TOTAL FACTOR PRODUCTIVITY-INFLUENCE FACTOR OF THE ECONOMIC GROWTH POTENTIAL . PRACTICAL APPLICATION ∗

Adequate to the new requirements of economy, the economic research has achieved progresses in addressing the issues regarding the growth and development, the economists drawing a number of theories and models, in order to find resorts that lead to sustainable growth. The paper refers to the means of assessment and forecast of the potential growth of an economy, by using a mathematical model, whose production function takes into consideration the role of three factors, being highlighted the role of the Total Factor Productivity, as an element of influence on growth with the other two factors. The study includes an application of the model use, for the analysis of the growth potential of the economy, at national level.


Introduction
The economic literature has given a particular interest to the analysis of growth problems and its determinants, trying to explain the forms of economic phenomena occurrence and provide alternatives concerning the ways to achieve growth.The emphasis was on measures which lead to performance achievement regarding the welfare and sustainable growth: capital investments, stimulate research and development activities and, respectively, technical progress, well-trained workforce etc.The economic research has achieved progresses in addressing problems regarding the development, economic growth, world trade, the economists initially, formulating theories and models based on perfect competition and, subsequently, moving to models of imperfect competition, according to the new requirements of economy, the aim being to find the springs which lead to sustainable growth.

Total Factor Productivity
The estimation and forecast of the growth of an economy potential, basically, takes into account: the available amount of labour, the amount of capital that can be used and the Total Factor Productivity, the latter being considered a "residual", respectively, that part of the output unexplained by the amount of inputs used in production.
Assimilated to technical progress, the Total Factor Productivity, more broadly, includes the other sources of growth, different from the factors, labour and capital, its level being determined by the extent of efficiency and intensity of the inputs used in production.The Total Factor Productivity (TFP) is based on the determination of estimated GDP, using the homothetic Cobb-Douglas production function.
Y = AK α L 1-α , where: Y -the output -GDP; α -the elasticity coefficient; A -the productivity; K -the capital stock; L -the workforce "Toupictionnaire"1 defines the concept of "Total Factor Productivity or multifunctional productivity, as a ratio of the production value to the total value of the inputs used (labour and capital)", allowing to measure the effectiveness of productive combination of labour and capital.The TFP is determined, in general, at a scale of a country or economic zone, its evolution, over time, allowing the evaluation of the relative growth, other than the one in relation to the use of production factors, labour and capital.The parties of capital and labour are dissociated by the elasticity coefficient, α.The capital and labour remain the major contributors of production, but the growth vector is considered the Total Factor Productivity (TFP), which can influence the economic growth, its corner stone being the technical progress.The technical progress determine the increase in the factors productivity, leading to their qualitative and not only quantitative growth, what gives growth an intensive nature.The production growth is superior to the growth of each factor, as such, the effectiveness of factors, respectively, the productivity increases due to the process of innovation or improvement of work setup.The difficulty in applying the model results from the assumptions taken into account and the interpretation of results: a number of elements may influence the quality of factors productivity (the technical progress), respectively, change of the production structure (the production of more goods and services, with saving of capital and labour) or of its setup, the education, research and development (R&D), the growth of skilled workforce, what makes it difficult to correctly determine the technical progress; the information required by the calculation of capital stock and labour development, also, of prices development; considering the elasticity rates taken in the series of that two factors.

Application for Romania
In the following, it is presented an application regarding the analysis of the potential of economy growth, at national level, using as model, the Cobb-Douglas production function with TFP.
The used model (Ghizdeanu, I.; Tudorescu, V.; Neagu, M.)2 : the Cobb-Douglas production function , where: Y = GDP N = the employed population K = the stock of capital TFP = the Total Factor Productivity For the expression of factors, in a single unit, it is using the linearly-homogeneous function, obtained by logarithm: For the time series of tfp (from the step 1) it is applied the TREND function and, thus, it is obtained the adjusted series of tfp, for the period taken into account (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012), as well as the ptf forecast for the years 2013-2015 (noted by tfp*).III.For the time series corresponding to n labour factor (the employed population) observed, based on the data from ASR (time series 2000-2012) it is applied the TREND function, achieving thus, the adjusted series of the factor -n -for the period taken into account (2000 -2012), as well as the forecast for the period 2013-2015 (noted by n*).
IV.The determination of the capital stock for each year of the period (2013)(2014)(2015), considering the forecast of the indicator gross fixed capital formation determined according to the relation: where: K t -the capital stock for the year t; δ -the rate of capital depreciation; I t -the investment for the year t.•The estimation of the size of current investment is accomplished by applying a constant rateβ -to the GDP value of the previous year.The calculations associated with the national level take place alternatively, every year in part, because the current I investment, is determined based on the previous year GDP.

Calculations and analysis associated with work steps
Following the previously announced work steps, the analysis highlights the following issues: The employed population had a sharp decrease in the year 2002 beside the year 2000 (1274 thousands people), respectively, 12%, unrecovered until the year 2012, the increases and decreases in the period, being sensitively contiguous.The evolution of the observed tfp shows a higher level of its, at the end of the period -2012 -beside the start 2000, respectively, 2.18 unto 1.78, the oscillations, increasing or decreasing , in the interval series, being correlated with the changes in other factors and expressing the contribution of tfp to GDP achievement, such as:

Capital (K)
•The tfp level increase in the years 2002,2004,2005, beside the previous years, given the conditions of a sensitive decrease of the employed population, expressing the contribution of tfp to GDP growth (the capital is also increasing).
•The tfp level decrease, in the year 2007, compared to the year 2006, the GDP being sustained by the growth both of the capital and of the employed population, compared to the previous year.
•The tfp increase in the year 2009 compared to 2008 (from 2.0 to 2.18) sustaining the GDP achievement that decreased, given the fact that both the employed and the capital had a substantial decrease, as an effect of the crisis.
• The adjusted tfp data, determined based on the trend, follow the same evolution, being sensitively contiguous to the observed tfp.
III.The determination of the adjusted n factor (the time series 2000-2012) and of the forecast n* , for the years 2013-2015, should be found in the Annex 4, represented according to the graphic in the Figure 5.
Adjusted n and forecast n* The evolution of the employed population, highlights, also, in the data determined based on the trend, the continuous decrease of the indicator, both in the period 2000-2012 and in forecast, 2013-2015.
IV.The determination of the capital factor -K and, respectively, GDP, alternatively, in forecast each year.
There are considered constant rates, throughout the forecast period, respectively: • the rate of capital depreciation -0.15 δ = 0.15 • the investment rate -0.048 According to the calculations above, for the period 2013-2015, the forecast values of the model factors, are presented in the Table.The forecast data show that, for national level, there is the possibility of a GDP growth due to the growth of capital and total factor productivity, the employed labor being in decrease.Taking into consideration the average annual growth rhythm during the 3 years period, the contribution of factors to potential GDP growth, is presented according to data in Table 2.The growth rhythm of GDP of 5.2%, is sustained by the capital, 4% and by the total factor productivity, 2.4%.The negative increase of the labour factor, 0.9%, is the consequence of the significant decrease of population in the series taken into account, respectively, from 10508 thousands people, in the year 2000, to 9263 thousand people, in the year 2012.
The calculations based on testing the parameters, respectively, the coefficients of elasticity, for labour and capital, the rate of investment and the rate of capital depreciation, followed to obtain values for the forecast GDP in the period 2013-2015, as close as to the values announced, in perspective, by Comisia Națională de Prognoză (CNP).Thus, the data forecast by calculation, for the years 2013, 2014 and 2015 are close to those forecast by Comisia Națională de Prognoză (CNP) 3 (March 5, 2014) (Table 3)

Conclusions
To estimate the forecast GDP and the contribution of factors to its achievement, there were taken into account, in the production function for national level, the following parameters: the coefficients of elasticity for labour and capital factors, α = 0.30, and, respectively, (1-α) = 0.70, the rate of capital depreciation, δ = 15%, the investment rate, β = 4.8%.
The analysis showed the contribution of the labour and capital factors to the national GDP achievement, but also, the total factor productivity contribution, in the case of this indicator, the participation degree being different, by years, depending on the level of the other two factors, the labour and capital.The data obtained reflect an increase in production, in the forecast period, higher to the growth of each of the labour and capital factors, the level of total factor productivity expressing the efficaciousness of factors use.
The results lead to the conclusion that, the use of the model, although it exposes some difficulties in implementation, as mentioned in the introductive part, may be relevant to such analysis, if should be taken into account a careful testing of the value of the used parameters and a statistical data base, large enough, to be considered methodologically satisfactory. Quelles values determined above shall be entered in the logarithmic production function to obtain the y values for the years for which the forecast it shall be accomplished.•Itshall be determined the Y value, respectively GDP, for the forecast years (by antilogarithm).

. The work steps of the application I.
⋅ The determination of the Total Factor Productivity, as a residual variable in the considered production function, at a given value of the parameter α; the tfp value is determined on each year, based on the values Y, N, K of ASR -INS, for the period 2000-2012; this is the time series of the observed tfp.