Revised Literature Review By Dr

Productivity Growth in Philippine Agriculture: A Literature Review

Submitted by Romeo G. Teruel

1

1. Introduction With the sizable contribution of agriculture to the Philippine economy, the country’s economic future will continue to be highly affected by agriculture’s performance.

In recent years, the agricultural sector has accounted for

approximately 20 per cent of the Gross Domestic Product (GDP) and about 14 per cent of the country’s export earnings. In addition, it employs almost half of the country’s labor force. Thus, the dependence of the majority of the rural poor on the agriculture as the major source of livelihood remains high. Recent discussions have expressed cause of concern regarding the future role of Philippine agriculture in the process of economic development. Agricultural production stagnated in the 1980s, growing at an average of 1 per cent annually. From 1990 to 1995, the average annual growth rate increased to 1.4 per cent; by 1996-2000, however, this declined to 0.60 per cent (David, 1996a;

Development

Indicators

for

the

Philippine

Agriculture,

2002).

Furthermore, the past and present agricultural scenarios seem to suggest that Philippine agriculture is lagging behind other agricultural economies in terms of comparative competitiveness. The Philippines has been transformed into a net agricultural importing country over the last decade. This trade scenario is the complete opposite compared to the scenarios observed in other neighboring countries, such as Indonesia, Malaysia and Thailand, which have consistently posted an increasing agricultural surplus since the 1970s.

It has also been

shown that the dismal growth of the agriculture correlates with the overall growth of the economy.

Several studies have shown that the decline in agricultural

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growth can be attributed to the continued deceleration of productivity (Mundlak, 2004 and Teruel and Kuroda, 2004, 2005). The objectives of this paper are as follows: 1.

To contribute a literature review on agricultural productivity analysis, providing a critical assessment of the state-of-the-art at both international and national levels;

2.

To describe the standard and emerging empirical techniques used in agricultural productivity studies, internationally and in the Philippines, including econometric analysis and growth accounting;

3.

To identify the similarities, relationships, and differences between the techniques within a coherent framework;

4.

To assess what is known about agricultural productivity growth in the Philippines, critical gaps in our knowledge and data on the nature, sources, and causes of productivity growth; and

5.

To propose a theoretical framework and empirical technique for use in the aggregate agriculture sector analysis of the PGPA

The review is composed of two stages: 1) theoretical and empirical. The first stage aims to examine the five theoretical approaches to measuring productivity growth such as: 1) the growth accounting, 2) index number, 3) econometrics, 4) the distance function based-Malmqvist approach and 5) the stochastic frontier approach. The second stage intends to review the empirical studies on productivity in Philippine agriculture that employ these approaches. The availability of data on output and input is essential for the accurate

3

measurement of productivity; hence, this paper also seeks to review the availability of agricultural data by looking at the different data sets assembled in previous studies, the data gaps in actual empirical productivity measurement, and other important data issues.

This paper ends with a synthesis,

recommendation and conclusion.

2. The Concept of Productivity This section discusses the concepts of and the issues surrounding productivity. It also proposes to differentiate partial productivity from total factor productivity (TFP). The basic definition of productivity is expressed as a quantitative relationship between output and input (Antle and Capalbo, 1988). It is also defined as the ratio of some measure of output to some measure of input use or simply an arithmetic ratio between the amount produced and the amount of any resources used in the process of production. This definition of productivity can be further simplified as the output per unit input or the efficiency with which resources are utilized (Samuelson and Nordhaus, 1995). As a concept, productivity can be a partial or total measure. The partial measure of productivity or partial factor productivity (PFP) relates output to any input implying that there will be as many definitions of productivity as inputs used in production. In this case, productivity is the amount of output per unit of a particular input or equally known as the average product. Commonly used partial measures are: yield (output per unit of land), labor productivity (output per economically active person or per agricultural per-hour) and capital productivity.

4

Yield is usually used to assess the success of a particular production technology. Labor productivity is used as an indicator to assess rural welfare or standard of living since this captures the ability to acquire income through agricultural production (Block, 1995). PFP can sometimes be misleading.

Changes in PFP can hardly be

explained since there is no clear indicator on why this measure of productivity changes.

An improvement for example in labor productivity can either be

attributed to the increased use of fertilizer or tractors. To account for at least some of these problems, one can use the total measure of productivity or the concept of total factor productivity (TFP). TFP relates the output produced with an index of composite inputs; meaning the sum of all the inputs used in the production process which may include land, labor, physical capital, livestock, fertilizers and pesticides. TFP is computed as the ratio of an index of agricultural output to an index of agricultural inputs.

The index of agricultural output

(agricultural input) is a value-weighted sum of all agricultural production components (conventional agricultural inputs). Growth in TFP is termed in the literature as the Solow residual and it is a measure of technological progress brought about by the changes in agricultural research and development, extension services, human capital development, infrastructure, government policies and environmental degradation. The change in TFP may also be attributed to unmeasured inputs or imperfectly measured inputs.

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3. Review of Methods There are several approaches or techniques that can be used to measure the change in output, to calculate the relative contribution of the different inputs used in production to output growth and to identify the Solow residual or output growth not due to increases in inputs.

These major approaches are: 1) the

growth accounting, 2) index number, 3) econometrics and 4) the distance function-based Malmquist approach and 5) the stochastic frontier approach. Each of this approach has different data requirements, is suited to address different questions, and has its relative strengths and weaknesses.

3.1 Growth Accounting Approach The growth accounting approach involves compiling detailed accounts of inputs and outputs, and aggregating these into input and output indices in order to calculate the TFP index (Diewer, 1976, 1980).

It decomposes the output

growth into two components: 1) the growth in different inputs like labor and capital and 2) growth in TFP.

This approach requires the specification of a

production function, which describes the technical relationship between the levels of output that can be produced using certain amount of inputs. This production function can be expressed as: Yt = At f ( K t , Lt )

1

where Yt is the output at time t, At represents the technology or TFP at time t, Kt is the capital stock at time t, and L is the amount of labor input at time t. Given this production function, the use of growth accounting approach requires the

6

following assumptions, namely:

1) the technology, as represented by At, is

separable as shown in Eq. 1, 2) the production function exhibits constant returns to scale (CRS), 3) the producers are efficient and they attempt to maximize profit, and 4) the markets are perfectly competitive. Differentiating (1) with respect to t gives •

•

Y = Af ( K , L ) +

∂f • ∂f • KA+ LA ∂K ∂L

2

where the dots indicate a first partial derivative with respect to time. Dividing Eq. 2 by Q gives: •

•

•

•

Y A ∂f K ∂f L = +A +A . Y A ∂K Y ∂K Y

3

Given the assumptions, the elasticity of output with respect to capital w k and the elasticity of output with respect to labor wL can be written as: wK = wL =

∂Y K ∂f K =A ∂K Y ∂K Y

4

∂Y L ∂f L =A ∂L Y ∂L Y

and therefore, Eq. 3 can be written as: •

•

•

•

•

•

Y A K L = + wK + wL Y A K L

5

•  A Solving for   , the growth rate of TFP is  A   •

•

A Y K L = − wK − wL . A Y K L

7

6

The TFP growth can be interpreted as the residual share of output growth after accounting for the changes in the production inputs.

One of the

disadvantages of using the growth accounting approach is that it imposes several strong assumptions like the Hicks-neutrality of technological change, constant returns to scale and long-run competitive equilibrium.

3.2 Index Number Approach An alternative way to compute for TFP is through the use of the Index Number Theory.

This theory describes how to derive a single index for the

quantity of different outputs or goods produced and of inputs used over time including their corresponding prices.

The index number approach involves

dividing an output quantity index by an input quantity index resulting to a productivity index. Therefore, At =

Yt Xt

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where At is TFP, Yt is an index of output quantities, Xt is an index of input quantities and subscript t denotes the time period. After obtaining At, the calculation of TFP growth rate is straightforward. The difficulty associated with using the index number approach is in the determination of the type of index to use and in gathering the price and quantity data necessary to construct them. There are several index procedures that can be used to measure productivity and these include the Laspeyres, Paasche, Fisher and the Törnqvist index procedures. What follows is the formulation of different output quantity indexes using the different index approaches. 8

Input

quantity indexes can be similarly constructed using the data on input quantities and prices. Given t

the

(

vectors

of

(

t

p = p1t , p 2t ....... p kt

prices

)

and

quantities

)

y = y1t , y 2t ....... y kt for the k different outputs produced in an economy at time t = 0,1,…….T, a Laspeyres index is computed as k

(

0

1

0

1

)

YL p , p , y , y =

0

1

0

0

p ⋅y p ⋅y

=

∑P Y 0

i =1 k

∑P Y 0

i

i =1

(

)

k  y1 0 1 0 1 YL p , p , y , y = ∑ si0  i0 i =1  yi

where

s = t i

1 i

i

8

0

i

  

9

pit y it m

∑p i =1

t i

y it

is quantity i’s nominal output share. Eq. 9 shows that the

Laspeyres index is a nominal share-weighted sum of quantities ratios. The Paasche index is calculated by using period 0 prices instead of period 1 prices. This index formulation is obtained by using the following equation: k

∑p

1 i

y i1

 k  y1 0 1 0 1 YP p , p , y , y = 1 0 = ik=1 = ∑ si1  i0 y p ⋅y ∑ pi1 yi0  i =1  i

(

)

1

p ⋅y

1

  

−1

  

−1

10

i =1

The Fisher index, on the other hand, is computed by getting the geometric average of the Laspeyres and Paasche indexes.

Finally, the Törnqvist index is

defined as

(

)

 y1 0 1 0 1 YT p , p , y , y = ∏  i0 i =1  y i 9

k

  

(

0.5 si0 s1i

) 11

One can either use the economic or the axiomatic approach to decide on what index formulation to use in constructing quantity indices for output and input. The economic approach selects an index number formulation on the basis of an assumed underlying production function given the price taking, profit maximizing behavior of producers (Diewert and Lawrence, 1999).

The

Laspeyres index procedure is believed to be exact for, or at least imply, a linear production function in which all inputs are perfect substitutes in the process. Similarly, the Törnqvist index, which is a discrete approximation to the more general Divisia index, implies a homogenous translog production function. On the other hand, a geometric index like the Fisher index exacts the Cobb-Douglas production function. The axiomatic approach requires a comparison of the properties of the different index number formulations with a number of desirable mathematical properties.

The index that satisfies the most tests is the “preferred” index

formulation. The axioms or desirable properties used for the test are as follows: 1. Constant quantities test: If quantities are the same in two periods, then the output index should be the same in both periods irrespective of the price of the goods in both periods; 2. Constant basket test: If prices are constant over two periods, then the level of output in period 1 compared to period 0 is equal to the value of output in period 1 divided by the value of output in period 0;

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3. Proportional increase in quantity test: If all quantities in period t are multiplied by a common factor, λ, then the quantity index in period t compared to period 0 should be increased by λ also; and 4. Time reversal test:

If the price and quantities in period 0 and t are

interchanged, then the resulting output index should be the reciprocal of the original index. Diewert and Lawrence (1999) noted that among the index number formulations, only the Fisher index passes all the axioms or desirable properties. Both the Laspeyres and Paasche indexes are found to be inconsistent with the time reversal test, while the Törnqvist index does not satisfy the constant basket test. They also noted that using a more extensive list of axiomatic tests, the Fisher index formulation continues to satisfy more tests than the other index formulations. Like the growth accounting approach, the construction of the output and input quantity indexes using the different index procedures requires restrictive assumptions such as the neutrality of technical change, constant returns to scale, competitive markets and the separability of the underlying transformation function in outputs and inputs.

Another disadvantage is that the statistical methods

cannot be used to evaluate their reliability because index numbers are not statistically generated. In addition, index numbers are not particularly informative in identifying sources of growth.

This approach however can be easily

implemented regardless of the number of observations.

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3.3

The Econometric Approach The econometric approach is based on an econometric estimation of the

production technology.

Thus, this approach requires the use of econometric

methodology; necessitates the specification of a function representing the technology and the estimation of such function, its derivatives or both to determine the value of the different parameters necessary for productivity estimation. The function can either be a primal function like the transformation function or the production function or a dual function like the cost or profit function. The estimation using the primal function involves the derivation of a factor demand and supply function based on the necessary conditions of optimization given a production function and the assumption of profit maximization or cost minimization. The estimation using dual functions on the other hand involves the derivation of a system of input demand and output supply by appealing to the theory of duality. The fundamental principle of duality in production is that the cost or profit function summarizes the economically relevant characteristics of a technology.

Thus, a firm’s technology as

represented by its production possibilities set or production function may also be characterized by its cost or profit functions, provided that these obey certain regularity conditions. To better understand the idea of this theory, the duality between a cost function and production possibilities set or production function will be discussed in turn1. 1

Between the two dual functions, cost function is frequently used in productivity estimation. Antle and Capalbo (1988) pointed out that TFP estimation using profit function is not straightforward. The link between TFP and cost function will be discussed in the latter part of this subsection.

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3.3.1 Duality Theory A production function is often assumed and used as a starting point in many researches on production relationship.

The analytical framework of

production functions can be extended with the inclusion of the duality theory under the assumption that firm chooses input quantities in order to minimize the cost of their production process, given the prices of these inputs. The duality between production and cost functions can be explained by following Diewert (1978): consider a production function with a single output given by Y = f(X) where Y is the maximum output which can be produced by a firm given a kdimensional vector of inputs X at a certain point in time. The function f can be said to describe the firm’s technology. On the other hand, if this firm has minimum total cost of producing the level of output Y given the vector of input prices P defined by C(Y,P), then its minimum C clearly depends on the underlying production function f. The duality theory establishes the duality of cost as well as production functions indicating that either of these functions, C or f, can adequately describe the economically relevant characteristics of the same underlying technology given certain restrictions on them. More formally, the dual relationship between cost and production (or transformation) functions implies that the minimum total cost of producing Y given the production possibility set T = (X,Y) and a vector of positive input prices P that

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correspond to X, that is, C(Y,P), can be constructed from T with C having the following properties2: (a) C(Y,P) is a negative real valued function defined for all finite Y ≥ 0, P ≥ 0k. (b) C(Y,P) is nondecreasing in input prices P. (c) C(Y,P) is nondecreasing in Y and tends to approach ∞ for every P ≥ 0k. (d) C(Y,P) is positively linearly homogenous and quasi-concave in the components P for every Y > 0. Similarly, given C with properties (a) to (d) above, the production possibilities set T with properties (i) to (iv) (please refer to footnote 2) can also be constructed from C.3 By Shephard’s lemma, the total cost function C with properties (a) to (d) above is related to the cost minimizing demand function for input X through its first partial derivative with respect to the input price P. Suppose the first partial derivative of C with respect to P is given by CP(Y, P).

If C is continuously

differentiable in P, then Cp equals the total cost minimizing demand for input X, at (Y,P). Moreover, if there is a unique cost-minimizing demand for input X at (Y, P), then CP exists.

The application of Shephard’s lemma produces a system of

2

The production possibilities set T has the following properties: (i) the set of producible outputs Y* is nonempty; (ii) for each Y in Y *, the input requirement set X(Y) is closed and for a nonzero output not contained the zero input vector; (iii) there is free disposal of inputs, that is, if an input vector X0 can produce output Y then a second input vector X 1 that is at least as large as X0 in each component can also produce Y; (iv) the input requirement sets are strictly convex from below, that is, two input vectors X0 and X1 are in X(Y), then for a weighted combination of X0 and X1, for instance, X2 = λX1+ (1-λ)X0 where the scalar λ is 0<λ<1, there is an input vector X 3 in X(Y) such that X2 is at least as large as X3 in every component. 3 Please see Diewert (1971, 1978) and McFadden (1978) for the proofs of these duality relations between cost functions and production possibility sets.

14

equation representing the output supply and input demand functions which is used to estimate parameters necessary for productivity measurement.

3.3.2 Primal and Dual Rate of Technological Change In the econometric approach to productivity measurement, technological change, which corresponds to the shifts of the production function, is synonymous with productivity change under the assumption that production is efficient. Technological change refers to changes in production process brought about by the application of scientific knowledge. Technological change occurs when there is an increase in output per unit of input due to the use of improved production methods resulting in an increase of efficiency in the use of resources, changes in input quality and the introduction of new processes and new inputs (Antle and Capalbo, 1988). This production function shifts or the technological change can actually be investigated using the duality relation by estimating the dual cost (or profit functions). What follows are discussions on an econometricbased productivity measurement drawn mainly from Antle and Capalbo (1988). For the productivity estimation, assume that the aggregate production function is given by 12

Y = F( X ,t)

where Y and X are the aggregate output and the aggregate input vector, respectively, and t denotes the state of technology.

The prime rate of

technological change under the assumption of efficient production is given by n   ∂ ln F /∂t = d ln Y /dt − 1 /F ∑ Fi dX i /dt  i =1  

15

13

where Fi is the marginal product of Xi. Under a competitive market where price equals marginal cost and inputs are paid in terms of their value of their marginal products, Eq.12 can be written as ∂ ln F /∂t = dlnY / dt − ( ∂ lnC /∂ ln Y ) where Si = Wi X i

∑W X i

i

i

−1

n

∑ S d ln X /dt i =1

i

14

i

is the factor cost share and the term ∂ ln C ∂ ln Y is the

elasticity of cost with respect to output indicating returns to scale. The primal rate of technological change given by Eq. 14 can be defined, therefore, as the rate of change in output minus the scale-adjusted index of the rate of change in input. In the case of the dual cost function4, the dual rate of technological change can be derived by differentiating totally the cost function C = C(Y, W, t) with respect to time and by invoking the Shepard’s lemma.

The dual rate of

technological change is algebraically expressed as −

n d ln Wi ∂ ln C dInY d ln C ∂ ln C = ∑ Si + − ∂t dt ∂ ln Y dt dt i =1

15

Eq. 15 shows that the dual rate is the sum of the index of the rate of change in factor prices and the scale effects less the rate of change of total cost. The relationship of the primal and dual rate of technological change can be shown by 4

The advantage of this so-called dual approach over the primal approach (use of production function) is that the derivation of the output supply and input demand functions is much simpler and easier. With this approach, it is not necessary to go through the sometimes bothersome algebra that is involved when solving the first order conditions as required in primal approach; one simply has to differentiate the cost function with respect to prices. Also, the cost function in general has factor prices as arguments or as independent variables rather than factor inputs as in the case of production function. The cost function, therefore, allows the use of input prices, which are actually exogenous to the firm instead of endogenous variables such as input quantities (Binswanger, 1974).

16

the total differentiation of total cost C = ∑ Wi X i with respect to time and by using Eq.15. The relationship is indicated by the following equation: − ∂ lnC/∂t = ( ∂ lnC/ ∂ ln Y ) ∂ lnF / ∂t

16

Thus, the primal and dual rates of technological change are equal if the elasticity of cost with respect to output, ∂ ln C ∂ ln Y , is equal to 1. This means that the primal and dual rates are equal if and only if the technology can be described by constant returns to scale. The derivation of the primal and dual rates of technological change can be generalized

to

multiproduct

technology

represented

by

the

following

transformation function

(

Y1 = F Y 2 , X , t where

)

Y 2 = ( Y2 ,.........Yk ) and X = ( X 1,..................... X n ) .

17 Hulten (1978) defines the

primal rate of technological change in the case of multiproduct technology as R1

∂ ln F ∂t

18

where R1 is defined as the revenue share of Y1 in total revenue. Here, the rate of technological change is measured in terms of Y1. Using the multiproduct cost function, C ( Y , W , t ) , where Y and W are vectors of outputs and factor prices, respectively, the dual rate of multiproduct technological change can be derived by getting the time derivative of the transformation function and by using the first order conditions for multiproduct profit maximization and the equilibrium

17

condition, pi = ∂C ∂Yi . The dual rate of multiproduct technological change can be expressed as  k  − ∂ ln C / ∂t =  ∑ ∂ ln C / ∂ ln Yi  R1∂ ln F / ∂t  i =1 

19

Eq. 19 shows that if the multiproduct technology exhibits constant returns

k

to scale, ∑ ∂ ln C / ∂ ln Yi = 1 , the primal and dual measures of the rate of i =1

technological change are equal. Following Capalbo (1988), the relationship between the definition of productivity as indicated by ∂ lnF ∂t , which is the measure of technical change,

• •  and the conventional definition of TFP =  Y − X  , which is the growth in outputs   not being accounted for by the growth in inputs, is shown by the following equation: •

[

TFP = ∂ ln F /∂t + ( ∂ lnC /∂ ln Y )

−1

] ∑ S d ln X /dt

−1

n

i =1

i

i

20

Under constant returns to scale, the measured growth rate of TFP is equal to the rate of technical change. As previously mentioned, for the single output case, the latter measures the marginal shift in the production function. On the other hand, if the production structure is characterized by increasing or decreasing returns to scale, then the TFP growth rate captures both the technical change as well as the scale effect. 18

Similarly, it is also possible to show the link between the dual definition of productivity ∂ lnC ∂t and TFP. Suppose the aggregate cost function is C = g ( w1 ,........., wn ,Y , t )

21

then by totally differentiating it with respect to time, invoking the Shephard’s

lemma, dividing everything by C and by simplifying, the expression for the proportionate shift in the cost function is given by •

•

B = C− ∑

• wi xi w − ε CY Y C

22

where B = ∂ lnC ∂t . Eq. 22 indicates that B is equal to the change in costs minus the change in aggregate inputs and the scale effect. Following Ohta (1974), this equation can be further simplified by the total differentiation of the cost equation C = ∑ Wi X i with respect to time, yielding wx wx C = ∑ i i x + ∑ i i w , or C C i i wx wx C − ∑ i i w = ∑ i i x ⋅ C C

23

By substitution, Eq. 22 becomes •

•

− B = ε CY Y − ∑ i

•

wi xi x i C •

− B = ε CY Y − X .

24

Combining Eq. 24 with the conventional definition of TFP, the dual cost functionbased definition of productivity is given as •

•

TFP = − B + (1 − ε CY ) Y

19

25

Using Eq. 14 and Eq. 24, one can show that − B = ∂ lnC ∂t = ε CY ( ∂ lnF ∂t ) . In the case of multiple outputs, the relationship between the shift in the cost function and the growth in TFP is indicated by the following equation:5

•

(

)

•

TFP = − B + 1 − ∑ ε CYJ Y .

26

3.3.3 The Translog Functional Form The use of the econometric approach in measuring productivity requires the use of functional form for econometric estimation.

The functional form,

however, should possess certain desirable properties, such as flexibility, consistency and linearity. A functional form is said to be flexible if it can provide a second order approximation to any arbitrary, twice continuously differentiable function (cost, profit or production) having the appropriate theoretical properties. The functional form should also be consistent, i.e. it must be consistent with the appropriate theoretical properties that the function must have. In the case of the cost function, these theoretical properties, as previously discussed, require compliance for linear homogeneity in factor prices, concavity in factor prices and monotonicity. Moreover, a functional form is desirable if the unknown parameters appear in a linear fashion in the function as well as in the output supply and input demand functions. A functional form that is linear in unknown parameters allows the application of linear regression techniques on the estimating equations of a particular function. 5

See Capalbo (1988) for the detailed derivation of the link between the primal and dual definition of productivity and the conventional TFP.

20

There are several functional forms that can be used for estimation: 1) the transcendental logarithmic (translog), 2) normalized quadratic and, 3) the generalized Leontief functional forms.

Among these forms, the translog is

commonly used in productivity estimation using the econometric approach and it also satisfies the flexibility, consistency and linearity properties. (Christensen, Jorgenson and Lau, 1973). In a manner similar to Cobb-Douglas, changes in TFP can be estimated using the translog production function specified as ln Y = α 0 + ∑ α i ln X i + i

1 1 α ij ln X i ln X j + β 0 t + β 1t 2 + t ∑ γ i ln X i . ∑∑ 2 i j 2 i

27

In this function, a time trend denoted by t is included, indicating that the technological change is not Hicks-neutral. Hicks neutrality can only be assumed if parametric restriction is imposed, that is γ i = 0 for all i . Applying Eq. 20 to Eq. 27, under the assumption of non-neutrality of •

technological change, the TFP ∗ is computed as  ∂ ln C  −1  •  − 1 X + β 0 + β1t + ∑ γ i ln X i . TFP = Y − X =  ∂ ln Q    •

∗

•

•

28

Assuming constant returns to scale, ∂ ln C / ∂ ln Q = 1 , Eq. 28 can be written as •

TFP ∗ = β 0 + β1t + ∑ γ i ln X i

29

On the other hand, if Hicks neutrality is assumed then •

TFP ∗ = β 0 + β1t.

21

30

As shown above, the cost function-based TFP can also be derived by appealing to the theory of duality. Specifically, a translog cost function can be used and specified as ln C = α 0 + ∑ α i ln Wi + i

1 ∑∑ γ ij ln Wi ln W j + ∑k β k ln Yk + 2 i i

1 ρ ik ln Wi ln Yk + α t t ∑ ∑ β kl ln Yk ln Yl + ∑∑ 2 k l i k 1 + α ii t 2 + ∑ α it ln Wi t + ∑ β kt ln Yk t. 2 i

31

Applying Eq. 25 to the translog cost function given by Eq. 31 and assuming constant returns to

scale, non-neutrality of technological change and

homotheticity, the cost function-based definition of productivity is given by •

TFP = α t + α ii t.

32

The econometric approach has the advantage of being statistical, thus, allowing inferential statistics or permitting hypothesis testing and calculation of confidence intervals in order to test the reliability of the model estimated. This approach specifically allows determining the contribution of each input to aggregate output. Furthermore, if the flexible functional form is used, then the use of the econometric approach would also mean the imposition of fewer restrictive assumptions about technology as opposed to the growth accounting and the index number approaches. The major disadvantage of the econometric approach, however, is that it is more demanding in terms of data requirement than the other approaches to productivity measurement.

Oftentimes, the

constraint on data availability may make it difficult to implement the econometric approach.

22

3.4 A Distance Function-based Malmquist Approach The Malmquist approach is a non-parametric approach used to measure productivity change. Unlike the Tornqvist-Theil index, the Malmquist productivity index does not presume that production is always efficient.

Hence, the

Malmquist index of productivity can be broken down into two components: 1) the changes in efficiency (firms getting closer to the frontier) and 2) the changes in technology (shifts in the frontier itself). In this approach, the productivity index is defined using two distance functions:

1) the input distance function or 2) the output distance function.

These functions allow one to describe a multi-input and multi-output production technology without assuming or specifying the cost-minimizing or profitmaximizing behavior of the producers. The Malmquist productivity index can be derived as follows: Assume a production technology that can be described using the output set, P(x). This output set P(x) represents the set of all output and input vectors that are feasible, meaning that output vectors y can be produced using input vectors x. For the sake of convenience, assuming that there is only one output and one input, then the output set can be written as P(x) = {y: x can produce y}

33

Given this output set, the output distance can be defined as   y  d O ( x, y ) = min δ :   ∈ P ( x )  .  δ  

23

34

If y is an element of the feasible production set, P(x), then the distance function d O ( x, y ) will take a value less than one or equal to one. In particular, if the value of d O ( x, y ) is unity, then y is located on the outer boundary of the feasible production set, otherwise, it is greater than one and located outside the set. This is the Malmquist productivity index defined by Caves, et al. (1982a and b) with reference to the base period that is: M OS ( x s , y s , xt , y t ) =

DOS ( xt , y t ) DOS ( x s , y s )

35

In particular, they defined their productivity index as the ratio of the two output distance functions both using the technology at time s (the base period). The numerator is the output distance function at time t based on technology of period s. On the other hand, the denominator is the output distance function at time s based on technology of period s. Thus, the Malmquist productivity index measures the distance between two data points of a particular unit (e.g. region or country in two adjacent time period) by calculating the distances of each data point relative to a common technology. Alternatively, instead of using period s technology as the reference group, it is also possible to develop the two output distance functions based on period t‘s technology. The Malmquist productivity index in this case is given by DOT ( xt , y t ) M ( x s , y s , xt , y t ) = T DO ( x s , y s ) T O

24

36

To avoid arbitrariness in the choice of benchmark technology, Fare et al. (1994) suggested that the Malmquist productivity index computed, based on output orientation, should be the geometric mean of the two indexes given by Eq. 35 and Eq. 36. That is 1

 DOS ( xt , y t )  DOT ( xt , y t )  2  T  M O ( x s , y s , xt , y t ) =  S ( ) ( ) D x , y D x , y  O s s  O s s 

37

The value of M0 will indicate whether there are positive or negative changes in productivity. If M0 is greater than one, this indicates positive productivity growth from period s to period t, whereas if the value is less than one, then this shows a decline in productivity. An equivalent way to writing this productivity index is 1

D T ( x , y )  D S ( x , y )  D S ( x , y )  2 M O ( x s , y s , xt , y t ) = OS t t ×  OT t t  OT s s  DO ( x s , y s )  DO ( xt , y t )  DO ( x s , y s ) 

38

Fare et al (1994) gave the following interpretation to the two terms on the righthand side of Eq. 38: Efficiency change =

DOT ( xt , y t ) DOS ( x s , y s )

39 1

 S  S  2 Technical change =  DO ( xt , y t )  DO ( x s , y s )  .  T  T   DO ( xt , y t )  DO ( x s , y s ) 

40

From Eq. 38, the Malmquist productivity index is just the product of the change in relative efficiency that occurred from period s to period t and the change in technology from period s to t.

25

One can estimate the distance functions necessary in the computation of the productivity index based on the Malmquist approach using the Data Envelopment Analysis (DEA). In their seminal paper, Charnes, et al.(1978) described DEA as a mathematical programming model applied to observational data that provides a new way of obtaining empirical estimates of relations such as production functions and/or efficient production possibility surfaces — the cornerstones of modern economics. DEA is, therefore, a non-parametric analysis. It is dataoriented and does not require the specification of any particular functional form to describe the efficient frontier or envelopment surface. DEA is used to evaluate the performance of a homogenous set of peer entities called “Decision Making Units” (DMUs). Under the DEA context, these DMUs are compared against each other because they can individually identify and vary their inputs and outputs. In this case, comparison is relative, meaning all DMUs are compared with best performing DMUs. DEA is a methodology that does not use central tendencies. Instead of fitting a regression plane through the center of the data as in statistical regression, one floats a piecewise linear surface to rest on top of the observations. The distance between the observed data point and the frontier measures the relative technical efficiency of each DMU. DEA is deterministic in nature and this approach does not differentiate technical inefficiency from statistical noise effects. DEA can either be input-oriented or output-oriented. In the input-oriented DEA, the frontier is defined by searching for the maximum possible reduction in

26

input usage, with output held constant. While, in the output-oriented DEA, it seeks the maximum proportional increase in output production, with input levels held fixed. The two measures will give the same technical efficiency scores under the assumption of constant returns to scale (CRS) technology, but will register different scores when variable returns to scale are assumed. The required distance measures necessary in the computation of output oriented Malmquist productivity index can be calculated by using DEA-like linear programs (Färe et al, 1994). A brief methodological explanation mainly taken from Coelli and Rao (2003) follows. In the single output and input case, the basis for the inefficiency measurement is usually the productivity δ that can be expressed as

δ=

Output . Input

41

If some DMUs are compared using the δ, then the one with a bigger δ is considered a better performer or more efficient because less input is used for a constant amount of output. The productivity δ is a relative measure because its interpretation is facilitated by making a comparison among the different DMUs in terms of efficiency. Typically, DMUs have multiple inputs y k ( k = 1,..., z ) that have to be weighted

(u

is expressed as

27

j

x j ( j = 1,..., m )

and outputs

, v k ) and can be summed up. Thus δ

z

δ=

∑v k =1 m

k

∑u j =1

yk

42

. j

xj

The numerator and denominator describe the sum of the weighted output and the sum of the weighted inputs, respectively.

In the case of the output-oriented

approach, the objective is to minimize the 1 δ , the reciprocal of the efficiency score, by increasing proportionally the amount of outputs given the level of inputs. The reciprocal of the efficiency score is just the ratio between the weighted sum of inputs and the weighted sum of outputs. Suppose there are n DMUs producing z outputs using m inputs. Then, under the constant returns to scale assumption, the reciprocal of the relative efficiency score of a hypothetical DMU p can be derived by solving the following CCR model proposed by Charnes, Coopers and Rhodes (1978): m

min

∑u j =1

j

x ji

j

y ki

j

x ji

z

∑v k =1 m

s.t

∑u j =1

≥ 1 i = 1,..., n

z

∑v k =1

43

k

y ki

vk , u j ≥ 0

∀k , j

The fractional model above can be converted to a linear program by setting the denominator equal to a constant usually unity. The resulting model is given by

28

m

min ∑ u j x jp j =1

s.t

z

∑v k =1

k

y kp = 1

44

m

z

j =1

k =1

∑ u j x ji − ∑ vk y ki ≥ 0 i = 1,..., n vk , u j ≥ 0

∀k , j

Every DMU has to choose input and output weights that minimize the 1 δ , the reciprocal of its efficiency score. Thus, the above model has to be run n times in order to calculate the reciprocal of the efficiency score of all the DMUs. Generally, a DMU is efficient when the reciprocal of its efficiency score is less 1, and it is inefficient when the score is greater than 1. However, the following dual form is the one usually calculated: max θ s.t

n

∑λ x i =1

i

− x jp ≤ 0

ji

n

∑λ y i =1

i

ki

j = 1,..., m

45

− θy kp ≥ 0 k = 1,..., z

λi ≥ 0

i = 1,..., n

where λ is the dual variable or dual multiplier and the variable θ is the factor by which DMU p’s output should be increased in order to achieve efficiency. A value of one indicates that DMU p is efficient relative to other DMUs considered, while a value higher than one indicates relative inefficiency. The ratio 1 θ coincides with the efficiency score δ which varies between zero to one. For pth DMU, four distance functions have to be calculated between periods s and t indicating solving four linear programming (LP) problems.

29

Following Färe et al (1994), under the assumption of constant returns to scale (CRS) technology, the pth DMU requires the following LPs:

[d ( x t o

p t

, y tp

n

s.t.

)]

∑λ i =1

−1

= max θ p

y tk ,i − θ p y tk , p ≥ 0

i, p t

k = 1,..., z 46

xtj , p − ∑ λit , p xtj ,i ≥ 0

j = 1,..., m

i =1

λit , p ≥ 0 i = 1,..., n

[d ( x s 0

p s

, y sp

n

∑λ

s.t.

i =1

x

j, p s

)]

−1

= max θ

p

y sk ,i − θ p y sk , p ≥ 0 k = 1,..., z

i, p s

n

− ∑ λ is, p x sj ,i ≥ 0

47

j = 1,..., m

i =1

λ is, p ≥ 0 i = 1,..., n

[d ( x t o

s.t.

p s

, y sp )

n

∑λ i =1

x

j, p s

]

i, p t

−1

= max θ

p

x tk ,i − θ p y sk , p ≥ 0 k = 1,..., z n

− ∑ λ xt ≥ 0 i =1

i, p t

j ,i

λ it , p ≥ 0 i = 1,..., n

30

48

j = 1,..., m

[d ( x s o

s.t.

p t

, y tp

n

∑λ i =1

)]

i, p s

−1

= max θ

p

y sk ,i − θ p y tk , p ≥ 0

k = 1,..., z 49

n

x tj , p − ∑ λis, p x sj ,i ≥ 0

j = 1,..., m

i =1

λis, p ≥ 0 i = 1,..., n The change in the technical efficiency can be further decomposed into two components: 1) the change in pure efficiency and 2) the change in scale efficiency. This decomposition can be done by using the variable returns to scale (VRS) version of the above model.

This version was introduced by Banker,

Charnes and Cooper (1984) and is denoted as the BCC model. This BCC model has additional convexity constraint: n

∑λ i =1

i

= 1.

50

This constraint allows capturing the returns to scale characteristics. The BCC model estimates the reciprocal of the pure technical efficiency, the overall technical efficiency estimated by the CCR model, net of the scale efficiency. The scale efficiency measures the capability of the DMU to fully exploit production possibilities and it is affected by external factors such as credit constraints, market demand and the likes. It can be obtained by calculating the ratio between the overall technical efficiency and the pure technical efficiency. If the values of the pure technical efficiency and the scale efficiency are less than one, then the DMUs are inefficient, but if the values are equal to one, then the units are efficient.

31

The change in the pure efficiency is, therefore,

d ot ( x t , y t ) pure

d os ( x s , y s ) pure

whereas the

s d ot ( xt , y t ) d o ( xt , yt ) pure ⋅ change in the scale of efficiency can be derived as s . d o ( x s , y s ) d ot ( x s , y s ) pure

The use of BCC model requires calculating two additional distance functions by solving the following two additional linear programming problems:

[d ( x t o

p t

, y tp

n

) ]

∑λ

s.t.

i, p t

i =1

−1

pure

= max θ p

y tj ,i − θ p y tk , p ≥ 0 n

x tj , p − ∑ λit , p x tj ,i ≥ 0

k = 1,..., z

j = 1,..., m

51

i =1

n

∑λ

=1

i, p t

i =1

λit, p ≥ 0 i = 1,..., n

[d ( x s o

p s

, y sp

n

s.t.

)

∑λ

i, p t

i =1

x

j, p s

n

]

−1

= max θ p

y sk ,i −θ p y sk , p ≥ 0 n

− ∑λis, p x sj ,i ≥ 0 i =1

∑λ i =1

pure

i, p s

=1

λis, p ≥ 0

i =1,..., n

32

k =1,..., z

j =1,..., m

52

DEA offers some benefits but also has certain limitations that have to be kept in mind when using it. DEA is able to handle multiple inputs and outputs cases and as mentioned earlier, it does not require a functional form that relates inputs and outputs nor any specific behavioral assumptions of the firms/unit under consideration often expressed as cost minimization, or profit or revenue maximization. It can also handle inputs and outputs without knowing their prices or weights. With regards to its limitation, DEA can only calculate the relative efficiency measures and as a non-parametric technique, statistical hypothesis tests are quite difficult (Charnes, A., et al., 1994, Schmid, F. A., 1994, Anderson, T. 1996, Hamburg, C., 2000). In DEA, it is also possible that some of the inefficient DMUs are in fact better overall performers than certain efficient ones. This is because of the unrestricted weight flexibility problem in DEA. Thus, a DMU can achieve a high relative efficiency score by being involved in an unreasonable scheme. Such DMUs heavily weigh few favorable measures and completely ignore other inputs and outputs. These DMUs can be considered as niche members and are not good overall performers.

3.5 Stochastic Frontier Approach In recent years, the measurement of technical efficiency with the use of the Stochastic Frontier Approach (SFA) has become a common approach. Like in the DEA-Malmquist productivity index approach, the level of technical efficiency of the firm in the SFA also refers to its ability to transform inputs into outputs

33

relative to a sample of similar firm. A firm is deemed efficient if it can potentially increase its output level without reducing its input level.

This potential is

dependent on the productive capabilities of comparable firms in the sector and is represented by a production frontier which displays the boundary or highest possible output levels for all input levels (Kumbhakar and Lovell, 2000 and Coelli et al., 2005). As a result, SFA differs with the other productivity measurement techniques but is similar with the Malmquist productivity index approach because it uses a frontier approach capable of capturing the two components of productivity: the efficiency change and the technical change. Unlike the DEAbased approach, however, the SFA is parametric in nature because it also depends on the choice of the estimation method, particularly on the specification of the functional form for technology and the choice of distribution for the inefficiency error term. The choice of functional form appears to be arbitrary, but the CobbDouglas (C-D) framework is generally adopted. The C-D functional form has been used by many researchers because of its parsimony and simplicity. But this simplicity comes with a cost due to strong restrictions imposed such as the unitary elasticities of substitution.

As a result, a number of alternative flexible

functional forms to C-D framework have been proposed in the literature, but the transcendental logarithmic form (commonly known as translog form) is by far the most popular despite the observation that the dominance of one functional form over the other depends on the data set (Kumbhabar and Lovell, 2000).

34

The many studies on efficiency measurement started from the seminal papers of Aigner, Lovell and Schmidt (1977) and Meeusen and Van den Broeck. The general stochastic frontier production function is expressed as Yi = X i b + vi − u i

i = 1,............., N

53

where i = l,……N indicates the units being studied, Yi is the output, Xi are factors of production and b is a vector of unknown parameters. The term, vi - ui, is the composed error term, where vi and ui capture the statistical noise and technical inefficiency in production, respectively. There are two models under the parametric SFA: the deterministic and stochastic frontier models.

The deterministic model involves a process of

enveloping all observations and identifying the distance between the observed production and the maximum production defined by the frontier and the available technology. This distance measures the technical inefficiency, hence, in the deterministic approach, v i will be equal to zero. There are several econometric techniques that can be employed to estimate the deterministic frontier model.

One can use the corrected ordinary

least square method where the parameters of the model, excluding the intercept term, can be estimated consistently by using the ordinary least squares. This method is considered robust even in the case of non-normality (Richmond, 1974). The consistent estimator for the intercept term can be obtained if the estimated intercept term is corrected by shifting it upward until no residual is positive and at least one is zero. Assume the following model: 54 35

y i = α + ∑ β j X ij + ε i

where ε i ~ N (0, σ 2 )

j

The corrected parameter estimates are given by Λ

Λ

B jcols = B jols Λ

Λ

Λ

α cols = α ols + max ε i Λ

Λ

55

Λ

µ icols = ε i − max ε i

then the individual efficiency can be computed as ^

TEi = e

− µ iCOLS

.

56

The stochastic frontier model differs from the deterministic model because the former can capture the effects of exogenous shocks not under the control of the units being investigated. In the stochastic model, other errors related to the data measurement are also being taken into account. The error capturing the statistical noise v i in Eq. (53) is assumed to be identical, independent and identically distributed. With respect to the one-sided (inefficiency) error u i the distributional assumption is a requirement. The commonly assumed distributions in the literature are: the half-normal, truncated from below at zero and the exponential distribution. If the two error terms are assumed to be independent of each other and of the input variables, and assuming a particular distribution, then the likelihood function can be defined and the maximum likelihood estimates can be determined. 36

From the estimation, one can obtain the fitted value for the composed error term v i − u i . These two error terms, therefore, have to be separated in order to facilitate the measurement of technical efficiency. Jondrow, Lovell, Materov and Shmidt (1982) separated the ramdomness or statistical noise from the technical efficiency by developing an explicit formula for the expected value of u i conditional on the composed error term ( E ( u i v i − u i ) ) in the half-normal and exponential cases.

Half-normal case:

E [ u i ei ] =

ei λ  σλ  φ ( ei λ / σ ) −  (1 + λ2 )  Φ( − ei λ / σ ) ς 

57

where Ø(۰) is the density of the standard normal distribution and Ф(۰) the cumulative density function. Exponential case:

[

σ v φ ( ei − θσ v2 ) / σ v E [ u i ei ] = ( ei − θσ ) + Φ ( ei − θσ v2 ) / σ v 2 v

where θ =

[

]

]

58

1 . σu

Truncated case: Following Greene (1993), the conditional technical efficiencies for the truncated model are obtained by replacing ei λ / σ in the expression for the halfnormal case, with

37

u i∗ =

ei λ

σ

+

ui

59

σλ

Finally, individual (conditioned) technical efficiency scores can be expressed as

TEi = e

− E [ ui ei ]

60

.

The measurement of technical efficiency has been extended to the panel data and this approach captures the behavior of the producer as it evolves across time. There are several benefits that can be derived from the use of panel data: there will be more data variability, collinearity is less of a problem and there will be more degrees of freedom necessary for econometric estimation (Baltagi, 1995). For the general panel data specification, the generic form of stochastic frontier production function given by Eq. (53) can be extended by adding the subscript t to the output, inputs and the error term.

The stochastic frontier

production function can then be expressed as:

γ it = f ( xit , t ) exp( vit − u it )

61

where yit is the output of the ith unit (i = 1,2,. . . . . ,N) in period t (t =1,2,. . . .,T); f(.) is the production technology; xit is a vector of j inputs; t is the time trend variable; uit is a non-negative random variable and output-oriented technical inefficiency term; and vit is assumed to be an iid N(0, σ v ) random variable, 2

independently distributed of the uit. The technical efficiency (uit) in Eq. (61) is assumed to be invariant through time. This time-invariant efficiency assumption is only plausible with very short 38

panels, but highly unlikely if the time-dimension of the panel data spans over a longer period of time. It can be argued that a firm’s efficiency or technology is less likely to remain constant over an extended period of time. This issue on technical efficiency (uit) has been addressed in the literature and several specifications have been proposed to make the technical inefficiency term uit time varying.

Kumbhakar (1990) and Battese and Coelli (1992), respectively,

proposed the following time-varying efficiency specifications

[

(

u it = u i / 1 + exp at + βt 2

)]

u it = u i × exp[ − η ( t − T ) ] where t is time and α, β, and η are the parameters to be estimated.

62.a 62.b The

shortcoming of these two specifications is the imposition of the same temporal pattern of efficiency across time making the efficiency rankings of the firms invariant through time. Cuesta (2000) has addressed this problem by proposing an efficiency specification following the firm-specific pattern as indicated by u it = u i × exp[ − ξ i ( t − T ) ]

63

where ξi are firm-specific parameters responsive to different patterns of temporal variation among firms. Battese and Coelli (1995) have further extended the approach of Kumbhakar, Ghosh and McGuckin (1991) to panel data by specifying the technical efficiency (uit) as a function of a set of explanatory variables zit, and an unknown vector of coefficients δ: u it = z it δ + wit .

39

64

They pointed out that the random wit is defined by the truncation of the normal distribution with zero mean and variance σ2, such that the point of truncation is -zitδ, that is, wit ≥ -zitδ. As a result, uit is obtained by truncation at zero of the normal distribution with mean zitδ and variance σ2. The normal assumption that the uits and vits independently distributed for all i =1,2,……N and t = 1,2, . . .,T is obviously a simplifying but restrictive condition. The measure for technical efficiency uit is the proportion by which the actual output yit falls short of the maximum possible output which is considered the frontier output f(x,t). Therefore technical efficiency (TE) can be defined by: TE it =

y it = exp( − u it ). f ( xit , t )

65

In addition to the measure of technical efficicency uit, the productivity change interpreted as the exogenous technical change can also be measured using the time trend variable appended in Eq. (61). It is specifically calculated by taking the log derivative of the stochastic frontier production function with respect to time (Kumbhakar, 2000). That is, technical change (TC) is defined as: TC it =

∂ ln f ( xit , t ) ∂t

66

Since the technical efficiency is time-varying, the overall productivity change is not only dependent on the technical change but also on the change in technical efficiency (TEit). That is, given the input level, the productivity change is given by ∂ ln y it = TC it + TEC it ∂t

40

68

where TEC it =

∂u it ∂ ln TE it = . ∂t ∂t

69

TCit is positive if the exogenous technical change shifts the production frontier upward given inputs. TECit is negative if technical efficiency (TEit) declines over time or positive if a producer is moving closer to the production frontier (technical efficiency increasing over time, ceteris paribus). When input quantities change, the productivity change can be measured by TFP change and is defined as: •

•

•

TFP it = y it − ∑ J S jit x jit

70

where Sjit is the share of the jth input for ith firm at time t. Following Kumbhakar (2000), the overall technical efficiency change is decomposed into a pure technical efficiency change effect and scale efficiency change effect. This overall technical efficiency can be measured by differentiating Eq. (61) totally and using the definition of TFP change in Eq. (70). The TFP change can be expressed as TFP = ( RTS − 1) ∑ J λ j x j + TC + TEC + ∑ J ( λ j − S j ) x j •

where RST = ∑

εj

inputs

j

•

•

71

∂ ln y ≡ ∑ j ε j is the measurement of the returns to scale and ∂ ln x j

elasticities

λ j = f j x j / RTS when

defined fj

at

the

production

frontier

f ( xit , t ) ,and

is the marginal product of input x j (assuming that

inefficiency effects u it are not functions of inputs). As shown by Eq. 71, TFP change is composed of different components: the first term is the scale effect, the

41

second term is the pure technical change, the third term is the technical efficiency change, and the last term is the input allocative effect. In this parametric SFA, the measures of technical efficiency and technical change can be used to calculate the Malmquist index via Eqs. 38-40.

Eq. (65)

can be employed to compute for efficiency change component.

Suppose

d Ot ( xit , y it ) = TE it

S and d O ( xis , y is ) = TE is , then the efficiency change can be

expressed as Efficiency change =

TE it . TE is

72

This measure is the same with Eq. 39. On the other hand, the technical change index between periods s and t for the ith firm can also be calculated using the parameter estimates derived by taking the time derivative of the production function. This index may vary for different input vectors due to the assumption of non-neutrality of the technical change.

Hence, there is a need to use the

geometric mean to measure the technical change index between two periods. This can be expressed as 1

 ∂f ( xis , s, B )   ∂f ( xit , t , B )   2 Techncial change = 1 +  x 1 +  ∂s ∂t    

73

This measure is related to Eq. 40. To compute for the Malmquist productivity index, the efficiency change and technical change indices can be derived using Eqs. (72) and (73), respectively, have to be multiplied together. This Malmqvist productivity index can also be compared with Eq. 38.

42

4. Review of Applications in the Philippines This section presents the results obtained in selected studies that have attempted to measure the productivity levels or growth rates of Philippine agriculture.

This does not attempt to explain the robustness of the estimation

results from these studies, rather, it demonstrates that a number of studies have already been done to measure the growth of productivity in Philippine agriculture using different data sets, timeframes and measurement techniques. This section also presents the different data sets used to estimate productivity estimates for Philippine agriculture. Researches on agricultural productivity in the Philippines can be classified according to the types of study conducted or the analysis used in the study. A research can be a cross-country study or a country-specific study. The first type is conducted purposely to examine productivity gaps among different countries or to analyze convergence. Thus, in this case, productivity estimates are usually

43

calculated at the national or aggregate level. Examples of these studies are those of Fulginiti and Perrin (1993, 1998), Craig, et al., (1997), Mundlak, et al. (2004), Arnade (1998), Suharriyanto and Thirtle (2001), Trueblood and Coggins (1997), and Coelli and Rao (2003). The second type intends to estimate countryspecific productivity levels or growth rates usually for purposes of a trend analysis and these can be either national or regional estimates (see Evenson and Sardido, 1986, Cororaton and Cuenca, 2001 and Teruel and Kuroda, 2004, 2005). In the Philippines, only a handful of empirical studies have dealt with productivity estimation in agriculture. This paper is limited to a review of the studies conducted since the 1980s onwards. Table 1 summarizes the different productivity studies in Philippine agriculture showing the different timeframes, productivity estimates and the productivity approaches used.

4. 1 Application in the Philippines 4.1.1 Cross-country Studies Pioneering cross-country studies started with the work done by Clark (1940) and Bhattachrjee (1953) followed by prominent studies by Hayami and Ruttan (1969, 1970).

Thereafter, most of the studies conducted were

refinements of the earlier ones through inclusion of variables missing in the previous models such as R&D, infrastructure, use of different functional forms, pooling techniques, as well as improved measurements of input and output with quality adjustment (Evenson and Kislev, 1975; Antle, 1983; Nguyen, 1979;

44

Mundlaak and Hellinghausen, 1982; Kawagoe, Hayami and Ruttan, 1985; Lau and Yotopolous, 1989; Craig, Pardey, and Roseboom, 1997). What follows are accounts of cross-country studies on productivity offering some estimates for Philippine agriculture. Using a Cobb Douglas production function, Fulginiti and Perrin (1993) specifically studied the effects of price discrimination and other related policies on agricultural productivity from 1961-1985 for eighteen (18) developing countries. Empirical evidence shows that price-depressing policies reduce productivity with an elasticity estimate of 1.3 per cent. They pointed out that those countries with higher taxation show more regression than those with little or no taxation at all. Based on their analysis, Philippine agricultural productivity could have been increased by 1.3 per cent through the elimination of direct government intervention (commodity price intervention) and 4.1 per cent through the removal of indirect intervention (real exchange rate distortion and protection afforded to the nonagricultural sector). Fulginiti and Perrin (1998) conducted another cross-country study to confirm previous findings that agricultural productivity is declining in developing countries. In this study, they covered the same time period and used four different productivity estimation procedures. The empirical results show that at least 50 per cent of the countries investigated have experienced a decline in productivity. For Philippine agriculture, wide discrepancy in results is observed as indicated by the estimated growth rates of productivity. Using the Malmquist index approach, the average annual productivity growth rate was -0.30 per cent

45

from 1961-85.

On the other hand, using the traditional growth accounting

approach, the average rate of growth was –2.50 per cent for the same period. Conversely, the production function- (variable and fixed coefficient) based estimations resulted in positive estimates of 0.1 and 1.80 per cent, respectively. Another, but more comprehensive, multi-country study using the Malmquist index approach was conducted by Trueblood and Coggins (1997). This study computed the productivity growth rates of 115 developed and developing countries. For the years covered 1961-1991, this study shows that most countries had modest agricultural productivity growth rates. The developed countries had an overall weighted average growth rate of 1.6 per cent for the entire period.

There was, however, a marked decline in productivity in

developing countries pointing to the widening gap of productivity among these countries.

The widening productivity gap was particularly evident during the

decades of the 1960s and the 1970s, though there was a reversion in this trend in the 1980s. When viewing the period as a whole, Trueblood and Coggins (1997) approximated a 1.19 per cent annual average productivity growth rate for Philippine agriculture. Arnade (1998) also investigated the productivity changes among the different countries.

Like Thirtle, et al. (1995) and Fulginiti and Perrin (1997,

1998), he used the conventional Malmquist approach by constructing an index with respect to a contemporaneous frontier technology, in which the frontier in year t+1 is compared with that of the previous year, t, while ignoring past history. Based on this study, Philippine agriculture recorded a negative productivity

46

growth rate of 0.40 per cent indicating a deceleration of productivity growth for the years 1961-93. This also indicates that productivity has not been the source of growth in Philippine agriculture for the entire period. Though the approach adopted by Arnade (1998) is used extensively in examining cross-country productivity differences, it is noted to suffer a dimensionality problem especially when the number of observations in the crosssection is small relative to the total number of inputs and outputs. This problem wa emphasized by Suhariyanto and Thirtle (2001) in their study and they addressed this by measuring the agricultural total factor productivity using the Malmquist index calculated with respect to the sequential frontier. Based on the empirical evidence, more than 50 per cent of the 18 Asian countries were found to have lost their productivity from 1965 to 1996. This is a corroboration of the empirical results on productivity loss obtained by Fulginiti and Perrin (1998) and Arnade (1998).

On the contrary, Philippines agriculture posted an annual

positive growth rate of 1.33 per cent. For the period 1962-1992, Martin and Mitra (1999) estimated the total factor productivity for the agricultural as well as the manufacturing sectors in a relatively wide range of countries for convergence analysis.

Under the

assumption of constant returns to scale, they used primal functions such as the translog and the Cobb Douglas production functions. They also computed for productivity growth rates using the growth accounting approach that is based on the actual factor shares. For the Philippines, agricultural productivity grew at an average annual rate of 1.64 per cent using the translog production function and

47

at 1.57 per cent based on the Cobb Douglas production function.

A relatively

higher annual growth rate of productivity of 2.07 per cent was calculated using the growth accounting procedure. Using the Malmquist index approach, Coelli and Rao (2003) examined the level and trends of productivity of 93 developed and developing countries that account for 97 per cent of the world’s agricultural output and 98 per cent of the world’s population. Using the Malmquist index approach on recent data from the Food and Agriculture Organization of the United Nations, they calculated an annual average rate of growth in productivity of 2.1 per cent from year 1980 to 2000.

They found little evidence of technological regression and this is in

contrast with the empirical findings of a number of studies.

For Philippine

agriculture, they computed 0.80 per cent annual rate of productivity growth for the same period. They, however, got a higher productivity growth rate of 1.3 per cent using the Törnqvist index number procedure. Mundlak (2002, 2004) estimated productivity growth rates that departed from the use of a traditional production function that assumes that technology is homogenous.

They argued that the level of output was dependent on the

implemented technology and the inputs used. Thus, the aggregate output is the sum of outputs produced using more than one technique, making the technology heterogeneous.

In the case of heterogeneous technology, Mundlak (2002,

2004) adopted an optimization problem at the firm level expressed as the choice of the techniques to be implemented and their level of intensity, given the available technology, product demand, factor supply, and constraints, referred to

48

as state variables. The state variables in this study were referred to as the carriers of the implemented technology and these included roads, representing the physical infrastructure, measures of education, health representing human capital and incentives. For the empirical estimation, the aggregate production function was specified and applied to three ASEAN Countries: Thailand and Indonesia.

Philippines,

This production function is like a Cobb-Douglas

function, but the coefficients are functions of the state variables and possibly of the inputs. Basing on the empirical evidence, the state variables accounted for an important part of the changes in the total factor productivity.

Decreasing

productivity was noted among the three countries, with the steepest decline observed in Philippine agriculture, from 0.98 per cent in 1961-80 to 0.13 per cent in 1980-98. On the average, the productivity growth rate was 0.25 for the entire period.

4.1.2 Country-specific Studies Using a growth accounting procedure, Evenson and Sardido (1986) conducted a country-specific study and obtained an estimated average annual productivity growth rate of 1.90 per cent for Philippine agriculture over the years 1955-1984. Cororaton and Cuenca (2001) also attempted to estimate the productivity growth rate for the entire Philippines and for the different sectors including agriculture. They also applied the growth accounting approach using national and sectoral databases covering years 1980-1998. The sectoral database was

49

constructed from the national level data using some distributional shares. In their productivity estimation, they only included two conventional inputs such as capital and labor. For the entire period, agricultural productivity growth rate was negative 0.56 per cent. This indicates that the growth in output for the period 1980-1989 was driven by production inputs. On the other hand, using a recent time-series cross-sectional agricultural data set covering 12 regions and covering the years 1974-2000, Teruel and Kuroda (2004, 2005) computed the productivity growth rates in Philippine agriculture by using a translog variable cost function (with land assumed to be a quasi-fixed input), a translog cost function (with price of land calculated as the residual of total revenue, net of measured costs for agricultural labor, fertilizer, seeds, and machinery and animal services), the growth accounting approach (the factor shares were based on a Cobb Douglas production function estimation) and an index number approach using the Törnqvist–Theil approximation method of the Divisia index. It is worth emphasizing, that Teruel and Kuroda (2005) applied these different approaches to the same dataset with the same timeframe. For the entire 27-year period, Teruel and Kuroda (2004, 2005) obtained a conservative estimate of the average annual productivity growth rate of 0.51 per cent based on the econometric approach using a translog variable cost function. The estimate based on a Cobb–Douglas production function approach is also modest, giving an annual average productivity growth rate of 0.99 per cent for Philippine agriculture.

For the translog cost function and index number

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techniques, they, however, obtained higher estimates of 1.42 and 1.62 per cent, respectively.

4.1.3 Productivity Estimates by Subperiod Evenson and Sardido (1986) and Teruel and Kuroda (2004, 2005) summarized and presented estimates of productivity by subperiods.

These

studies were conducted to assess productivity growth and trends across time. These estimates are presented in Table 2. Evenson and Sardido (1986) reported productivity estimates using a 5-year and 10-year subperiods, while

Cororaton

and Cuenca (2001) maintained 9-year subperiods. Teruel and Kuroda (2004, 2005), on the other hand, computed productivity growth rates by considering the following time periods: 1974-1980, 1981-1990 and 1991-2000. Mundlak, et al. (2004) for their study maintained longer episodes such as 1961-1980 and 19801998. Using a growth accounting procedure and agricultural data from 19501984, Evenson and Sardido (1986) obtained positive estimates for the different 5-year subperiods except for 1980-1984. The agricultural sector performed better during the 1950s as indicated by productivity growing at an annual rate higher than 2 per cent, followed by a decline in the 1960s and a recovery in the 1970s. The productivity growth rate particularly was at its peak during the period of 1975-1979 with a growth rate of 5.3 per cent.

This subperiod, however,

considered as the post Green Revolution period by Evenson and Sardido (1986), was followed by a deceleration of productivity as evidenced by a negative annual

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growth rate of 1.10 per cent during the subperiod 1980-1984.

This poor

performance of the agricultural sector in the early 1980s seems to find support from the study carried out by Cororaton and Cuenca (2001). They computed an annual productivity growth rate of -5.36 per cent for years 1980-1989 followed by a positive growth during the 1990s at 4.25 per cent. Teruel and Kuroda (2004, 2005), based on a translog variable cost function, found that the highest productivity level of 0.77 per cent in Philippine agriculture also occurred during the post-Green Revolution period (1974–1980). From this subperiod, the productivity growth declined in the 1980s and even further in the 1990s as evidenced by the computed annual average rate of 0.50 and 0.35 per cent, respectively.

This further indicates that productivity level

during the Green Revolution era has not been sustained or paralleled, despite substantial policy changes put in place since 1986 to invigorate agriculture in the Philippines.

These productivity trends are also reinforced qualitatively by

estimates derived from the translog cost function as shown by growth rates 2.01, 1.16 and 0.84 per cent for the subperiods 1974-1980, 1981-1990 and 1990-2000, respectively. On the other hand, these temporal patterns of productivity are not supported by estimates obtained from productivity measurement using the growth accounting and the Törnqvist index approaches.

For the growth

accounting approach, Philippine agricultural productivity grew annually at a rate of 2.19 per cent in the late 1970s and then followed by a deceleration and recovery in the 1980s and 1990s as explicitly shown by annual growth rates of

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-0.53 and 1.44 per cent, respectively.

Similarly, for the Törnqvist index

approach, the calculated productivity growth rates are 2.50, 0.50 and 2.60 per cent across time periods. However, Mundlak, et al (2004), using Cobb-Douglas production function with state variables, seem to validate the evidence on declining productivity as shown by their estimates indicating a relatively rapid growth during years the 1961-1980 (0.98%) and slower growth during the years 1980-1998 (0.13%).

4.1.4 Regional Productivity Estimates. Table 3 presents productivity estimates for different regions. Evenson and Sardido (1986) reported estimates for productivity growth rates for 9 regions using the growth accounting approach.

For the entire 1950-1984, the rapid

productivity growth was observed in Northern-Eastern Mindanao (2.54%), followed by two regions in Luzon, namely: Southern Tagalog (2.39%) and the Ilocos region (1.60%). Western-Southern Mindanao and Eastern Visayas had productivity growth rates within the range of 1.09 to 1.46 per cent. Other regions showed modest growth with a rate of less than 1 per cent except for Central Luzon that did not reflect any productivity growth. Teruel and Kuroda (2005) also computed for the productivity estimates of the different regions using the translog variable cost function and the index number approach.

Compared with Evenson and Sardido, the empirical

estimates based on the translog variable cost function show a marked difference

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in terms of the productivity performance of the different regions over the period 1974-2000. The highest annual average productivity growth of 1.56 per cent was posted by the Ilocos region, followed by Central Luzon with productivity growing at a rate of 1.45 per cent. On the other hand, negative productivity estimates were noted in three of the twelve regions, namely: Bicol, Western Visayas and Western Mindanao. Using the index number approach, among the regional production areas, Central Luzon had the highest annual productivity rate of growth of 3.28 per cent. This region was followed by Ilocos, Southern Tagalog and Northern Mindanao having an annual productivity growth rate of 2.16 per cent.

Other regions with

productivity growth rates above 2 per cent per annum were Cagayan Valley and Southern Mindanao.

The remaining regions with positive productivity growth

rates included Western Visayas (0.55%), Central Visayas (1.07%), Eastern Visayas (0.91%), Western Mindanao (0.17%) and Central Mindanao (0.85%). On the contrary, between the years 1975 to 2000, only Bicol region posted an annual negative productivity growth rate of 0.29 per cent. It can be noted from Table 3 that out of the 12 regional agricultural production areas, eight has productivity levels explaining more than 50 per cent of output growth and these included all the regions in Luzon and two regions each from the Visayas and Mindanao. This illustrates that agricultural production in the Philippines during this period was driven by productivity and the regions in Luzon were relatively more productive than those in the Visayas and Mindanao.

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On the average, productivity contributed 59 per cent to output growth with the remaining 41 per cent attributed to the increased use of inputs.

4.1.5 Productivity Estimates by Approach This subsection classifies productivity studies by type of approaches used in the estimation. As indicated by Table 4, four studies used growth accounting approach to estimate productivity growth. Regardless of timeframes and data sets, the average productivity growth rate based on this approach fell within the range of -2.50 to 2.07 per cent For the index number approach, two studies attempted to compute for the rate of growth of productivity using the Tornqvist-Theil index number procedure. The mean growth rate was relatively higher at 1.46 per cent annually. There are five studies identified to have used the econometric approach using both the primal and the dual functions. These studies adopted one or a combination of these functions for empirical exposition purposes. Three studies estimated productivity based on a production function either using the CobbDouglas or the Translog functional forms.

On the other hand, two studies

employed a dual cost function using a translog functional form. Ignoring the differences in the methodologies, the time periods, the functional forms and the data used in the estimation, the productivity growth rate based on the econometric approach averaged 1.14 per cent; lower than the average estimate based on the index number approach.

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Moreover, a number of productivity studies conducted more recently offered productivity estimates for Philippine agriculture using the DEA-based Malmquist approach. With this approach, the productivity estimates fell within the range of -0.30 to 1.19 per cent and averaged 0.32 per cent. This indicates that average annual productivity growth rate calculated using DEA-based Malmquist approach generated more conservative than results than those obtained using other productivity measurement techniques.

4.2 Contribution of Non-conventional Inputs to Productivity This section discusses the non-conventional inputs in relation to productivity. The concept of TFP, as residual share of output growth after accounting for the changes in production inputs, originated from the seminal papers of Tinbergen (1942) and Solow (1957). Abromovitz (1956) called this residual part of the output growth as “measure of our ignorance”, since it does not only contain technological change but also other unnecessary components, namely measurement errors, omitted variables, model misspecification, etc. Accurate measurement is at the heart of productivity estimation and comparison. There are two types of measurement errors: in factor utilization and in the quality changes of the production factors. Thus, given the importance of TFP in understanding the growth process, one of the recent directions taken by researchers, as indicated in the literature, has been on measuring better the

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factors of production, including corrections for quality of factors (Jorgenson and Griliches, 1967; Greenwood and Jovanovic, 2000).

Some researchers have

addressed the issues pertaining to omitted variables and model specification by incorporating non-conventional inputs to TFP estimation.

These non-

conventional inputs include education, research and development, extension, government programmes and policies and infrastructure.

Several empirical

studies have been conducted to determine their contribution to productivity. Some of these non-conventional inputs have been used to account for input quality changes. This will be discussed in turn. Education is always assumed to be related to the quality of the agricultural labor force.

Education is an investment in “human capital”.

individuals with general skills to solve problems.

It provides

However, data on the

educational level of the agricultural labor are not available especially in most developing countries. Consequently, for productivity analysis, national proxies are usually used in empirical studies: literacy and life expectancy (Craig, Pardey and Roseboom, 1997), historic calorie availability (Frisvold and Ingram, 1995) and the number of agricultural college graduates as a proxy for the level of advanced technical education in agriculture (Hayami and Ruttan, 1985). Many researchers also have attempted to account for land quality in productivity estimation in order not to attribute the differences in production that are actually due to changes in land quality to other inputs. Some tried to control for differences in land quality by including a land quality index in productivity estimation. Developed by Peterson (1987), in this land quality index, land quality

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is characterized

as a function of historic precipitation and the share of a

country's land area devoted to pasture and crops. Other researchers have made adjustments for the impact of land quality on productivity by using proxy variables such as the mean rainfall and the percentage of land area that is arable and irrigated. Research and development is also undertaken to improve the production capacity of the agricultural sector given resource constraints and to minimize the environmental degradation caused by agricultural production.

Research and

development has been shown to have significant contribution to productivity. On the average, the productivity contribution of agricultural research ranged from 20 to 60 per cent (Ruttan, 1980, 1982; Echeverria, 1990; Huffman and Evenson, 1993; and Fuglie et al., 1996).

For productivity analysis, public agricultural

research expenditures are generally used as proxy for research and development. To measure the impact of research and development to productivity, expenditures in research are lagged for a number of years to account for the time required for research to reach fruition.

This is done

specifically because a particular research may require several years for completion and the farmer’s learning curve for the new innovation may also take time.

This approach of lagging agricultural research expenditures, however,

does not account for the spillover effects of research to other countries or regions. Agricultural research is performed both by public and private sectors. Private agricultural research is equally important but related information is incomplete or not yet available especially in the case of developing countries. It

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has been shown in the productivity literature that public investment in research stimulates private research efforts (Pray, Neumeyer and Upadhyaya, 1988). Related to research are extension services. This non-conventional input has been shown to have positive contribution to agricultural productivity. Agricultural extension involves the dissemination of agricultural information, the demonstration of new production technologies as well as direct consultation with farmers regarding specific problems related to production and farm management. Agricultural extension is undertaken to reduce the time lag between the development of new technologies and adoption. It is assumed that the impact of extension on productivity is more immediate than research. Based on empirical findings, the contribution of extension to agricultural productivity is more mixed than research and this problem is data-related since reports on public extension expenditures are incomplete and even more non-existent than research especially in most developing countries. On the other hand, the effects of government programs and policies to productivity have also been revealed by a number of studies (Fulginiti and Perrin, 1993; Hu and Antle, 1993; Block, 1995; Fulginiti and Perrin, 1997; Frisvold and Ingram, 1995). It has been indicated that the prices of agricultural outputs and inputs affect the technology chosen by the farmers and thus the productivity trends.

These prices may be affected by government policies that tax or

subsidize agriculture. In some productivity estimation studies, the depreciation of the real exchange rate, past export growth rate and export instability are used as proxies for government policy and policy reforms. Relatively, little research has

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attempted to investigate the impact of government programs on productivity in agriculture, but some have shown evidence of positive relationship (Huffman and Evenson, 1993 and Makki and Tweeten, 1993). Like other non-conventional inputs, public investments in infrastructure can also increase agricultural productivity by lowering the cost of inputs at the farm level and increasing farmers' access to marketing opportunities. To account for the impact of the provision of public infrastructure to productivity, proxy variables are also used such as the paved road density adopted by Craig, Pardey and Roseboom (1997) and the gross domestic product of each country's transportation and communication sectors employed by Hu and Antle (1993). Other proxy variables include water and sewer systems, schools, hospitals, conservation structures and mass transit.

Using a Cobb-Douglas (C-D)

aggregate production function, Aschauer (1989) was the first to empirically show the strong positive impact of the ratio of the public to the private capital stock to productivity in the United States. Specifically, he found out that a 1 per cent increase in the public capital stock would result in an increase in total factor productivity (TFP) by almost 0.40 per cent. Thus, he attributed the decline in US TFP growth in the 70s to lower public investment spending. In the Philippines, some studies attempted to incorporate these nonconventional inputs to account for the changes in the quality of production inputs and to determine their contribution to productivity. One empirical study was conducted by Evenson and Quizon (1991) and they employed a normalized quadratic profit function with infrastructure,

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technology and policy or program variables and used pooled dataset covering the years 1948-1984 and 9 regions.6 Infrastructure variables include roads, rural electrification and general rural development expenditures.

To capture the

impact of policies or programs to productivity, they used variables such as land transfers under the agrarian reform program.

On the other hand, they also

included technology variables such as high-yielding rice varieties, the regional and national research stock variables and extension.

Evenson and Quizon

(1991) have evaluated the productivity effects of infrastructure, technology and policy via the output supply and input demand equations using elasticities, but not in the sense of productivity decomposition analysis. The major findings can be summarized as follows: i.

HYVs stimulated input demands and had positive impact on output;

ii.

Regional research program had substantial impact to output relative to national research program, although though combined research investment had a higher marginal rate of return of 70 per cent;

iii.

The net impact of extension was positive but small, indicating a lower rate of return;

iv.

Roads were shown to have a significant impact on inputs and outputs with a substantial net profit effects;

v.

Rural electrification appeared to have minimal impact on output; and

6

Evenson and Quizon (1991) used the data set constructed by Evenson and Sardido.

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vi.

Land reform had a small but significant output and net productivity effect.

Teruel and Kuroda (2000) also examined the impact of public infrastructure on the productivity performance of Philippine agriculture. Instead of the profit function, they used a translog cost function framework augmented with public infrastructure such as irrigation, roads and rural electrification7. They used more a recent data set covering 12 regions and period 1974-2000. From their study, a higher TFP estimate was noted during the late 1970s, but this was followed by a discernible decline in the 1980s and 1990s. The higher productivity growth in the period 1974-1980 was driven by public infrastructure. Its productivity contribution, however, decreased markedly in the 1980s. During this decade, it was technological change that spurred the growth of productivity, although its contribution was not sufficient to sustain the higher productivity level of the late 1970s. On the other hand, in the last decade, there was a recovery of contribution of public infrastructure to productivity, though this did not reverse the overall trend in TFP growth. For the entire period, TFP grew with an annual average growth rate of 1.42 per cent. The contributions of technological change and public infrastructure to TFP were comparable (1.81 and 1.99 per cent respectively), with provision of farm-to-market roads seen to play an important role. This is in line with the findings of Evenson and Quizon (1991) emphasizing the importance of roads relative to rural electrification in effecting significant changes in input demand, output supply as well as in profit. Overall, in this study, 7

Teruel and Kuroda (2005) also estimated a profit function. However, we did not further pursue this line of inquiry since there were negative profits in some regions for some years.

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Teruel and Kuroda (2005) provided empirical evidence showing that the decline of productivity in Philippine agriculture could be partly explained by the reduced provision of rural infrastructure.

4.3. Data Sets In order to estimate productivity levels or growth rates, data are needed on agricultural output and input.

In the case of the cross-country or even the

country-specific study using time and cross sectional data, comparable and consistent data are necessary to make comparisons over time and space. This subsection deals with the measurement of inputs and outputs that may influence measured productivity. First, it begins with a discussion of the measurement of the quantity of output and proceeds with a discussion of the measurement of the different inputs. Discussion will be done by type of productivity studies starting with cross-country and moving on to country-specific studies. Specifically, the different data sets will be presented: those used by cross-country studies to include that of Mundlak, et al. (2002) in their study involving three ASEAN countries, and those employed for country-specific analysis such as the works of Evenson and Sardido (1986) and Teruel and Kuroda (2004, 2005).

6.1 Cross-country Studies For the past decade, the number of cross-country studies examining the differences in agricultural productivity levels and their growth rates has increased significantly. This can be attributed to three factors: 1) the availability of some

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panel data sets, 2) the development of new empirical techniques to analyze this type of data, and 3) the desire to assess the impact of Green Revolution and other programs to agricultural productivity in developing countries (Coelli and Rao, 2003). Most of the cross-country studies reviewed in this paper used the Food and Agriculture Organization of the United Nations (FAO) panel data, spanning for several decades from the 1960s to 1990s8. Most of these data are typically measured in relatively simple physical terms especially the conventional inputs. The shortcomings of the FAO data have been cited in the literature (Thirtle, et al., 1995; Fulginiti and Perrin, 1997, 1998; Arnade, 1998). This data set does not account for the differences in input quality especially land, the chemical inputs considered only fertilizers and excluded other chemicals for crop protection like pesticides, and the machinery did not include animal draft power, equipment and other machinery.

6.1.1 FAO Data Set The FAO developed a measure of output that aggregates each country’s output in a manner that minimizes exchange rate distortions and facilitates intercountry comparisons.

This measure is called the “international dollar.” This

measure involves the calculation of weighted world prices for each commodity, and multiplies each country’s commodity quantities by their weighted world prices. Aside from the international dollar measure, there are other ways to aggregate agricultural output and these include the wheat unit approach and the 8

Other researchers used the data set from Hayami and Ruttan series of studies.

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use of official exchange rates. The former was developed by Hayami and Ruttan (1985) and this involved the calculation of the ratio of each individual commodity price to the price of wheat in India, the United States and Japan, while the latter converted output in local currency units to dollars. Land typically is measured as hectares of agricultural land that is arable and permanent cropland. Some studies exercised control over the differences in land quality by using the international land quality index of Peterson (1987). Fertilizer input is measured as the sum, in nutrient-equivalent terms, of nitrogen (N), potassium (P2O2), and phosphate (K2O) contained in the commercial fertilizers consumed in each country. Labor includes economically active agricultural population. Economically active population is defined as all persons engaged or seeking employment in an economic activity, whether as employers, own-account workers, salaried employees or unpaid workers assisting in the operation of a family farm or business. Specifically, the FAO definition of economically active population in agriculture includes workers in agriculture, forestry and fisheries. A few researchers have attempted to correct for the quality of the agricultural labor force by considering non-conventional inputs such as national-level measures of education or literacy.

In addition, other researches adjusted the quality of

agricultural labor force directly by sex and age. Livestock in the FAO dataset are measured by aggregating different animals (Cattle, sheep, goats, pigs, mules, horses, asses, buffaloes, camels,

65

ducks, chicken, and turkeys) using different weights usually taken from Hayami and Ruttan (1985). Machinery is measured as the total number of wheel and crawler tractors used in agriculture. This, however, excludes garden tractors.

6.1.2 The Mundlak, et al. Data Set For Mundlak, et al. (2002), the data set included time series data on the quantity of output and inputs such as agricultural land, fertilizers, capital stock in agricultural machines and in non-agricultural origin (livestock and orchards), and labor.

The data were taken from the different sources: National Statistical

Coordination Board (NSCB), FAO, Fertilizer and Pesticide Authority (FPA) and from different surveys conducted by National Statistics Office.

From the

Mundlak, et al. study (2002), the data series construction will be discussed in turn. The agricultural Gross Domestic Product series includes Forestry and Fishery. National accounts were obtained in constant and current market prices (pesos) from the Economic and Social Statistics Office of the National Statistical Coordination Board (NSCB). Data on the area in hectares of agricultural land were taken from the statistical databases found in FAO's website. This data series included the arable and permanent cropland, along with permanent pastures. Data on the area in hectares of irrigated land were also downloaded from the statistical databases of

66

the FAO website. Data on the consumption of fertilizers in metric tons were reported by the FPA. The data series on the agricultural capital stock in agricultural machines as well as in livestock and orchard were estimated using the method of Larson, Butzer, Mundlak, and Crego (2000). Data on gross domestic capital formation in agricultural machinery and tractors in current pesos were taken from the Philippine Statistical Yearbook. These were used to calculate capital stock. The investment data were then converted to constant values using the agricultural, fishery, and forestry GDP deflator before aggregating these to the capital stock series.

On the other hand, the data on gross domestic capital formation in

breeding stock and orchard development were in constant and current market prices (pesos) taken from NSCB. These were also used in calculating capital stock. Labor force data were obtained from the Philippine Statistical Yearbook and the Bureau of the Census and Statistics' (BCS) Survey of Households, now known as the National Statistics Office (NSO). When available, data on total agricultural employment were taken from the October survey of NSO.

6.2 Country-specific Studies For country-specific studies,

several data sets were assembled for

Philippine agriculture for the analysis of production structure and for productivity estimation. Evenson and Sardido (1986) constructed a data set for years 19481974 for 9 regions. They also assembled agricultural data series for the years

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1974-1984 using a 12-region classification.

The most recent data set can be

attributed to Teruel and Kuroda (2004, 2005). This cross-sectional and timeseries dataset on Philippine agriculture included 12 regions and spanned 27-year period.

This period spans the post-Green Revolution era and the period

characterized by substantial changes in policies affecting Philippine agriculture. Teruel and Kuroda’s (2004, 2005) data set was constructed using assumptions mostly taken from Evenson and Sardido (1986).

6.2.1. The Evenson and Sardido’s Data set Evenson and Sardido (1986) define agricultural output as the gross value of production of agricultural crops and livestock. Most of the data for this series were taken from the Raw Materials Resources Survey for Agriculture (RMRSA) of the Department of Agriculture and Natural Resources (DANR) and from the Crop and Livestock Survey (CLS) of the Bureau of Agricultural Economics (BAEcon), DANR. The data on agricultural output were reported on a calendar year basis. Regional agricultural crop production included palay, corn, coconut, sugarcane, fruits, and other crop production such as root crops, onions, potatoes, beans and peas, vegetables, coffee, cacao, peanuts, abaca, tobacco, cotton, kapok, ramie, rubber, maguey, and other commercial and food crops. Annual crop prices were computed by dividing the crop value by the quantity of production.

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For the regional livestock and poultry production, Evenson and Sardido (1986) included meat, milk and egg production of farm households as well as changes in the livestock and the poultry inventories. Annual changes in the inventories from 1948 to 1984 were computed using the annual regional population estimates of carabaos, cattle, hogs, horses, goats, sheep, chicken, ducks, geese, and turkeys from the RMRSA and the CLS. Dressed weights of the slaughtered livestock and poultry in each region were also obtained from the RMRSA and the CLS. Missing years were filled in by using the ratios of dressed weights of slaughtered animals to their corresponding January populations. Prices of livestock and poultry were computed in the same manner as crop prices. Meat prices were computed as the price of a particular animal divided by the average dressed weight of similar slaughtered animals. These dressed weight equivalents were obtained from the DANR. The input series were subjected to the following qualifications: 1. Agricultural land was classified as either (a) land planted to temporary and permanent crops or cultivated land, and (b) all other agricultural land (land under temporary and permanent pastures, land temporarily idle/fallow, etc.). Area measures of other agricultural land were not available from the RMRSA and the CLS. This series was constructed by initially using the regional estimates of all other agricultural land from the 1948, 1960, 1971 and 1980 Censuses of Agriculture. Interpolation and extrapolation were used to complete the missing years.

69

2. Cultivated land is reported as crop area capturing the effects of multiple cropping. Evenson and Sardido (1986) converted this crop area into physical land area by first computing the multiple cropping indices as the ratio of crop area to physical area in each region. Then, these multiple cropping indices were completed for the missing years by interpolation and extrapolation using the 1948, 1960, 1971 and 1981 BCS Censuses of Agriculture. Finally, to purge the land data series of the effects of multiple cropping, crop areas were subsequently divided by their respective multiple cropping indices. For each type of land, they constructed a rental series for the 1948-74 data and assumed constant shares for each type of land for recent period fixed at 0.3. 3. Labor was measured in equivalent man-days spent in agricultural production. The labor data series was based on annual data from the Philippine Statistical Survey of Households (PSSH) of the BCS.

However, the PSSH

surveys (labor force survey) reported employment in agriculture, forestry, hunting and fishing, as a group. Evenson and Sardido (1986) assumed that labor employment in agriculture was a constant-proportion (92%) of the reported total employment for this group of economic activities. This assumption was adopted from Paris (1971). 4. Prior to the construction of the series of equivalent man-days spent in agriculture, several adjustments or estimations were employed to come up with regional data on employment in agriculture purposely to complete the missing years. This was done especially for the years prior to 1967.

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In computing for the equivalent man-days (LMDt), the regional employment in agriculture had to be broken down by age and sex. For age distribution, Evenson and Sardido (1986) used the national percentage distribution of agricultural employment by age for each year and applied this uniformly to the different regions.

On the other hand, the within-region

distributions of employment by sex were used to estimate the distribution of employment by sex for each age group in each region. Equivalent man-days spent in agriculture per year were computed using the equation: LMDt = 23

mt f C Mat + 15 t ( 0.75) Fat + t ( 0.50 )( Mct + Fct ) 8 8 8

74

where M = number of male workers, F = number of female workers, a = adult, i.e., 15 years and above, c = children, i.e., 14 years and below, m = average number of hours worked per week by male adults, f = average number of hours worked per week by female adults, c = average number of hours worked per week by children, t = time This equation implies that females and children have working capacities equal to 75 and 50 per cent, respectively, of the working adult males.

The

equation further assumes that the adult male workers work 23 weeks a year while female adults and children work only 15 weeks a year. This assumption

71

was adopted from Oppenfeld, et al. (1957). Regional agricultural wages were taken from BAEcon surveys and referred to wages without meals. The farm machinery data series was based heavily on the annual national stock data for four-wheel tractors, hand tractors, plows, harrows, and other implements. To estimate the annual national stock of farm equipment, the following formula was used: Kt = (1-d) Kt = 1 + I t

75

where K refers to the stock of farm equipment, I to gross domestic capital formation, d to the annual rate of depreciation and t to the time subscript. To construct this input series, Evenson and Sardido (1986) gathered the data on the stock of farm equipment from the 1948 Census of Agriculture and the data on gross domestic capital formation from the 1956 Capital Formation Study of BaEcon and from the annual estimates of gross domestic capital formation in durable agricultural machinery as well as implements from the National Economic and Development Authority’s National Income Account. Evenson and Sardido (1986) computed the annual depreciation rate using the 1948 and the 1956 benchmarks and the annual gross domestic capital formation data. In a similar manner with the labor input, adjustments or estimations were done to fill in data gaps in the farm machinery data series. The amount of capital services of agricultural machinery in each region was assumed to be 16.2 percent of the total value of each region's agricultural capital stock. This was based on the interest rate assumed to be 10 per cent and the depreciation rate of 6.2 per cent.

Implicit price indices for farm equipment

72

were computed from the National Income Accounts. They were assumed to be equal across regions in any given year. The fertilizer input series was constructed using data from the different sources. For the years 1956-1975, the total supply of fertilizer in nutrient equivalents (the sum of domestic production and imports unadjusted for year-end stocks) was taken from Anden (1976). This series was extended backwards to 1948 by converting total supply of fertilizer (unadjusted for yearend stocks) available for the years 1948 to 1955 into their nutrient equivalents using the constant conversion factor computed as the average ratio of total nutrient supply to total fertilizer supply for the years 1956 to 1960. For the years 1974-1984, fertilizer consumption was based on the fertilizer sales of the distributors obtained from the Fertilizer and Pesticide Authority. Regional series construction was done by distributing the total sales to the different regions using the regional proportion of fertilizer distributors.

The

regional fertilizer sales by nutrient were then computed based on the proportion of N, P, and K to the total nutrient demand and then multiplied by the total sales. The series on work animal was based on the 1948, 1960, 1971 and 1980 Censuses of Agriculture. Working carabaos and cattle stocks were estimated for each region by interpolation between censuses. The service flow included an adjustment for feed.

6.2.2 Teruel and Kuroda’s Data Set

73

A regional data set on agricultural products and inputs was assembled for the years 1974-2000. Like Evenson and Sardido (1986), the data were reported on a calendar year basis using the 12-region classification for the Philippines9. The data set accounted for 88 per cent of the total volume of crop production and almost 100 per cent of the total poultry and livestock production. The data on the quantities and prices of the different agricultural products, inputs, and areas planted were sourced from the several occasional publications of the Bureau of Agricultural Statistics (BAS). These publications include the Crop Statistics, Selected Crop Statistics, Prices Received by Farmers, Rice Statistics Handbook and Selected Statistics on Agriculture.

In the data set,

quantities were reported in thousands of metric tons, prices in pesos per kilogram, and areas in hectares. The crop categories include rice, corn, sugarcane, coconut, tobacco, rootcrops (camote, cassava, gabi, pao galiang, tugui, and ubi or yam), fruits (banana, mango and pineapple), and vegetables (cabbage, eggplant, garlic, radish and tomato). Livestock and poultry products, on the other hand, included meat of cattle, carabao, hogs, goat, chicken, and ducks, as well as chicken and duck eggs. The prices reported in the data set were farmgate prices. Gaps in the price data were filled in through estimation. The data on land variable is the sum of the areas for all the crops (i.e. rice, corn, sugarcane, coconut, tobacco, rootcrops, fruits, and vegetables).

9

The twelve regions are as follows: Ilocos, Cagayan Valley, Central Luzon, Southern Tagalog, Bicol, Western Visayas, Central Visayas, Eastern Visayas, Western Mindanao, Northern Mindanao, Southern Mindanao and Central Mindanao.

74

Labor was reported in terms of equivalent man-days (MD) spent in agricultural production.

Equivalent man-days were computed based on the

number of male and female workers aged 15 years old and over who were employed in agriculture. Equivalent man-days spent in agricultural production were computed using MD = 160∗ M + 105∗0.75∗ F

76

where M refers to the number of male workers and F refers to the number of female workers, following Quizon (1980) and Evenson and Sardido (1986).10 The equivalent mandays equation reflected the assumption that a female worker had 75% of the working capacity of a male worker, and that an adult male agricultural worker worked 160 days in a year while an adult female worked 105 days in a year.11 Regional agricultural wages referred to the average daily wage (without meal allowance) received by farm workers in all agriculture, 12 as reported by the Bureau of Agricultural Statistics. Equivalent animal work days were computed based on the number of work carabaos and work cattle by assuming that these animals worked an average of 220 and 150 days a year, respectively. 13 The cost of services of work animals per work day was assumed to be one-half of the daily wage rate of agricultural labor.14

10

These authors included the number of male and female children who were employed in agriculture in their computation of equivalent mandays. This was not done in this study however due to the unavailability of such data for most of the years covered by the data series. 11 The latter assumption on the number of workdays of males and females was based on a study by Oppenfeld, et. al.(1957). 12 This is a weighted average of the wages received by farm workers in rice, corn, coconut and sugarcane farms. 13 The assumptions on the number of workdays were adopted from Quizon (1980). 14 This was the assumption used in the Evenson data set.

75

Fertilizer quantities were reported in metric tons of nutrients, i.e. nitrogen, phosphorus and potassium. Raw quantity data were taken from the Fertilizer Statistics, a publication of Fertilizer and Pesticide Authority (FPA) and were reported by fertilizer grade (e.g. 46-0-0, 14-14-14, etc.). The data on the volume of consumption/sales15 by fertilizer grade were converted to their nutrient equivalents. The fertilizer grade indicates the nutrient content of the fertilizer. For example, let x-y-z be a fertilizer grade. Then the nitrogen content of this fertilizer is X% of its weight, phosphorous is y%, and potassium is Z% of its weight. Regional consumption of nitrogen, phosphorus, and potassium fertilizers was computed by getting the nutrient content of all the fertilizer grades consumed in the region, and summing these by type of nutrient (i.e. nitrogen, phosphorus and potassium) for all the grades. Fertilizer prices were reported in the data set in pesos per kilogram of nutrient.

For a given region, the price per kilogram of nutrient in a particular

fertilizer grade was computed as follows: Let x-y-z be a fertilizer grade, and let Px-y-z be its retail price per kilogram in region i. Then the price per kilogram of nitrogen in x-y-z is P x-y-z/x%; of phosphorus is Px-y-z/y%; and of potassium is Px-y-z/z%. These prices were computed for all the fertilizer grades consumed in the region. Thus, for a given region, there were as many prices per kilogram of particular nutrient as there were fertilizer grades containing this nutrient.16 To 15

FPA defines consumption/sales as withdrawals from importers’ and manufactures’ warehouses. No data on actual consumption were available. 16 For example, for the year 1974, there were five fertilizer grades containing nitrogen (46-0-0, 210-0, 16-20-0 and 14-14-0, 14-14-14), two fertilizer grades containing phosphorus (16-20-0 and 14-14-14), and two fertilizer grades containing potassium (0-0-60 and 14-14-14). Thus there were four computed prices of nitrogen, one for each grade, and two prices each of phosphorus and potassium.

76

derive the final price estimates for a given region, the prices per kilogram of a particular nutrient, say nitrogen, computed for the various fertilizer grades were weighted by the ratio of the nitrogen content of a particular grade to the total nitrogen content of all the grades consumed in the region. For example, the computation of the price per kilogram of nitrogen for region i in 1974, denoted by PN,i is as follows: PN , i = ∑ PN , g ∗ g

Ng total N

77

where PN,g is the region’s price per kilogram of nitrogen in fertilizer grade g, g= 46-0-0, 21-0-0, 16-20-0, 14-14-14; Ng is the nitrogen content of fertilizer grade g; and total N = N46-0-0 + N21-0-0 +N16-20-0 +N14-14-14. The data on seeds, which included rice and corn seeds, were taken from the Supply-Use data of BAS. The price of seeds was based on the farmgate prices of corn and rice. The sources of the data they used to construct the data series on agricultural machinery were: (i) the 1978 BAEcon Capital formation Study and (ii) the annual national estimates of gross domestic capital formation17 from the Economic and Social Statistics Office (ESSO) of the National Statistical Coordination Board.

17

Based on the Manual on the Philippine System of National Account, gross domestic capital formation consists of two major components; the gross fixed capital formation and the change in stocks. The gross fixed capital formation refers to the outlays on construction, durable equipment and breeding stocks, orchard development and afforestation. Change in stocks, on the other hand, refers to the difference between ending and beginning inventories such as finished goods, work-in-progress, and raw materials, which have been produced or purchased but not yet sold or consumed as intermediate inputs during the accounting period.

77

To estimate the national stock values of agricultural machinery for 19742000,18 the following equation was used: K t = (1 − d ) K t −1 + I t

78

where K refers to the stock value of agricultural machinery, I to investment in agricultural machinery, d to the depreciation rate, and t to the time subscript. The benchmark figure used for k was the 1973 value of agricultural machinery (=185.6 million pesos, in current prices) reported in the 1978 BAEcon Capital Formation Study, and the depreciation rate was assumed to be 10%.

The

investment data used were the data on gross domestic capital formation in agricultural machinery and tractors (in current prices) taken from Economic and Social Statistics Office (ESSO) of the National Statistical Coordinating Board. The estimated annual national stock values of agricultural machinery in current prices were deflated using implicit price indices computed from the ESSO data. The amount of capital service of agricultural machinery in each region depended on the (deflated) value of the capital stock, the interest rate and the depreciation rate. The relationship can be expressed as K st = ( d + r ) K t

79

where Kst is the value of capital service in year t, Kt is the deflated value of capital stock in year t, d is the annual depreciation rate which they have assumed to be 10% and r is the annual interest rate, also assumed to be 10%. Implicit price indices were computed from the ESSO data as the ratio of the current price to

18

The ESSO reported data on gross domestic capital formation separately for agricultural machinery and for tractors other than steam. We define agricultural machinery to be inclusive of tractors, so the sum of the gross domestic capital formation data for these two categories of durable equipment were used in the estimation.

78

the constant price estimates of gross domestic capital formation in agricultural machinery and tractors. The computed indices had 1985 as base year; these indices were rebased to 1974.

6. Literature Gaps 6.1 Key General Findings Most of the cross-country and country-specific studies reviewed offer evidence of positive productivity growth rates for Philippine agriculture. Numerically, however, there were marked discrepancies among these estimates. These can be attributed to the differences in the theoretical constructs or methodologies used or probably due to the use of different data sets assembled using different assumptions and time periods. Although this paper highlights the alternative approaches to productivity measurement and data sources, a consistent general picture emerges with regard to the recent agricultural productivity performance of the Philippines.

79

The performance during the 1950s was generally good. This was followed by a decline in the decade of the 1960s and a recovery between 1970s and 1980s as shown by a relatively strong growth in productivity. A subsequent decline, however, followed through until 2000. These empirical results seem to corroborate relatively few studies arguing that the poor performance of agriculture can be attributed to the prolonged and relatively rapid decline in agricultural productivity, which characterizes many developing countries (Fulginiti and Perrin, 1997, 1998, 1999; Kawagoe et al., 1985; Lau and Yotopoulos, 1989 and Kawagoe and Hayami, 1985). At the regional level, the regions in Luzon are generally more productive than in the Visayas and Mindanao especially in recent years. The regions of Ilocos and Central Luzon are identified as the relatively more productive regions. Bicol region, on the other hand, is consistently the least productive of the regions and in some years experienced negative growth rates.

6.2 Estimation In addition to cross-country studies, there are a handful of country-specific studies on productivity estimation conducted in the Philippines.

From 1980

onwards, the common approaches to productivity measurement used by these studies are the growth accounting approach and the econometric approach. The latter approach specifically employed the Cobb-Douglas production function, the translog production function and the dual translog cost function. All dual estimations dealt with a single output case, indicating that multiple output dual

80

models have not been fully exploited in studying agricultural productivity in Philippine agriculture. The index number procedure is also seldom used, while the DEA-based Malmquist index procedure has not been applied so far to Philippine agriculture using regions as the DMUs in spite of its advantage of handling inputs and outputs without requiring information on prices and weights, which are often problematic under the Philippine context. A number of these studies based on non-parametric approach were considered cross-country studies.

Just like the DEA-based Malmquist index approach, the stochastic

frontier approach has not also been used to empirically estimate productivity levels or growth rates in Philippine agriculture.

6.3 Data Regardless of the source of data, there are several data issues that are widely recognized in estimating productivity in Philippine agriculture, to wit: 1.1 The constraint imposed by data availability or small data dimension indicating limited number of observations which consequently diminishes the number of options for sophisticated approaches to productivity measurement or the use of more advanced techniques such as the econometric and the parametric SFA. 1.2 The insufficient disaggregation of the inputs implies the inability to assign inputs to particular outputs.

81

Given the diverse and highly

specialized nature of modern agriculture, it will be interesting to have forecasts of the productivity growth of the different commodities. 1.3 Missing data on some intermediate inputs such as pesticides, herbicides, organic fertilizers and on non-conventional inputs affecting productivity, among them, research and development, extension, government programs and education is also a concern.

Missing

variables will have an upward bias on productivity estimates. Likewise, the problem on measurement errors also needs to be addressed in the estimation process. One technique is by accounting for the changes in the quality of inputs over time or by through minimizing under/over measurement of inputs. 1.4 The most recent data set maintained a 12-region classification. There is also a need to look at the possibility of reconstituting the data to come up with a panel data for the current classification composed of 14 regions or, if possible, even for a more detailed dimension like at the provincial level. 1.5 The use of the following assumptions in constructing the data set need to be validated: i.

The assumption used in the computation of the equivalent man-days regarding the working capacity of a female worker relative to the working capacity of a male worker.

ii.

The assumption that an adult male agricultural worker works 160 days a year while an adult female works 105 days.

82

iii.

The assumption used in the calculation of the equivalent animal work day that the carabao and the cattle work an average of 220 and 150 days a year, respectively.

iv.

The cost of services of the work animals per workday was assumed to be one half of the daily wage of agricultural labor.

v.

The assumption that labor employment in agriculture is a constant-proportion (92%) of the reported total employment in the agricultural sector.

vi.

The use of fertilizer consumption/sales data (withdrawals from importers’ and manufactures’ warehouses) in lieu of data on the actual fertilizer consumption.

vii.

The assumption regarding the depreciation as well as the interest rates used for the computation of the amount of capital service of the agricultural machinery.

viii.

The imputation of land price as the residual of total revenue net of measured costs for agricultural labor, fertilizer, seeds, and machinery and animal services.

1.6 The implication of the use of interpolation, extrapolation and other techniques such as the application of regional shares to distribute national data to the different regions to fill in the missing years. An example of this is the distribution of deflated capital stock figures to the regions using the regional distribution of interpolated number of

83

tractors. These techniques are commonly used and these might have caused some biases in the estimates for productivity growth or levels.

7. Recommendations and Conclusion In spite of the fact that all studies reviewed in this paper used different data sets, time frames and theoretical constructs, most of these studies revealed positive growth rates for Philippine agriculture. A review of the existing literature, however, poses a challenge with regard to the veracity of productivity estimates offered by the studies due to the reported problems such as the data gaps or difficulties in constructing relevant data series especially at the regional level and also in terms of the use of restrictive assumptions to fill in the missing years, the measurement errors attributed to missing variables and over/under measurement of the output and input data, to name a few. In order to provide better estimates of productivity, particularly in Philippine agriculture, more work needs to be done on the following areas: 84

On the issue of methodology, there is a need to highlight the use of models with functional forms that are flexible enough to take into account the complexity of relations between output and input and between various inputs to include intermediate inputs such as pesticides, herbicides, organic fertilizers, etc. due their increasing importance in agricultural production. These relationships can be easily investigated by using parametric approaches like the econometric and the SFA. Aside from productivity estimates, these approaches can provide information on the production structure and the nature of technology in Philippine agriculture not readily available when using for example the index number procedure.

For Philippine agriculture, one can also use the DEA-based

Malmqvist productivity index approach to address the issue on the availability of quality input data series.

This approach provides additional information on

efficiency which is assumed to be constant in the case of econometric approach. There is also a need to identify the data requirements for chosen methods and conduct a detailed quality assessment of all readily available data series and consider alternatives for correcting the common data problems. The econometric approach is more demanding in terms of data requirement than the Malmquist index approach. The former requires both data on quantity and prices of output and input, while the latter provides options to use either the data on output or input quantity.

However, both are sensitive to measurement errors due to

missing variables and over/under measurement.

These measurement errors

have been shown to cause biases in the parameter estimates that are used in productivity estimation.

85

In preparing for the data series, there is also a need to develop options for obtaining the missing data of interest and to assess the feasibility of obtaining the required data. The missing data problem is more common in all inputs than in output data and more conspicuous in pooled time-series and cross-sectional data set. The measurement of agricultural productivity growth has been in the policy agenda for the longest time due to its welfare implication.

Because of its

importance, a huge literature on agricultural productivity measurement has been developed.

In spite of the extensiveness of the literature, one important

characteristic stands out, that is, most publications measure sectoral productivity and neglect commodity-specific productivity growth. This observation also holds true in Philippine agriculture and this can be attributed to the difficulty of allocating inputs to individual outputs.

There is a need, therefore, to review

research studies addressing this empirical issue such as those of Lence and Miller 1998; Paris and Howitt, 1998 and Just, Zilberman and Hochman, 1983). The studies reviewed in this paper, particularly the country-specific studies, that have focused on Philippine agriculture constitute a small part relative to the extensiveness of a broad body of international work that has been published with regard to productivity since the 1980s. The attempt to investigate key issues related to data and estimation will not only bring research on Philippine agricultural productivity at par with international studies, it will also provide broader evidence significantly to rejuvenate Philippine agriculture.

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Table 1: Productivity Studies on Philippine Agriculture: 1986-2005 Authors

Year

Years Covered

Productivity Estimates

Methodology

Cross-country Studies Trueblood and Coggins Arnade Martin and Mitra

1997

1961-1991

0.0119

Malmqvist Index

1997 1999

1961-1993 1967-1992

-0.0040 0.0164

Malmqvist Index Translog Production Function

0.0157

Cobb-Douglas Production Function Growth Accounting (Actual Factor Share) Growth Accounting Method

Martin and Mitra

1999

1967-1992

0.0207

Fulginiti and Perrin Fulginiti and Perrin

1998

1961-1985

-0.0250

1998

1961-1985

0.0010

Production Function (Variable Coefficient)

0.0180

Production Function (Fixed Coefficient)

87

Fulginiti and Perrin Coelli and Rao Coelli and Rao

1998

1961-1985

-0.0030

Malmqvist Index

2003 2003

1980-2000 1980-2000

0.0080 0.0130

Malmqvist Index Index Number Approach (Törnqvist Index Procedure) Production function

Mundlak, Larson 2004 1961-1998 0.0025 and Butzer Country-specific Studies Evenson and 1986 1950-1984 0.0190 Growth Accounting Method Sardido Cororaton and 2001 1980-1998 -0.0056 Growth Accounting Method Cuenca Teruel and 2004 1974-2000 0.0051 Translog Variable Cost Kuroda Function Teruel and 2005 1974-2000 0.0162 Index Number Approach Kuroda (Törnqvist Index Procedure) Teruel and 2005 1974-2000 0.0091 Cobb-Douglas Production Kuroda Function Teruel and 2005 1974-2000 0.0142 Translog Cost Function Kuroda Table 2: Productivity Estimates Across Subperiods in Philippine Agriculture Authors Year Years Productivit Methodology Covered y Estimates Evenson and 1986 1950-1954 0.021 Sardido 1955-1959 0.024 (5-year subperiod) 1960-1964 0.018 Growth Accounting Method 1965-1969 0.008 (Land Rents Based) 1970-1974 0.014 1975-1979 0.053 1980-1984 -0.011 Evenson and 1986 1950-1954 0.027 Sardido 1955-1959 0.025 (5-year subperiod) 1960-1964 0.019 Growth Accounting Method 1965-1969 0.010 (Fixed Share = 0.3) 1970-1974 0.021 1975-1979 0.053 1980-1984 -0.011 Evenson and 1986 1955-1964 0.021 Sardido 1965-1974 0.013 Growth Accounting Method (10-year subperiod) 1975-1984 0.021 (Land Rents-based) Evenson and 1986 1955-1964 0.022 Sardido 1965-1974 0.016 Growth Accounting Method (10-year subperiod) 1975-1984 0.021 (Fixed Share = 0.3) Corroraton and 2001 1981-1989 -0.054 Growth Accounting Method

88

Cuenca Mundlak, Larson and Butzer Teruel and Kuroda Teruel and Kuroda

2004 2004 2005

Teruel and Kuroda

2005

Teruel and Kuroda

2005

1990-1998 1961-1980 1980-1998 1974-1980 1981-1990 1991-2000 1974-1980 1981-1990 1991-2000 1974-1980 1981-1990 1991-2000 1974-1980 1981-1990 1991-2000

0.042 0.0098 0.0013 0.0077 0.0050 0.0035 0.0219 -0.0053 0.0144 0.0250 0.0050 0.0260 0.0201 0.0116 0.0084

Production Function (With State Variables) Translog Variable Cost Function Cobb-Douglas Production Function Index Number Approach (Törnqvist Index Procedure) Translog Cost Function

Table 3: Productivity Estimates by Regions in Philippine Agriculture Regions Growth Accounting Translog Variable Index Number Approach Cost Function Approach (Evenson and Sardido, 1986)

(Teruel and Kuroda, 2004)

(Teruel and Kuroda, 2004)

9-Region Classification

12-Region Classification

12-Region Classification

1950-1984

1974-2000

1974-2000

Ilocos

0.0160

0.0156

0.0216

Cagayan Valley

0.0073

0.0084

0.0204

Central Luzon

0.0000

0.0145

0.0328

Southern Tagalog

0.0239

0.0066

0.0216

Bicol

0.0047

-0.0025

-0.0029

Western Visayas

0.0083

-0.0059

0.0055

89

Central Visayas

-

0.0059

0.0107

Eastern Visayas

0.0146

0.0021

0.0091

Northern-Eastern Mindanao Western-Southern Mindanao Western Mindanao

0.0254

-

-

0.0109

-

-

-

-0.0028

0.0017

Northern Mindanao

-

0.0085

0.0216

Southern Mindanao

-

0.0082

0.0201

Central Mindanao

-

0.0032

0.0085

Table 4: Productivity Studies on Philippine Agriculture by Approaches: 1986-2005 Authors Year Years Productivity Methodology Covered Estimates

Growth Accounting Approach Evenson and Sardido

1986

1950-1984

0.0190

Growth Accounting Method

Fulginiti and Perrin Martin and Mitra

1998 1999

1961-1985 1967-1992

-0.0250 0.0207

Cororaton and Cuenca Index Number Approach Teruel and Kuroda

2001

1980-1998

-0.0056

Growth Accounting Method Growth Accounting (Actual Factor Share) Growth Accounting Method

2005

1974-2000

0.0162

Coelli and Rao

2003

1980-2000

0.0130

1998

1961-1985

0.0010

Index Number Approach (Törnqvist Index Procedure) Index Number Approach (Törnqvist Index Procedure)

Econometric Approach Fulginiti and Perrin

90

Production Function

(Variable Coefficient) 0.0180 Martin and Mitra

1999

1967-1992

0.0164 0.0157

Production Function (Fixed Coefficient) Translog Production Function

Mundlak, Larson and Butzer Teruel and Kuroda

2004

1961-1998

0.0025

2004

1974-2000

0.0051

Teruel and Kuroda

2005

1974-2000

0.0091

Teruel and Kuroda Malmquist Approach Trueblood and Coggins Arnade Fulginiti and Perrin Coelli and Rao

2005

1974-2000

0.0142

Cobb-Douglas Production Function Production Function (With State Variables) Translog Variable Cost Function Cobb-Douglas Production Function Translog Cost Function

1997 1997 1998 2003

1961-1991 1961-1993 1961-1985 1980-2000

0.0119 -0.0040 -0.0030 0.0080

Malmqvist Index Malmqvist Index Malmqvist Index Malmqvist Index

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