ri=ftvi(t)+vi(t-0]
The average rate o f productivity growth T F P ) is therefore given by the translog rate o f productivity growth
ri-=\[vHi)+
v'rit-i)]
TFP growth or the shift o f the production function is sometimes called residual growth or multifactor productivity growth: output growth due to factors other than in put growth. It is impossible in practice to include all factors in a production function estimation due to limits on the availability o f data on all factors concerned. Omission o f minor production factors will not, however, have a significant effect on the results o f the TFP growth estimation, as long as major input variables are included. TFP growth o f the agricultural sector is estimated both with and without fertilizer as a factor and TFP estimates varied very little (Chapter 4). The reason for the small change in the estimated TFP growth might be due to the imposition o f constant return to scale which implies that all weights sum to one. The added fertilizer variable in the model o f agri-
cultural TFP growth estimation affects changing in the contribution o f closely related input such as land. The main purpose o f this study is not merely to estimate the abso lute size o f TFP growth, but to compare the size and indicators o f TFP growth in sec tors, industries and crops, and so to explain the major sources o f growth in Thailand and draw policy implications.
The framework o f input variables included in the TFP estimation follows the framework adopted by Gollop (1983). The alternatives o f the aggregate productivity studies is based on the measures o f value added versus on deliveries to final demand. While the final products included in national products should be the objective o f pro duction, the sum o f sectoral deliveries to fmal demand should therefore be the appro priate measure. Gollop (1983) shows that existence o f imported intermediate inputs may cause TFP studies based on value added measures to yield upward bias in their estimation o f productivity growth (Appendix CH 3 Section 3.1).
Sectoral deliveries to intermediate demand could be excluded from the aggre gated productivity estimation if they are viewed as self-cancelling transactions. The self-cancelling property in fact follows the assumption that the economy is closed to trade in foreign - produced inputs. Once trade in foreign - supplied inputs is intro duced, however, domestic deliveries to intermediate demand and intermediate input purchases are not offsetting transfer.
Since the data on domestically produced and imported intermediate inputs is unavailable, the study will include only prim ary capital and labour inputs in the estima tion. This, however,could make a little upward bias o f TFP growth estimation.
TFP estimation methodology adopted in the study
There are studies estimating TFP growth in Thailand, however, most o f them using non-parametric approach; i.e. they used factor shares as the weight o f each input factor in calculation o f TFP growth (Equation 3.6). This study will directly employ output elasticity o f each input factor estimated from production function to be the weights. An advantage o f this method is that the data on w age and rent (factor returns) normally are not much reliable.
Chapter 3
Page 39
The main task in estimating TFP growth is to determine the factor weights to be used in the TFP growth estimation equation, ß/cand ßz, in Equation (3.6). In equilib rium and with perfect competition, factor shares (wage shares and rent shares for la bour and capital) are equal to the output elasticity o f that factor, and these factor shares can be used to estimate Equation (3.6) (as used in some papers including Denison 1967, 1976). Nevertheless, the most direct method o f TFP estimation is to estimate the production function and use the estimated values o f output elasticities o f factors as the weights in calculating Equation (3.6). In addition, since the cost function has a duality property with respect to the production function, the cost function can also be used to calculate TFP growth. These two methods o f TFP calculation will be equal under the constant return to scale condition (Equation 3.12).
Production functions can be o f the form
y(t) = F(X lt,X 2t,. . . , X nt, t ) (3.8)
Alternatively, the cost function, according to microeconomic theory, may be chosen as a dual o f the production function
c
=C[y(t),
Pit, P2t, P nt,t]
(3.9)
where
X it = factor input
F i t= the ith factor input price i - 1 , 2 , . . . , n
Assuming that F and C satisfy differentiability and curvature characteristics, the growth o f total factor productivity can be measured by:
T F P = y =
d u y (t) _ d y 1
d t
dt y
where
y(t) is the output o f the production function
y(t) = F (X it, X 2 t,... X nt,t)
th
X i is the i input
Therefore y indicates how the maximum output changes over time, under the given inputs used.
Or using the duality property
t t p — r —
ck\C
_dC
1 T F ? ~ r ~ ~ ~ ä ~ ~ ~ ~ ä cwhere
C(t) is the minimum total cost o f producing output Y(t)
(3.11)
Therefore V is the change over time in the minimum cost o f producing a given level o f output, at given input prices.
y is related to T b y
r
Y 0
(3.12)where
0 = InC/lny = an index o f returns to scale (Ohta 1974).
When constant returns to scale are imposed, y = Vsince 0 = 1 . The cost func tion can be obtained by the solution o f the cost minimization condition for competitive producers who face given input prices. Therefore T, which is estimated from the cost function, must give the same result as y which is estimated from its primal production function under conditions o f constant returns to scale.
TFP growth estimates are based on the production function to obtain elasticities o f output which are then used as the weights o f the factor inputs in TFP growth estima tion. The prime reason for choosing the production function to estimate TFP growth is that some time-series data on input prices are unavailable and unreliable. In this study, TFP growth will be estimated by Equation (3.5).