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Intellectual Capital Growth Model,Economics, Economic Growth Theory, Endogenous Growth model, AK Model, Intellectual Capital, Total Factor ProductivityThe theory of intellectual capital has experienced a boom in the first decade of 21st century. Most of theresearch work in this area focuses on enterprises and organizations, although there is an effort, especially lately, to provideanswers concerning development of national economy. This theory has a lot of potential to create new insights and it isexpected that it becomes even more incorporated into mainstream economics. This paper is an attempt to incorporateintellectual capital theory insights into endogenous growth theory as part of modern macroeconomics. In this paper,simple AK endogenous growth model is used as a basis. The intellectual capital growth model presented here also takes“A” or Total Factor Productivity as an average total productivity but with one fundamental distinction. It is using the logicof Calculated Intangible Value and/or Knowledge Capital Earnings by Baruch Lev where higher than average returnsindicate higher intellectual capital. The model presented here applies this logic to Total Factor Productivity. In cases whereTFP is equal to the average, the intellectual capital performance is also equal to the average, and the model is withconstant returns as the AK model. But in cases where TFP is larger than average, the intellectual capital performance is alsobetter than average, and the model is with increasing returns, and in cases where TFP is less than average, the intellectualcapital performance is worse, and the model is with diminishing returns. The most important implication of the model isthat savings and investments have a long‐term effect on growth only if intellectual capital performance is equal or betterthan average. If intellectual capital is worse than average there is no such an effect because of diminishing returns. In sucha situation the policy should be first to increase intellectual capital to at least average performance and then to increaseinvestments.
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Intellectual Capital Growth Model: Using IC Measurement Logic on AK Endogenous Model
Stevo Pucar Faculty of Economics, University of Banja Luka, Banja Luka, Bosnia and Herzegovina [email protected] Abstract: The theory of intellectual capital has experienced a boom in the first decade of 21st century. Most of the research work in this area focuses on enterprises and organizations, although there is an effort, especially lately, to provide answers concerning development of national economy. This theory has a lot of potential to create new insights and it is expected that it becomes even more incorporated into mainstream economics. This paper is an attempt to incorporate intellectual capital theory insights into endogenous growth theory as part of modern macroeconomics. In this paper, simple AK endogenous growth model is used as a basis. The intellectual capital growth model presented here also takes “A” or Total Factor Productivity as an average total productivity but with one fundamental distinction. It is using the logic of Calculated Intangible Value and/or Knowledge Capital Earnings by Baruch Lev where higher than average returns indicate higher intellectual capital. The model presented here applies this logic to Total Factor Productivity. In cases where TFP is equal to the average, the intellectual capital performance is also equal to the average, and the model is with constant returns as the AK model. But in cases where TFP is larger than average, the intellectual capital performance is also better than average, and the model is with increasing returns, and in cases where TFP is less than average, the intellectual capital performance is worse, and the model is with diminishing returns. The most important implication of the model is that savings and investments have a long‐term effect on growth only if intellectual capital performance is equal or better than average. If intellectual capital is worse than average there is no such an effect because of diminishing returns. In such a situation the policy should be first to increase intellectual capital to at least average performance and then to increase investments. Keywords: intellectual capital growth model, endogenous growth model, AK model, total factor productivity, calculated intangible value, knowledge capital earnings
1. Introduction The theory of intellectual capital has experienced a boom in the first decade of 21st century. In 1997 Sveiby published his book "The New Organizational Wealth," Stewart published his book "Intellectual Capital" and Edvinsson and Malone published book "Intellectual Capital". After that and after Bontis and McMaster University, Hamilton, Canada organized the World Congress on Intellectual Capital, from 1998 until today we have an abundance of articles, books, studies and conferences dealing with intellectual capital. Most of the research work in this area focuses on enterprises and organizations, although there is an effort, especially lately, to provide answers concerning development of national economy.
On the other hand, the new growth theory or endogenous growth theory, as part of mainstream macroeconomic growth theory, argues that economic growth is an endogenous result of the economic system, especially concerning relation of human capital and technology. What should be stressed here is that there is still an intensive work on developing new growth models, so that the endogenous theory still cannot be considered completed. This presents an opportunity to incorporate new insights from the theory of intellectual capital into the endogenous growth theory. This paper is an attempt in that direction.
First part of this paper elaborates simple AK endogenous model as basis for new model that is presented in a third part. Second part of the paper explains intellectual capital measurement logic as basis for advancing AK model. Third part is presenting a new model – Intellectual Capital Growth Model and at the end there are some concluding remarks.
2. AK model
AK model is one of endogenous models within the macroeconomic theory of growth. Endogenous growth theory has emerged as an upgrade of the standard neoclassical theory of growth. Specifically, the neoclassical growth model, the so‐called Solow model is based on the law of diminishing returns, where capital and output per capita reach a steady state regardless of the initial conditions.
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The key feature of the AK endogenous growth model (Rebelo, 1992, and others) is that this model assumes that there are no diminishing returns to capital. Unlike the neoclassical model, the AK model uses a linear model in which the output is a linear function of capital.
AK model is based on a simple premise. For each additional unit of capital, income will increase by constant amount, and the relationship between income and capital will always be proportional. To model this, it is only necessary to assume that share of capital in factor income equals 1. The income will depend on the capital
(1) or in per capita terms
(2)
A is a positive average that reflects the level of total productivity K is capital L is labor
The Figure 1 is showing the production function, savings and depreciation the same way as the Solow model.
Figure 1: Production function, savings and depreciation in AK model
In this model, there are no diminishing returns on capital and production function is linear. With the growth of capital, output rises proportionately, and since savings are proportional to output, the savings function is also linear. The depreciation is linear as in the Solow model. The income here depends on the capital and the growth rate of output is equal to the growth rate of capital. First, growth of capital is (for the simplicity we will assume that population is constant):
kksfk δ−=Δ )( (3)
s is rate of savings δ is rate of depreciation of capital
When we substitute f(k) with Ak we get:
ksAkk δ−=Δ (4)
Growth rate of capital gk is:
kkksAkkk /// δ−=Δ
δ−= sAgk (5)
Since gk = gy then
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δ−= sAgy
(6)
The basic implication of the model is the fact that the savings function and the function of depreciation are straight lines which never intersect. As there is no intersection, savings will always, except at the origin, will be higher of depreciation and capital will continue to grow.
When we are talking about the AK model, the most interesting implication in terms of economic policy is the fact that the increase in the national savings rate raises living standards. Every public policy that increases the rate of savings accelerates economic growth. The model also implies a divergence between economies. If two economies start with different initial capital stocks, then the absolute gap will be increasing.
3. Intellectual capital measurement logic
According to Bontis (1998) claims, the term "intellectual capital (IC)," was first introduced by John Kenneth Galbraith, who considered that, in addition to the classic, pure knowledge, creative knowledge is of great importance for the economic activity. The difference between the human capital and intellectual capital is in the fact that intellectual capital is not just knowledge and skills that can be acquired by learning and training. It is a whole set of intangible assets used to create value.
The theory of intellectual capital began to be more present in international public during the late 1990s of the last century. At that time one of the pioneers in this field, Stewart (1997) described intellectual capital as a brand new topic for that era, in which there are a lot of wandering.
Together with human capital, theory of intellectual capital is based on the structural and customer capital (Bontis, 1998, Edvinsson and Malone 1997, Stewart, 1997, etc.). Structural capital is created by work of human capital in the past and it consists of patents, concepts, models, networks, systems, and organizational culture. Customer capital includes relationships with customers and suppliers, brand names, trademarks and reputation or image of the company.
The study of intellectual capital means the study of the thing that is immaterial. Therefore the key problem in this area is its measurement. Unfortunately, the fact that it is intangible, regardless of the simplicity of the concept, becomes a problem for researchers when it is necessary to measure it.
According to Sveiby (2001, 2010) there are four categories of measurement approaches.
Direct Intellectual Capital methods (DIC) asses the monetary value of intangible assets through identification of its various components. Components are directly evaluated individually and/or as an aggregated coefficient.
Scorecard Methods (SC) also asses the intangible assets through identification of its various components. The difference from DIC method is that there is no monetary valuation since indicators of components are reported in scorecards.
Market Capitalization Methods (MCM) use difference between market capitalization and the book value as the value of intellectual capital of a company.
Return on Assets methods (ROA) divide average pre‐tax earnings by the average tangible assets of the company and then compare it with its industry average. The above‐average earnings are divided by the average cost of capital and the result is an estimated value of intellectual capital of the company.
Here we will pay attention to Return on Assets methods (ROA). It has always been recognised that the balance sheet of a company certainly does not represent the real value of an enterprise. Determining the value of a company by using Return on Assets methods has been common practice among investors for many years and is still used today. The method for ROA based intellectual capital calculation divides average pre‐tax income into average assets employed over a period in order to establish the rate of return achieved by the enterprise. This rate of return is then compared to the industry average to establish the performance of the enterprise in relation to its peers. Where the return generated by the enterprise is higher than the industry average, this is deemed to be as a result of the intellectual capital of the enterprise and the excess return is discounted using an appropriate
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discount factor in order to arrive at a present value for intellectual capital or the intangible asset value of the enterprise.
Stewart (1995) explains Calculated Intangible Value methodology by using an example of company Merck:
Calculation of average pre‐tax earnings for three years – $3.7 billion.
Calculation of average year‐end tangible assets for three years – $12.9 billion.
Dividing earnings by assets to get the return on assets (ROA) – 29 percent.
Calculation of industry’s average ROA for the same three years. For pharmaceuticals the average is 10 percent.
Calculation of the “excess return”. The industry average ROA is multiplied by the company’s average tangible assets – 10 percent x $12.9 billion. These are earnings of average drug company with the same tangible assets. This is subtracted from the company’s pre‐tax earnings. For Merck this is an excess of $2.4 billion. According to Stewart (1995), this is how much more that company earns from its assets than the average drug manufacturer.
Calculation of the three‐year‐average income tax rate, which has to be multiplied by the excess return. This result is subtracted from the excess return to get an after‐tax figure. This is the premium attributable to intangible assets. For Merck, with an average tax rate of 31 percent, this is $1.65 billion.
Calculation of the net present value (NPV) of the premium. This is done by dividing the premium by an appropriate percentage, such as the company’s cost of capital. Using an arbitrarily chosen 15 per cent rate, this yields Merck $11 billion. This is the CIV of Merck’s intangible assets.
Knowledge Capital Earnings (KCE) is methodology proposed by Lev (2001). First, he calculates earnings of the company (an average of earnings 3 years before and the forecasted earnings for 3 years after). From that earnings, he subtracts earnings of financial assets using given average after‐tax return on financial assets and earnings of physical assets using given average after‐tax return on physical assets. The result are earnings that cannot be atributed either to financial assets or to physical assets. According to Lev (2001) these earnings are knowledge capital earnings. He is using these earnings to calculate intellectual capital of the company and various other indexes and ratios. It must be emphasized here that the rate of return on financial assets and the rate of return on physical assets are taken as given averages.
4. Intellectual capital growth model
4.1 Description of the model
Underlying thought of the model presented here is an assumption that ideas, i.e. intellectual capital plays a crucial role in economic growth. We will begin with equations (1) and (2) shown in AK model
or in per capita terms
A is a positive average that reflects the level of total productivity and represents all intangible factors of production, i.e., ideas. K is capital, and represents all tangible factors that are used in production process, i.e., things L is labor Until now everything is the same as in AK model. Now we make a crucial distinction. We will express Ak in the following way:
Ai k=( A k)α (7) Ai is total factor productivity for a specific country
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A is average supranational total factor productivity (of the world or of group of similar countries or based on some specific criteria, structure of economy, etc.) α is an exponent or power that shows value of output with TFP of specific country as an α power of output with average supranational TFP We are now going to apply logic of IC measurement in explanation of this concept. In Calculated Intangible Value we use industry average ROA, use it to calculate earnings of average company within the same industry with the same tangible assets, compare it to actual ROA (same assets in both cases) and determine the difference which represents performance of intellectual capital.
In this growth model the same logic is used. Output A k represents output that would be produced with average supranational total factor productivity. Output AiK is actual output produced with country specific total factor productivity using the same capital. The relation of those two outputs is considered as an indicator of intellectual capital performance in this model. Using this logic, power α is showing to what extent intellectual capital performance of specific country is better or worse than average intellectual capital performance. If α=1 intellectual capital performance is equal to average, if α>1 intellectual capital performance is better than average and if α<1 intellectual capital performance is worse than average. Since α is a power that shows a performance of intellectual capital we shall call it Intellectual Capital Power. We are going back to the model. First we will formulate the model: (8)
The Figure 2 is showing the production function, savings and depreciation for this model with α=1 when intellectual capital performance is equal to average.
Figure 2: Production function, savings and depreciation with α=1
This model is with constant returns and behaves as simple AK model. With the growth of capital, output rises proportionately, and since savings are proportional to output, the savings function is also linear. The depreciation function is also linear. The Figure 3 is showing the production function, savings and depreciation for this model with α<1 when intellectual capital performance is worse than average.
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Figure 3: Production function, savings and depreciation with α<1
This model is with diminishing returns. With the growth of capital, output function is with diminishing returns, and since savings are proportional to output, the savings function is also diminishing returns. The depreciation function is linear.
The Figure 4 is showing the production function, savings and depreciation for this model with α>1 when intellectual capital performance is better than average.
Figure 4: Production function, savings and depreciation with α>1
This model is with increasing returns. With the growth of capital, output function is with increasing returns, and the savings function is also with increasing returns. The depreciation function is linear. Concerning growth rate, as similar as in simple AK model, the income will depend on the capital and the growth rate of output is equal to the growth rate of capital. This is why we first have to determine the growth rate of capital.
First, we will use the equation (3) and substitute f(k) with ( A k)α to get:
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(9)
Growth rate of capital gk is:
(10)
Since gk = gy then
(11)
It has to be noted that is average/marginal product of capital calculated as ratio of output to capital
(y/k). Now, for the case when α=1 growth rate is determined as similar as in simple AK model:
(12)
The Figure 5 is showing the growth rate gy for this model with α=1 when intellectual capital performance is equal to average.
Figure 5: Growth rate gy with α=1
The growth of output is constant here and can be continued infinitely. For the case when α<1 growth rate is
decreasing because with growth of capital k output‐capital ratio is decreasing.
The Figure 6 is showing the growth rate gy for this model with α<1 when intellectual capital performance is worse than average.
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Figure 6: Growth rate gy with α<1
The growth of output can be continued here only until investments become equal to depreciation. This is similar to the Solow model.
For the case when α>1 growth rate is increasing because with growth of capital k output‐capital ratio is
increasing. The Figure 7 is showing the growth rate gy for this model with α>1 when intellectual capital performance is better than average.
Figure 7: Growth rate gy with α>1
The growth of output is increasing here and can be continued infinitely.
The most important implication of the model is that savings and investments have a long‐term effect on growth only if intellectual capital performance is equal or better than average. If intellectual capital is worse than average there is no such an effect because of diminishing returns. In such a situation the policy should be first to increase intellectual capital performance to at least average and then to increase investments.
4.2 Discussion of the model
This model claims that if the country keeps up with growth of knowledge, ideas, technology, i.e. intellectual capital or, even better, pushes its boundaries, it will grow in the long term. On the other hand, if it fails to do so, it will face diminishing returns and growth problems.
It must be emphasized here that this model is the one of the first attempts to introduce intellectual capital as a concept to macroeconomic growth theory. Even concerning knowledge, macroeconomic growth theory did not include it as a concept for many years. In the early nineties, mainly based on the work of American economist Paul Romer (1986, 1990, 1993), a new paradigm, now commonly known as "endogenous growth theory" is created.
Romer's crucial contribution to economic theory is the creation of growth model in which ideas play a crucial role in economic growth. Romer (1993) divides factors into ideas and things. Things are all physical objects that exist around us, whether natural or manmade. They are scarce, behave by the law of diminishing returns and cannot create economic growth by themselves. On the other hand, ideas are not scarce. He claims that human beings have unlimited ability to use new “recipes” for rearrangement of things. The fact of central importance, according to Romer (1993), is that the possibilities for new ideas are almost inexhaustible.
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As we said before, underlying thought of the model presented here is also an assumption that ideas, i.e. intellectual capital plays a crucial role in economic growth. This model is based on the assumption that TFP and intellectual capital are two sides of the same coin.
Since it was created, TFP is the one of most important issues in economic growth theory. Тhe impact of TFP on economic growth is also well documented. Among many others, Easterly and Levine (2002) find that Total Factor Productivity, measured as Solow residual, “accounts for most of the income and growth differences across nations.” The crucial problem of TFP is its real meaning. This is still an open question. TFP is still measured as a residual and is still “a measure of our ignorance” (Abramovitz, 1956). We still need deeper insights of what TFP really is, since Solow residual gives us pretty dismal notion of it. The stream of papers that treat TFP in alternative way as index number (Caves et al. 1982; Fare et a.l 1994; and others) offers more space to comprehend this issue.
The similar thing is with intellectual capital, since its definition is also dismal. As noted earlier, Sveiby (2001, 2010) systemized many different approaches to intellectual capital. The one of them considers intellectual capital as the sum of human, structural and customer/relational capital. The other one is defining intellectual capital of a company as difference between its market capitalization and the book value. There is also an approach that relates intellectual capital to above‐average earnings. Within those 3 approaches Sveiby (2001, 2010) distinguishes 42 different concepts of intellectual capital and its measurement.
Concerning national intellectual capital, first studies were based on the methodology created by Edvinsson and Malone (1997). Thus Rembe (1999), analyzed intellectual capital in Sweden. In other Scandinavian countries, similar projects were promoted (Malhotra, 2003). Israeli scientists have also identified the importance of intellectual capital for economic development (Pasher, 1999; Pasher and Shachar, 2007). A similar report was made in Poland and was based on the same methodology (Boni, 2009). Another group of studies examines the macroeconomic impact of intellectual capital as an economic driver. There are several such studies. For example Bounfour and Stahle (2008) measure the economic effects of intellectual capital on the macro level using a large number of indicators, on the sample of 51 countries. Some other studies have applied measurement models that were originally developed for the micro level. Corrado et al (2009) estimate intangible capital in the U.S. economy expanded by using their own methodology for microeconomic research. Recently, the large share of the national intellectual capital research use complex unique indexes created on the basis of a large number of different indicators. These models also rely on microeconomic foundations. The most common taxonomy that is used here is Edvinsson and Malone (1997). For example, Bontis (2005) has created a unique index that measured the situation in the Arab countries. Andriessen and Stam (2005) used a similar approach in assessing the state of intellectual capital in the European Union. All other studies of national intellectual capital used this methodology to a greater or lesser extent (Bounfour, 2005a; Lin and Edvinsson, 2011; Veziak, 2007). However, the key problem with the use of composite indexes is that they lack firm theoretical foundations which brings into question their validity (M'Pherson and Pike, 2001, Malhotra, 2003, Stahle, 2006). Based on our review of the literature, we can see that there is only one study that attempts to integrate this type of indicators in the framework of macroeconomic growth theory (Muhsam, 1970).
Since TFP is one of the most important topics in the theory of growth, a key direction in creation of this model was to connect the concept of productivity with the concept of intellectual capital. Concerning TFP, Romer (1990) sees it as set of instruction, designs or recipes, basically set of ideas for rearrangement of things. Although there are many definitions of intellectual capital, here in this paper we consider intellectual as a set of ideas (and relations) used to create value.
There is also more essential connection of these two concepts. The productivity, in essence, is the relation of output and inputs. Since it shows how much of output is created with given inputs, in value terms it entirely depends on the amount of new value that is created out of those given inputs. And the concept of intellectual capital is all about the creation of value. Intellectual capital represents an active transformation of knowledge into a new value, value‐added products or services. This is the reason why these two notions are linked in this model. If we prove that this is true then intellectual capital offers deeper explanation of what TFP really is and TFP could become the most important performance measure of intellectual capital on aggregate level.
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5. Conclusion In one of his famous papers on ideas and things Romer (1993) says: “A nation that lacks the knowledge used to create value in a modern economy suffers from an idea gap.” This thought was a leading thought in creation of this model. The model presented here gives theoretical framework in which it is clear that ideas or intellectual capital performance, measured as productivity, is most important for a long‐term growth. Intellectual Capital Power α is an indicator of idea gap. If it is less than 1, country suffers from an idea gap.
What could this model mean in the real world? Intuitively, this could mean that most enterprises in economies with α larger than 1, are leaders in competitiveness. In these economies enterprises do things in most effective and efficient way, push boundaries of existing technologies, innovate and create new technologies. Also it is probable that most enterprises in economies with α equal to 1 keep up with productivity changes or intellectual capital performance of their competition. In these economies most enterprises operate with average effectiveness and efficiency. For example, they could use up‐to‐date technologies but do not innovate enough to be able to push things beyond current technology. In both cases the policy would be to increase investments in order to achieve higher standard of living, since intellectual capital performance is enabling long‐term growth.
On the other hand, most enterprises in economies with α less than 1 probably lag behind productivity or intellectual capital performance of their competition. In other words, in these economies most enterprises do thing in less effective and efficient way or use older technologies. These economies suffer from an idea gap and, as we said, the policy should be first to increase intellectual capital performance to at least average and then to increase investments.
In spite of the simplicity of the concept that is underlying the model presented in this paper, empirical testing will probably be much more difficult. The current growth accounting methodologies and data sets that are adapted to those methodologies do not offer too many possibilities for empirical testing of the model. This is because Total Factor Productivity (TFP) is most often empirically measured as Solow residual, representing TFP growth rate. In order to make sense of this model, further theoretical and empirical work on TFP is needed especially using the intellectual capital theory. We need deeper insights of what TFP really is, since Solow residual gives us pretty dismal notion of it.
Another problem is the definition of the supranational average values. It is an open question shall we use averages of the world or of group of similar countries or based on some specific criteria, structure of economy, etc. This will need a careful analysis, since different averages can completely change whole picture. In addition to work on TFP, this will also need both theoretical and empirical analysis.
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