Marginal product of capital and growth theory: accumulation versus assimilation with a special case for NICs

(1)

UNIVERSITY OF GRONINGEN – FACULTY OF ECONOMICS AND BUSINESS MASTER THESIS - INTERNATIONAL ECONOMICS AND BUSINESS

Marginal product of capital and growth theory:

accumulation versus assimilation with a special case

(2)

1

ABSTRACT

This paper examines the role of capital in GDP growth by applying natural capital and price level corrections to the Marginal Product of Capital (MPK) and compares the development of the MPK with predictions that flow from the neoclassical ‘accumulation’ theory versus the modern ‘assimilation’ theory using data from 77 countries during 1990-2011. We argue that the neoclassical theory assumes diminishing returns to capital while modern theory predicts that this does not have to be the case due to productivity increases. The results suggest that modern theory holds unless we remove Newly Industrialized Countries (NICs) from the analysis.

(4)

3

1 – INTRODUCTION

Economic growth policy strategies have come and gone. Starting in the 1950s, the emphasis on industrialization has been common policy advice around the globe for about three decades, based on the success of experiences in the US and Western Europe and it was thought that developing countries in Africa, Latin America and Asia could achieve similar growth rates by enforcing the same strategy that successful western societies had implemented years before (Kohli, 2004). This policy advice, commonly termed as the ‘Industrialization Push Strategy’ (Murphy and Schleifer, 1989) aimed at an active role for the government including the implementation of import-substitution policies; export promotion; restricted international trade and often rather specific government support for export-oriented industries that the government deemed desirable (Kohli, 2004). Initially, the strategy seemed to work, with annual growth rates of 2% or higher in Africa, Latin America and Asia between 1950 and 1970 (Maddison, 2003). However, with the exception of South-East Asia, annual growth rates of these regions slowed down drastically and were even negative in some sub-Saharan African countries between 1970 and 1990 (Maddison, 2003).

Following the failure of the industrialization push in most areas, governments decided to let go of this strategy and let market mechanisms improve economic growth, which is known as the Washington Consensus of the 1980s. International trade and FDI were allowed to run more freely and governments were to focus on implementing structural reforms to improve macro-economic stability. This policy theorized that markets would take care of the inefficient industrial sectors that were often the case under the industrialization push regime (Gore, 2000). Especially in Latin America, structural reforms increased rapidly from 1985-2000 (Rodrik, 2013). Disappointingly, growth did not ensue, as annual growth in Latin America was only 1% between 1990 and 2003 (Maddison, 2003). The former USSR even saw its economy decline during that same period. On the other hand, countries in South-East Asia have seen incredible results from shifting (agricultural) workers to industrial and services sectors, from opening up their markets to foreign investment and from structural reforms.

(5)

4

Related to the idiosyncrasy of growth paths and why some countries are economically successful and others are not is the Lucas Puzzle, which was originally conceptualized by Lucas in 1990. In neoclassical comparative economics, economists would argue that capital flows from countries where it relatively abundant to where it is relatively scarce and where it can be used more productively to harvest larger returns. Lucas argues that the contrary is true; capital flows from poor to rich countries rather than the other way around. He shows the marginal product of capital (MPK) differences between India and the US, which is a measure of the return in income from an increase in capital. Because of the lower income and capital per worker in India, the marginal product of capital should be 58 times as high as that of the US if neoclassical models of trade and growth were true (Lucas, 1990). This figure, however, is not anywhere close to being accurate and therefore there must be underlying reasons why capital does not flow from rich to poor countries. Critical to our understanding of economic growth path idiosyncrasy and the effect of growth policies is the analysis why this occurs. Consequently, there has been much research that tries to solve this puzzle.

Alfaro, Kalemli-Ozkan, and Volosovych (2005) argue that a significant contributing factor is that poor countries are more likely to have weaker institutions (e.g. fewer property rights, lower financial development) where capital is not effectively allocated to productive uses and foreign investment is less likely. Reinhardt, Ricci and Tressel (2013) find that the degree of financial openness is important in explaining why capital does not flow from rich to poor countries, as less developed countries that have open capital accounts gain net capital inflows and more developed countries tend to have net capital outflows. But with a closed capital account, this does not hold as capital inflows and not correlated with the level of economic development. A third strand of research focuses on differences in human capital. Owen & Yawson (2010) argue that human development in a country plays an important role. In particular, they find that the Human Development Index, life expectancy, school enrolment and telephone usage are all significantly positively related to cross-border acquisition decisions for US firms.

(6)

5

MPK, it can at least partially be explained why capital does not flow from rich to poor countries.

The empirical part of this paper builds and expands onto the work of Caselli and Feyrer in three ways: firstly, the development of the MPK over time. This is relatively new in the literature. Several attempts have been made, however none that directly analyses the effect of capital inputs on the MPK. Secondly, we use a wider set of countries. Due to data restrictions, Caselli and Feyrer were not able to include important transitioning economies such as China. Finally, data used in the calculation of the MPK has been refined and expanded, allowing for a more accurate calculation of MPKs. We will then use our time series estimation of the MPK to make inferences about a countries’ ability to grow from capital inflows and neoclassical versus modern growth theories. Throughout this paper, we use the words country and economy interchangeably, but mean the same.

2 – LITERATURE REVIEW

2.1 - Marginal Product of Capital

The Lucas Puzzle refers to the inconsistency of economic logic behind global capital flows. This logic goes back to (neo)classical macro-economic thinkers such as Ricardo’s and the Heckscher-Ohlin comparative advantage models that go back to the 19th and early 20th century, respectively. The latter expanded on Ricardo’s theory of why specialization and international trade is beneficial by adding factor endowments (i.e. labour and capital). The model says that a country will export products that use factor endowments in which it is relatively abundant (and therefore cheap) and import products that use factor endowments in which it is relatively scarce. As poor countries are relatively abundant in labour and scarce in capital, while rich countries are relatively abundant in capital and scarce in labour, economists assume that capital flows from rich to poor countries. The logic behind these models and its implications for international trade are explained in many basic macro-economic textbooks. See, for example, Helpman (2011) for an overview.

(7)

6

not as different between countries after correcting the MPK for land and natural resources and price differences than was previously thought. In other words, there is a certain convergence of MPK levels. They then argue that human capital is the driving factor explaining the remaining differences in output per capita for the same stock of capital per capita.

Ferreira (2011), who builds on the work of Caselli & Feyrer (2007), offers a complementary explanation by looking at the credit side of MPK differences; smaller economies can have MPKs above the rest of the world without capital flowing to these countries, since they also have higher risk premiums. Ferreira showed for a subset of countries that MPKs are almost fully converged when they are risk-adjusted. Interestingly, Ferreira also add to the literature by looking at the development of the MPK over time. In his analysis, he finds that in general the mean GDP-to-capital ratio declines, with the exception of the USA. Another study by Chatterjee and Naknoi (2010) also look at the time series development of capital inflows and find that both low-income and high-income countries reap gains from capital inflows, but only on a very small scale. These findings are in line with Caselli and Feyrer, who also did not find gains from reallocating capital across countries because the MPK is almost the same everywhere when adjusted.

There are two important limitations to these studies discussed above. Firstly, the set of countries used was narrowed down, because some data were based off a study by Bernanke and Gürkaynak (2002), who calculated the labour share of income (from which the capital share of income is derived) for a restricted number of countries. Moreover, they somehow miss a lot of economies that experienced very rapid growth somewhere during the last half-century. Countries included in these studies are either economies located in the western world or are small economies (in terms of GDP), mostly located in Central America and Africa. In particular, they miss most Newly Industrialized Countries (NICs), which are countries characterized by having not yet reached developed country status but have, in a macroeconomic sense, outpaced their developing counterparts in terms of income increases (Behera, 2015). Later on, we will discuss how the growth of NICs is especially relevant for MPK calculations over time and its relevance for growth theory.

The second limitation relates to the calculation of the MPK over time by Ferreira (2010). Ferreira assumes that the capital share in income (αk) remains constant because of data

(8)

7

World Table, however, that the capital share in income generally increases over time (Feenstra, Inklaar and Timmer, 2015). So, his argument that the MPK declines over time might be because of a possible underestimation of the MPK in the years after the determination of capital shares by Bernanke and Gürkaynak in 1996. We describe how an underestimation of the capital share in income results in a lower MPK in the ‘MPK Estimation’ section below. Fortunately, new data offer a solution for both limitations, since The Penn World Table recently published its own estimation of the labour income share, which fluctuates over time.

2.2 - MPK Estimation

To correct the MPK for natural capital and price level differences, we follow Caselli and Feyrer (2007) and correct for a number of factors in the standard, neoclassical estimation of the MPK, which was used by Lucas (1990). In neoclassical growth models, the MPK is the rental rate of capital, meaning that it is the return of capital to income. If Y is GDP, K is the capital stock and α is the capital share in GDP, then

MPK = 𝛼 ∗𝑌 𝐾

The capital share in GDP is commonly backed out from estimations of the labour share in income (i.e. one minus the labour share), which usually stem from the work of Gollin (2002) and Bernanke and Gürkaynak (2002). However, this capital share includes payments to both reproducible and non-reproducible capital, for example payments to land and natural resources. On the other hand, the capital stock K is calculated using the perpetual inventory method from investment and is thus only the capital that is reproducible. Therefore, using the equation above would overestimate the MPK. As developing countries are usually much more dependent on agricultural and natural resources, the overestimation of the MPK can be especially significant for these countries. This is a critical correction, since it leads to false assumptions about the Lucas Paradox and actual MPK differences.

(9)

8

(1) MPK𝑁 = 𝛼_𝑤 ∗𝑌 𝐾 (2) MPK𝐿 = 𝛼_𝑘∗𝑌 𝐾

In the first equation, the mnemonic N stands for naïve and in the second equation, L stands for land and natural resource corrected. αw is the capital share backed out from the labour share,

while αk is the capital share that is corrected for land and natural resources. However, the

equations above still do not account for price level differences. This is relevant, since the price of capital relative to the price of consumption goods is higher in developing countries than in developed countries. To show why this is an important correction, we can consider an economy that produces J final goods that require the input of capital and other factors. Capital can be imported, produced at home or both. A firm can decide to purchase capital to use it in the production of a final good. The return on this transaction is:

𝑃₁(𝑡)𝑀𝑃𝐾1(𝑡) + 𝑃𝑘(𝑡 + 1)(1 − 𝛿)

𝑃_𝑘(𝑡)

Where P1(t) represents the domestic price of the good at time t, Pk(t) is the domestic price of

capital goods, δ is the depreciation rate, and MPK1 is the physical MPK in the production of a

good. In a frictionless international capital market, firms in all countries have alternative investment possibilities with a common rate of return R*. This implies that

𝑃₁𝑀𝑃𝐾₁

𝑃𝑘 = 𝑅

∗_{− (1 − 𝛿)}

From the two equations above, observe that the value of the MPK in any final good, divided by the price of capital is constant across all countries. We can incorporate this condition into our analysis by first noting that the total capital income is Σj PjMPKjKj, where Kj is the

amount of capital used in producing good j. We also note that PjMPKj = P1MPK1 if capital is

efficiently allocated domestically, so total capital income is P1MPK1ΣjKj = P1MPK1K, where

K is the total capital stock in a country. Since capital income is P1MPK1K, the capital share in

income is α = P1MPK1K / (PyY), where PyY is GDP at domestic prices. So, the following

holds:

𝑃1𝑀𝑃𝐾1

𝑃_𝑘 =

(10)

9

To put this more simply, this model stresses that the MPK should be corrected for the relative price level of final goods (PyY) and the capital stock (PkK). Clearly, the difference with equation 1 lies in the relative prices of final goods and the capital stock (Py/Pk). We can now define two more definitions of the MPK:

(3) 𝑃MPK𝑁 = 𝛼_𝑤∗ 𝑃𝑦𝑌 𝑃_𝑘𝐾 (4) 𝑃MPK𝐿 = 𝛼_𝑘∗𝑃𝑦𝑌

𝑃_𝑘𝐾

Where the P stands for price-corrected. Naturally, the best measure of the MPK is the latter as it is corrected for both land and natural resources and price level differences. Therefore, it will be the main unit of analysis in answering all hypotheses. We do argue, however, that we retain the other MPK estimations in our analysis, as it will allow for implications about the effects of the MPK adjustments.

2.3 - Growth theory and MPK

Now that we have established the reasoning behind MPK estimation in general, we turn more specifically to the role of capital in economic growth and the growth theories underlying this relationship. In growth economics, there have been many attempts to measure reasons for growth by using growth accounting, which is an empirical method to decompose growth into contribution of growth in production factors introduced by Solow (1956). These neoclassical models typically use a Cobb-Douglas production function, in which the change in output is caused by a change in the capital, labour and a term known as total-factor productivity (TFP/MFP), which is measured as a residual and embodies the effectiveness of the production inputs capital and labour to economic growth (Bosworth and Collins, 2008). It is therefore a measure of efficiency that depends on technological change, reallocation of production factors and terms-of-trade.

(11)

10

meaning that the input driven growth process (accumulation) will stagnate in the long run due to a decreasing productivity effect of extra capital. This implies that there can also be underinvestment when the investments are not large enough to maximize possible gains in outputs, and overinvestment when the value of investments are larger than the value of additional gains from the investment. A representation of this hypothesized relationship is given in figure 1:

Figure 1: Diminishing returns to capital

An additional characteristic of Solow’s model is that technological change is disembodied from the production curve, implying that technological change is exogenous to the relationship of capital to growth. Bosworth and Collins (2008) is an example of an accumulistic, Solow-type approach to growth differences between China and India from 1978 until 2004. While they do expand the original Solow model by looking at sector differences (sectors were aggregated in Solow’s work), they calculate the technology effect as a residual, something that is completely different from another approach to economic growth. A key finding of the article was that China’s rapid growth was mainly attributable to the growth in physical capital and growth in TFP. But, because overinvestment is a possibility in the Solow-model, growth due to of physical capital accumulation may erode in the future if there are diminishing marginal returns. On the other hand, economic growth due to increases in TFP is sustainable, since according to Solow they are exogenous to the production curve of capital per worker. A challenge for countries wanting to grow from the Solow perspective can be related to Rodrik’s (2013: 2) ‘fundamentals’ challenge: ‘how to accumulate the skills and broad institutional capabilities needed to generate sustained growth’. Essentially, this model argues that there are diminishing returns to capital and therefore the MPK declines over time.

Output per worker

y1

y0

Capital per worker

(12)

11

The second and modern economic growth theory disagrees with the exogeneity of technology. In this view, technology is embodied in the production function. At the base of this theory lies that there are multiple sectors in an economy, different from Solow’s aggregated economy, and production factors contributing to growth vary greatly between these sectors. This type of dual economy approach dates back to Lewis (1954) and argues that accumulation and productivity growth take place in modern sectors (i.e. industry and services) while traditional sectors (i.e. agriculture) remain technologically backward (Rodrik, 2013). Therefore, economic growth depends in large part on the rate at which resources can shift from the traditional to the modern sector.

In a study of the ‘Asian Miracle’, the rapid growth of several East Asian economies (Hong Kong, Singapore, South Korea and Taiwan) between 1960 and 1996 by Nelson and Pack (1999), it is argued that economic growth was mainly caused by the assimilation of technology, caused by learning effects. This ‘assimilation theory’ stresses the endogeneity of technology in the capital-output function and argues that capital per unit of labour differs greatly between the traditional and modern sector. The shift in the proportions of capital in the two sectors is the key to economic growth, which is driven by learning, innovation and entrepreneurship (Nelson and Pack, 1999). Contrary to Solow’s ‘assimilation’ theory, growth in the capital stock does not have to suffer from diminishing marginal returns if it is moved from the traditional to the modern sector. This theory relates to Rodrik’s ‘structural transformation challenge’: how to ensure that resources flow rapidly to the modern economic activities that operate at higher economic productivity’ (2013: 2). The MPK does not have decrease over time if there is a significant impact of productivity.

(13)

12

productivity over the entire economy. Nelson and Pack (1999) argue that the growth involved learning to use new machinery and production processes. It is the assimilation of technology that causes economic growth and the reallocation of resources from traditional to modern sectors with higher profitability and productivity. Ventura (1997) proposes a similar argument in which these export-oriented East Asian economies were able to exploit capital to reallocate from labour-intensive to capital-intensive sectors. This ensures that while the capital stock per worker grows in the economy as a whole, it remains unchanged within each industry. So, the MPK does not decline. Many assimilationists point at the continued growth of the East Asian countries to prove their point.

Clearly, the two theories view the development of the MPK over time differently. In general, accumulationists expect a declining trend in MPK as a result of capital inputs, as the steady increase of the capital stock implies diminishing returns. On the other hand, assimilationists argue that because of productivity increases and the shift towards capital-intensive sectors, the MPK does not have to decrease over time as a result of capital increases. In fact, it may even increase. The main argument of this paper is that this partition in macro-economic theory regarding its effect on the MPK has not been explained and needs further investigation.

(14)

13

systems converge MPK level differentials. This is also what Caselli & Feyrer (2007) theorize: differences in MPKs are the result of credit frictions in the world allocation of capital. Therefore, theory suggests that MPKs will converge over time as financial systems improve. So, in MPK terms, some countries may gain from improved financial systems while others may lose. On average, however, it can be expected that the MPK increases over time when financial systems improve, as higher financial development implies that capital is more efficiently allocated which raises the marginal product of capital if nothing else changes over time. However, if there is a declining trend in MPK because of factors other than financial development, financial development may have a seemingly negative effect depending on the influences of other variables in the model.

A second factor that influences the MPK are shocks to the global rate of return. Remember from the theory of the relevance of price-level adjustment in MPK calculations that:

𝑃₁𝑀𝑃𝐾₁

𝑃_𝑘 = 𝑅∗− (1 − 𝛿)

(15)

14

theory is true because it does not prove diminishing returns to capital or productivity increases. Risk shocks occur with regular frequency in the timeframe of our dataset, most dominantly during the 1990s and late 2000s (Alpanda, 2013). We therefore argue that we need to control for these shocks.

Finally, high inflation rates have a negative effect on the MPK. The reason is that higher inflation discourages the use of money, which reduces the marginal product and the output of physical capital. This theory stems from papers on the effect of inflation on economic growth, for example that of Mundell (1963) and Tobin (1965). In a survey on the theoretical literature on inflation and growth, Gillman and Kejak (2005) refer to the role of inflation in that it acts as a tax on capital which decreases the marginal product of capital and lowers growth. Fischer (1983) in an analysis of inflation and growth confirms that higher inflation is associated with lower returns to capital because it reduces the efficiency of factors of production.

In the presence of the effects that financial development, world interest rates and inflation have on the development of the MPK, which we will account for, we are now able to specify the main hypotheses regarding the accumulationist versus assimilationist theory:

Hypothesis 1.1: Changes in the MPK are negatively related to changes in the capital stock over time, therefore there are diminishing returns to capital and the accumulistic theory has the most ground.

Hypothesis 1.2: Changes in the MPK are not or positively related to changes in the capital stock over time, therefore there are significant productivity increases and the assimilistic theory has the most ground.

(16)

15

NICs provide a special case for MPK calculations over time. These countries typically rapidly accumulate human and physical capital, and in doing so their share of world production and exports of capital-intensive goods rises and their share of unskilled-labour-intensive production falls (Romalis, 2004). This shift during our timeframe in the analysis is a unique property of NICs (or, at least, is most substantial in NICs). To see why this shift is important for the development of MPK over time, consider the corrections that we make to MPK in section 2.2. Firstly, if the share of unskilled-labour-intensive production (i.e. agriculture) falls, the share of natural resources in the capital share in income must also fall while the reproducible share rises. Secondly, the price-level correction for NICs also alleviates over time, as the price gap of capital relative to consumption goods must fall when it moved to capital-intensive industries, because of the increasing investment possibilites. Therefore, ceteris paribus, the MPK increases over time. Note that the addition of ceteris paribus in the last statement is important, as the changes in conditions mentioned above do not imply that there are no diminishing marginal returns. In fact, a recent study by Fernald and Neiman (2011) provides evidence that productivity has had a negative effect on growth in Singapore when it was a NIC in the 1970s and 80s. So, while the MPK may initially increase when moving to capital-intensive sectors, it may decrease over time if there are decreasing rates of return to investments and no significant productivity increases to alleviate this. Still, we expect that the shift to capital-intensive sectors plays an important role in the development of its MPKs and that this ‘catch-up’ with developed economies causes a boom in returns to capital, because of their increasing share of reproducible capital and cheaper capital. Therefore, PMPKL is likely to react differently to changes in the capital stock in NICs than other economies and we structure the following hypothesis accordingly:

Hypothesis 2: The relationship between the PMPKL and the capital stock, established in testing of hypothesis 1, does not hold for NICs.

(17)

16

PMPKL measure, since it corrects for relative price levels and natural capital which is essential for the development of MPKs in NICs as theorized above.

Hypothesis 3.1: Without NICs, changes in the PMPKL are negatively related to changes in the capital stock over time, therefore there are diminishing returns to capital and the accumulistic theory has the most ground when NICs are disregarded.

Hypothesis 3.2: Without NICs, changes in the PMPKL are not or positively related to changes in the capital stock over time therefore there are significant productivity increases and the assimilistic theory has the most ground when NICs are disregarded.

3 – DATA AND METHODOLOGY

3.1 – PWT Data

The data are compiled from a combination of data from the most recent edition of the Penn World Table (PWT 8.1), which were released on April 13th, 2015 (Feenstra, Inklaar and Timmer, 2015), and data from a World Bank report named The Changing Wealth of Nations, which was released in 2011. Our dataset is framed between 1990 and 2011, whereas the PWT has data available that go back as far as 1950. The motivation for the shortened timeframe is twofold: firstly, wealth data from the World Bank are only available for the years 1995, 2000 and 2005. We cannot provide wealth estimates much earlier than 1995 due to reliability issues that will be discussed in detail later on. Secondly, some economies only have data available from 1990 onwards. Including these economies is important since they might provide useful evidence on the MPK of these countries since they are rather unique in the sense that they are in a turbulent growth phase. After combining data from the PWT, World Bank and other sources, 77 countries remain with data of 22 years ranging from 1990 to 2011. An overview of countries included is listed among the appendices.

Variables Y, K, aw, Py and Pk all come from the PWT. Since the publication of Caselli &

(18)

17

intended to measure differences in standard of living across countries. Thus, we will use output-based GDP since MPK is a measure of the capital’s productivity in a country. The second distinction is between ‘Real GDP’, based on prices that are constant across countries and over time, ‘Current-price Real GDP’, based on prices that are constant across countries in a given year and ‘National Account GDP’ that is constant over time, but not over countries. For our measure of Y, we use the output-based current-price GDP at current national prices in millions of 2005 US$ (which is named CGDPo). We choose this measure since the price level of GDP (Py) is based on this measure of GDP. In our analysis of price-level corrected MPKs,

we multiply Py with Y, creating a nominal measure of GDP and we multiply Pk with K,

creating a nominal measure of the capital stock. This makes Y and K comparable. For an overview of measurements of GDP and other variables, see Feenstra, Inklaar and Timmer (2015: 7).

Like Y, Capital stock K is the capital stock at current national prices. It is based on cumulated investment in structures and equipment (Feenstra, Inklaar and Timmer, 2015) and it is calculated using the perpetual inventory method. In the estimation of capital stocks, investment and depreciation are distinguished by type of asset. This is an important contribution to our estimations, as this makes it possible to account for the difference in asset composition and relative prices of asset type between countries. For example, our MPK estimations may be biased downwards for poor countries if long-lived assets, such as buildings, are given too much weight. The PWT corrects for several groups of assets, including slowly depreciation assets such as structures (2%) and rapidly depreciating assets such as software and computers (31,5%) (Inklaar and Timmer, 2013).

(19)

18

MPK in countries experiencing a turbulent period of GDP growth, as was discussed in the literature review. Additionally, the PWT improves on previous work by allowing the labour income share to change over time. Interestingly, they find that the labour income share declines over time for 89 of the 127 countries. Ceteris paribus, this hints at an increase of the MPK in these countries over time. The final two variables are directly taken from the PWT and account for price level differences in our MPK estimations with variable Py reflecting the

price level of GDP, which is a measure of the PPP divided by the exchange rate. Pk is the

price level of the capital stock. So essentially, Py/Pk reflects the price level of consumption

goods to the price level of capital in any country at any given point of time.

3.2 – World Bank Data

To adjust for land and natural resources and to allow only reproducible capital to be taken up in the capital income share, we need wealth data that divide between the two. In 2011, the World Bank has published a comprehensive report named The Changing Wealth of Nations. They diverge from standard measures of economic growth, GDP, because they argue that there is a need for a sustainable measure for economic growth by accounting for, amongst other things, depletion of natural resources. For example, a country could grow its GDP by depleting stocks of forests and minerals, but this growth would not be sustainable (World Bank, 2011). For policy makers, the main implication of the report is that while overall wealth, like GDP, would appear to be growing steadily, the decomposition of a countries wealth suggests that some growth paths are not sustainable due a trend of decreasing natural resources. Total wealth (variable W) is defined as ‘the measure of total (or comprehensive) wealth is built upon the intuitive notion that current wealth must constrain future consumption’ (World Bank, 2011: 4). Total wealth includes (1) Intangible capital, which is measured as a residual and constitutes human-, social-, and institutional capital. In almost every instance, intangible capital is the largest contributor to total wealth. (2) Produced capital includes machinery, structures and equipment. It is the sum of physical capital and urban land (3) Net foreign assets, which are calculated as total assets minus total liabilities and (4) Natural capital, which is the sum of rents from cropland, pastureland, timber, non-timber forest, protected areas, oil, natural gas, coal and minerals. Like Caselli & Feyrer (2007), we define wealth as produced capital plus natural capital and correct for land and natural resources:

𝛼𝑘 = (

𝑃𝑘𝐾

(20)

19

We adjust the capital share in income (aw) for land- and natural resources using the same logic

as Caselli & Feyrer (2007). Total wealth is the reproducible capital plus natural wealth (i.e. W = (PkK+ L), then payments to reproducible capital is PkK*r and payments to natural resources

L*r. Assuming that differences in capital gains for natural and reproducible capital are relatively small, reproducible capital’s share of total capital income is proportional to reproducible capital’s share of wealth, since all units of wealth pay the same return. So, 𝑃_𝑘𝐾/𝑊 is estimated using data from the World Bank, and aw stems directly from the PWT.

The average constitution of wealth of the countries in our dataset is:

Average 1995 2000 2005 Reproducible capital 58,2% 59,4% 56,3% 58,9% Urban land 14,2% 14,3% 14,1% 14,1% Natural capital 26,5% 26,3% 26,1% 27,0% of which: Cropland 8,1% 8,4% 9,1% 6,7% Pasture land 3,3% 4,0% 3,4% 2,6%

Timber and other forest 2,4% 2,2% 2,9% 2,0%

Protected land 2,8% 2,7% 3,2% 2,5%

Oil 3,4% 3,3% 3,0% 4,0%

Natural gas, coal and minerals 1,7% 1,2% 1,3% 2,6%

Subsoil assets 5,1% 4,5% 4,3% 6,6%

Table 1: Constitution of wealth

Over time, the average wealth distribution remains rather constant. Only the components of natural capital change substantially: the relative value of crop- and pasture land decreases, while oil, natural gasses and subsoil assets have increased. As was theorized, the constitution of wealth differs greatly between countries. For example, wealth in rich countries such as Germany, the UK and Switzerland consists of over 90% of reproducible capital, while the wealth for poorer countries, such as Burundi and the Central African Republic consists mostly of natural capital. Less than 20% of total capital is reproducible in these countries.

Unfortunately, the World Bank only has wealth data available for three years: 1995, 2000 and 2005. We need to tread carefully with the estimation of wealth for the remaining years as an overestimation of the share of natural resources in wealth leads to an underestimation of ak,

(21)

20

in wealth data. To adequately cope with these data restrictions we propose the following method: for data points between 1995-2000 and 2000-2005, we let the share of reproducible capital increase or decrease with a constant factor until the reference point in 2000 or 2005 is reached. For the remaining years, i.e. before 1995 and after 2005, we let the reproducible capital share remain constant. We cannot adequately predict the share of reproducible capital in the wealth data for these years. Firstly, because this share is dependent on many economic factors which are out of the scope of this paper. Secondly, a second source of natural capital is available for some countries (e.g. the US Office of Management and Budget publishes accounts of land and natural resources), but for most countries, the World Bank is the only institution that publishes worldwide accounts as far as we know of. The World Bank does publish a yearly indicator of natural capital in GDP but it includes only a few elements of natural capital and it does not include urban land. Finally, we cannot accurately predict values of reproducible capital, because of the low amount of data points that are factual and the unreliability that such predictions would produce.

A fair criticism would be that the constant share of reproducible capital for these years ignores the fact the MPK may be affected by the assumption that this share does not fluctuate. For example, the financial crisis may have had a temporal small negative effect on the share of reproducible capital (World Bank, 2011). While this is certainly a limitation, it should not matter for our research questions. Our dataset consists of 22 years and shocks that only last a few years on the reproducible capital share during these years will have a limited effect on the MPK regression estimations within a country. In any case, we deem our method of estimating the reproducible capital share more reliable then Ferreira’s (2011) estimations, where the share is constant across the entire period.

3.3 – Data for other independent variables

(22)

21

issued to governments, government agencies and public enterprises (Levine, 2005). So, private credit is an effective measure of the allocation of capital to where it is productive. Levine and Zervos (1998) and Levine, Loayza and Beck (2000) use the same or similar measures for financial development. The literature review by Levine (2005), on which our definition of financial development is based, remains positive about private credit as proxy for financial development in panel data analysis (Levine, 2005: 54). It is also one of the World Bank’s core indicators of financial development (Čihák et al., 2013). Therefore, we argue that private credit is the best proxy for financial development that is available in our data frame. Not surprisingly, there is enormous cross-country variation in private credit. In 2011, it is less than 10% of GDP in Sierra Leone, while it is almost 200% in countries such as the UK, US and the Netherlands. The private credit data is missing for some years in some countries, but normally not for more than 1 or 2 years. We interpolate the data for these years because we do not expect large shocks in private credit. Data in years for when there are financial crises are never missing.

Inflation data are also available from the World Bank Database. We use the GDP price deflator inflation as it measures the price level of total production in the economy instead of a basket of consumer goods and services in the consumer price index (World Bank, 2015). This is relevant as it is expected that inflation affect the MPK by changes in prices for the economy as a whole, not just by consumer prices. Also, inflation is not already incorporated into our measure of Y since we chose to use current-price GDP. Finally, to allow for fluctuations in the world interest rate we will incorporate year-dummies that capture these fluctuations.

In our analysis we shortly mention the difference in MPK between developed and developing countries. This categorization is taken directly from the most recent version of the World Economic Outlook from the IMF (2015), and, like Caselli & Feyrer’s paper, is based on income level.

3.4 – Methodology

(23)

22

2008). The pooled model is one where the data on different countries are simply pooled together with no provision for individual differences that might lead to different coefficients. From the literature review, it should be clear that this is not what we try to measure, as we know that there may be country-specific differences in MPK development and the influence of capital. The standard model that does incorporate this characteristic is a fixed-effects model (Hill, Griffiths & Lim, 2008). Fixed-effects models explore the relationship between predictor and outcome variables within the country and each country has its own individual characteristics that may or may not influence the predictor variables. To empirically test if the fixed-model is preferred (vis-à-vis the random effects model) we run a Hausman test where the null-hypothesis is that the preferred model is random effects vs. the alternative the fixed effects. So, we test whether the unique errors are correlated with the regressors, the null hypothesis is they are not. Therefore, if the null hypothesis is true, both the coefficients of the random effects and the fixed effects are consistent, while only the fixed effects model is consistent when the null hypothesis is rejected. We will explain why this is especially important in our model further along the methodology.

The Hausman test requires coefficients to be on a similar scale to be accurate, and since MPK estimations are much smaller than the capital stock, we momentarily transform these variables. Other variables need not to be transformed. The Hausman test gives a χ2 of 15.61 with a p-value of 0.0014, indicating that the null-hypothesis must be rejected, as it is significant at the 1% level. Therefore, the fixed-effects model is appropriate. This makes it possible to further specify our model (as there is no ui error term in fixed effects models) and

write down the following regression equation:

𝑀𝑃𝐾𝑖𝑡 = 𝛽0+ 𝛽1𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑆𝑡𝑜𝑐𝑘𝑖𝑡+ 𝛽2𝐹𝐷𝑖𝑡+ 𝛽3𝛱𝑖𝑡+ 𝛿𝑡𝑇𝑡+ 𝑒𝑖𝑡

Where dependent variable MPK can be either MPKN, MPKL, PMPKN or PMPKL, CapitalStock is K transformed to trillions (1012) of US$ to make coefficients easier to interpret, FD is level of financial development and Π is inflation, all in country i in year t. T is the time dummy variable that captures year-specific shocks. Furthermore, βk is the coefficient

for the independent variables; δ the coefficient for the binary time regressors and e is the error term. All but the time dummies are continuous variables.

(24)

23

and as our data are relatively ‘long’ (T = 22) and ‘wide’ (N = 77) according to the standards of Hill, Griffiths & Lim (2008: 538), implications about MPK development are reliable. The only exception to this is when we test for hypothesis 2. NICs are relatively few in number (N = 9) and therefore country-specific characteristics that influence the MPK in a way that is different from what we expect from NICs may impose threats to the conclusions we derive from testing this hypothesis. For example, NICs did not all start shifting to capital-intensive sectors at the same time and several had already started doing so at the beginning of our timeframe. We argue, however, that hypothesis 1 and 3 are the main hypotheses to test in this paper. The second hypothesis serves more to show that MPK development in NICs can be different from that of the RoW and can therefore significantly affect conclusions from the main hypothesis.

A second issue regarding the estimation of the model is that K is used both as an independent variable and in the construction of the MPK, causing, to some degree, a form of endogeneity known as simultaneity bias (Hill Griffiths and Lim, 2008). Therefore we expect the error term eit to be partially correlated with the variable CapitalStock. Under normal circumstances, one

would create a model using an instrumental variable for CapitalStock to counter this problem and estimate the model accordingly. However, there are no valid instruments as there are none that affect the MPK only through the CapitalStock, thus satisfying the exclusion restriction and are exogenous to the model (i.e. that do not correlate with the error term eit). For example,

higher financial development may generally increase K, but it can also directly affect Y, Pk or

other variables that constitute MPK, and because of this it is not a viable instrument. Treating it as an instrumental variable does therefore not improve the validity of our estimations. Alternatively, if we choose an instrument that is highly related to changes in the capital stock, for example gross capital formation, there is no reason to assume that this is not related to the error term if changes in the capital stock are, and is therefore not exogenous. Another common practice in applied econometrics work to avoid simultaneity bias is using lagged values. Reed (2013) and Bellemare, Masaki and Pepinsky (2015) show that this does not solve simultaneity bias. In contrast, the problem may even become more hazardous if the model is characterized by serial correlation, which is the case in this model, as we will prove shortly hereafter.

(25)

24

is consistent even in the presence of correlation between CapitalStock and ui, because the

fixed effects models treats this as fixed parameters to be estimated (Hill Griffiths and Lim, 2008). Consequently, fixed effects results are consistent even if ui correlates with

CapitalStock. Besides, the model includes accounts for several factors that may influence MPK levels besides capital stock changes, including year dummies, financial development and inflation. So, capital stock coefficients do reflect the relationship between capital stock changes and MPK changes as best as possible in the presence of these factors, that may identify part of the bias in the estimation.

To clarify, we do not defy the notion that simultaneity bias does not have an effect in our model, nor do we try to do so. It is, however, preferable to the alternative, which is using a model with an instrumental variable, as we cannot be sure that such a variable does not violate the properties that instrumental variables should have or use lagged variables that may even exacerbate the problem. Therefore, the fixed effects model provides the most consistent estimation. Fortunately, we can determine the direction of the bias, which we will discuss thoroughly in the discussion of the results.

(26)

25

4 – RESULTS

4.1 – Summary statistics

Before moving to the testing of the hypotheses, we will provide some summary statistics of the MPK data. Firstly, we can show differences in the four MPK measures by taking country-averages (so that standard deviation is cross-country only) and categorizing these geographically and (socio)-economically:

MPKN MPKL PMPKN PMPKL

N Mean (SD) Mean (SD) Mean (SD) Mean (SD)

World 77 .197 (.091) .105 (.047) .176 (.072) .098 (.047)

Africa 21 .243 (.106) .092 (.069) .187 (.087) .073 (.060)

Asia 18 .198 (.054) .112 (.038) .196 (.077) .110 (.045)

Australia 3 .188 (.062) .094 (.014) .176 (.057) .089 (.008)

Europe 20 .123 (.036) .107 (.029) .126 (.037) .111 (.033)

North and Central America 8 .244 (.093) .126 (.046) .208 (.069) .114 (.048)

South America 7 .212 (.114) .099 (.047) .194 (.033) .093 (.025)

Developed country 27 .133 (.039) .115 (.035) .136 (.038) .119 (.037)

Developing country 50 .231 (.092) .100 (.051) .197 (.077) .087 (.048)

NIC 9 .219 (.048) .113 (.032) .200 (.023) .104 (.023)

Non-NIC 68 .194 (.095) .104 (.048) .173 (.076) .098 (.049)

Table 2: Differences in MPK measures

Overall MPK estimates significantly drop when corrected for natural capital. Especially in regions such as Africa, Central America, South America and developing countries in general, this correction is significant as it drops MPK levels with over 50%. The price-level correction also differs greatly between countries; in Europe and in developed countries, capital is cheaper than consumption goods (i.e. Py/Pk > 1), but in developing countries capital goods are

more expensive than consumption goods. This correction is especially strong for African countries, as it drops the MPK estimate with almost 25%, on average.

(27)

26

Figures 2.1 to 2.4: Scatterplots of MPK measures and the ln of GDP per engaged person

All graphs above are in line with Caselli & Feyrer’s conclusions: MPKs are not higher in developing countries (in terms of income level) than in developed countries. Contrarily, MPKL and PMPKL seem to increase with income level. We can also show the development of the best measure of MPK, PMPKL, over time, using the same categorizations as in table 1:

1990 2000 2010

N Mean (SD) Mean (SD) Mean (SD)

World 77 .089 (.046) .097 (.054) .103 (.051)

Africa 21 .060 (.049) .068 (.072) .088 (.067)

Asia 18 .107 (.058) .107 (.049) .113 (.050)

Australia 3 .075 (.013) .079 (.013) .101 (.008)

Europe 20 .102 (.026) .115 (.039) .107 (.036)

North and Central America 8 .098 (.038) .118 (.048) .117 (.057)

South America 7 .083 (.022) .088 (.029) .095 (.034)

Developed country 27 .114 (.037) .121 (.040) .116 (.042)

Developing country 50 .075 (.044) .084 (.056) .096 (.054)

NIC 9 .095 (.040) .097 (.028) .112 (.030)

Non-NIC 68 .088 (.047) .097 (.028) .102 (.053)

(28)

27

According to the data, PMPKL has increased in every category. More interestingly, however, is that MPKs also seem to have converged over time. While MPK levels in developed countries have remained relatively constant, MPKs in developing countries have been on a steady rise since the 90s. This may be caused by several factors, for example the capital share in income has risen in most economies according to the authors of the PWT database (Inklaar and Timmer, 2013). Therefore, increasing MPK does not necessarily point to a rejection of diminishing returns – which is perhaps slightly counterintuitive – but can also result from increasing capital shares in income, declining share of natural capital in total capital, reducing capital price levels vis-à-vis consumption price levels or factors such as improving financial development, increasing world interest rates or reduced inflation. We show how the natural capital and price level corrections show in the development of the MPK, taking yearly averages, in the figure below:

Figure 3: Development of different MPK measures

Figure 3 shows that much changes when the MPK is corrected. In fact, the price level corrected MPKs show an increasing trend over time, while the other two measures decrease. We also observe a negative shock in all MPK measures at the end of the 2000s, around the time, possibly showing the consequences of the 2007 financial crisis. The next section deals with answering the question if there are diminishing returns, which is examined by testing how changing capital stocks influence the MPK.

(29)

28 4.2 – Hypothesis testing

We now move on to the testing of the hypotheses using the fixed-effects model specified in section 3.4. If there are diminishing returns to capital (hypothesis 1.1), changes in the capital stock must be negatively related to the MPK. We estimate the regression coefficients for all measures of MPK. Time dummy estimations are left out of the output report, due to the lengthy list of dummy variables, but are included in the model. The regression output is given below: (1) (2) (3) (4) VARIABLES MPKN MPKL PMPKN PMPKL CapitalStock -0.00239*** -0.000898*** -0.00153*** -0.000373 (0.000730) (0.000337) (0.000520) (0.000245) FD -0.000104 -1.81e-05 -0.000241*** -5.11e-05**

(6.55e-05) (3.02e-05) (4.67e-05) (2.20e-05)

Π -5.96e-06 -8.26e-07 -8.14e-06* -3.27e-06

(6.80e-06) (3.14e-06) (4.84e-06) (2.28e-06)

Constant 0.224*** 0.115*** 0.169*** 0.0921***

(0.00659) (0.00304) (0.00469) (0.00221)

Observations 1,694 1,694 1,694 1,694

R-squared 0.777 0.813 0.817 0.893

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 4: Core model regression output

In three out of four MPK measures we accept hypothesis 1.1 as capital stock changes are significantly and negatively related to MPK changes with p-values of 0.001 (MPKN), 0.008 (MPKL) and 0.003 (PMPKN). The model explains most of the variance for all MPK measures with R2 ranging between 0.78 with dependent variable MPKN and 0.89 with dependent variable PMPKL. Unfortunately, it is our best measure of MPK, PMPKL, that is not aligned with the results of regression estimations of other MPK measures. The results below do show that the capital stock is negatively related to PMPKL, but is not statistically significant on any level with a p-value of 0.128. We therefore cannot determine whether there are diminishing returns to capital with this measure of MPK and therefore reject hypothesis 1.1 and accept hypothesis 1.2 for dependent variable PMPKL. Because there are no significant diminishing returns, there have to be productivity increases that counter diminishing returns, at least in some economies.

(30)

29

sectors. We use the model to estimate the relation of changes in PMPKL to changes in the capital stock, but only for NICs:

(5) (6) (7) VARIABLES PMPKL (only NICs) PMPKL (only NICs) PMPKL (only non-NICs) CapitalStock 0.00042 0.00092** -0.00325*** (0.000407) (0.00041) (0.000411) FD 0.00059*** (0.000107)

Π -6.48e-06 -3.58e-06 -3.80e-06

(5.48e-06) (5.91e-06) (2.56e-06)

Constant 0.0687*** 0.0949*** 0.0921***

(0.00823) (0.00728) (0.00203)

Observations 198 198 1,496

R-squared 0.659 0.597 0.906

Table 5: NIC regression output with adjustments

Based on the results above (regression 5), we cannot directly accept hypothesis 2. While the coefficient of the capital stock turns from negative to positive, it is not significant on any level (p-value of 0.28) and therefore does not significantly differ from estimations including all countries. Problems with this estimation due to the relatively small N have been discussed in the methodology section. As expected, the R2 is also considerably lower than in the other regression estimations, indicating that the data fits the model less than in other regressions.

(31)

30 (8) VARIABLES PMPKL (only non-NICs) CapitalStock -0.00289*** (0.000407) FD -7.03e-05*** (2.21e-05) Π -3.54e-06 (2.50e-06) Constant 0.0945*** (0.00223) Observations 1,496 R-squared 0.912

Table 6: Non-NIC regression output

Clearly, excluding NICs has a major effect on the significance of the capital stock. Changes in the capital stock is now highly significantly and negatively related to changes in PMPKL with a p-value of <0.001. For every additional trillion of US$ worth of capital, our best measure of MPK is expected to decrease with almost 0.003, on average. Therefore, we accept hypothesis 3.1 that changes in the PMPKL are negatively related to changes in the capital stock over time and the accumulistic theory has the most ground.

4.3 – Robustness tests

To test the robustness of the results in the previous section we employ three methods of doing this. Firstly, we will test whether the relations motivated in the previous section hold when reducing the timeframe to 1995 until 2005. Remember from the data section that we hold the share of reproducible capital constant for years outside this frame. Major developments in the constitution of capital in years before 1995 or after 2005 may therefore have consequences for the development of MPK, which we cannot directly account for.

(9) (10) (11) (12) (13) VARIABLES MPKN MPKL PMPKN PMPKL PMPKL (only non-NICs) CapitalStock -0.00444*** -0.00219** -0.00258** -0.000808 -0.00278*** (0.00159) (0.000870) (0.00120) (0.000607) (0.000857) FD 0.000146 0.000222*** -0.000161** 1.87e-05 -3.00e-05

(9.19e-05) (5.04e-05) (6.94e-05) (3.52e-05) (3.67e-05)

Π 8.26e-05 -3.23e-05 4.64e-05 -2.80e-05 -2.28e-05

(0.000151) (8.30e-05) (0.000114) (5.80e-05) (6.34e-05)

Constant 0.193*** 0.0951*** 0.175*** 0.0940*** 0.0976***

(0.00648) (0.00356) (0.00489) (0.00248) (0.00260)

Observations 847 847 847 847 748

R-squared 0.891 0.897 0.905 0.945 0.955

(32)

31

The robustness test is applied to all models used in hypothesis 1 (regressions 9 to 12) and hypothesis 3 (regression 13). The estimates above suggest that none of the conclusions from section 4.2 change. Only the level of significance changes for dependent variables MPKL and PMPKN with p-values of 0.012 and 0.032, respectively.

Secondly, we can test whether the change in significance of the capital stock (after removing NICs from the dataset) is robust by reviewing its performance by systematically removing variables that also affect the PMPKL. The motivation for this type of robustness test is that we should doubt the causality of capital stock changes to PMPKL if the conclusions we derived from models in section 4.2 change when other variables are dropped (White and Li, 2010). For example, there may be confounders that significantly change the relationship between the capital stock and PMPKL, as we saw in regression (6). Note that we only apply this robustness test to regression (8), as it was the only significant relation for hypothesis testing for PMPKL to begin with. Off course, the robustness test does not imply that increases or decreases in capital stock coefficient significance is directly attributable to the hypothesis testing, but serves to show that if there are confounders that move the coefficient in the opposite direction, the model may be wrongly specified as multicollinearity has a significant effect in this case. We firstly remove the time dummies in model (15), after which we remove inflation in (16) and financial development in (17).

(14) (15) (16) (17) VARIABLES PMPKL (only non-NICs) PMPKL (only non-NICs) PMPKL (only non-NICs) PMPKL (only non-NICs) CapitalStock -0.00289*** -0.00152*** -0.00151*** -0.00106** (0.000407) (0.000428) (0.000429) (0.000412)

FD -7.03e-05*** 7.36e-05*** 7.45e-05***

(2.21e-05) (2.09e-05) (2.09e-05)

Π -3.54e-06 -5.89e-06** (2.50e-06) (2.67e-06) Constant 0.0945*** 0.0953*** 0.0952*** 0.0991*** (0.00223) (0.00134) (0.00134) (0.000745) Observations 1,496 1,496 1,496 1,496 R-squared 0.912 0.895 0.895 0.894

Table 8: Confounder robustness test

(33)

32

(17) to be only significant on the 5% level. Still, its p-value of 0.010 is still very close to significance on the 1% level.

The final sensitivity analysis deals with the heteroskedasticity and autocorrelation in the data. Regression (18) shows that regression (8) remains statistically significant when standard errors are clustered within countries, although the level of significance drops to 5% with a p-value of 0.021. (18) VARIABLES PMPKL (only non-NICs) CapitalStock -0.00289** (0.00124) FD -7.03e-05 (4.95e-05) INF -3.54e-06*** (7.35e-07) Constant 0.0945*** (0.00367) Observations 1,496 R-squared 0.912

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 9: Heteroskedasticity and autocorrelation robustness test

Indeed, the table above suggests that even with the arguably unreliability of the heteroskedasticity and autocorrelation tests specified in the methodology section, the result is robust.

4.4 – Discussion of results

(34)

33

have shown that the corrected measure for MPK tends to increase with income level. In figure 3, we show that the development of MPK changes when the corrections are applied, as it tends to decrease for the uncorrected measure and increases when it is corrected for natural capital and price levels.

In regard to the PMPKL calculations over time, we find that MPK levels have increased in every category, although less developed countries have risen more sharply. We argue that contributors to this are the increasing capital share in income, which according to Feenstra, Inklaar and Timmer (2015) has risen for 89 out of 127 countries in the PWT, and the decreasing price level of capital relative to consumption goods. Our findings are different than that of Ferreira (2011) who showed that the GDP-capital ratio has actually declined. However, the findings of Ferreira are not mutually exclusive from ours, as Ferreira reports a declining GDP-capital ratio that does not include the (rising) capital share in income and therefore his conclusion that the MPK has declined is not necessarily correct. Ferreira also uses a different timeframe (1950-2003) and while the GDP-capital ratio has been declining rapidly since the 1950s, he argues, it has been relatively stable around the start of our timeframe in 1990 (Ferreira, 2011: 470). Thirdly, Ferreira uses a smaller set of countries that excludes most NICs, which may also affect the mean MPK trend.

The first set of regressions in table 3, including all 77 countries, show that for the three lesser MPK calculations, there is a significant negative relationship between the capital stock and MPK and therefore we accept hypothesis 1.1 that there are diminishing returns to capital and the accumulistic theory has the most ground. The corrected measure of MPK, however, is negative but not statistically significant and thus we fail to accept hypothesis 1.1 and accept hypothesis 1.2 instead that the assimilistic theory has the most ground, however with little validity. At this point it is probably appropriate to discuss what the effect of the simultaneity bias, which was discussed at length in the methodology section, may be. We cannot argue against the notion that the bias makes the estimators inconsistent to some degree. However, this does not imply that the estimates are of no use as, instead of using invalid and/or exogenous instruments, we are able to provide the direction of the bias.

(35)

34

‘feedback loop’, which causes the bias in the coefficient in K is negative and the bias is thus downward on the capital stock. This allows us to safely assume that the inferences we make about the coefficient of the capital stock when the dependent variable is PMPKL in regression (4) are consistent, especially in the presence of simultaneity bias. In reality, the capital stock may even be significantly positively related to PMPKL if the effect of the bias is substantial, which would improve the validity of hypothesis 1.2 and strengthen the assimilistic theory. So, we argue that there are no significant decreases in the PMPKL as a result from capital stock increases, and therefore the assimilistic has the most ground.

The reverse is true when we consider regression (8) where we find significant evidence in favour of hypothesis 3.1 that says that there are diminishing returns to capital if we disregard of NICs in the data. The downwards bias makes the coefficient of CapitalStock excessively negative, which in an extreme case might lead to a Type II error, where we fail to reject hypothesis 3.1 (accumulation) and should have supported hypothesis 3.2 (assimilation). We remain positive, however, that hypothesis 3.1 is consistent, as the simultaneity bias has to be very substantial for a Type II error since the coefficient is significant on the 1% level and even on the 0.1% level. We argue that the use of a fixed effects model and inclusion of other variables that influence the MPK has diminished the severity of such bias and therefore assume, with caution, that hypothesis 3.1 is consistent.

Even if the impact of simultaneity bias is substantial, the impact that removing NICs from the data has on regression estimation is irrefutably causing accumulation to be more grounded compared with when NICs are included in the data. This proves a core argument in the literature that NICs follow a different growth path in terms of capital stock to MPK changes. Especially when financial development is removed in regression (6) and (7), which acts as a confounder, we find that the influence capital has is distinctly different in NICs and NICs, since the sign is significantly positive for NICs, while significantly negative for non-NICs.

Marginal product of capital and growth theory: accumulation versus assimilation with a special case for NICs