The paper discusses several problems of estimating the total factor productivity included in the aggregate production function used in the Romanian macroeconomic model. The author suggests an improvement of the formula adopted in the version 2005 of this macro-model.total factor productivity

Emilian Dobrescu

English

Research Papers in Economics

￿￿  Estimating the Total  Factor Productivity  in Romanian Economy 
 
Amfiteatru Economic  512 
 
￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿
 
Emilian Dobrescu 
Macroeconomic Modelling Centre - Romanian Academy 
E-mail: emiliand@clicknet.ro 
 
 
 
Abstract 
The paper discusses several problems of estimating the total factor productivity included in 
the aggregate production function used in the Romanian macroeconomic model. The author 
suggests an improvement of the formula adopted in the version 2005 of this macro-model. 
Keywords: total factor productivity 
JEL Classification: C22, E23 
 
 
Estimating the Total Factor Productivity in Romanian Economy 
 
1. The last operational version of the Romanian macro-model (Dobrescu 2006) included a 
specific  form  of  Cobb-Douglas  production  function.  It  tried  to  combine the  classical 
conceptual framework with the recent modelling approaches [Aghion and Howitt; Allen; 
Apel and Jansson; Baxter and King; Burnside, Eichenbaum, and Rebelo; Cechetti; Claus 
(2000a, b); Denis, Mc Morrow and Rõger; Elmeskov; European Commission 1995; Forni 
and  Reichlin;  Froyen;  Gerlach  and  Smets;  Gordon;  Hodrick  and  Prescott;  Hulten; 
Kuttner; Nordhaus; OECD 2000; Scott; Solow; Turner, Richardson, and Rauffet; Pindyck 
and Rubinfeld; Proietti, Mussoy, and Westermanny]. Indeed, some peculiarities of the 
Romanian economy were also incorporated.  
 
1.1. The starting point of this attempt was a common formula with capital and labour, 
expressed in yearly indices: 
   
IGDPc=IE^alpha*ICKc^(1-alpha)*ITFP          (1) 
where: 
IGDPc – index of gross domestic product at constant prices; 
IE – index of employment;  
alpha – elasticity of output with respect to labour, approximated by the extended share of 
labour income in gross value added;  Economic Interferences  ￿￿ 
 
Vol XI • Nr. 26 • June 2009  513 
ICKc - index of tangible fixed assets at constant prices; and 
ITFP – index of the total factor productivity. 
• There are reliable statistical data concerning IGDPc and IE.  
•  For  alpha  and  ICKc  such  information  are  not  yet  available.  They  were  replaced  by 
author’s indirect estimations. 
• The total factor productivity, as an index, has been deduced from the relationship:  
ITFP=IGDPc/(IE^alpha*ICKc^(1-alpha))          (2) 
 
1.2. Two categories of determinants are involved in the econometric determination of the 
total factor productivity: on one hand, the level of alpha itself and, on the other, some 
variables which essentially influence the dynamics and utilisation of the productive 
capacities.  
1.2.1. Regarding alpha, it seems realistic to assume that: 
·  if  actual  alpha  is  less  than  its  long-run  (equilibrium)  level,  the  labour  force  is  not 
stimulated to reach the highest potential output;  
· if alpha exceeds such an optimal point, the firms are obliged to restrain their activity, 
which also has negative repercussions on the total factor productivity. 
Starting from these considerations, the econometric relationship of the index of total factor 
productivity (ITFP) was built according to the following restrictions: 
- if alpha=0 or =1 (that is when the production would be nonsensical for labour force or, 
respectively, for capital), ITFP tends to zero;   
- ITFP depends non-linearly on alpha, admitting a maximum when alpha reaches its long-
run (equilibrium) level. 
The simplest functional form has been adopted: 
ITFP=(alpha-alpha^a)*RV              (3) 
                  (+/-)            (+) 
where RV captures the effect of other variables. The influence of the expression (alpha-
alpha^a) depends on the position of actual alpha comparatively to its long-run (equilibrium) 
level.  
The first mentioned assumption (when alpha=0 or =1, ITFP=0) is automatically observed. 
The second one is also satisfied for a>1. The long-run (equilibrium) level of alpha was 
noted  alphao.  It  has  been  estimated  separately,  using  a  specific  procedure 
(alphao=0.653821). On this basis, the parameter a has been determined from  
¶ITFP/¶alpha=0                     (4) 
and respectively: 
(1/a)^(1/(a-1))=alphao                   (5) ￿￿  Estimating the Total  Factor Productivity  in Romanian Economy 
 
Amfiteatru Economic  514 
1.2.2.  Concerning  RV,  the last  version  of  the  Romanian macro-model  has  retained the 
following factors:  
•  investment  intensity,  approximated  by  the  index  of  gross  fixed  capital  formation  at 
constant  prices,  computed  as  a  moving  geometrical  average  of  two  successive  terms 
(AIGFCFc); 
• domestic demand pressure (DDP), as a ratio of the domestic absorption index to gross 
domestic product index;  
• unemployment rate; this is represented by its moving arithmetic average of two successive 
years (maru). 
The  first  factor  influences  the  dynamics  of  tangible  fixed  assets;  the  second  has  an 
important impact on the utilisation degree of productive capacities, and the third variable 
acts on labour-intensity of employed workers.       
The effect of transitional reforms was captured by the time (t); a constant has also been 
included in order to reflect the trend. 
 
1.3. Finally, the expression (6) has been regressed. 
ITFP=(alpha-alpha^a)*(c(1)+c(2)*rAIGFCFc+c(3)*rDDP(-1)+c(4)*maru(-1)+c(5)/t)    (6) 
where rAIGFCFc=AIGFCFc-1 and rDDP=DDP-1.  
The following coefficients have resulted (using the statistical series for 1990-2004 years): 
a=4.582357 
c(1)=1.975529 
c(2)=0.393543 
c(3)=0.533134 
c(4)=1.240195 
c(5)=-0.529765 
The sign of c(5) attests the increasing positive influence of institutional changes on the 
global efficiency of the Romanian economy.  
 
2. In case of data covering the whole 1990-2008 time frame, the specification (6) generates 
parameters with low statistical significance. Consequently, the present paper proposes 
several changes in this equation. 
2.1. In order to aproximate alphao, a VAR for alpha series has been applied:   
alpha=0.301332+0.541104*alpha(-1)             (7) 
from  which  yields  alphao=0.301332/(1-0.541104)=0.656645.  A  similar  level  would  be 
obtained using the previous methodology, based on econometric estimates of the first order 
differences of alpha. In the new determination of alphao, the coefficient a changes slightly: 
a=4.657958. This will be included in the updated regression. Economic Interferences  ￿￿ 
 
Vol XI • Nr. 26 • June 2009  515 
2.2. Regarding other variables, it seems more suitable to involve not only the gross fixed 
capital formation, but the whole volume of the tangible fixed assets. On the other hand, 
the degree of utilization of productive capacities depends greatly on exports, which are 
absent in the relationship (6). Consequently, the total demand pressure in real terms 
(TDPc) will be introduced:      
TDPc=[(DAD+X)/(PGDP*(DAD(-1)+X(-1))]/ICKc        (8) 
where 
DAD – domestic absorption at current prices; 
X – exports in national currency at current prices; and 
PGDP – gross domestic product deflator. 
We prompt that the index of tangible fixed assets at constant prices (ICKc) is computed as 
follows: 
ICKc=(CK(-1)*(1-dfa)+GFCFc)/CK(-1)=1-dfa+GFCFc/CK(-1)     (9) 
where: 
CK(-1) – tangible fixed assets of previous year in prices of the same year; 
dfa – depreciation rate of the tangible fixed assets; 
GFCFc – gross fixed capital formation at previous year prices (its value in current prices is 
deflated by the corresponding price index - PK). 
Normally, TDPc substitutes rAIGFCFc and rDDP used in (6).  
2.3.  As  it is  known, the  weight  of the sectors providing natural raw materials remains 
significant. Their output depends on climatic conditions. Such a circumstance cannot 
be neglected. A possible way to take it into account is to include, among explicative 
factors of ITFP, the variation registered by the index of gross value added (at constant 
prices) produced in agriculture, forestry, fishing, and hunting (AG1-AG1(-1)).  
2.4. We can also admit that t - as a separate independent variable (reflecting the influence 
of transitional changes) - has ceased to be representative. However, it will be attached 
– as an amortizing factor - to (AG1-AG1(-1)). The economic development attenuates 
step by step the impact of climatic oscillations on global output.  
2.5. Therefore, the ITFP function could be defined as follows: 
ITFP=(alpha-alpha^4.657958)*(c(6)+c(7)*TDPc+c(8)*maru+c(9)*(AG1-AG1(-1))/t)   (10) 
This  new  specification  has  been  regressed  using  statistical  series  for  1990-2008  years 
(Appendix). The obtained results are presented in Table no. 1 
 
Table no. 1 
Dependent Variable: ITFP     
Method: Least Squares     
Sample (adjusted): 1992 2008   ￿￿  Estimating the Total  Factor Productivity  in Romanian Economy 
 
Amfiteatru Economic  516 
ITFP=(alpha-alpha^4.657958)*(c(6)+c(7)*TDPc+c(8)*maru+c(9)*(AG1-AG1(-1))/t) 
  Coefficient  Std. Error  t-Statistic  Prob. 
c(6)  1.030516  0.085412  12.06522  0 
c(7)  0.617856  0.081938  7.54052  0 
c(8)  5.130551  0.606539  8.458727  0 
c(9)  2.373125  0.319154  7.435671  0 
R-squared      0.94755 
Adjusted R-squared    0.93545 
 
All the retained factors, including the variation of agriculture output, are significant. The 
Jarque-Bera statistics of residuals shows as follows: 
 
Table no. 2 
0
1
2
3
4
-0.03 -0.02 -0.01 0.00 0.01 0.02
Series: RESID
Sample 1990 2008
Observations 17
Mean       -4.02e-06
Median    0.000112
Maximum   0.020175
Minimum  -0.025066
Std. Dev.    0.011803
Skewness   -0.321605
Kurtosis    2.732682
Jarque-Bera  0.343667
Probability  0.842119
 Economic Interferences  ￿￿ 
 
Vol XI • Nr. 26 • June 2009  517 
3. In order to establish if the expression (10) is suitable or not, two simulations will be 
processed. 
3.1. One of them confronts the estimations for ITFP1 (specification and parameters for (6)) 
with those for ITFP2 (specification and parameters for (10)). The updated series 1990-
2008 are used in both cases. The results are compared with the corresponding statistical 
data (ITFP) in the following Graph: 
0.85
0.90
0.95
1.00
1.05
1.10
1.15
90 92 94 96 98 00 02 04 06 08
ITFP ITFP1 ITFP2  
Graph ITFP 
It is clear that ITFP2 reflects better the actual series. The correlation coefficient ITFP2-
ITFP is 0.954113, while the correlation coefficient ITFP1-ITFP represents only 0.216619. 
3.2. The second simulation compares the behaviour of ITFP in both formulas, depending on 
variation of alpha. This exercise is based on data for 2007, namely: 
rAIGFCFc=0.251787 
rDDP(-1)=0.009420  
maru(-1)=0.072244 
t=19 
TDPc=1.016068 
maru=0.068837 
AG1-AG1(-1)=-0.199 
Only  alpha  is  changing  (from  0  to  1).  The  results  are  noted  with  prefix  s.  They  are 
presented in Graph salpha. 
 ￿￿  Estimating the Total  Factor Productivity  in Romanian Economy 
 
Amfiteatru Economic  518 
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
salpha
sITPF1
sITPF2
 
Graph salpha 
The estimations obtained using formula (10) seem to be more realistic, in the sense that 
they are comparable with the similar coefficients used in the macro-models of other UE 
countries (normally, for closed alpha). 
Our experiment confirms again the need to re-examine periodically the specification of a 
model especially under frequently changing statistical series.  
 
Appendix 
Statistical Series 
 
Year  ITFP  alpha  AIGFCF  DDP  maru  TDPc  AG1 
1990  0.950555  0.721966  -  1.131312  NA  1.075781  1.366347 
1991  0.884687  0.68395  0.665499  0.953015  NA  0.874546  0.875098 
1992  0.912989  0.574054  0.871786  1.043864  0.033317  1.049447  0.858203 
1993  1.024945  0.60137  1.090631  0.967632  0.058166  0.868805  1.137795 
1994  1.030434  0.608583  1.1421  0.972695  0.07759  1.021459  1.030115 
1995  1.105212  0.646958  1.136446  1.034519  0.081767  1.171229  1.050228 
1996  1.04819  0.639608  1.062692  1.026819  0.072574  1.050883  0.961066 
1997  0.963765  0.634923  1.036982  0.987439  0.061303  0.918839  0.997348 
1998  0.9907  0.668191  0.977913  1.009007  0.059696  0.9955  0.886009 Economic Interferences  ￿￿ 
 
Vol XI • Nr. 26 • June 2009  519 
Year  ITFP  alpha  AIGFCF  DDP  maru  TDPc  AG1 
1999  1.087856  0.680407  0.945929  0.970421  0.065213  1.16205  1.031173 
2000  1.061419  0.704771  1.002052  1.007609  0.070778  1.188215  0.819548 
2001  1.114863  0.67385  1.077838  1.020071  0.070969  1.13345  1.273484 
2002  1.074492  0.656387  1.091039  0.980694  0.076336  1.099262  0.938407 
2003  1.044469  0.684953  1.084034  1.017407  0.07638  0.994834  1.050558 
2004  1.088066  0.671309  1.098922  0.985458  0.075745  1.050741  1.201029 
2005  1.023196  0.686882  1.118745  1.041238  0.076261  1.03433  0.826344 
2006  1.069076  0.667355  1.159518  1.00942  0.072244  1.053753  1.034 
2007  1.030701  0.682341  1.251787  1.029859  0.068837  1.016068  0.835 
2008  1.063896  0.65303  1.288952  0.983507  0.061227  1.040494  1.214 
Source: National Institute of Statistics, National Commission for Prognosis, author’s estimations 
 
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Estimating the Total Factor Productivity in Romanian Economy

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Estimating the Total Factor Productivity in Romanian Economy

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