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This article attempts to disaggregate and explore the components of TFP growth that contribute to changes in output, scale of production, and allocative efficiency and technical efficiency of the Malaysian manufacturing sector. The total factor productivity (TFP) concept defined as total output per unit of all inputs used in the production of an industry has gained a prominent place in academia. The investigation on TFP growth is obviously useful for identifying sources of output growth in the development of an industry. The TFP growth is often interchangeably understood as the technical progress or changes in technology as the sole contributor to economic development. Nonetheless there are other factors contributing to its substance. Knowledge on these technical changes would help decision makers to realize the strengths and weaknesses that contribute to the growth and development of an industry. Alternatively this research would be more beneficial in the case of cross-industry or cross-country comparative studies in order to plan for developmental goal. In such a case a model industry or country can be chosen that exhibits special growth features.

Growth and development, and later sustainable development had always been in the forefront of attainment goals of world’s economies. Historic attentions were given to multifaceted issues of growth of prominent economic constraints in achieving development objectives. In the oldest profession of agriculture, Robert Maltus [

where L is the working-age population, P is the participation rate and S is the number of schooling and e^{0.1S} is a weight used to reflect the impact of education and the size of labor force on the labor input, which is assumed to be exponential. Several findings particularly in Korea suggest that each additional year of schooling raises labor’s productivity by 10 percent. Even though education is relevant to the productivity improvement it will not be so for all situations. With higher education the farmer’s productivity could have declined due to the possibility of better off farm employment. Educated labor tends to be less committed to agriculture and thus its productivity. Experience and on job trainings can be another factor that contribute to higher productivity. Health condition of the workers deteriorates with limitations of medical facilities which in turn impede worker’s productivity. Types of education and trainings that contribute directly to the development of human capital should be differentiated from the ordinary workers. Labor should at least be classified according to skilled and non-skilled labor. No attempt is made in the current study to classify labor according to skilled and non-skilled because of the lack of time series data.

Total factor productivity (TFP) growth is the residual of output growth not accounted for by capital and labor. The derivation of TFP growth components is relevant in order to unveil the unexplained sources of economic growth beyond that reflected in the production function. The residual growth component from the microeconomic perspective can be attributed to technical progress, technical efficiency, scale of firm operation and other socioeconomic factors not captured by the variables used in the production function. In macroeconomics, sources of TFP growth can be categorized into education and training, changes in demand, economic restructuring, technical progress and capital structure [

The measurement of TFP growth is closely associated with the growth of economic activities. One could not understand TFP growth without first understanding the methodology for estimating growth. The growth concept involves time and its measurement can either be discrete or continuous depending on the extent of pronouncement of the state variables. According to Dowling [_{t} refers to the current year variable, y_{o} is the base year variable, r is the rate of growth and n is the number of years of the target projection. This discrete growth equation is less pronounced than the continuous growth equation which is represented in natural exponential function such as that of. Throughout this article the discrete growth equation will be used for the estimation of the relevant policy variables in the TFP growth.

Theoretical formulation of the TFP growth is based on a simplified production process with only capital (K) and labor (L) utilized as inputs in the production of a commodity, q. Defining q as the product of and where refers to all influences that go into determining output Q besides capital (machine hours) and labor (labor hours). This mathematical relationship can be presented as

The concept of the total factor productivity (TFP) is defined as total output divided by the total inputs. Based on the above simple production function TFP which is should be equal to total output divided by the total input function. Assuming that all variables are a function of time, the derivative of output with respect to time yields the following equalities,

Substitute and from Equation (1) and expand the derivation of capital and labor with respect to time yields the equation below,

Dividing through the above equation by Q and setting, the output growth equation is obtained as

As shown in (2) the formulated identities yield the required total output growth that will be used for the estimation of TFP growth. Terms of Equation (2) can be further simplified to arrive at the final result of the output growth equation as in Equation (3)

where is the total output growth due to technical progress, is the total factor productivity growth, is the output elasticity of capital is the output elasticity of labor, while and are capital and labor growth rates respectively. The equation for TFP growth is defined as in Equation (4) below

This is one of the techniques whereby TFP and its growth are normally estimated. Obviously there are other techniques; one of which is the Malmquist index as discussed in Coelli [

Decomposition of the TFP growth acknowledges the reference of the article written by Rukmani Gounder and Vilaphonh Xayavong [_{it}” which denotes the technical inefficiency of the industry i in year t, and “V_{it}” the white noise systematic error term. They are independently and identically distributed with. A higher value of U implies an increase in the technical inefficiency of the industry i and a small value is otherwise. Production function with capital (K) and labor (L) as inputs and the two error terms is presented as

Technical inefficiency (TE_{it}) is further defined as the exponential of negative U_{it} that is. The rate of technical inefficiency growth is obtained after taking the logarithm of Equation (6.1) and differentiating it with respect to time. The technical inefficiency result is shown in Equation (6.2) which will be used throughout the discussion henceforth. The estimation of technical inefficiency for the manufacturing industry is obtained from the stochastic frontier production function.

Disregarding it subscripts for the time variables Equation (5.2) is usually presented in its simplified identity as

TFP growth in actual estimation uses Equation (8) where s_{K} and s_{L} denote the share of capital and labor on production respectively. Substituting Equation (7) into (8) the TFP growth can be further disaggregating into additional components as derived in Equation (9)

Add and subtract 1 from equation (10.2) above and with manipulation and rearranging of the terms equations (11.1) and (11.2) are finally arrived at as shown below:

where and, RTS = return to scale,

, and. is the technical advancement over time, represented by the shift in the intercept of the production function. This shift can be represented by the time variable but the result of such output may not truly depict the technical progress experienced by an industry or state of a country analyzed.

Some argued that technical progress is already imbedded in the utilization of physical capital. A technically experienced labor is capable of operating machine to produce a product with precision that saves time, minimizes cost and raises productivity. For computational purpose, further decomposition of the TFP growth Equation (11.2) can be performed by substituting the equivalent of technical progress element as in Equation (4). The final result of TFP growth equation is shown in Equation (12)

Equation (12) is utilized in the final estimation of TFP growth with the help of Excel spreadsheet. Under an optimal production and assuming that the industry operates in a perfectly competitive market the share of capital and share of labor in production are identical to the output elasticity of capital and output elasticity of labor respectively. Defining profit (π) as the difference between total revenue and the total cost, share of labor (s_{L}) and capital (s_{K}) under the assumption of perfect competition should be equivalent to and where p is price of output, r and w stand for unit price of capital and labor respectively.

Technical progress (TP) is normally estimated from the effect of time on the total output, which is obtained from the first term on the RHS of Equation (12). The second term following technical progress represents the return to scale level of the industry with respect to changes in capital and labor over time.

Since double logarithmic function is used in the analysis, RTS is equivalent to the sum of capital and labor coefficients which are their respective elasticities. For a sum of elasticity greater than one, the production operates under increasing return to scale (RTS). While a sum of one is a constant RTS and that less than one is decreasing RTS.

This third item represents the allocative efficiency component of the industry since changes in output price and input costs of capital and labor are considered here. The fourth item refers to changes in technical efficiency of the industry. Annual changes in technical efficiency are obtained from the stochastic production frontier using the Cobb-Douglas production function which had included the technical inefficiency variables in the model such as exchange rate, interest rate and the dummy a proxy for impact of outbreak of the financial crisis on the manufacturing sector. Changes in the random error term V refer to the external disturbance not captured in the model. The rest of the notations are as defined above.

Data for the analysis of manufacturing industry is obtained from Key Indicators of Developing Asian and Pacific Countries, the Economics and Development Resource Center, Asian Development Bank. Since the objective of this paper is to disaggregate the measurement of the TFP growth the principal industries in the manufacturing sector will not be the focus. Instead, the general representation of the industry at two-digit level is presumed sufficient for the illustration needed. The data gathered for the analysis comprise the value of the total output, fixed assets excluding buildings and land, and the number of employed workers for the period 1980 to 2007.

Annual growth in total output, fixed assets, labor and labor productivity, capital productivity and capital-labor ratio for the period 1981-2007 is shown in

Evidently both fixed assets and employed workers had experienced remarkable growth just as did the total output during the late 1980s and the early 1990s. Capital invested in the manufacturing industry grew around 15

percent to 30 percent annually during the period of 1988- 1995, while the employed workers representing labor grew at much lower percentage for this period. By 1997 growth rates for these factors as expected were negative particularly after the outbreak of economic crisis of 1997 through 1999. Unpredictable fluctuations and volatility in their growth rates appear to follow after this period.

The annual trends in labor productivity, capital productivity and capital-labor ratio for the period 1981 to 2007 are shown in

With the information on elasticity and the growth rate of inputs, that is capital and labor, one should be able to calculate the TFP and its growth using the formula in Equation (4). Mahadevan [

The inefficiency variables were used in the stochastic production frontiers, namely exchange rate, interest rate and the dummy representing the period economic crisis whereby 1 = crisis year and 0 = otherwise. As evident statistical tests of t-ratios show that the Cobb-Douglas SPF is a better estimator for the manufacturing sector.

The SPF was adopted specifically in this investigation in order to estimate the annual technical efficiency and its annual changes for the TFP growth component. The Cobb-Douglas SPF was chosen for the analysis.

The annual TFP growth components are shown in

some impact on the TFP growth.

This paper is specifically focused on the methodology of disaggregating the technical components of TFP growth for the manufacturing sector of the Malaysian industry for the period of 1980 to 2007. Since the investigation is centered on the measurement technique limited data was utilized, obtained from the Key Indicators of Developing Asia and Pacific Countries, Asian Development Bank. Methodology for measuring TFP growth is first presented in this investigation. This was followed by the discussion on theoretical development of the TFP growth with the objective of deriving and expanding this simple model to disaggregate TFP growth components. These components comprise the technical progress, industrial return to scale with respect to the use of capital and labor over time, the allocative efficiency given output price and input costs of capital and labor, and changes in technical efficiency of the industry. Finally the stochastic production frontiers (SPFs) were estimated to obtain the necessary parameters from empirical data. It is also emphasized that measuring TFP growth can only be done practically when researchers understand how growth rate is derived and calculated. The discrete growth function is utilized throughout the discussion, as its usage is handy and not easily exploded. The measurement of TFP growth is important from the economic standpoint in order to identify the unexplained contribution to the total output growth other than those explained by capital and labor. This unexplained growth is the technical progress. Nowadays as human resource development is becoming dominant in influencing output growth, intellectual capital besides that of physical capital has been recognized as an essential variable to sustain economic growth. The TFP growth is important for decision makers in identifying sources of technical growth in the private corporation, local government for national planning and for international comparison. Even so the ability to measure and interpret these sophisticated techniques will not be of much use to real world decision making when data sources are insufficient and not reflective of the reality. Thus, the first stage requires data collection and source that is reliable and up to date, while the second stage requires ability to measure and interpret the results obtained from the analyses. As we realize that TFP growth can be estimated by other techniques such as the index numbers, different methods of TFP measurement might produce different results. The estimation technique adopted in this study utilizing the stochastic frontier production with inefficiency model provides a way of estimating TFP growth and component of technical efficiency is probably robust and most appealing currently.