Empirical Evidence From Swedish Manufacturing Firms Relationship between R&D and Productivity doc

According to the endogenous growth theory the most important factor for determining the economic growth rate is the rate of advance of a country's use of knowledge stock and its importan

Masters of Economics of Innovation and Growth

Thesis Empirical Evidence From Swedish Manufacturing Firms

Relationship between R&D and Productivity

CESIS

Royal Institute of Technology (KTH)

Acknowledgement

This dissertation is the partial fulfilment of Master programme in Economics of Innovation and Growth at The Royal Institute of Technology (KTH), in Stockholm Sweden The paper

was the result of a series of meeting with my supervisor Professor Hans Lööf I am grateful

to him for kind direction I am also grateful to Professor Borje Johansson, Almas Heshmati, Martin Anderson and other professor in the department of Economics of Innovation and Growth during my programme I got help from them I would like to thank you from my heart for the support, guidance, invaluable suggestions throughout this study

My special thank to Professor Hans Lööf for giving me an opportunity to work on the firm level data set and his valuable instruction Mr Lööf strongly impressed me during this programme I highly appreciate to Sofia Norlander and Joanna Wasilewska for their great help in my whole study period in KTH, Sweden Lots of thanks to my classmates in this program

Content Page

1 Introduction ……… 5-7

2 Literature review … 7-15

2.1 The history of economic growth theory ……… 7-11

2.2 Empirical evidence of R&D and productivity relationship … 11-15

3 Objectives and hypothesis ……… 15-16

4 Data and methodology analysis ……… 16-24

4.1 Data and variable analysis ……… 16-19

4.2 Research methodology analysis ….……….……… 19-24

5 Empirical result analysis ……… 24-26

Abstract

Many empirical studies have been introduced to show the relationship among R&D and productivity at the firm level The motivation of this paper is to extend the literature of the relationship between R&D and productivity level at the firm level This research paper deals only firms direct benefits that actually gains from conducting the research The paper

is based on 6665 Swedish manufacturing firms’ unbalanced panel data set during the period 1992-2000 To estimate the R&D impact on productivity level this study uses the autoregressive model or dynamic model This model works on where large number of firms and small number of period’s data are observed The study employs the econometrics tools OLS, fixed effect and generalized method of moment (GMM) estimators The research is conducted with and without industry dummy in the model The empirical results confirm that the R&D expenditure has significant impact on the firm level productivity at the 5% level of significance The empirical result suggests that industry specific effect has no impact on significant level

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Key words: OLS, fixed effect, generalized methods of moment (GMM)

1 Introduction:

Research and development (R&D) spending have been increasing all over in the world It increases the stock of useful knowledge through research and development activity It is one of the crucial determinants of productivity and economic growth The neo-classical growth model argues that the long run growth is exogeneously determined by either saving rate or rate of technological change Neoclassical economics state that technological progression and other external factors are the main sources of economic growth On the other hand, endogenous growth theory agrues that economic growth is generated from within a system as a direct result of internal processes Endogenous growth theory explains that growth is usually determined by the production of new technologies and human capital given to the production More specifically, the theory refers the enhancement of a nation's human capital that will lead to economic growth through new forms of technology, process of specialization, efficient and effective means of production According to the endogenous growth theory the most important factor for determining the economic growth rate is the rate of advance of a country's use of knowledge stock and its important determinant is R&D productivity Because R&D expenditure is the source of valuable knowledge that leads to improve innovation, specialization and productivity Innovation increases product market competition and stimulates the process of creative destruction which brings new business opportunities of the firms Innovation induces firms

to enter and exit from the market

R&D provides benefits two ways: one is direct productivity benefits and another

is indirect benefits The direct productivity benefit occurs through conducting research such as automobile or aircraft manufacturers industry and the indirect benefits come through new technology spreading to others parts of the economy In the present monopolistic competition market, firms achieve monopolistic power through product differentiation R&D has a crucial role to obtain product variety R&D investment result is invention, new ideas, design and productivity increment which can be a source of competitive advantages in the global market economy The firms can sustain growth through investment in R&D Productivity is one of the key driving forces of economic growth The term productivity refers to measures the output from production process per unit of input

To measure the gains from R&D spending the researchers rely on firm level productivity measurement analysis The available empirical studies have generally confirmed the significant role of R&D investment on productivity level at the firm level Most of the studies can be divided into two categories Production function based studies and cost function based studies The production function based studies show the impact of R&D on productivity level that is R&D elasticity and the cost function based studies show the R&D impact on production cost Some studies have estimated the rate of return in R&D (CBO -2005) From the literature of productivity measurement studies it can be observed that there is no single measurement of productivity Broadly, productivity measurement can be classified into two categories: - single factor and multi-factor productivity (MFP) measure The single factor productivity measure is also called partial productivity measure Multi-factor productivity again can be two forms one is value added based capital-labour MFP measure and another one is gross output based capital, labour, energy and material (KLEMS) MFP productivity measures In case of value added concept where value added is considered as firms out put (OECD Manual-2001) The most frequently used productivity measurement methods can be expressed by the following tree diagram:

Figure-1: productivity measurement methods:

Source: Measurement of aggregate and industry level productivity growth: OECD manual (2001)

Among those measurements, most of the studies uses value added based productivity measure To explore the relationship between R&D and productivity level this research paper uses the value added concept The research paper will be organized by using seven sections where section two provides literature review, section three present the objectives and hypothesis of this paper, section four explains the data and methodology analysis of the study, section five contains empirical result, Section six focuses on limitation of this study Finally, in the last section gives some conclusions

2 Literature review:

2.1 The evolution of growth theory:

The growth theory and growth empirics are attractive subjects in economics The modern concept of economic growth started with the critique of Mercantilism, especially

by the physiocrats During the 16th to 18th century the mercantilist believed that nation wealth and power were best served by increasing export and collecting precious metals in return The mercantilism focused on ruler’s wealth, accumulation of gold or the balance of trade Physiocracy is a school of thought founded by François Quesnay (1694-1774) This theory originated in France and was most popular during the second half of the 18thcentury Physiocracy is the first well developed theory in economics This doctrine was dominated by Marquis de Mirabeau, Mercier de la Riviere, Dupont de Nemours, La Tronse, the Abbe Baudeau and others The main theme of this doctrine was Francois Quesnay’s (1759) axiom that only agriculture yielded a surplus- what he called a net product The physiocrats believed that the wealth of nations was derived solely from the value of land agriculture or land development From the viewpoint of modern economics the main weakness is that they only consider agricultural labor to be valuable Physiocrats viewed the production of goods and services as consumption of the agricultural surplus, while modern economists consider these to be productive activities which add to national income.The most important contribution of the physiocrats was emphasis on productive work as the source of national wealth The productive capacity itself allows growth and increment of national wealth

The classical economics is the first modern school of economics of thought Adam Smith “The Wealth of Nations” in 1776 is considered the beginning of this school Adam Smith, David Ricardo, Thomas Malthus and John Stuart Mill are founders of this school

The "Classical" school is sometimes called the "Surplus" school Often classical economics school expanded up to William Pretty, Johann Heinrich Von Thunen and Karl Marx Classical economists explained the growth and development Adam Smith explained a supply side driven model of growth This model can be expressed by simple production function:

Y = f (L,K,T)

Where Y is the output, L is labour, K is capital and T is land The out put growth (gY) was driven by population growth (gL), investment (gK) and land growth (gT) and increases overall productivity (gf) Smith suggested that growth was related to capital accumulation, technological progress and institutional and social factors

gY = φ(gf, gL, gK, gT)

Where time was endogenous it depends on the sustenance available to accommodate the increasing workforce Investment (gK) was also endogenous: determined by the rate of savings; land growth (gT) was dependent on the conquest of new lands or technological improvements of fertility of old lands Technological progress could also increase growth overall Smith also emphasized improvements in machinery and international trade as engines of growth as they facilitate further specialization He stated that the division of labour improves growth, was a fundamental argument

David Ricardo (1817) modified Smith idea including diminishing return to land His most important assumption was that economic growth must decline and end due to the scarcity of land and its diminishing marginal productivity He showed that how distributional changes between wages, rent, interest and profit affected the prospects for long run capital accumulation and growth According to Ricardo’s idea output growth requires growth of factor input But land supply is limited Land can not be produced or created As a result two effects occur on growth Firstly, landowner rents increases overtime reducing the profit of capitalist and secondly, wage goods will be rising in price and this reduces profit as workers require higher wages As the economy continued to grow, then, by his theory of distribution, profits would be eventually squeezed out by rents and wages In the limit, Ricardo argued, a "stationary state" would be reached where capitalists will be making near-zero profits and no further accumulation would occur

Ricardo suggested that this decline can be checked by technological improvements and foreign trade

Ricardo first claimed that technical improvements would help push the marginal product of land cultivation upwards and thus allow for more growth But in his later third edition of his principles, Ricardo modified his position on machinery He noted that machinery displaces labour and that ‘set free’ might not be reabsorbed elsewhere and thus merely generate downward pressure on wage and thus lower labour income In order to reabsorb this extra labour without this effect, then the rate of capital accumulation must be increased

Malthus (1796) in his ‘Essay on the Principle of Population." In essence, Malthus said that any growth in the economy would translate into a growth in population He claimed in his hypothesis that population growth exceed the growth of mean of subsistence Actual population growth is kept in line with food supply growth by positive checks If the population growth was not easily checked and would quickly outstrip growth and increasing misery all around

John Stuart Mill (1806-1873) improved little upon Ricardo, Mill first adopted Ricardo's view that the average wage is determined by a fixed amount of capital divided by the number of workers, he stated that other factors play a role in determining wages,

among them workers' expectations as well as various institutional factors

Karl Marx (1818-1883) modified the growth theory through his reproduction scheme He believed that all production belong to labour because workers produce all value within society The market system allows capitalists, the owner of machinery and factories, to exploit workers denying them a fare share of what they produce He predicted

_ Note: http://cepa.newschool.edu/het/essays/growth/growthcont.htm

that capitalist compete for profit that led capitalist to adopt labour saving machinery He used the multi sectoral context and provided the steady state growth equilibrium Marx did not believe that labour supply was endogenous to wage Marx claimed that wage is not determined by necessity or natural factors but rather by bargaining between capitalist and workers Marx also saw that the profit and raw material as the determinant of savings and capital accumulation

John Maynard Keynes (1936) distinguishes his theory from classical economics

He developed theory that explains determinants of saving, consumption, investment and production In that theory, the interaction of aggregate demand and aggregate supply determines the level of output and employment in the economy According to Keynes investment demand is one of the determinants of aggregate demand and that demand is linked to output via the multiplier He argued that without market imperfections, aggregate demand might fall short of the aggregate productive capacity of its labour and capital

Keynes theory of demand determined equilibrium first extended Sir Roy F Harrod (Harrod in 1939, Domar in 1946) into a theory of growth that is the ‘Harrod-Domar’ model of growth The Harrod –Domar model was initially created to help analysis the business cycle Harrod-Domar (1946) model is used in development economics to explain an economy’s growth rate in terms of the level of savings and productivity of capital It suggests that there is no natural reason for an economy to have balanced growth Its implication was that growth depends on the quantity of labour and capital; more

investment leads to capital accumulation, which generates economic growth

The neo-classical model was an extension of Harrod-Domar model (1946) that includes new term, productivity growth The most important contribution was given Robert Solow (1956) Solow and T.W Swan developed neo-classical model of economic growth which is also called Solow-Swan model or exogenous growth model The exogenous model shows how economies will naturally tend to steady state This model explains the long-run economic growth Solow extended the Harrod-Domar model by including: (a) labour as a factor of production; (b) Diminishing return occur to labour and capital separately And constant return to scale for both factor combined; and (c) A time varying technology distinct from capital and labour Capital output ratio is not fixed as they are in

the Harrod-Domar model In neo classical growth model the long run growth rate is exogenously determined, in other words it is determined out side of the model The common prediction of this model is that an economy will always converge towards steady state rate of growth which depends on the rate of technological progress and the rate of labour force growth

The endogenous growth theory is also called new growth theory that was developed in the 1980s as a response to criticism of the neo-classical growth model Romer (1986) developed the model of increasing returns in which there was a stable positive equilibrium growth rate that resulted from endogenous accumulation of knowledge The most important work of this model that distinguishes itself from neoclassical growth by emphasizing that economic growth is an endogenous outcome of an economic system, not the result of forces that impinge from outside The importance is usually given to the production of new technologies and human capital Endogenous growth theory argues that economic growth is generated from within a system as a direct result of internal processes This was an important break with the existing literature, in which technological progress had largely been treated as completely exogenous More specifically, the basic mechanism

of endogenous growth theory is productive externalities The enhancement of a nation's human capital will lead to economic growth by means of the development of new forms of technology and efficient and effective means of production Endogenous growth theory demonstrate that policy measure have an impact on the long run growth rate of an economy Subsidies on research and development or education increase the growth rate by increasing the incentive to innovation R&D has a special economic significance apart from its conventional association with scientific and technological development R&D investment generally reflects a government and organization willingness to forgo current operation or profits to improve future performance or returns and its ability to conduct research and development This is necessary due to technology change and development as well as other competitors and the changing preference of customers

Note: http://en.wikipedia.org/wiki/Economic_growth

http://en.wikipedia.org/wiki/Endogenous_growth_theory

2.2 Empirical evidence of R&D and productivity relationship:

Many studies have consistently proved that R&D investment and firm’s performance has positive correlation A large number of empirical studies have estimated the effect of R&D investment on productivity Most of the studies are based on production function

Griliches (1980) investigated the R&D elasticises on the 883 U.S firms during the period 1957 to 1965 Author has found the R&D elasticity is positive and approximately 0.08 In another study, author (Grillchese-1986) explored the relationship between R&D investment and productivity on 1000 largest US manufacturing company during the period 1957-1977 Later study used the Cobb-Douglas production function and found that output elasticity with respect to R&D investment is 0.086.Griliches and Mairesse (1984) worked

on 133 US manufacturing firm during the period 1966-1977 and found the R&D elasticity

is 0.08(without year dummies) and 0.09 (with year dummies) Minasian (1969) conducted the study on 17 US manufacturing firms during the periods 1948-1957 This study uses the multiple regression models and estimated the R&D elasticity on value-added and found R&D coefficient is 0.08 and statistically significant

Jaffe (1986) explored the relationship between R&D and productivity on 432 US firm for the period 1973-1979 This study uses patent data to classify the firms in technology- based categories and found significant and positive R&D coefficient (0.098) Hall & Mairesse (1995) examined the R&D elasticity on 197 French manufacturing firms for the period 1980 to 19870 The study found the productivity of R&D spending for French manufacturing firms is positive (0.07) Kafouros (2004) focused on the 78 UK manufacturing firms for the period (1989-2002) This study examined the contribution of R&D is approximately 0.04 The elasticity for large firm (0.44) is and for small firm is 0.035 The R&D-elasticity is considerably high for high-tech sectors (0.11), but statistically insignificant for low-tech sectors Beneito (2001) investigated the R&D elasticity on 501 Spanish manufacturing firms The empirical result suggests that R&D elasticity of productivity is 0.07 and statistically significant

Klette & Kortum (2002) use the dynamic model and showed that R&D as a fraction of revenues is strongly related to firm productivity and largely unrelated to firm size or growth Mogens et al (1999) have used a production function approach to estimate

the effects of the R&D capital on output They use 684 Danish manufacturing firms during the period 1987 to 1995, the empirical findings was a positive and output elasticity of R&D capital is 0.08 and statistically significant Heshmati and Lööf (2006) using the multivariate vector autoregressive model have found the significant heterogeneity between the firms’ investment and performance behaviour by their size The study was conducted in Swedish manufacturing firm it also refers that relationship between investment and firm performance is existed in both case of cross-sectional and time series analysis The empirical result shows that a significant and positive elasticity of productivity with respect

to human capital, physical capital and knowledge capital

Wakelin (1997) worked on 170 UK manufacturing firms Using Cobb-Douglas production function the study demonstrated that a positive and significant relationship between R&D expenditure and productivity when no control is made for sector effects But the relationship is insignificant when sector dummy variables are introduced (fixed effects are included) The study also showed that innovative firms spent more on R&D expenditure relative to sales than non-innovating firms (2.3% against 0.8% in the period

1988 to 1992)

Wang and Tsai (2002) estimated the impact of R&D on productivity within the private sector, Based on a sample of 136 large manufacturing firms listed in the Taiwan Stock Exchange (TSE) during the period 1994-2000 In this research authors uses the Cobb-Douglas production function and estimated R&D output elasticity was around 0.18;but, when the whole sample is classified into two categories, high-tech and other firms, The study found a statistically significant difference in R&D elasticity between the two samples The R&D elasticity for high-tech firms is around 0.3, but only 0.07 for other firms The study also demonstrated that the Schumpeterian hypothesis, that the impact of R&D on productivity is an increasing function of firm size, is also tested within this study; however, the empirical results do not support the proposition at the 5 per cent significance level

Lesley et al (2008) have used an unbalanced longitudinal database on 532 top European R&D investors over the six-year period 2000-2005 They divided the panel data into three subgroups high, medium and low- tech group This study compared between the

POLS (pooled ordinary least square) and the random effect model The empirical results of random effect model suggest that knowledge stock has a significant positive impact on a firm's productivity, with an overall elasticity of about 0.125 The estimated elasticity coefficients of the high, medium and low- tech firm are 0.160, 0.146 and 0.068 respectively Where as the POLS estimated elasticity for overall sample is 0.123 The estimated elasticity for high, medium and low tech is 0.18, 0.138 and 0.048 respectively.

Bond et al (2003) use the dynamic production function approach and estimated the impact of R&D on productivity between German and UK firms The study conducted on more than 200 firmsGerman and UK in each country during the period 1987 -1996 After

Table-1: Firms R&D elasticity in different studies:

elasticity

Firm and periods

Griliches (1980) 0.08 883 U.S firms; 1957 to 1965

Griliches and Mairesse (1984) 0.09 133 U.S firms; 1966 to 1977

Jaffe (1986) 0.098 432 U.S firms; 1973 to 1979

Griliches (1986) 0.086 1000 largest US manufacturing company

1957-1977

Minasian (1969) 0.08 17 U.S firms; 1948 to 1957

Hall and Mairesse (1992) 0.07 197 French manufacturing firms; 1980 to

1987 Wang and Tsai(2002) 0.18 136 large manufacturing firms listed in the

Taiwan Stock Exchange (TSE) during the period 1994-2000,

Beneito(2001) 0.07 501 Spanish manufacturing firms

1990-1996 Potters et al (2008) 0.13 532 top European R&D investors over the

six-year period 2000-2005

Kafouro(2004) 0.04 78 firms in UK, (1989–2002),

Mogens et al (1999) 0.08 684 Danish manufacturing firms

(1987-1995) Kwon and Inui (2003) 0.093 3830 Japanese manufacturing

Firms for the period between 1995 and

1998

Bond, et al (2003) 0.079(Ger

many) 0.065(UK)

200 firms in German and UK

In each country, 1987 -1996

controlling for firm size and industry effects This study has found that the R&D output elasticity is approximately the same in both countries In UK, they obtain a preferred estimate of 0.065 (SE 0.024) while the estimate for the German sample is 0.079 (SE 0.042)

Doraszelski, and Jaumandreu, (2006) uses the dynamic model on 1800 Spanish manufacturing firms in nine industries during the 1990s Empirical findings indicate that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity across firms R&D expenditures stimulate productivity The growth in expected productivity corresponding to observations with R&D expenditures is often higher than the growth corresponding to observations without R&D they estimate this difference in expected productivity to be around 5% in most cases and

up to 9% in some cases The following table-1 provides the empirical evidence of some studies about the R&D elasticity on productivity level

Kwona and Inui (2003) estimated a Cobb-Douglas production function, this paper investigated on 3,830 Japanese manufacturing firms for the period between 1995 and 1998

A positive and significant role is found on R&D expenditure and productivity The R&D elasticity is 0.09 This study also showed that the roles are different by the firms’ sizes and characteristics of technology The empirical result showed that the effects of R&D on productivity improvement are larger for the large sized and high-tech firms than they are for the smaller sized andlow-tech firms

The evidence from these studies indicates that R&D expenditure has a positive and significant impact on firm level productivity in US, UK, Spain, Germany, French, Denmark and Japan

3 Objectives:

Since many studies in different countries has confirmed the significant relationship between R&D and firm level productivity Hence the motivation of this research work is to examine the relation between R&D and productivity level using dynamic model in case of Swedish manufacturing industry The research will be conducted on 6665 Swedish firms during the period 1992-2000.This research paperinvestigates the following hypothesis:

a) Ho: The null hypothesis is that R&D spending has no impact on productivity b) Ha: The alternative hypothesis is that R&D spending has a positive role on

Productivity

4 Data and methodology analysis:

4.1 Data and variable analysis:

The data set contain different kinds of information of Swedish manufacturing

firms for the period 1992-2000 The data set include many firms among many industries

The following table-3 provides the summary statistics for the variables those are used in this study analysis

Table 3: Number of observations and variables:

Variable Observations Mean Standard

Note: EBIT: Earning before income tax R&D: Research and Development expenditure

It is unbalanced panel data and consists of various information such as value added, sales, wage, employment, R&D expenditure, gross investment, labour cost, production cost, earning before income tax (EBIT), human capital, subsidy and others Some of the extreme value of the variable can affect result of the research Hence the data set has been trimmed outliers using different techniques The data set contain the negative wage value that is required to be positive The study also trimmed out the variables those which are not necessary for this model analysis After shorting the data set it contains 6665 Swedish

manufacturing firms for the period 1992-2000 All the variables in the table-3 have been reported in the log form The brief descriptions of the variables are as follows:

Value added (Per employee log value added):

The original data set was given in total value added form The total value added of every firm in each period is divided by their corresponding employee number and then log value has been taken

Capital (log value of per employee net capital):

The data set report the physical capital of every firm which is transformed into net capital through perpetual inventory method and the constant rate of depreciation is applied

In this case I follow the same procedure conducted by Hall and Mairesse (1995), Lööf (2008), Hyeog Ug Kwon and Tomohiko Inui (2003) The perpetual inventory method as follows:

NECA= Kt-1 (1-δ) + It

Where, NECA is consist of the last year depreciated tangible assets and the gross

investment Kt-1 is the last year net capital investment; δ is the depreciation rate and It is the gross investment The depreciation rate is constant overtime (0.15) The net capital has been transformed into per employee net capital by divided with employee number of this firm

Employment (log value of employee):

The preferred measure of labour input is hours worked, but some researchers use number of people employed if hours are unavailable For the firm level data most of the uses hours as measures of labour unit If working hours is not available researcher uses the researcher number of people employed in these establishments Here, the data set report the number of employee according to the establishment This paper uses log value of employee

definition:(The perpetual inventory method (PIM) IMF, OECD, Eurostat, ILO): The perpetual inventory method (PIM)

produces an estimate of the stock of fixed assets in existence and in the hands of producers by estimating how many of the fixed assets installed as a result of gross fixed capital formation undertaken in previous years have survived to the current period

R&D( log value of per employee R&D spending):

The data set covers every firms every firm which reported positive R&D expenditure and the number of employees are more than 49 This study has trimmed outsome of the extreme observation of R&D spending that may influence result The author observed that a few number of firms per employee spending was more than 2000 million and these observations have been removed from the data set Then log value of R&D spending has been taken

Human capital(engineering knowledge and general knowledge):

The human capital is consisted of engineering knowledge and general knowledge

The employees who have university degree are counted as engineering knowledge and the

employees those who are undergraduate are counted as general knowledge

The table-4 provides the correlation result of the main variables which have been used in this study The auto correlation table have been presented in the appendix part A correlation is a single number that describes the degree of relationship between two variables The correlation coefficient indicates the strength and direction of a linear relationship between two random variables The closer the coefficient is either-1 or 1, the stronger the correlation between the variables

Table-4: correlation matrix:

The correlation matrix -4 report that the sales and EBIT is highly correlated with value added In case of productivity measurement value added, sales and earning before income tax (EBIT) are considered as productivity of firms The correlation between productivity and R&D is 0.2037, in case of capital and employment these coefficients are, 0.3719 and 0.1201 respectively

4.2 Research methodology analysis:

Most of the research paper uses Cobb-Douglas production function approach to estimate the contribution of R&D on productivity that is a mathematical equation which explain how inputs are combined to produce output (See for example, Griliches (1986); Mairesse and Sassenou (1991), Lichtenberg and Siegel (1989); Goto and Suzuki (1989), Wang and Tsai (2002), Mogens et al (1999), Kwon and Inui (2003), Wakelin (1997)) The extended form of Cobb- Douglas production function is:

Qit = Aeλτ Kαit-1 Lβit Rγit-1 e Өit +εit (i)

The definition of the variables differs depending on the study The studies that use firm-level data tend to use firms’ revenues, production or sales, or value-added a measure

of output (Q) L is the labour input, K is the physical capital input, R is the R&D capital investment Where Α is the level of technology of firms that is constant (TFP) α, β and γ are the elasticity of production with respect to capital, labour and R&D expenditure

respectively and e is the disembodied technological change and λ is the rate of

disembodied technological change and λt means the time trend is usually replaced by time dummies in the estimation that capture common technological change, shocks, such as strikes and weather, and allow such aggregate shock to have flexible effects on Q and free correlation with K and L (Kwona and Inui, 2003) Өit is the firm specific variables The

notation i-represents the firms or sectors and t- represent the period or year The subscript t-1 is the lagged values on the physical capital and R&D capital and εit is the disturbance

term The logarithmic form of the equation (i) is as follows:

Log (Qit)=log (A) + λt+ Өit + α log (Kit-1) + β log (Lit) + γ1 log (Rit-1) +εit (ii)

Within this framework the studies focus mainly on the estimated elasticity γ of R&D capital The coefficient of the R&D variable γ measures the elasticity of output with respect to R&D effort

In order to examine the R&D impact on productivity this paper uses the autoregressive model In the time series regression analysis it is playing an important role

to explain how the dependent variable and independent variables are related The model works well when panels are large and time period is small The impact of independent variable on dependent variable can not occur immediately the total effect is distributed over serial periods of time R&D capital has been viewed as a measurement of the current state of technical knowledge that is determined by current and past R&D expenditure (Griliches, 1979) But it is difficult to determine the appropriate lag structure Most of the studies consider R&D has a significant impact on productivity two years later This paper uses autoregressive model with three inputs such as physical capital, labour and knowledge capital (R&D) The model is as follows:

yit= αyit-1 + βxit + (ηi + vit) |α|<1 ; i = 1,2 N; t = 1, 2 T (iii)

The above equation contains a lagged dependent variable as an explanatory

variable Where the certain time period is t, the previous period is t-1 This model specifies that in the period t, y is determined by the value of previous year y and by the t previous

values of x Therefore, the effect of x variable is distributed over t+1 periods of time yit is

the log value of output for firms i in period t, yit-1 is log value of previous year output of

the firms i The variable xit is the log value of explanatory variables α, and β are the parameters to be estimated The error component is consisted of two parts; one (ηi) that is unobserved individual time invariant effects and another (vit) which is common disturbance term In the equation (iii) this study assumes that (ηi) is stochastic term and the disturbance term (vit) is serially uncorrelated The number of firms (N) are sufficient large and time period (T) are small

The coefficient α and β can be estimated by the method of ordinary least squares (OLS) In the presence of the lagged dependent variable the OLS estimation rule does not give a linear unbiased estimator The ordinary least square (OLS) of the dynamic model