per GDP/capita. Data were obtained from Penn World Table, by selecting all countries for the time period from 1996 until 2010 for the variable ‘pi’ which is the price level of investment6. The Penn World Table is provided by the Center for International Comparisons of Production, Income and Prices, University of Pennsylvania.
Initial human capital is approximated by Barro by the school-enrollment rates in 1960 (Barro 1991 p. 409). Accordingly, data for this variable is collected by using data from the Worldbank that state the primary school enrollment rate in 1996. This paper choses the net enrollment rate over the gross enrollment rate (GER), because the former states that the “Total is the ratio of children of the official primary school age who are enrolled in primary school to the total population of the official primary school age.”7 In contrast, the latter states that “Total is the total enrollment in primary education, regardless of age, expressed as a percentage of the population of official primary education age. GER can exceed 100% due to the inclusion of over-aged and under-aged students
3http://data.worldbank.org/indicator/NY.ADJ.NNAT.GN.ZS 4 http://data.worldbank.org/indicator/NY.GDP.PCAP.PP.CD 5 http://data.worldbank.org/indicator/NE.CON.GOVT.CD 6 https://pwt.sas.upenn.edu/php_site/pwt71/pwt71_form.php
because of early or late school entrance and grade repetition.”8 Therefore, the former is being found a more accurate measure.
Human capital accumulation is according to Mankiw Romer and Weil measured by the percentage of working-age population in secondary school (Mankiw Romer Weil 1992 p. 419). However, as Kwon (2009) points out, “Romer (1990) suggested the ratio between skilled-adults and total adults to measure the stock of human capital in the national economy” (Kwon 2009 p. 6). Moreover, Kwon argues, “Organization for Economic Cooperation and Development (OECD) utilizes International Adult Literacy Survey (IALS), the ratio between literate adults and total adults, to measure the stock of human capital” (Kwon 2009 p.6). Therefore, this paper choses to use the Adult Literacy Rate to measure human capital accumulation, in order to avoid high multicollinearity with the measure for initial human capital. Data for the IALS is obtained from the Worldbank, using the adult total, measured as a percentage of people ageing fifteen years and older.9 The literacy rate measure the rate of investment in human capital, or in symbols .
Data for inflation was acquired from the Worldbank where inflation is being described as “the annual growth rate of the GDP implicit deflator that shows the rate of price change in the economy as a whole”. “The GDP implicit deflator is the ratio of GDP in current local currency to GDP in constant local currency”. 10
Unfortunately, data on tax evasion could only be found for OECD countries. These data were obtained from table 4 in the appendix of Size and development of tax evasion in 38 OECD countries by Buehn and Schneider (2012). Data on tax evasion is measured as tax evasion as a percentage of GDP. The table is also included in the appendix 2of this paper.
The variables crime and corruption are measured by the Worldwide Governance Indicator Project (WGI) created by the Worldbank.11 According to the WGI, Rule of Law “reflects perceptions of the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence” (WGI 2013). Therefore, rule of law is used as a measure of crime. Furthermore, the WGI describes corruption as follows: it “reflects perceptions of the extent to which public power is exercised for private gain, including both petty and grand forms of corruption, as well as "capture" of the state by elites and private interests” (WGI 2013). For both variables Rule of Law and Control of Corruption, the data ranges from -2.5 to 2.5 for -2.5 indicating a weak and 2.5 indicating a strong government performance.
8http://data.worldbank.org/indicator/SE.PRM.ENRR/countries/1W-KH?display=graph 9 http://data.worldbank.org/indicator/SE.ADT.LITR.ZS 10 http://data.worldbank.org/indicator/NY.GDP.DEFL.KD.ZG 11http://info.worldbank.org/governance/wgi/index.aspx#home
Finally, data for economic growth was deducted from data for GDP/capita by taking log difference between the value of GDP/capita in 2010 and 1996. Again, this data was acquired from the Worldbank12.
4.2.2 Sample Groups
As written before, this paper follows the same approach as the research by Mankiw, Romer and Weil. The first group of countries consists of countries “other than those for which oil production is the dominant industry” (Mankiw Romer Weil 1992 p. 413). The reason that they excluded those countries is that oil production does not influence the value added of the countries, is it the extraction of resources, which they do not consider economic growth (Mankiw Romer Weil 1992 p. 413). The countries in this group are labelled ‘N’ for non-oil. This group had 98 countries in it, and this paper assumes the number of countries where non-oil is the dominant industry did not change much over time and therefore the same group is countries is used.
The second sample group excludes “countries whose populations in 1960 were less than one million or countries who data received a grade “D” from Summers and Heston” (Mankiw Romer Weil 1992 p. 413). In 1960 this sample consisted of 75 countries. However, since the time span of the data of this research is from 1996 until 2010, this paper excludes countries where the population was less than one million in 1996. The reason for this, as Mankiw Romer and Weil argue, is that the income in countries with a population smaller than one million “may be dominated by idiosyncratic factors” (Mankiw Romer Weil 1992 p. 413). As for the second part of the description of the sample, the reason for countries to received grade “D” from Summers and Heston was that their “real income figures are based on extremely little primary data; measurement error is likely to be a greater problem for these countries” (Mankiw Romer Weil 1992 p. 413). In this paper, the newest version of the System of National Accounts is being used, and therefore countries that received a “D” in this version13, are excluded from the sample (System of National Accounts, 2008, p. 13-16). As a side note, this paper wants to mention that the version used here is the version from 2008; however there does exist a newer version from 2012 but for this version the appendix with the grading list could not be found. Therefore, the version from 2008 is used here. This group of countries is called I for intermediate. In the Penn World Table version 7.1 some more countries received grade ‘D’, which were Algeria, Haiti and Papua New Guinea. Therefore, the composition of this group changed to some extent, and the group consists of 72 countries now instead of 75.
Furthermore, it would be interesting to examine whether countries with populations less than one million actually are subject to idiosyncratic factors. Therefore, another group is created
12
consisting of the non-oil sample group including countries with populations less than one million now. This group is called ‘non-oil small’.
The fourth group consists of “OECD countries with populations greater than one million” (Mankiw Romer Weil 1992 p. 413). Again, because of the different time period, the fourth group consists in 2010 of 35 OECD countries. However, the population of Luxemburg and Iceland is less than one million so those two countries should be excluded. Mankiw, Romer and Weil included New Zealand in their OECD-group sample, although the country was an OECD country only from 1971, and the same goes for Australia. The latter points out that Mankiw Romer and Weil measured the number of OECD countries at the end of fifteen year period. Therefore, it is reasonable to also include countries that became OECD members during the period 1996-2010.
Alternatively, following the reasoning by Motley, a fifth and sixth group needs to be created. According to Motley, the fifth group is an enlargement of the OECD group with “seven countries in the High Quality sample that have income levels above that of the poorest OECD country (Portugal). The countries added are Hong Kong, Israel, Mexico, Singapore, South Korea, Syria, and Venezuela.” He calls this sample group ‘OECD+’. One needs to note that the paper written by Motley was written in 1998, while Mexico became an OECD member in 199414. Hence, Mexico is already included in the OECD sample group. With the same reasoning, South Korea became an OECD member in 199614, therefore in this research it is also included in the OECD sample group. The same goes for Israel who became a member in 201014. When the latter is taken into account, there are only three additional countries in this group. The sixth sample group, called ‘Rest of the World’, includes the countries that are not in the OECD+ sample but whose data is High Quality. These countries are Uruguay, Chile, and Argentina. This paper assumes that Motley means grade A and B with high quality, since he does not specify this in his paper. However, a group that is composed of only three countries will most likely not produce very significant results. Therefore, this paper choses to leave the sixth group out of the analysis. By the same reasoning, a group that differs from another group by only four countries will most likely not produce very different results. However, the fifth group will still be analyses to confirm this expectation.
14
5. Empirical Results
In this section, first the results of the regression are given. Then, an explanation on these results follows. Finally, the results are compared to each other and to the results found by Mankiw, Romer and Weil. N.B. to be clear, the augmented Solow model refers to the model described by Mankiw, Romer and Weil, while the extension of the augmented Solow model, or the extended model, refers to the model developed in this paper.
5.1 Results and Data Analysis
As is done by Mankiw, Romer and Weil, this paper takes the average of the variables of interest over the time period. Therefore, the data is not panel data anymore, and this research is able to make a simple linear regression. The distinction between conditional and unconditional convergence is made here, as well as in Mankiw, Romer and Weil (1992). As stated in section 3.2, conditional convergence is the convergence in steady state income controlling for determinants of the steady state. Unconditional convergence equals convergence while not controlling for the determinants of the steady state. In table one and two, first the value for the parameters are given, then in brackets its standard error and below the p-value. In this section, the adjusted r-square, significance level and F-statistic are discussed. The adjusted r-square is the proportion of variance of the dependent variable explained by the independent variable(s). In other words, it measures how well the model fits the data. The significance level is a criterion used to reject the null hypothesis. Usually, a five per cent significance level is used. However, here the criterion is ten per cent. Stock and Watson (2012) describe the F-statistic as being “used to test joint hypotheses about regression coefficients” (Stock and Watson, 2012, p. 263). The null hypothesis is that all coefficients are jointly zero, the alternative hypothesis is that at least one coefficient is different from zero (Stock and Watson, 2012, p. 269). When the p-value is very low (for example lower than one per cent), the null hypothesis is rejected.
In the progress of analyzing the data, first the values for the independent variables were taken as non-natural logarithmic values. Also, economic growth, the dependent variable, was calculated by subtracting GDP/capita in 2010 from the value in 1996 and dividing by GDP/capita in 1996. The approach used in this analysis, which gives the results below, however, is to use natural logarithmic values of all independent variables. Economic growth was calculated by taking the log difference of GDP per capita between 1996 and 2010. The disadvantage of the second, and current approach, is that one cannot take the natural logarithm of a negative value. The values of some parameters are negative, so they are not taken into account in the analysis. However, the same approach is used by
Mankiw, Romer and Weil. Therefore, this paper adopts the same method of working. Interestingly, the values for the adjusted r-square for the second approach are higher than for the first approach. For the first approach, under conditional convergence, they are 0.466, 0.351, 0.024, 0.411 and 0.585 respectively for the N, I, NS, OECD and OECD+ sample groups. Also, in the second approach, the F-statistic is significant at one per cent in all groups, while it is not significant in the NS group in the first approach. For the first approach under unconditional convergence, the r-square values are 0.081, 0.108, 0.005, 0.347 and 0.398 for respectively the N, I, NS, OECD and OECD+ sample group. Those values are 0.092, 0.09, -0.06, 0.696 and 0.676 in the second approach. The second approach is better especially for the OECD and OECD+ sample groups.
In the tables it is indicated whether the variables are significant and if so, at which percentage. When the p-value is bold, it is significant at ten percent. When it is bold and has one asterisk, it is significant at five per cent, and then it is bold and has two asterisks, it is significant at one per cent.
5.1.1 Results and Analysis on Unconditional Convergence
It is expected that all previously discussed parameters (n+δ+g, sK, sH, government consumption, initial
human capital, investment, tax evasion, inflation, crime and corruption) have an influence on the steady state income. Therefore, controlling for those, when testing for unconditional convergence, only the initial GDP/capita is regressed on the change in income from 1996 to 2010. One needs to note that in group N the countries Somalia and Myanmar are excluded because no data could be found on GDP per capita, therefore economic growth could not be calculated. The results are as follows.
Sample
Observations
N
95
I
76
NS
148
OECD
32
OECD+
36
Constant 1.185 (0.148) 0.000** 1.166 (0.169) 0.000** 0.630 (0.099) 0.000** 3.650 (0.350) 0.000** 3.453 (0.320) 0.000** Ln(GDP/capita_1996) -0.062 (0.019) 0.002** -0.060 (0.021) 0.005** 0.003 (0.013) 0.797 -0.308 (0.036) 0.000** -0.288 (0.033) 0.000** Adjusted R-squared 0.092 0.090 -0.006 0.696 0.676 F-statistics p-value 10.495 0.002** 8.446 0.005** 0.067 0.797 71.955 0.000** 74.141 0.000** Table 1 – Unconditional ConvergenceFrom the table it can be seen that the constant term is significant in all groups. However, no conclusion can be drawn from this because the constant term does not have a marginally positive or negative effect on the dependent variable. The parameter on Ln(GDP/capita)1996) is significant at one per cent for the groups N, I, OECD and OECD+. The reason that it is only not significant in the NS group is because of the inclusion of the very small countries. As stated before, in section 4.2.2, in the Solow model those countries are excluded from the analysis because countries with populations less than one million are subject to idiosyncratic factors. This is true to the extent that it makes the coefficient insignificant. Also, the parameter is negative is all groups except in the NS groups. This confirms the previously stated.
When looking at the values for the adjusted r-square, in this analysis the OECD+ sample group has the highest explanatory power. Interestingly, the adjusted r-square for the NS group is negative. This can be the case when the fit of the model is worse than by just fitting a horizontal line through the data. Considering the numbers of the F-statistic and its significance, one can see that the F-statistic is significant at one per cent in all groups but NS. The reason for this is the same as before. For all groups except NS the coefficients are jointly different from zero. In the case of unconditional convergence, there is only one coefficient determining economic growth; therefore the F-test gives the same result as a t-test. In conclusion, for the N, I and NS sample groups, there is no tendency for poor countries to grow faster on average than rich countries. However, for the OECD and OECD+ sample groups, there is a significant tendency.
5.1.2 Results on Conditional Convergence
Below the results can be seen from the regression analysis.
Sample
Observations
N
95
I
76
NS
148
OECD
32
OECD+
36
Constant 3.428 (0.656) 0.000** 2.713 (0.890) 0.003** 0.209 (0.106) 0.051 5.751 (1.451) 0.001** 5.116 (1.158) 0.000** Ln(Government Consumption/GDP/capita) 0.004 (0.061) 0.947 0.035 (0.062) 0.578 0.013 (0.043) 0.756 0.031 (0.151) 0.840 0.034 (0.114) 0.768 Ln(π) 0.151 (0.028) 0.000** 0.162 (0.039) 0.000** 0.249 (0.036) 1.888 0.142 (0.081) 0.095 0.191 (0.059) 0.004** Ln(n + g + δ) 0.031 (0.103) 0.764 0.159 (0.252) 0.530 0.014 (0.055) 0.806 -0.210 (0.261) 0.430 -0.178 (0.218) 0.423 Ln(sh) -0.024 (0.020) 0.245 -0.031 (0.021) 0.136 0.007 (0.020) 0.725 -0.020 (0.025) 0.431 -0.011 (0.016) 0.502 Ln(Initial Human Capital) 0.004(0.020) 0.834 0.007 (0.021) 0.750 0.040 (0.021) 0.063 -0.022 (0.025) 0.400 -0.035 (0.019) 0.079 Ln(Tax Evasion) 0.045 (0.072) 0.529 0.036 (0.070) 0.613 -0.060 (0.106) 0.573 0.035 (0.065) 0.594 0.018 (0.050) 0.717 Ln(Investment/GDP/capita) -0.356 (0.065) 0.000** -0.308 (0.065) 0.000** -0.044 (0.030) 0.148 -0.434 (0.212) 0.054 -0.392 (0.142) 0.011* Ln(sk) -0.057 (0.026) 0.030 -0.044 (0.028) 0.126 -0.054 (0.033) 0.099* -0.095 (0.056) 0.109 -0.111 (0.047) 0.025* Ln(Crime) -0.016 (0.033) 0.642 -0.027 (0.033) 0.428 -0.043 (0.045) 0.336 0.074 (0.051) 0.165 0.096 (0.043) 0.063 Ln(Corruption) 0.032 (0.023) 0.172 0.031 (0.022) 0.166 0.047 (0.035) 0.183 0.014 (0.040) 0.730 0.023 (0.027) 0.402 Ln(GDP/capita_1996) -0.337 (0.066) 0.000** -0.295 (0.069) 0.000** -0.003 (0.014) 0.851 -0.528 (0.149) 0.020* -0.463 (0.122) 0.000** Adjusted R squared 0.575 0.524 0.338 0.767 0.825 F-statistic p-value 12.583 0.000** 8.514 0.000** 7.827 0.000** 10.276 0.000** 15.987 0.000** Table 2 – Conditional Convergence
One can see from the table that only a few coefficients are significant at 10 per cent. This is probably due to the fact that the data was taken from multiple sources. Although the largest part of the data was collected from the Worldbank, still some other sources were used as well. Therefore it might be not entirely consistent. Also, data on investment could only be found for both private and public investment combines, while investment as described by Barro (1991) contains only public investment. Furthermore, data on tax evasion was only found for OECD countries. In addition, the measure for sk is not perfect: is it measured by the interest rate, see section 4.2.1, which was
extremely high for example for Zimbabwe from 2004 (252 per cent), 2005 (219 per cent) and 2006 (509 per cent).
For the variable ‘initial human capital’ there is no observation in 1996 for some countries, therefore this research takes the first observed value. Even if the first observation is for example only in 2000, this value is still taken.
The adjusted r-square is the highest for the OECD+ sample group. It means that the designed model has the highest explanatory power in this sample group. One should note that the adjusted r-square of the NS group is low. This is due to the inclusion of very small countries, as mentioned above. The F-statistic is significant at one per cent in all groups. Again, this means that in the coefficients are not jointly equal to zero. It is interesting to note the difference in the value of the adjusted R-square between the OECD and OECD+ sample groups. The difference is 0.825 – 0.767 = 0.058, which is 5.8 per cent, while the only difference between the groups is four countries.
In conclusion, there is a weak tendency for poor countries to grow faster on average than rich countries in the NS sample group. The tendency is larger for the N and I sample groups but still not very strong. For the OECD and OECD+ sample groups, the tendency is very strong.
5.2 Comparisons
5.2.1 Comparison of Conditional and Unconditional Convergence
Adjusted R square N I NS OECD OECD+
Conditional Convergence 0.575 0.524 0.338 0.767 0.825 Unconditional Convergence 0.092 0.090 -0.006 0.696 0.676
Above, the values for the adjusted r square for the conditional and the unconditional convergences are summarized. When comparing the values, one can see that the values for conditional convergence are much higher than for the unconditional convergence in all sample groups. The reason for this is most likely that in the unconditional convergence, there is only one independent variable, namely the initial GDP per capita. In the conditional convergence however, there are ten variables explaining the variation in economic growth. Therefore, the more explanatory variables, the better the model is at explaining variation in the dependent variable, economic growth.
5.2.2 Comparison of Unconditional Convergence with Mankiw, Romer and
Weil
Here, a comparison follows between the current research and research done by Mankiw, Romer and Weil to examine weather adding more variables and using a newer data set improves the fit of the model for unconditional convergence.
In the augmented Solow model, the values for the adjusted r-square in the unconditional convergence for the groups Non-oil, Intermediate and OECD are respectively 0.03, -0.01, and 0.46 (Mankiw, Romer and Weil, p. 425). In this paper those values are respectively 0.092, 0.090 and 0.696, as can be seen in table three. In the augmented Solow model, the explanatory power of the model is lower for all three sample groups, compared to the extension of the augmented Solow model. So in the augmented Solow model, there was a more significant tendency for poor countries to grow faster than rich countries, especially for the OECD sample group. For the N and I sample group, there is no significant tendency towards convergence. It is interesting though to note that for the N and I sample group the r-squared value is low, while the coefficient on the initial level of income per capita is significant at one per cent.
5.2.3 Comparison of Conditional Convergence with Mankiw, Romer and
Weil
Here, a comparison follows between the current research and research done by Mankiw, Romer and Weil to examine weather adding more variables and using a newer data set improves the fit of the model for conditional convergence.
In the augmented Solow model the values for the adjusted r-square in the conditional convergence for the groups Non-oil, Intermediate and OECD are respectively 0.46, 0.43 and 0.65 (Mankiw, Romer
and Weil, p.426). In this paper those values are respectively 0.575, 0.524 and 0.767, as can be seen in table three. The values for both models are quite alike, where the values are higher in the extended model for all three groups.
5.3 Convergence Parameter
Recall equation (7) on page 15:
( )) ( )) ( ) ( ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ( ) ) ) ) ) ))
For ; GC is government consumption, ihc is initial human capital, I is investment, τ is tax evasion, π is inflation, cri is crime, cor is corruption, and the rest of the symbols are used as before.
The convergence parameter λ can be calculated as follows. Each model has its own coefficient for the variable ln(GDP/capita_1996). From the equation above it can be seen that this coefficient equals ). So when equating this with the corresponding value of the coefficient, one can solve
for λ. The results are shown in the table below. The calculation for number of years to come halfway the steady state is based on the calculation done by Mankiw, Romer and Weil. They write that when λ = 0.02, a country will reach halfway its steady state in about 35 years. Likewise, they argue, when λ = 0.04, the number of years is 17. Following the same reasoning, the following results are found.
Unfortunately, the values do not correspond with the values found by Mankiw, Romer and Weil. Also, the values for the convergence parameters vary widely, from 0.003 to 0.75. Furthermore, the
Sample
N
I
NS
OECD
OECD+
Coefficient -0.337 -0.295 -0.003 -0.528 -0.463
λ 0.41098 0.34956 0.00300 0.75078 0.62176
Number of years halfway to the Steady State
1.71 2 233.333 0.93333 1.129
λ MRW 0.0137 0.0182 0.0203
values for the number of years to halfway the steady state vary from smaller than one to over two hundred.
5.4 Conclusion
One can conclude that adding working-age population growth, human capital accumulation (sh), tax
evasion, crime and corruption do not improve the performance of the model; these variables are not significant in any of the groups. But, combining parameters of interest from the Solow model and research by Barro (1991) does improve the explanatory power of the model to a certain amount, as expressed by the partly significance of initial human capital and investment and insignificance of government consumption. Inflation improves the fit of the model only for all groups except NS. The variables marginal product of capital (sk) is significant in the N, NS and OECD+ group. It is interesting
to note that in the NS group, the only two significant variables (neglecting the constant term) are initial human capital and marginal product of capital, where the latter is also significant in the N group but initial human capital not. The variable initial human capital improves the fit of the model in all groups except the NS sample group, for the reason mentioned before. In the conditional convergence, the tendency for poor countries to grow faster on average than rich countries is weak in the NS sample group, intermediate for the N and I sample groups yet not very strong, and quite strong for the OECD and OECD+ sample groups. As for the unconditional convergence, there is no tendency whatsoever for the N, I and NS sample groups. On the contrary, there is a significant tendency for the OECD and OECD+ sample groups.
