____W S I g29
POLICY RESEARCH WORKING PAPER 1827
The Determinants Capital is important to
agricultural production, so
of Agricultural Production policies that improve acccss to
agricultural capital will
A Cross-Country Analysis facilitate growth, if the capital
is used efficiently
Yatr Mundlak
Don Larson
Ritz Butzer
The World Bank
Development Research Group
September 1997
Pocy RESEARCH WORKING PAPER 1827
Summary findings
In this analysis of capital's role in agricultural and choice of technology. The legacy of past policies that
production, a new construction of data on capital distorted the relative returns to economic activity is
allowed Mundiak, Larson, and Butzer to advance the enshrined in current stocks, which may respond slowly
cross-country study of production functions. The model to pouicy reformr.
reveals the relative importance of capital, a finding quite The analysis assumes that the production technology is
robust to modifications of the model and the heterogeneous and the implemented technology is
disaggregation of capital to its two components. The endogenous and determined jointly with the level of
model is also consistent with the view that lack of unconstrained inputs. T hus, a change in the state
physical capital serves as a constraint on agricultural variahles affects both the technology and the inputs, so
growth. the production function is not identified. To overcome
The shift to more productive techniques is associated that problem, changes in productivity are decomposed to
with a decline in labor, reflecting labor-saving technical three orthogonal components caused hy the
changes. This is not news, but it is emphasized here fundamentally different processes underlying panel data.
because it comes out of an integral view of the process The statistical framework expiains the unstable results
which distinguishes between the core technology and the observed in production functions derived from panel
changes that took place over time and between countries, data. Statistically, the results depend on how the data are
LNot only is capital important to agricultural projected. Comparisons between units over time or of
production, and agricultural development dependent on deviations from unit-means or time-means all describe
the economic environment, but agriculture is more cost- different processes. This is based on theory but has an
capital-intensive than nonagriculture. intuitive appeal as well.
Capital is all the more important as a factor of In this case, the spread in productivity among
production in that land (also important) varies little over countries is different from the spread in productivity for
time. The availability of agricultural capital determines a country through time. The factors explaining the
whether the gap between available and applied spread will differ. The modeling approach should
technologies can be closed. explicitly recognize the fact that panel data measure a
Prices have little direct, immediate impact on combination of economic phenomena.
agricultural growth, beyond their impact through inputs
This paper - a product of the Development Research Group - is part of a larger effort in the group to examine the
determinants of growth in agriculture. The study was funded by the Bank's Research Support Budget under the research
project "Determinants of Agricultural Growth" (RPO 679-03). Copies of the paper are available free from the World Bank,
1818 H Street NW, Washington, DC 20433. Please contact Pauline Kokila, room N5-030, telephone 202-473-3716, fax
202-522-3564, Internet address pkokila Qworldbank.org. September 1997. (40 pages)
The Policy Research Working Paper Series disseminates the findings of w ork in progress to encourage the exchange of ideas about
I development issunes. An objective of the series is to get the findings out quickil, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
co ntries they re present.
Produced by the Policy Research Dissemination Center
THE DETERMINANTS OF AGRICULTURAL PRODUCTION: A CROSS-COUNTRY ANALYSIS
Yair Mundlak, Donald F. Larson, and Rita Butzer
Yair Mundlak is a professor in the Economics Department, University of Chicago;
Donald F. Larson is an economist in the Commodity Policy and Analysis Unit at the
World Bank; and Rita Butzer is a consultant at the World Bank. The authors would like
to thank Al Crego for valuable research assistance. This research was conducted at the
World Bank as part of a larger research effort on the determinants of agricultural growth
(RPO 679-03).
Summary findings
This study is triggered by the desire to shed light on the role of capital in
agricultural production, a neglected topic due to lack of appropriate data. The
construction of the data on capital allowed us to advance the cross-country study of
production functions in what turns out to be an important direction. The analysis is based
on the premise that the production technology is heterogeneous and the implemented
technology is endogenous and determined jointly with the level of the unconstrained
inputs. Therefore, a change in the state variables affects both the technology and the
inputs, and consequently the production function is not identified. To overcome this
problem, we decompose the changes in productivity to three orthogonal components
caused by the fundamentally different processes underlying panel data and thereby gain
meaningful economic insight.
The statistical framework provides an explanation for the unstable results
observed in production functions derived from panel data. Statistically, the results
depend on how the data are projected. Underlying this is the fact that comparisons
between units, over time or of deviations from unit-means or time-means all describe
different processes. This is based on theory, but has an intuitive appeal as well. In the
case at hand, the spread in productivity among countries is a different economic
phenomenon or process from the spread in productivity for a country through time. In
turn, the factors explaining the spread will differ. Panel data measures a combination of
these economic phenomena-a fact which should be recognized explicitly in the
modeling approach.
The most striking result is the relative importance of capital. This result is quite
robust to various modifications of the model and to the disaggregation of capital to its
two components. Our findings are also consistent with the view that physical capital
serves as a constraint to agricultural growth. At the same time, the between-time
regression shows that the shift to more productive techniques is associated with a decline
in labor, which is an indication of the labor-saving technical change in agriculture. This
is not news, but it is emphasized here because it comes out of an integral view of the
process which separates between the core technology and the changes that took place
over time and between countries. These results highlight the importance of capital in
agricultural production, an attribute critical in the understanding of agricultural
development and its dependence on the economic environment.
The introduction of the appropriate state variables to account for technology,
prices and physical environment produced a production function that displays constant
returns to scale and thus avoided the pitfalls of previous studies and the misguided
conclusions that followed. The contribution of inputs to growth should be judged by
their contribution to output under a constant technology, attributing the rest of the growth
to technical change. Our results support the view that agriculture is cost-capital-intensive
as compared to nonagriculture. We provide estimates of factors' productivity that can be
compared to the factors' price. Comparing our results to the factor shares, it seems that
on the whole there is a surprising agreement. We do find that the growth calculations are
sensitive to the weight of land, and this is where earlier results erred the most. Still, after
all these years of intensive work on production functions, there is no hard evidence that
estimated elasticities do a better job than the factor shares as were originally used by
Solow (1957).
Finally, our results have important implications for policy. First, we can say that
agricultural capital is directly an important determinant of agricultural production. This
is especially significant, since land, another important determinant of production, varies
little over time. Moreover, agricultural capital is also important in closing the gap
between available and applied technologies. Therefore policies facilitating access to
agricultural capital will facilitate growth, provided the capital is used efficiently. This
implies that the overall economic environment must be conducive to the efficient use of
capital. Second, we find that prices have little immediate and direct impact on
agricultural growth, beyond their impact through inputs and the choice of technology.
Consequently, past policies that distort the relative retums to economic activity leave a
legacy enshrined in current stocks that may respond slowly to policy reforms.
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THE DETERMINANTS OF AGRICULTURAL PRODUCTION: A CROSS-COUNTRY ANALYSIS
Yair Mundlak, Donald F. Larson, and Rita Butzer
Introduction
Knowledge of the production structure, as reflected in the production elasticities,
is essential in the discussion of several key topics such as:
1. The contribution of inputs to output and, in a dynamic context, to growth.
2. The existence of returns to scale.
3. The sensitivity of the cost of production to changes in factor prices.
4. The relationships between factor prices and their productivity.
The discussion in this paper and the results bear directly on the first three subjects and
indirectly on the last one.
Empirical studies utilize data collected at various levels, from micro data at the
firm level to macro data at the national level. Cross-country studies utilize national data,
and their potential contribution comes from the large spread in inputs and other important
variables which helps to increase the precision of estimates. However, cross-country
studies have suffered from lack of sectoral capital data. To overcome this deficiency,
data on agricultural capital were constructed and used here in the estimation (Crego,
Larson, Butzer and Mundlak, 1997). The results are striking in that it becomes clear that
capital plays a major role in agricultural production.
The practice in empirical studies has been to assume that technology is
homogeneous and is represented by a production function applicable to all the
observations in the sample. This assumption is not supported by the data. For instance,
when panel data have been used, the results vary according to whether country or time
dumnmies are introduced. Such dependence on the specification has been discussed in the
literature within the framework of statistical properties under the assumption that all the
versions provide information on the same function. We take here the alternative view
which differentiates between functions estimated from observations within country and
time and those obtained from variability across countries and over time. Again, the
results are striking.
The recognition of the variability of the function relates to a more general view
that technology is heterogeneous and the choice of the implemented technology is
determined by the economic and physical environment. Earlier empirical applications of
this approach utilize factor shares, which we do not have. We therefore settle for less and
formulate the problem in a way that allows us to estimate the function.
1
The plan of the paper is as follows: we begin with a brief literature review of cross-
country studies of the agricultural production function. This is followed by an outline of
the model, a discussion of the statistical aspects, data description, presentation of the
results, a discussion of the results and conclusions.
Cross-country studies1
Analysis of agricultural production functions began in 1944 with the work of
Tintner(1944), Tintner and Brownlee (1944), followed by Heady (1944). These studies
were based on farm data. Subsequent work was extended to cover aggregate data, and in
1955 Bhattacharjee presented the first analysis based on cross-country data. The
underlying notion for these early studies was that all observations were generated from
the same production function. In an effort to get a definitive statement on the agricultural
production function, Heady and Dillon (1961, Chapter 17) compared the result of
Bhattacharjee's study with numerous other studies and discovered that the notion of a
homogenous technology was elusive. Thus they concluded "Still, the variations shown
among the elasticities ... bears witness to the dangers associated with the use of any such
global production function." (Op. cit., p.633).2
The use of cross-country data to estimate a global production function gained
impetus with the work of Hayami (1969, 1970) and Hayami and Ruttan (1970) -- studies
which sought to explore the causes of cross-country differences in agricultural
productivity. Again, the assumption underlying these studies is that all countries use the
same production function. This assumption does not stand, and we find considerable
disparities between their results and those obtained in country studies.
Since Bhattacharjee's study, with the passage of time, it was possible to increase
the sample size and thus estimate the functions for different periods and additional
countries. Also researchers have introduced new subjects, including: checking the
robustness of the estimates and the returns to scale, improving the specification by adding
state variables and using different methods of estimation, and doing away with the
assumption of constant technology.
Table 1 summarizes results obtained in a series of cross-country studies where the
quantities (outputs and inputs) are expressed either as country totals or in per worker
terms.3 Studies using data for a single period provide estimates for the between-country
regression for that particular year. This is also the case for studies which use panel data
and introduce time dummies (within-time regressions) but not country dummies. Studies
with panel data which contain country dummies (with or without time dummies) provide
estimates for the within-country (or within-country and time) regression. We elaborate
on this point below.
1 For a survey of agricultural production functions see Mundlak (1997).
2 Clark (1973) assembles many results of factor shares in a nonformal framework but with extensive
international coverage. It is very clear that the estimates depend on the economic environment which is a
major theme of the discussion.
3 We do not include studies where the quantities are expressed as averages per farm because this would
raise issues unessential to our discussion
2
We will try to characterize some of the results. The study by Bhattacharjee does
not include any measure of capital items nor shifters, technology or others, and therefore
the results cannot be compared meaningfully with the other studies. The remaining
studies have some shifters such as schooling, research and extension, infrastructure and
the like. In a way of generalization, the table shows that the between-country estimates
of land elasticity are low in absolute terms and relative to estimates obtained from the
within regression (compare the two versions of the Evenson and Kislev study). Two
measures of capital have been used in most studies, machinery and livestock. The
elasticity of machinery varies around 0.1 (a little higher for the between-country
regression) and that of livestock concentrates in the range of 0.2-0.3. The estimates for
the labor elasticity are less stable. Of course, this is a very general evaluation but
sufficient to provide a background for the discussion.
The model
The underlying premise is that producers at any time face more than one
technique of production and their economic problem is to choose the techniques to be
employed together with the choice of inputs and outputs. The outline of the approach
follows Mundlak (1988, 1993). Letx be the vector of inputs and Fj(x) be the production
function associated with the jth technique, where Fj is concave and twice differentiable,
and define the available technology, T, as the collection of all possible techniques, T =
{Fj(x); j=l, ... , J}. Firms choose the implemented techniques subject to their constraints
and the environment. We distinguish between constrained (k) and unconstrained (v)
inputs, x = (v, k), and assume for simplicity, without a loss of generality, that the
constrained inputs have no alternative cost. The optimization problem calls for a choice
of the level of inputs to be assigned to techniquej so as to maximize profits. To simplify
the presentation, we deal with a comparative statics framework and therefore omit a time
index for the variables. The extension to the intertemporal version is conceptually
straightforward. The Lagrangian equation for this problem is:
L = pj F.(vj,kj)- wvj - A(kj -Ic0), (1)
j j j
subject to Fj(.) E T; vj 2 0; kj 0,
where pj is the price of the product of techniquej, w is the price vector of the
unconstrained inputs and k is the available stock of the constrained inputs. The solution
is characterized by the Kuhn-Tucker necessary conditions. Let s=(k,p,w,I) be the vector
of state variables of this problem and write the solution as: vy*(s), kj*(s), X*(s), to
emphasize the dependence of the solution on the state variables. The optimal allocation
of inputs vj*, kj* determines the intensity of implementing the jth technique. To the
extent that the implementation of a technique requires positive levels of some inputs,
when the optimal levels of these inputs are zero, the technique is not implemented. The
3
optimal output of techniquej is: yj* - Fj(vj*, kj*) and the implemented technology (iT) is
defined by
IT(s) = {Fj(vj,kj); Fj(vj *,k*) X 0, FjT}7
The empirical analysis can provide estimates of the production function that
corresponds to the implemented technology. The aggregate production function
expresses the aggregate of outputs, produced by a set of micro production functions, as a
function of aggregate inputs. This function is not uniquely defined because the set of
micro functions actually implemented, and over which the aggregation is performed,
depends on the state variables and as such is endogenous. Let the aggregate production
function be written as:
EpjYj*(s) = F(x*,s) = v(s). (2)
This production function is defined conditional on s, but changes in s imply
changes in x* as well as in F(x*,s). It is therefore meaningless in this framework to think
of changes in x, except by 'error', which are not instigated by changes in s. This means
that it is impossible to reveal a stable production function from a sample of observations
taken over points with changing available technology. Consequently, in general, the
aggregate production function is not identifiable.
The empirical aggregate production function can be thought of as an
approximation in a specific way. For (2) to be a production function in the usual sense, x
should be disjoint from s. Such a separation requires a discrepancy between x and x*
that will allow us to write for the observed output:
vpj y _= F(x, s). (3)
Strictly speaking, F(x, s) is not necessarily a function since x can be allocated to
the various techniques in an arbitrary way. It is only when we have an allocation rule
leading to x * that uniqueness can be achieved. With this caveat, we view F(x, s) as a
function of s, since s determines the techniques to which the inputs are allocated. A
discrepancy, x-x*, produces information on a given implemented technology, and such a
discrepancy is also the source of information for identifying a given production function.
It has been shown (Mundlak, 1988) that F(x, s) can be approximated by a function
which looks like a Cobb-Douglas function, but where the elasticities are functions of the
state variables and possibly of the inputs:
lny = 1(s) + B(s,x) lnx + u (4)
where y is the value added per worker, B(s,x) and F(s) are the slope and intercept of the
fimction respectively and u is a stochastic term.4
4 This expression can be given a more descriptive structure which leads to an approach in its estimation.
However, we do not have the factor shares needed for this approach and therefore we do not go into it.
For the utilization of factor shares, see Mundlak, Cavallo and Domenech (1989) and Coeymans and
Mundlak (1993).
4
Variations in the state variables affect F(s) and B(s,x) directly as well as indirectly
through their effect on inputs. The state variables may not be independent, a change in
one state variable may be associated with a change of the others. This is illustrated by
evaluating the elasticity of average labor productivity with respect to a given state
variable (say si):
olny I dj = E {T I °Sh + In x[oB(s) I °Sh] + B(s)(oln xlk )I aS)h / aSi (5)
h
The first two terms in the brackets show the response of the implemented
technology to a change in the state variables, whereas the last term in the brackets shows
the output response to a change in inputs under constant technology. The elasticities in
(5) have a time index, which is suppressed here, indicating that they vary over the sample
points. The innovation in this formulation lies in the response of the implemented
technology to the state variables. To isolate this effect, we rewrite (5), assuming
independence between the state variables, namely aSh/aSi = 0 for h i, and holding x
constant to yield the elasticities
Ei = oT(s) I aij + In x[OB(s) I osj] (6)
The effect captured by (6) is part of the unexplained productivity residual in the standard
productivity analysis under the assumption of constant technology.
When the available technology consists of more than one technique, a change in
the state variables may cause a change in the composition of techniques in addition to a
change of input used on a given technique. In this case, the empirical function is a
mixture of functions and as such may violate the concavity property of a production
function.
Statistical aspects
The dependence of the implemented technology on the state variables causes it to
vary across countries and over time in any given country. Countries differ in their natural
endowments such as weather and soil quality-differences which remain roughly
constant over time. They also vary in their constraints and the economic environment.
We should therefore expect different coefficients from cross-country and from time-series
analyses. An examination of the empirical distribution of the various variables reveals
that between-country variability is considerably larger than the variability over time. To
gain insight, it is useful to review the various forms of analyses within a uniform
framework. We label W, B(i), W(i), B(t), W(t) and W(it) projection (symmetric and
idempotent) matrices that generate residuals. They can be defined in termns of their
operation on an arbitrary vector x={xit} of order NT. Let xi. and x t denote the averages of
xit over t and i respectively and the terms in parentheses contain the typical elements of
the vectors in question:
Wx = (X1, - X), W(i)x = (x, - xi), W(t)x = (xi, -x,),
W(it)x = (x, -xi -x, + x..),
5
B(i)x = (x;. - x.), and B(t)x = (x., - x..), i=l,...,N, t=l,..., T.
The following identities can then be derived:
W= W(i) + B(i) (7)
W= W(t) + B(t) (8)
W= W(i) + W(t) - W(it) (9)
W= B(i) + B(t) + W(it) (10)
Let y be the vector of observations of the dependent variable and X be the matrix of
observations of the explanatory variables. The regression coefficients of interest can be
written in a generic form for a projection matrix P as:
b = (X'PX) - X'Py
where P can be any one of the projection matrices of interest listed above with rank not
smaller than rank X. To introduce the notation for the regression coefficients, we present
in the brackets the projection matrix and the corresponding vector of coefficients:
Pooled: [W b]; within-time and country: [W(it), w(it)]; within-country: [W(i), w(i)];
within-time: [W(t), w(t)]; between-time: [B(t), b(t)]; between-country: [B(i), b(i)].
It is well-known (Maddala, 1971) that the pooled regression can be presented as a matrix-
weighted average of within and between regressions. For instance, use (7) and simplify:
b = (X'WX)-' X'Wy = Gw(i) + (I - G)b(i), (11)
where G = (X'WA)-' X'W(i)X.
When, G, the share of the within component of variance X, is relatively small, the
coefficients of the pooled regression will reflect largely the between-regression
coefficients.
The common practice in empirical analysis is to use dummy variables for time or
country and to obtain b, w(i), w(t) and w(it) from pooled data without dummies, with
country dummies, with time dummies and with country and time dummies respectively.
Referring to the identities presented above, it appears that data generated by W(it) (using
country and time dummies) is cleaned from the between-time and between-country
variations in the data and as such should best represent a measure of the more stable
technology, referred to as the core implemented technology. Data generated by W(i)
(using country dummies) are cleaned of the between-country variations but contain the
variability over time. Similarly, data generated by W(t) are cleaned of the time variability
but contain the cross-country variability. This can be seen by rearranging the identities in
(7)-(1 0):
W(i) = W(it) + B(t) (12)
W(t) = W(it) + B(i) (13)
To determine the empirical importance of this distinction, we estimate and present
the three canonical regressions of this problem: b(i), b(t) and w(it). There is however a
6
practical problem with the estimation of the b(t), as we have only 21 years, and as such
the sample size is small for estimating the full model. However, we can obtain an
approximation of the time-effect on the regression coefficients by comparing w(it) and
w(i).
Data description
Output and inputs
We estimate a cross-country agricultural production function where agricultural
output depends on inputs, agricultural technology and the state of the economy.
Agricultural output is measured as agricultural GDP in 1990 US dollars. Inputs to
agricultural production include land, capital, labor and fertilizers and pesticides.
Hectares of arable and permanent cropland, along with permanent pastures, are
used for the measure of land. Agricultural labor is defined as the economically active
population in agriculture. Fertilizer consumption is often viewed as a proxy for the
5
whole range of chemical inputs and more.
Data on agricultural capital have been scarce. Commonly, crude data on tractors
or machinery have been used in cross-country analyses of agricultural production
functions. To overcome this problem, Crego, Larson, Butzer and Mundlak (1997)
constructed a series of capital in agriculture. National accounts data on investment were
used to construct a measure of the stock of fixed capital, consisting primarily of
structures and equipment. The fixed capital stock used here is measured in 1990 US
dollars. FAO data were used to construct a series of capital in livestock and in trees.
Livestock is measured in value terms by multiplying the quantities of livestock in a
country by the regional trade prices. The value of an orchard in any period is assumed to
be the discounted stream of future revenues that it will yield less production costs. We
use data on the value of production and harvested land area for major tree crops. The net
revenue associated with each acre of tree crops is imputed forward in time (with
discounting) and aggregated to yield the value of capital in the form of trees.
Not only does fixed capital differ from capital of agricultural origin-livestock
and orchards-in the method of construction, the two types of capital can also differ
fundamentally in terms of markets and pricing. Capital of agricultural origin is produced
largely by resources in agriculture and therefore its cost of production is largely
independent of the markets for nonagricultural inputs, which are often imperfect. As
such, farmers may face noncompetitive prices for their fixed investment inputs. Also,
fixed investments depend more on outside finance and are frequently hindered by credit
constraints.
5 "We first observe that the correlation between research and fertilizer variable is .95, reflecting the well-
known association between agricultural research and the introduction of modern inputs." (Antle, 1983,
p.613).
7
Environment
Agricultural production depends on the physical environment or natural
conditions. As observed by Mundlak and Hellinghausen (1982), this feature is usually
omitted in empirical analysis. In part, such an omission can be rationalized for time-
series studies where the basic features of the environment are constant and changes over
time, such as weather-distinguished from climate-are transitory in nature. However,
this rationalization is invalid for cross-sectional analysis, and it is therefore important to
try to capture the impact of the environment. In our analysis, we follow Mundlak and
Hellinghausen (1982) by using two variables extracted from Buringh, van Heemst and
Staring (1979). The variables are potential dry matter (PDAM) and a factor of water deficit
(FWD).6 The first variable is motivated by the desire "to compute theoretical potential
production, that is the production of a healthy, green, closed, standard crop, well supplied
with nutrients, oxygen, water and foothold and therefore only limited by the daily
photosynthetic rate, that depends on the state of the sky, the latitude and the date." (Op.
cit., p.8).
The production of dry matter requires moisture. Arid areas may have a large
value for PDMbut actual production is small due to water deficit. The relative water
availability is measured by the ratio of actual transpiration to potential transpiration
where the potential transpiration "depends only on the climate and is defined as the
amount of water which will be lost from a surface completely covered with the vegetation
if there is sufficient water in the soil in all times. On the other hand, the actual
transpiration is also based on rain data and calculated by evaluation of monthly water
balance, ... The difference between potential and actual evapotranspiration is moisture
deficit during the growing season." (Op. cit., p.9). The variable, referred to as FWD,
measures relative availability of moisture rather than deficit; the lower is the value of the
FWD the larger is the deficit. Thus the variable is expected to be positively correlated
with productivity.
Technology
As indicated above, the tacit assumption that all the observations are generated by
the same technology is a very strong one and should be tested empirically. This can be
done by introducing variables that will account for important differences in technology in
the sample. To do this, we experimented with several variables.
The most common variable used in empirical studies as a carrier or representative
of technology is some measure of human capital. The application of the concept of
human capital in empirical analysis is quite problematic for a variety of reasons. In
practice, it is mostly represented by a measure of schooling. The basic idea is that higher
levels of education are conducive for technological progress. However, the causality
could go in either direction in that economic progress generates a demand for schooling.
Therefore, the interpretation of a schooling variable in empirical analysis is somewhat
6 Binswanger, Mundlak, Yang, and Bowers (1987) used the same source to construct somewhat different
variables.
8
ambiguous. We include the mean school years of education of the total labor force as a
proxy for the human capital stock for the overall economy.
In addition to schooling, we include several variables whose meaning are
somewhat more specific and perhaps easier to interpret. In the case of agriculture, there
is a natural variable to measure the level of technology for a given crop; this is the yield
or output per unit of land. Extending this concept to aggregate output, we construct an
aggregate peakyield. For each country and each commodity, the maximum ofthe past
yields is computed. Country-specific Paasche indices (1990=1) are constructed of these
peak commodity yields, weighted by land area. A Paasche index is used since changing
the composition of output changes the relevance of existing technologies. This index is
intended to capture country-specific variations in technology over time but, as measured,
it is inadequate to represent variability across countries in technology in a given year.
However, we can capture the cross-country variability in growth rates. To do this, we
calculate the average rate of growth in the index over the period by regressing the log of
the peak yield on time. This variable is used in the between-country analysis.
Countries do not always perform on the technology frontier. Deviation from the
peak yield may be due to economic considerations or to natural disturbances. Be the
reason what it may, the deviation may affect the productivity of the various inputs. To
allow for such an effect, we measure the difference between the actual yield and the peak
yield for each crop, obtain a land-weighted sum of these differences and divide by the
peak yield. This ratio is calculated for each country in each year and referred to as the
yield gap.
Agricultural productivity is likely to be affected by the overall technological level
of the country. As economies develop generally, the physical, legal, regulatory
infrastructure and institutions which support agriculture develop as well. We measure
this influence with two variables. The state of development is measured by the per capita
output in the country relative to that in the United States. The main variability of this
measure is across countries, but it also varies over time. To supplement the variability of
the overall technology over time in each country, we use the maximum past average labor
productivity in non-agriculture in the country and refer to this variable as na-peak. It
turns out that this variable was only of marginal importance and will not be discussed
here.
Incentives
We introduce two measures of incentives to allow for the direct effect of
incentives on productivity over and above their indirect effect that comes through
resource allocation and accumulation. The measures are the terms of trade between the
agricultural and manufacturing sectors obtained as the ratio of the sectoral prices, or the
relative price, (agricultural GDP deflator to manufacturing GDP deflator, lagged one
period) and its fluctuations, calculated as a moving standard deviation from the three
previous periods. For the between-country analysis, we modify the measures, and use the
average rate of growth in the relative price over the period, calculated by regressing the
log of the price ratio on time. Also the standard deviation of the relative price over the
9
entire period is used in place of the moving standard deviation. The variability in
agricultural prices reflects the market risk faced by agricultural producers. In addition to
the sector-specific risk, there is an economy-wide market risk, that of price volatility for
the economy as a whole as measured by the rate of inflation. This is calculated as the rate
of change in the total GDP deflator.
Expected improvement of future profitability encourages investment and thereby
augments the capital stock which appears as a variable in the analysis. The regression
coefficients of the incentive variables represent only the direct effect of prices that is not
captured in input changes. To obtain the full impact of the incentives on productivity, it
is necessary to add their indirect effect through investment, but this is not done here.
The data are more fully described in Annex I.
Sample description
The sample was determined by the data availability and the preference for a
balanced data panel in order to simplify the analysis. It consists of annual data from 37
countries, listed in Annex I, for a 21-year period (1970-90). The information conveyed
by the sample is summarized in Table 2. The first column presents the average annual
growth rate of the variables over the sample period. Output grew at a rate of 3.82
percent. Capital has the highest growth rates among the inputs, 4.25 percent. This is a
weighted average of its two components, where the growth rate of structures and
equipment is 5.42 percent. On the other hand, the growth rate of schooling is 1.8 percent
and that of the peak yield is 1.9 percent. The gap in the level of development compared
to the US has widened over the period and the terms of trade of agriculture deteriorated at
an average rate of 0.3 percent. There has been little change in land and less so in the
labor force. It should be noted that these rates are for the sarnple as a whole and there are
differences among countries as we can learn from the decomposition of the sum of
squares.
The remaining columns of the table present a decomposition of the total sum of
squares to its components that corresponds to equation (10) above. To standardize the
results, we divide the components by the total sum of squares so that the numbers give
the percentage of each component in the total sum of squares. The terms are
SS total = SS(xit - x ), SSW(it) = SS(xit - Xi - X t + x ), SSB(i) = SS(xi - x),
SSB(t) = SS(x t - x ), where, for any variable z, we use the notation: SS(z) = E
i t
The between-country differences account for most of the variability of the output
and the inputs. Thus, just by allowing for a country effect, and without introducing any
input to the regression, the R2 is 0.9617 so that the unexplained residual from country
averages accounts for only 3.83 percent of the total sum of squares of output. Similarly,
the between-country variability accounts for 95 to 98 percent of the variability of capital
and practically all of the variability in land and labor. The situation is similar when the
output and inputs are measured per worker. The relative importance of the country and
time components is different for the state variables; the between-country component is
10
important in schooling and development and less important in the other variables. In
part, this difference is due to the way the variables are measured. Schooling and
development are measured in units that allow cross-country comparisons, and
interestingly, the relative importance of the between-country component in the total sum
of squares is similar to that of inputs. On the other hand, peak yield, prices and price
fluctuations were measured differently for the variability over time and for that over
countries as explained above. In short, peak yield varies largely over time. This variable
is measured as an index for each country, so that the between-country variability reflects
differences in the rate of growth of the peak yield rather than differences in the level. The
yield gap is a derived measure from the peak yield, but here most of the variability is in
the transitory component of within-country-time. This suggests that the deviations from
the peak yields are affected considerably by local conditions, some of which are weather
triggered and the others can be attributed to the economic environment. Be the case what
it may, these variables show variability over time and also have a strong transitory
component.
To sum up, the relative importance of the between-country component is
dominant. This can lead to the erroneous conclusion that the within analysis has little to
contribute. As a matter of principle, this conclusion is not well founded because the
precision of the estimated coefficients depends not only on the spread in the regressors
but also on the variance of the equation shock and this usually contains a component that
is time invariant. Consequently, the variance of the within component is considerably
7
smaller than the total variance. Indeed, as we see below, the within estimates are
meaningful empirically and informative substantively.
Empirical results
The estimates for a base model are given in Table 3 which, in line with the
specification in equation (10), consists of three blocks. The first block presents the
within-country-time estimates, w(it), which summarize the changes that took place over
time and over countries after allowing for country and time effects. As such, these
estimates are based on observations taken from the more stable, or core technology. The
second block presents the between-time estimates, b(t), obtained from a short time-series
of the sample means for each year. This represents the time-series component, common
to all countries and as such it captures the impact of changes in the available technology.
The last block presents the between-country estimates, b(i), based on the between-country
variations which constitute the major component of the total sum of squares. It
summarizes the locus of points that go across the different techniques implemented by the
countries, all operating under the same available technology.
The within estimates are obtained under the constraint of constant returns to
scale', whereas both between regressions are unrestricted. Variables that remain constant
over time, such as the environment, are not included in the first two blocks. By
7 This point was taken into account in the comparison of the within and the dual estimators in Mundlak
(1996).
8 We tested and were not able to reject the constant-returns-to-scale hypothesis. See Table 4.
11
construction, variables in different blocks are orthogonal to each other and therefore the
estimates in one block are unaffected by the omission or addition of variables in the other
blocks.
The first question is whether we can do away with any of the three
aforementioned regressions. The answer to this question is given in Table 4 which
presents results for several F-tests. The null-hypotheses that blocks can be omitted are
rejected and therefore we should interpret the information embedded in all of the blocks.
The second question is whether the coefficients of the variables common to the various
equations are the same. Casual inspection indicates that they are quite different,
confirming the basic initial hypothesis that the regressions summarize the combined
effect of changes in inputs and technology and therefore the within and between
regressions summarize different processes. We now turn to interpret the results.
Inputs
The results are striking in several respects. Perhaps the most interesting result is
the magnitude of the elasticity of capital, 0.37 in the within regression, 0.34 in the
between-country and 1.03 in the between-time regression. Thus, it is high and significant
in all three blocks, which is not the case with the other inputs. The between-time
estimate is particularly high, and it indicates that the implementation of changes in the
available technology, which can not be observed directly, were strongly affected by
investment in agriculture.
The effect of capital becomes even stronger when capital is disaggregated to the
two components as seen in Table 5. The within coefficient is 0.29 for structures and
equipment and 0.13 for livestock and orchards, a sum of 0.42. The relative importance of
the two components is almost the same in the between-time regression, and their sum is
similar to that of the elasticity of total capital. The relative importance takes on a
different form in the between-country regression, where livestock and orchards is the
dominant component.
The land elasticity in the within regression is 0.47 for the aggregate capital (Table
3) and 0.44 for the disaggregated capital (Table 5). Thus we find no empirical support for
the idea, originally expressed by Schultz (1953) and echoed by others (see for instance
Kawagoe and Hayami, 1985, p.91), that land has lost importance in modem agriculture.
Indeed, the land coefficient is negative, though small, in the between-country regression.
This indicates that the techniques used by the more productive countries were land
saving.9 However, with a given technology, the marginal productivity of land is positive,
9 To illustrate possible consequences of imperfect knowledge of the production process we bring an
example from a study of cross-country differences in agricultural productivity. "Depending on the weight
to be applied to land, the total productivity of new continental countries becomes higher or lower than
other DCs." (Kawagoe and Hayami, 1985, p.91). They use three alternative weight systems in their
productivity exercise, where land weights (elasticities) are 0.1 (obtained from cross-country production
function), 0.3 (less developed countries "in which factor shares are high for land and low for modern inputs
such as fertilizers and machinery") and 0.05 (the "situation in the highly advanced stage of economic
development" relying on Schultz that at this stage the importance of land declined). (Kawagoe and
12
or else there would be no cultivation. Finally, land is not included as a variable in the
between-time regression in view of the low variability of land over time as indicated in
Table 2.
The coefficient of fertilizers is particularly high in the between-country regression
and much lower in the other two. A value of 0.08 obtained in the within regression for
the elasticity of fertilizers may seem to be low, but this is not the case. A point estimate
of 0.08 means that about 8 percent of the within changes in agricultural output are to be
attributed to fertilizers. It is to be noted that this result is obtained for the aggregate
agricultural output whereas fertilizers are used only on plant products. It is likely that a
production function for plant products alone would show a larger elasticity for fertilizers.
Thus, a value of 0.08 for aggregate output may even be a bit high. One possibility is that
fertilizers capture the impact of other chemicals and more generally, the modem inputs,
as indicated above. As such, it is possible that the variable also captures some inter-
technology effects. Another possibility is that the elasticity reflects a high shadow price
of fertilizers, which is a signal for constraints that prevent optimal use.
The striking result is the high value of the fertilizers elasticity obtained from the
between-country regressions. This means that the locus of country means represents a
changing technology package where the improvement in the implemented technology is
fertilizer using. At the same time it is also capital using but land saving
Referring to Table 3, the elasticity of labor, obtained in the within regression by
imposing the assumption of constant returns to scale, is relatively low, 0.08, and it is 0.26
for the between-country regression. The corresponding results for Table 5 are 0.10 and
0.22 respectively. Thus, the variations of output in each country are largely accounted for
by variations in capital and land and less by labor.
The within regressions were obtained under the constraint of constant returns to
scale. The constraint was tested empirically and it is not rejected, as can be seen from the
results in Table 4. The between regressions are unconstrained, and it is interesting that
the sum of the elasticities of the inputs of the between-country regressions is practically
one in Tables 3 and 5. This is in contrast to the results of those cross-country studies
which show increasing returns to scale (for instance, Kawagoe, Hayami and Ruttan, 1985,
p.120). This indicates that our specification succeeds in capturing the impact of cross-
country differences in technology and thus eliminates the spurious result of increasing
returns to scale.10
Hayami, 1985, p.88). There is no theoretical basis for this classification, but we bring this reference to
indicate that the higher value is close to that obtained in the within analysis and the low value is not far
from that obtained from the between-country analysis. There is a similar ambiguity with respect to the
other weights. Therefore, without gaining a clearer view with respect to the appropriate weights, the whole
exercise does not convey any clear message.
10 The finding of increasing returns to scale in cross-country analysis found justification of sirnilar finding
by Griliches (1963b) in cross-regions analysis for the US. For more evidence, see Kislev and Peterson
(1996).
13
Technology
The technology variables play a dual role in the analysis. First they serve as
technology shifters and as such reduce, or eliminate completely, the bias of the estimated
input coefficients that is caused by the correlation of inputs and technology. Second, we
can examine empirically how well they describe the data and thereby guide us in the
search for appropriate technology indicators. The test of the null hypothesis that the
technology block can be omitted is rejected, as reported in Table 4.
Turning to the individual components, the estimated elasticities in Tables 3 and 5
give the same message. The peak yield serves well as a shifter of the agricultural
productivity, as measured by the core technology, with an elasticity of about 0.83. The
level of development of the country relative to the US is also an important explanatory
variable of agricultural productivity. Note that the contribution of this variable is over
and above that of the peak yield which shows that the yield level is not the only indicator;
first, the yield variable does not represent the productivity in livestock production which
accounts for about one third of output and second, there is a scope for improving
efficiency under a given technology by coming closer to the frontier, as represented by
the performance of the US.
The between-time regression shows that, for the sample as a whole, none of the
technology variables was important in accounting for the changes in agricultural
productivity over time. The work is done by physical capital. The implication is that
even though schooling and peak yields increased with time (Table 2), we get no evidence
that they contributed to the benefits harvested from improvements in the available
technology. It is the changes in the available technology that caused the increase in these
variables, at least in peak yield and perhaps in schooling. But it was capital availability
that was crucial for the countries to take full advantage of the available technology. This
sheds light on the importance of physical capital in accounting for the changes in
agricultural productivity in the study period.
The results are different for individual countries, as seen from the between-
country regression, where the level of development is important in accounting for the
productivity variations. This is a statement of the importance of the various attributes of
the overall level of development of a country in determining the level of agricultural
productivity. This may also be the reason that schooling appears to be irrelevant. To the
extent that schooling matters, it may have an indirect effect through the development
variable. However, to what extent schooling matters and how it can be measured using
aggregate data is still an open question and was recently highlighted by Pritchett (1996).
The peak yield is a measure of the frontier of the implemented technology, but
countries do not always operate at the frontier. We thus introduced the yield gap variable
described above, whose average for the sample as a whole is 9 percent of the peak yield.
As seen in Table 2, this variable varies considerably within country and time. We add
this variable to the regression and report the results in Table 6. The variable has a
negative effect on output in the within regression. This is of no surprise, operating off the
frontier has a negative effect on productivity. The reason for introducing the variable is
14
to allow for a shift of the function to account for the unfavorable environment and
thereby relieve the inputs from accounting for this outcome. Interestingly, the effect on
the input elasticities is minor, except for labor, as can be seen by comparing Tables 6 and
3. It thus leads to the conclusion that the within-country-time yield gap was caused by
transitory effects that could not be anticipated or were anticipated to be transitory and
therefore there was no reason to make major changes in the inputs. The main change in
the within analysis is in the peak yield coefficient, which increases from 0.83 (Table 3) to
0.93 (Table 6). The latter number is obtained by freeing the variable from the noise of
the transitory conditions and thus is thought to be more reliable.
The results are different for the between-country regression where the coefficient
of the yield gap is positive, significant and sizable, 1.24, higher than the coefficient of
peak yield in the within regression. To understand this result, we have to go back to the
definition of the variables. In the between-country regression, we use the average growth
rate of the peak yield in place of the peak yield index and therefore we do not control for
the level of technology as we have done in the within analysis. Thus, the gap captures
some of this effect. An increase in the gap occurs either by an increase in the peak yield,
which is of a permanent nature, or by a transitory decline in the performnance in a given
year. In the between-country regression the relative gap is measured as the country
average gap over the 21 year of the study period and as such it summarizes permanent
effects, rather than the transitory ones which dominated the within variations. Therefore,
a larger permanent increase in the gap seems to reflect larger peak yields and this explains
the positive regression coefficient of this variable in the between-country regression.
What countries find it difficult to stay closer to their own frontier? The answer can be
found by examining the correlation coefficients of the gap and the other variables given
in the appendix. The correlation coefficients are close to zero for the within deviations,
which is consistent with the interpretation that these deviations in the yield gap were
transitory. On the other hand, they are significantly negative for the country averages,
particularly with capital and fertilizers, and to a lesser degree with schooling and
development. It is the poorer countries that had on average a larger yield gap.
Prices
The test of the null hypothesis that the price block can be omitted from the
analysis is rejected. It appears however that the allocation of the effect to the individual
components is problematic. On the whole, the signs of the coefficients are in line with
expectations but the precision is low. The coefficient of relative prices is positive and
that of its variability is negative. The magnitude of the price elasticity is small, 0.04 in
the within regression. This indicates a small quantitative effect on agricultural
productivity, but note that this effect is obtained conditional on given inputs and on
technology. Thus, there is little scope for additional price effects. The fact that this
effect is at all detected is of prime importance. The channels for the price effect are the
level of inputs and the choice of technology, and these are represented by explanatory
variables. Therefore, when evaluating policies that alter the relative returns to economic
15
activity, it is important to realize that the legacy of past policies become enshrined in
cutrent stocks.
Two measures of market-risk, inflation and relative price volatility, dampen
agricultural production (as seen by the within estimates); however both effects are
quantitatively small. The coefficient of the measure of price volatility is negative, but it
is significantly different from zero only in the between-country regressions. The effect of
inflation is ambiguous in that it is negative and insignificant in the within regression, and
it is positive and significant in the between-country analysis.
Environment
The two environment variables introduced to the between-country regression,
have a positive and significant effect in the analysis with aggregate capital but the effect
of potential dry matter becomes unimportant when capital is disaggregated. This may
suggest that this measure is not sufficiently robust.
Interactions
As indicated by equation (4), for the aggregate production function to serve as an
appropriate second order approximation of technology, the coefficients of the inputs
should be made functions of the state variables. To estimate the coefficients, it is useful
to have data on factor shares which are used for estimating the dependence of the shares
on the state variables. (Mundlak, Cavallo and Domenech, 1989 for Argentina and
Coeymans and Mundlak, 1993 for Chile). However, we do not have data on factor
shares, which by itself is a serious deficiency of the international data sets related to
agriculture. Therefore, this approach is not feasible here. In principle, as an alternative,
we can add cross products of the variables to the regression. However, such variables, by
construction, are highly correlated with the variables which are already in the regression.
Moreover, even without such cross products, the degree of the explanation of the
regressions is rather high. Consequently, the scope for such an extension is limited,
restricting the number of variables that can be added. We report here the cross products
of peak yield with schooling, capital and labor (Table 7). Three coefficients of the cross
products are significant at an acceptable level-schooling in the within regression, capital
and labor in the between-country regressions. The mean elasticities differed only slightly
from the elasticities of the base regression but, nevertheless, the results are suggestive.
The negative coefficient on the schooling cross product indicates that an increase in peak
yield, or more generally in the level of technology, is schooling saving in the within
regression. Similarly in the between-country regression, an increase in peak yield is
capital saving and labor using. These results are reasonable, but we do not elaborate on
them further because of the limitations mentioned above. The main message from this
experiment is that there is a scope for investigating the nature of the dependence of the
elasticities on the state variables, but for this we need data on factor shares.
16
Robustness
In the tables we presented all the regression coefficients without eliminating those
coefficients which are insignificantly different from zero (no pretesting). Recall that in
the present model, the inputs and technology are determined jointly by the state variables,
so that the data reflect such joint changes. Thus, instead of eliminating individual
variables, we impose zero restrictions on linear combinations of the coefficients using the
method of principal components (PC) in Mundlak (1981). The results in Table 8 are the
PC versions of Table 3, with an imposition of constant returns to scale in the within
regression. The last line in the table shows the maximum number of zero restrictions that
could be imposed jointly at the 5 percent level of significance. For example, 4 such
restrictions could be imposed on the 10 coefficients of the within regression.' Thus, the
within and between-time regressions are being affected more than the between-country
regression where only two restrictions are imposed. In this block, the main effect is on
the coefficients in the price block.
In spite of the imposed restrictions, the main results of the analysis are
maintained. As before, there is a considerable difference between the within and between
regressions. The capital elasticity declined slightly in the within and between-time
regressions, but it is still high. In the within regression, the decline in the capital
elasticity is offset by an increase in the elasticities of labor, fertilizer, peak yield and
development. In the between-time regression, the important change occurs in the
coefficients of schooling and peak yields which become positive and significant. Also,
the labor coefficient is now larger but with a negative sign. This pattern reflects the
changes that took place over time in these variables (Table 2), a growth of schooling and
peak yield, and a decline of labor. It is thus consistent with the view that the between-
time regression traces the locus of production plans across technologies. However, this
result differs from that of the OLS regression and makes tentative our conclusion on the
role of schooling in the implementation of changes in the available technology. The
reason for this difference in results can be found in the high values of the correlation
coefficients of the between-time changes in capital, schooling, peak yield, and fertilizer
(Appendix table, last block). The OLS estimates placed the explanation with capital
whereas the PC procedure sorted it out and allocated some of the explanation to the other
variables as well.
However, the PC version of the disaggregated capital did not confirm the results
obtained for the aggregate capital as can be seen by comparing Tables 9 and 5. The PC
estimates in this case increased the importance of capital at the expense of the other
components.
To conclude, the most robust results are the relative importance of physical capital
and land in the within-country-time regression, capital in the between-time regression and
the irrelevance of land, the importance of capital and fertilizer in the between-country
regression.
11 The restrictions are imposed on the coefficients of the principal components rather than on the
coefficients of the original regressions.
17
Comparing to conventional analysis
Often, regressions are presented with either time or country dummies, which
amounts to running a within-time or within-country regression. The relationships
between such regressions and ours is established by combining equations (12) and (13)
with one similar to (11). This will show that w(i) is a matrix-weighted combination of
w(it), and b(t), and similarly, w(t) is a matrix-weighted combination of w(it) and b(i).
The implication is that allowing for only one effect results in regression coefficients
which reflect some between effects. The importance of the between component is
determined by its relative weight in the total sum of squares (see Table 2). Thus, the
regression coefficients obtained with time dummies reflect largely the between-country
regression because the relative weight of the between-country sum of squares is
dominant. Similarly, the regression coefficients obtained with country dummies reflect
the between-time regression, but not to the extent of the previous case because the
variations in the variables over time are much smaller than those across countries as can
be seen from Table 2. In any case, the mere fact that a regression is done with some
dummies does not guarantee that it identifies a stable function.
Table 10 presents within regressions for the specifications in Tables 3 and 5
respectively. Comparing the within-country regression in the second column in Table 10
to that of the within-country-time regression in Table 3, we see the impact of the
between-time regression. In a way of generalization, the between-time sum of squares of
output and input is of the order of magnitude of twice as much as that of the within-time-
country. The coefficient of capital increases from 0.37 to 0.53, and many of the
coefficients of the within-country regression are insignificantly different from zero
reflecting the influence of the between-time coefficients. This comparison provides a
framework for interpreting empirical results obtained under different specifications of
effects.
With this interpretation we can now compare our results to those presented in
Table 1. In this we ignore the first study by Bhattacharjee because it has no measure of
capital nor of state variables; thus it is not very comparable to the other studies. Most of
the studies are strictly cross-country and as such are comparable to the between-country
results. The similarity is in the low land elasticity, and also the sum of the elasticities of
machines and livestock is close in most cases to the value of 0.4 we obtained for the sum
of structures and equipment and livestock and orchards in the between-country
regression. This similarity is consistent with our interpretation that these studies describe
only the between-country changes; hence they provide a limited and incomplete picture
of the production process. In any case, they do not provide coefficients of a stable
production function and as such, do not provide the appropriate weights for growth
accounting, as they were intended to do.
It is always useful to check the results against all available information. The
Global Trade Analysis Project (GTAP) reported factor shares of land and labor in
agriculture for 1992 for 24 regions (Hertel, 1997). The data needed to compute factor
shares are not available for all countries. The more available data are on labor costs, and
18
these were used as a pivot to generate the other shares relying on "other sources" where
available (op. cit., p. 11 3). Applying the appropriate regional data to the 37 countries in
our study, we summarize this information in Figure 1 in terms of the empirical
distributions. The median values are 0.24 for land, 0.39 for labor and 0.39 for capital.12
Another source of information is the OECD which reports "compensation of employees"
by sectors. Computing labor shares from these series for 19 countries for the period
1970-90 (for 7 countries the period is somewhat shorter) yields a median value of 0. 19.
The labor share in these statistics is higher than the estimated elasticity from the within
regression, but nevertheless, these values are conveniently close to the within estimates
and are conspicuously far away from the between-country estimates. This seems to
provide independent support for our interpretation.
Summary and conclusions
This study is triggered by the desire to shed light on the role of capital in
agricultural production, a neglected topic due to lack of appropriate data. The
construction of the data on capital allowed us to advance the cross-country study of
production functions in what turns out to be an important direction. The analysis is based
on the premise that the production technology is heterogeneous and the implemented
technology is endogenous and determined jointly with the level of the unconstrained
inputs. Therefore, a change in the state variables affects both the technology and the
inputs, and consequently the production function is not identified. To overcome this
problem, we decompose the changes in productivity to three orthogonal components
caused by the fundamentally different processes underlying panel data and thereby gain
meaningful economic insight. The between-time process captures changes that are
induced by changes in the available technology (technical change). The between-country
process captures the changes that take place when the available technology is held
constant but other state variables differ across countries and account for their differences
in the implemented technology. Finally, the within-country-time process represents the
changes in outputs, inputs and state variables when the available technology is held
constant as well as the fundamental changes across countries and as such comes closest to
a production function. This framework also allows us to reinterpret results from earlier
studies of cross-country productivity in a new way.
The most striking result is the relative importance of capital. This result is quite
robust to various modifications of the model and to the disaggregation of capital to its
two components. Capital seems to account for about 40 percent of total output in the core
technology. This indicates that agricultural technology is cost-capital intensive compared
to non-agriculture. This result is further reinforced by the magnitude of the land
elasticity in the core technology and is at variance with the view that land is not an
important factor of production in modem agriculture. This view is based on an incorrect
12 The median values obtained using the unweighted regional data were similar (0.25 for land, 0.31 for
labor and 0.42 for capital).
13 We say that a technology is cost-capital intensive with respect to a reference technology if the factor
share of capital is larger than that of the reference technology.
19
reading of the data where no distinction is made between changes in technology and a
movement along a given production function. The sum of capital and land elasticities is
around 0.8 in various formulations, making it clear that agriculture should be more
sensitive than nonagriculture to changes in the cost of capital, and less to that of labor
(Mundlak, Cavallo and Domenech, 1989). The value we obtained for the sum is a bit
high compared to the literature. Consistent with our view of heterogeneous technology, it
is possible that a different choice of countries and time periods would lead to somewhat
different results. However, a sum of 0.8 for land and capital elasticities leaves a lot of
room for the conclusion on the importance of capital to remain intact.
The capital elasticity in the between-time regression is much higher than in the
within regression and this is consistent with the view that physical capital serves as a
constraint to agricultural growth. This is well illustrated by McGuirk and Mundlak
(1992) in the context of the Green Revolution. At the same time, the between-time
regression shows that the shift to more productive techniques is associated with a decline
in labor, which is an indication of the labor-saving technical change in agriculture. This
is consistent with the observed slight decline of labor over time (Table 2) while output
grew at a brisk pace. This is not news, but it is emphasized here because it comes out of
an integral view of the process which separates between the core technology and the
changes that took place over time and between countries. These results highlight the
importance of capital in agricultural production, an attribute critical in the understanding
of agricultural development and its dependence on the economic environment.
The introduction of the appropriate state variables to account for technology,
prices and physical environment produced a production function that displays constant
returns to scale and thus avoided the pitfalls of previous studies and the misguided
conclusions that followed.
The statistical framework provides an explanation for the unstable results
observed in production functions derived from panel data. Statistically, the results
depend on how the data are projected. Underlying this is the fact that comparisons
between units, over time or of deviations from unit-means or time-means all describe
different processes. This is based on theory, but has an intuitive appeal as well. In the
case at hand, the spread in productivity among countries is a different economic
phenomenon or process from the spread in productivity for a country through time. In
turn, the factors explaining the spread will differ. Panel data measures a combination of
these economic phenomena-a fact which should be recognized explicitly in the
modeling approach.
While we are specifically dealing with these issues in the context of agricultural
production, the arguments probably extend to other applications as well. The
decomposition of the sum of squares to their canonical components most likely will tell
the importance of the various processes. It is however important to emphasize that even
if one of the components carries only a small weight in the sum of squares, it can still
convey a great deal of meaningful information, as we have demonstrated in the case of
the within-country-time regression.
20
To sum up, we can now return to the key topics listed at the beginning of the
paper. The contribution of inputs to growth should be judged by their contribution to
output under a constant technology, attributing the rest of the growth to technical change.
After all these years of intensive work on production functions, there is no hard evidence
that estimated elasticities do a better job than the factor shares as were originally used by
Solow (1957). In terms of our work here, the within estimates come closest to the little
evidence we have on factor shares. Also, it is clear that the weights obtained from
between regressions by Hayami and Ruttan (1970, 1985), and earlier by Griliches (1963a,
1963b), give a distorted picture. We have pointed above to the sensitivity of the growth
calculations to the weight of land, and this is where the between results erred the most.
Not independently, our results indicate no evidence of increasing returns to scale. The
increasing returns to scale inflated the contribution of the inputs and reduced the role of
the residual technical change in the growth calculations ala Griliches, Hayami and Ruttan.
Our results support the view that agriculture is cost-capital-intensive as compared
to nonagriculture. We provide estimates of factors' productivity that can be compared to
the factors' price. Comparing our results to the factor shares, it seems that on the whole
there is a surprising agreement.
Finally, our results have important implications for policy. First, we can say that
agricultural capital is directly an important determinant of agricultural production. This
is especially significant, since land, another important determinant of production, varies
little over time. Moreover, agricultural capital is also important in closing the gap
between available and applied technologies. Therefore policies facilitating access to
agricultural capital will facilitate growth, provided the capital is used efficiently. This
implies that the overall economic environment must be conducive to the efficient use of
capital. Second, we find that prices have little immediate and direct impact on
agricultural growth, beyond their impact through inputs and the choice of technology.
Consequently, past policies that distort the relative returns to economic activity leave a
legacy enshrined in current stocks that may respond slowly to policy reforms.
21
Annex l: Description of Variables
Output - agricultural GDP in 1990 US dollars. Original source of the GDP data: National
Accounts of the World Bank, the UN and the OECD, the International Financial Statistics
of the IMF and various country sources.
Structures and equipment - stock of fixed agricultural capital (structures and equipment)
in 1990 US dollars. The mapping from fixed investment to fixed capital follows the
methodology of Ball, Bureau, Butault and Witzke (1993). The capital stock is
represented as a weighted sum of past investments where the sequence of relative
efficiencies of capital of different ages serves as the weights. The following function of
physical depreciation is chosen to describe the relationship between the efficiency of an
asset and its age:
(L - t)
SI = IJ) OL,
where S is the relative efficiency of an asset with a lifetime of L at age t. ,8 is the decay
parameter. If 0<,8<1, the function is concave, that is, it exhibits gradual losses in
efficiency in the early life of the asset and more rapid losses as it ages (accelerating
physical depreciation). A truncated normal distribution of service lives of capital around
a mean is assumed. For the construction of the agricultural capital stocks, the mean
lifetime of an asset was assumed to be 20 years with a standard deviation of 8. The decay
parameter was set at 0.7. The capital stock in any given year is the sum of the relative
efficiency for that year of all past investments. This method requires a certain amount of
extrapolation of the investment data. The series (in logs) of GDP and the ratio of
investment to GDP are backcasted to 1913 using OLS regressions of the data series
against time. The extrapolated investment series is calculated from these. Original
source of investment data: National Accounts of the UN, the World Bank and the OECD
and various country sources.
Livestock and orchards - livestock and orchards in 1990 US dollars. Livestock: Data on
trade volume and trade quantities of livestock are readily available at the regional level.
By dividing volume by quantity, regional trade prices were obtained. Quantities of
livestock in each country are valued at the corresponding trade prices for the region.
Orchards: Using data on the value of production and harvested land area for major tree
crops, an indirect measure of the value of orchards is constructed. The value of a tree in
any period is the discounted stream of future revenues that it will yield through
production, less production costs. The net revenue associated with each acre of tree crops
is imputed forward in time (with discounting) and, when aggregated, taken as the value of
capital in the formn of trees. To obtain net revenue, profits are assumed to be 20% of
revenues. Additionally, the simplifying assumption is made that at any point in time the
average tree is halfway through with its assumed lifetime. Original source of production
data: FAO Production data set. Original source of trade data: FAO Trade data set.
22
Capital - total stock of agricultural capital in 1990 US dollars. Total agricultural capital
is the sum of the fixed capital stock, livestock and orchards. (Capital = Structures and
equipment + livestock and orchards). Original source of investment data: National
Accounts of the UN, the World Bank and the OECD and various country sources.
Land - agricultural area (arable and permanent cropland and permanent pastures) in
hectares. Original source: FAO Fertilizer data set.
Labor - agricultural labor force. Labor is defined as the economically active population.
The data are reported for various sectors as well as for the overall economy for every ten
years (1950-90). The data for other years are estimated by using straight-line
interpolations of the total labor series and the ratio of agricultural labor to total labor, and
calculating agricultural labor from these. Original source: ILO data set.
Fertilizer - total fertilizer (nitrogenous, phosphate and potash) consumption in metric
tons. Original source: FAO Fertilizer data set.
Schooling - economy-wide human capital proxied by the mean school years of education
of the total labor force. This data series was constructed by Nehru, Swanson and Dubey
(1993) from enrollment data using the perpetual inventory method. "The average
education stock measures the mean school years of education of the working age
population (defined as the population between the ages of 15 and 64), and is the sum of
primary, secondary, and post-secondary average education stock.. .The series are built
from enrollment data using the perpetual inventory method, adjusted for mortality.
Estimates are corrected for grade repetition among school-goers and country-specific
dropout rates for primary and secondary students." (Op. cit., p.8). This data series is
available up to 1987. The data for 1988-90 are forecast by fitting the data using an OLS
regression of human capital on time. Original source: Nehru, Swanson and Dubey
(1993).
Peak yield - country-specific index of peak yield to measure available agricultural
technology. Compute yields of each commodity for each country in each year by
dividing the production of the commodity in metric tons by the hectares of land used in
the commodity. Find the maximum of past yields of each commodity for each country in
each year. Construct Paasche indices of the peak yields for each country in each year by
multiplying the peak commodity yields by the area of land used in the commodity and
then summing over the commodities, and dividing by the peak commodity yields in the
base year (1990) multiplied by this year's area of land in the commodity, summed over
all the commodities. Original source on commodity production and land usage: FAO
Production data set.
NA-peak - peak of nonagricultural productivity to measure available general technology.
Calculated as the maximum of past ratios of nonagricultural GDP in 1990 US dollars to
the nonagricultural labor force. Nonagricultural GDP is the difference between total GDP
and agricultural GDP, nonagricultural labor is the difference between total labor force and
agricultural labor. Original source of the GDP data: National Accounts of the UN, the
World Bank and the OECD, the International Financial Statistics of the IMF and various
country sources.
23
Development - development indicator. Calculated as the ratio of the country's total GDP
per capita in US dollars to total US GDP per capita. Original source of the GDP data:
National Accounts of the UN, the World Bank and the OECD, the International Financial
Statistics of the IMF and various country sources.
Yield gap - relative gap between available and implemented technology. Calculate the
difference between the peak commodity yield (maximum of past commodity yields) and
the actual commodity yield of each commodity for each country in each year. Construct
an index of the gap for each country in each year by multiplying the gap for each
commodity by the area of land used in the commodity and then summing over the
commodities, and dividing by the peak commodity yields multiplied by the area of land
in the commodity, summed over all the commodities. Original source on commodity
production and land usage: FAO Production data set.
Relative prices - relative sectoral prices. Calculated as the ratio of the agricultural GDP
deflator to the manufacturing GDP deflator, lagged one period. Original source of the
GDP data: National Accounts of the UN, the World Bank and the OECD, the
International Financial Statistics of the IMF and various country sources.
Variability in prices - fluctuations in the relative sectoral prices. Calculated as a moving
standard deviation of the ratio of the agricultural GDP deflator to the manufacturing GDP
deflator from the three previous periods. Original source of the GDP data: National
Accounts of the UN, the World Bank and the OECD, the International Financial Statistics
of the IMF and various country sources.
Inflation - inflation (or deflation). Calculated as the rate of change in the total GDP
deflator. Original source of the GDP data: National Accounts of the UN, the World Bank
and the OECD, the International Financial Statistics of the IMF and various country
sources.
PDM- potential dry matter production. Output in kilograms per hectare per year in
roots, stems, leaves, flowers and fruits that can be achieved if precipitation and soil
conditions are optimal. Original source: Buringh, van Heemst, and Staring (1979).
FWD - factor of water deficit. Measured by the ratio of actual transpiration to potential
transpiration. Original source: Buringh, van Heemst, and Staring (1979).
The following variables are expressed in natural logs: output, capital, structures
and equipment, livestock and orchards, land, labor, fertilizer, schooling and NA-peak.
The following variables were converted from nominal local currencies to nominal
US dollars using exchange rates obtained from the International Financial Statistics of the
IMF: output, capital, structures and equipment, livestock and orchards, NA-peak and
development.
The following countries are included in the sample: Australia, Austria, Canada,
Chile, Colombia, Costa Rica, Cyprus, Denmark, Egypt, Finland, France, Great Britain,
Greece, Honduras, Indonesia, India, Italy, Jamaica, Japan, Kenya, Korea, Sri Lanka,
Morocco, Mauritius, Malawi, Netherlands, Norway, Pakistan, Peru, Philippines, El
Salvador, Sweden, Tunisia, Turkey, Tanzania, Uruguay and the United States.
24
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27
TABLE 1 -- COMPARISON OF RESULTS
Bhattacharjee Hayami & Evenson & Yamada & Antle Hayami & Nguyen Evenson & Mundlak &
Ruttan Kislev Ruttan Ruttan Kislev Hellinghausen
Date of study 1955 1970 1975 1980 1983 1970 1979 1975 1982
Sample:
Number of countries 22 37 36 41 43 36 40* 36 58
Time period 1949 1960 1955, 60, 1970 1965 1955,60,65 1955,60,65 1955,60, 1960, 65,
65, 68 70, 75 65, 68 70, 75
Estimation method OLS OLS OLS OLS PCR OLS OLS OLS PCR
Data specification S; N M; N M; N M; N S; N M; PW M; N M; N M; N
Fixed effects included year year country country#
Elasticities
Structures&equipment/Machinery/Tractors 0.12 0.10 0.11 0.11 0.14 0.06 0.07
Livestock & orchards/Livestock 0.23 0.30 0.23 0.14** 0.28 0.33 0.35 0.19
Land 0.42 0.08** 0.04** 0.02** 0.16 0.07 0.02** 0.14 0.16
Labor 0.28 0.41 0.23 0.33 0.38 0.40 0.39 0.03** 0.46
Fertilizer 0.29 0.12 0.10 0.24 0.07** 0.14 0.10 0.09 0.11
Irrigation 0.01
Schooling/General education 0.32** 0.08** 0.25** 0.24 0.10**
Technical education 0.14 0.04 0.14 0.12 0.17 0.00**
Research and extension 0.14 0.17 0.07
Infrastructure 0.21
Policy variable
Peak yield index
Development
sum of input elasticities 0.99 0.96 0.77 0.93 0.75 1.00*** 0.98 0.67 1.00***
* sample is not balanced, n= 183 for Nguyen study
** not significant at P=.05 for one-tailed test
*** homogeneity constraint imposed
# Country effects on slopes and intercept
OLS and PCR are ordinary least squares and principal components regressions.
S and M represent single year observations and multi-year averages.
PW represents per-worker averages of national aggregated data, N represents national aggregates.
28
TABLE 2 -- GROWTH RATES AND THE DECOMPOSITION OF THE SUM OF SQUARES
Average Annual Decomposition of the Sum of Squares
Growth Rate (expressed as a percentage of total)
Variable (%) SSB(t) SSB(i) SSW(it)
Output:
GDP 3.82 2.49 96.17 1.34
Inputs:
Capital 4.25 2.67 95.77 1.56
Structures & equipment 5.42 3.00 95.24 1.76
Livestock & orchards 2.17 0.96 97.83 1.21
Land 0.12 0.00 99.95 0.05
Labor -0.04 0.01 99.35 0.64
Fertilizer 3.04 1.14 96.76 2.09
Technology:
Schooling 1.80 4.14 93.48 2.38
Peak yield 1.90 58.10 24.64 17.27
Development -0.29 1.41 94.18 4.41
Yield gap 8.97 30.91 60.12
Prices:
Relative prices -0.30 3.01 41.98 55.00
Price variability 2.48 15.78 81.75
Inflation 2.38 10.65 86.97
Per Labor Output and Inputs:
GDP 2.67 95.00 2.33
Capital 2.14 95.46 2.40
Structures & equipment 2.17 95.86 1.98
Livestock & orchards 1.14 96.78 2.07
Land 0.01 99.41 0.58
Fertilizer 0.98 97.78 1.24
29
TABLE 3 -- BASE MODEL
Within
time and country Between time Between country
Variable Estimate t-score Estimate t-score Estimate t-score
Inputs:
Capital 0.37 6.90 1.03 6.01 0.34 13.13
Land 0.47 3.78 -0.03 -2.82
Labor 0.08 -0.16 -0.16 0.26 13.67
Fertilizer 0.08 1.53 0.14 0.33 0.43 21.91
Technology:
Schooling 0.09 0.55 -0.28 -0.06 0.02 0.52
Peak yield 0.83 3.80 -0.32 -0.07 0.06 4.19
Development 0.52 3.36 -0.21 -0.33 0.31 2.97
Prices:
Relative prices 0.04 1.78 0.02 0.09 0.01 1.95
Price variability -0.03 -0.97 -0.07 -0.26 -0.08 -2.82
Inflation -0.00 -0.75 0.04 0.71 0.07 4.25
Environmental:
Potential dry matter 0.16 2.68
Water availability 0.44 7.96
Note: R-square for 777 obs. .9696
30
TABLE 4 -- STATISTICAL TESTS
Tests of significance of blocks of variables
R-square k h F-statistic 5% critical value outcome
Full regression 0.9696 31
Null hypothesis is that the following block is not significant.
within time & country 0.9643 22 9 14.45 1.89 reject
between time 0.9448 22 9 67.62 1.89 reject
between country 0.0302 19 12 1921.03 1.77 reject
technology block 0.9676 22 9 5.45 1.89 reject
price block 0.9685 22 9 3.00 1.89 reject
environmental block 0.9670 29 2 31.90 3.01 reject
Number of observations, n, is 777.
k represents the number of parameters estimated.
h represents the number of constraints imposed by omission of a block of variables.
Test of constant returns to scale for within-time and country analysis
Input Estimate
Capital 0.36
Land 0.42
Labor 0.08
Fertilizer 0.08
Sum 0.94
F-statistic 0.04
5% critical value 3.84
The null hypothesis of constant returns to scale is not rejected.
31
TABLE 5-- ALTERNATIVE MODEL, DISAGGREGATED CAPITAL
Within
time and country Between time Between country
Variable Estimate t-score Estimate t-score Estimate t-score
Inputs:
Structures & equipment 0.29 6.51 0.58 2.95 0.11 5.62
Livestock & orchards 0.13 2.09 0.44 1.81 0.29 9.04
Land 0.44 3.62 -0.06 -4.35
Labor 0.10 -0.58 -0.55 0.22 11.05
Fertilizer 0.04 0.79 0.09 0.22 0.42 20.41
Technology:
Schooling -0.07 -0.43 1.08 0.26 0.05 1.07
Peak yield 0.78 3.60 -1.64 -0.33 0.01 0.69
Development 0.46 3.01 -0.02 -0.02 0.28 2.73
Prices:
Relative prices 0.04 1.78 0.01 0.03 0.05 5.91
Price variability -0.02 -0.76 -0.12 -0.42 -0.15 -4.87
Inflation -0.00 -0.84 0.01 0.22 0.11 6.15
Environmental:
Potential dry matter -0.03 -0.49
Water availability 0.55 9.41
Note: R-square for 777 obs. .9703
32
TABLE 6-- ALTERNATIVE MODEL, INCLUDES YIELD GAP
Within
time and country Between time Between country
Variable Estimate t-score Estimate t-score Estimate t-score
Inputs:
Capital 0.37 7.13 1.03 6.02 0.39 14.04
Land 0.44 3.55 -0.05 -3.85
Labor 0.12 -0.18 -0.18 0.24 12.52
Fertilizer 0.07 1.44 0.17 0.38 0.44 22.66
Technology:
Schooling 0.11 0.65 0.06 0.01 0.02 0.57
Peak yield 0.93 4.24 -0.82 -0.15 0.07 4.91
Development 0.54 3.55 -0.29 -0.39 0.20 1.95
Yield gap -0.42 -2.90 0.17 0.20 1.24 4.39
Prices:
Relative prices 0.04 1.68 0.02 0.12 0.01 2.24
Price variability -0.02 -0.74 -0.05 -0.20 -0.05 -1.92
Inflation -0.00 -0.63 0.05 0.73 0.06 4.04
Environmental:
Potential dry matter 0.18 3.09
Water availability 0.46 8.45
Note: R-square for 777 obs. = .9707
33
TABLE 7-- ALTERNATIVE MODEL, INCLUDES CROSS PRODUCTS
Within
time and country Between time Between country
Variable Estimate t-score Estimate t-score Estimate t-score
Inputs:
Capital 0.32 3.54 0.24 0.12 0.42 11.25
Land 0.51 3.81 -0.03 -2.38
Labor 0.09 -2.87 -0.54 0.19 5.99
Fertilizer 0.08 1.62 -0.07 -0.12 0.45 15.46
Technology:
Schooling 0.36 1.61 6.39 0.39 -0.05 -0.52
Peakyield 1.18 1.61 4.92 0.08 0.65 2.38
Development 0.49 3.16 -0.36 -0.36 0.21 1.63
Peak yield*schooling -0.56 -2.10 -6.64 -0.44 0.04 1.05
Peak yield*capital 0.06 0.63 0.84 0.37 -0.05 -3.82
Peak yield*labor -0.06 -0.98 -0.24 0.04 2.31
Prices:
Relative prices 0.04 1.71 0.05 0.23 0.01 0.99
Price variability -0.03 -0.92 -0.12 -0.41 -0.09 -3.18
Inflation -0.00 -0.64 -0.01 -0.06 0.06 3.82
Environmental:
Potential dry matter 0.16 2.39
Water availability 0.46 7.25
Note: R-square for 777 obs. = .9704
Mean Elasticities
Capital 0.37 0.96 0.32
Labor 0.04 -3.72 0.26
Schooling -0.12 0.66 0.03
Peak yield 0.73 -1.24 0.02
34
TABLE 8 -- PRINCIPAL COMPONENTS ANALYSIS OF BASE MODEL
Within
time and country Between time Between country
Variable Estimate t-score Estimate t-score Estimate t-score
Inputs:
Capital 0.26 17.25 0.87 8.10 0.34 29.54
Land 0.46 15.85 -0.03 -2.94
Labor 0.16 -0.70 -1.71 0.26 20.59
Fertilizer 0.12 2.54 -0.33 -3.26 0.43 22.74
Technology:
Schooling -0.08 -1.27 0.32 8.83 0.02 0.52
Peak yield 0.99 6.38 0.36 8.05 0.06 5.55
Development 0.87 16.10 -0.02 -0.07 0.31 4.91
Prices:
Relative prices 0.03 2.34 -0.01 -0.07 0.01 2.45
Price variability -0.01 -0.40 0.03 0.13 -0.08 -3.28
Inflation -0.00 -0.92 -0.01 -0.36 0.06 4.05
Environmental:
Potential dry matter 0.15 2.59
Water availability 0.44 8.44
Number of restrictions 4 4 2
35
TABLE 9 -- PRINCIPAL COMPONENTS ANALYSIS OF DISAGGREGATED CAPITAL
MODEL
Within
time and country Between time Between country
Variable Estimate t-score Estimate t-score Estimate t-score
Inputs:
Structures & equipment 0.25 8.56 0.25 10.43 0.12 6.60
Livestock & orchards 0.19 4.79 0.73 7.20 0.24 25.89
Land 0.47 9.28 -0.05 -3.93
Labor 0.05 -1.75 -4.27 0.25 17.35
Fertilizer 0.04 0.84 0.00 0.03 0.42 20.73
Technology:
Schooling 0.07 0.75 0.26 7.87 0.04 0.94
Peak yield 0.61 3.67 0.32 8.81 0.03 2.83
Development 0.51 7.49 -0.68 -4.01 0.37 4.15
Prices:
Relative prices 0.02 1.38 0.08 0.55 0.04 7.12
Price variability 0.00 0.11 -0.03 -0.12 -0.12 -4.55
Inflation -0.01 -8.05 0.04 2.45 0.10 5.93
Environmental:
Potential dry matter 0.02 0.34
Water availability 0.53 9.12
Number of restrictions 5 6 1
36
TABLE 10 -- WITHIN-TIME AND WITHIN-COUNTRY ANALYSES
Aggregate Capital Disaggregated Capital
Within time Within country Within time Within country
Variable Estimate t-score Estimate t-score Estimate t-score Estimate t-score
Inputs:
Capital 0.44 19.04 0.53 11.51
Structures & equipment 0.18 10.82 0.38 9.21
Livestock & orchards 0.23 10.48 0.21 3.50
Land -0.04 -4.08 0.51 1.81 -0.06 -4.81 0.57 2.06
Labor 0.31 19.37 0.13 1.16 0.35 21.11 0.08 0.76
Fertilizer 0.29 16.70 0.03 0.68 0.28 14.65 0.00 0.07
Technology:
Schooling 0.15 3.83 0.07 0.42 0.15 3.6g -0.10 -0.58
Peak yield 0.37 2.42 0.82 4.24 0.32 1.94 0.84 4.41
Development 0.34 4.45 0.21 1.60 0.66 8.80 0.22 1.69
Prices:
Relative prices 0.06 2.71 0.03 1.05 0.04 1.80 0.02 1.01
Price variability -0.05 -1.71 -0.01 -0.50 -0.05 -1.47 -0.01 -0.36
Inflation -0.01 -1.30 -0.00 -1.07 -0.00 -0.96 -0.00 -0.98
37
Factor shares in agriculture
0.9
0.8- r
0.7
Qc7-0.6 - land
, 0.5- - u-+labor
capital
-g 0.4 -___-+ +-+median
S0.3
0.2- -
0.1
0
CDOC-) C\ C.D CC C \2 co C-Q CL
O O R -'2CD CD C'D C t CZ TZ CC C.O
shares
38
APPENDIX - CORRELATION MATRICES OF VARIABLES
Within-time and country variables
Capital S&E L&O Land Labor Fert School Peak Dev Gap Price Var Inf
Capital 1.0000 0.7645 0.6685 -0.2508 -0.3368 -0.0225 -0.1091 0.0183 0.4650 0.0340 0.1360 -0.0100 -0.0051
Structures and equipment 1.0000 0.3153 -0.2194 -0.2493 0.0790 0.0727 0.0968 0.4187 0.0607 0.1086 -0.0444 0.0301
Livestock& orchards 1.0000 0.0508 0.1458 0.2369 0.1160 0.0820 0.1172 0.0799 0.1478 0.0278 -0.0949
Land 1.0000 0.4811 0.3184 0.2852 0.0445 -0.2464 0.0958 0.0640 0.1247 -0.0078
Labor 1.0000 0.5475 0.6058 0.0780 -0.4282 0.1370 0.0322 0.0260 0.0746
Fertilizer 1.0000 0.4224 0.0791 -0.1957 0.0468 0.1203 -0.0057 -0.0213
Schooling 1.0000 0.3847 -0.2472 0.1483 0.0771 0.0185 0.0490
Peak yield 1.0000 -0.0436 0.1736 0.1362 0.0447 -0.0921
Development 1.0000 0.0057 0.0275 -0.0207 -0.0575
Yield gap 1.0000 0.0167 0.0767 0.0573
Relative prices 1.0000 0.5050 -0.1696
Price variability 1.0000 0.0556
Inflation 1.0000
Between-country
variables
Capital S&E L&O Land Labor Fert School Peak Dev Gap Price Var Inf PDM FWD
Capital 1.0000 0.9478 0.8776 0.6892 0.4252 0.9295 0.2629 -0.0748 0.5687 -0.5241 -0.0311 -0.1920 -0.0921 -0.4006 0.1300
Structures and equipment 1.0000 0.6998 0.5113 0.2340 0.9075 0.4382 -0.1904 0.6977 -0.5353 -0.0406 -0.2096 -0.0736 -0.5573 0.1667
Livestock & orchards 1.0000 0.8588 0.6404 0.8001 -0.0622 0.0852 0.2229 -0.4211 -0.0716 -0.0946 -0.0524 -0.0040 -0.0801
Land 1.0000 0.5777 0.6049 -0.2126 0.0290 0.1107 -0.1901 -0.0605 -0.0891 0.1345 0.1484 -0.2284
Labor 1.0000 0.4207 -0.5609 0.1434 -0.4083 -0.1180 0.3384 -0.2066 0.0294 0.3917 -0.3126
Fertilizer 1.0000 0.3016 -0.2128 0.5433 -0.4949 -0.0326 -0.1952 -0.1303 -0.3876 0.1028
Schooling 1.0000 -0.2815 0.7290 -0.2788 -0.3559 0.0693 -0.0103 -0.6327 0.5629
Peak yield 1.0000 -0.3339 -0.1620 0.3774 -0.0295 -0.1991 0.1934 -0.0610
Development 1.0000 -0.2695 -0.2785 -0.1345 -0.1721 -0.8191 0.4957
Yield gap 1.0000 -0.0707 -0.1254 0.1648 0.2261 -0.1611
Relative prices 1.0000 -0.1122 -0.3581 0.1794 -0.2631
Price variability 1.0000 0.2480 0.1943 0.0576
Inflation 1.0000 0.1646 -0.1156
PDM 1.0000 -0.5812
FWD 1.0000
39
APPENDIX -- CORRELATION MATRICES OF VARIABLES (Continued)
Between-time variables
Capital S&E L&O Labor Fert School Peak Dev Gap Price Var Inf
Capital 1.0000 0.9950 0.9694 -0.0117 0.8797 0.9328 0.9343 0.3586 0.7104 -0.4599 0.1404 0.3356
Structures and equipment 1.0000 0.9460 -0.0265 0.8787 0.9333 0.9363 0.3337 0.6902 -0.4584 0.1443 0.3490
Livestock & orchards 1.0000 0.0901 0.7925 0.8512 0.8525 0.3305 0.6862 -0.4232 0.1882 0.2460
Labor 1.0000 -0.0648 -0.0847 -0.0809 0.0837 0.2056 0.4814 0.4866 -0.5916
Fertilizer 1.0000 0.9803 0.9796 0.4538 0.7869 -0.4501 -0.0408 0.3765
Schooling 1.0000 0.9992 0.4344 0.7804 -0.4878 -0.0270 0.4416
Peak yield 1.0000 0.4064 0.7844 -0.4969 -0.0335 0.4254
Development 1.0000 0.3980 0.2995 0.3867 0.4636
Yield gap 1.0000 -0.2585 -0.0143 0.0787
Relative prices 1.0000 0.5881 -0.2840
Price variability 1.0000 -0.1308
Inflation 1.0000
40
Policy Research Working Paper Series
Contact
Title Author Date for paper
WPS1801 Regional Integration as Diplomacy Maurice Schiff August 1997 J. Ngaine
L. Alan Winters 37947
WPS1 802 Are There Synergies Between Harry Huizinga August 1997 P. Sintim-Aboagye
World Bank Partiai Credit 38526
Guarantees and Private Lending?
WPS1 803 Fiscal Adjustments in Transition Barbara Fakin August 1997 M. Jandu
Economies: Social Transfers and the Alain de Crombrugghe 33103
Efficiency of Public Spending: A
Comparison with OECD Countries
WPS1804 Financial Sector Adjustment Lending: Robert J. Cull August 1997 P. Sintim-Aboagye
A Mid-Course Analysis 37644
WPS1805 Regional Economic Integration and Junichi Goto August 1997 G. llogon
Agricultural Trade 33732
WPS1806 An International Statistical Survey Saivatore Schiavo-Campo August 1997 M. Guevara
of Government Empioyment and Giulio de Tommaso 32959
Wages Amitabah Mukherjee
WPS1807 The Ghosts of Financing Gap: William Easterly August 1997 K. Labrie
How the Harrod-Domar Growth 31001
Model Still Haunts Development
Economics
WPS1808 Economic Transition and the Francisco H. G. Ferreira August 1997 M. Geller
Distributions of Income and Wealth 31393
WPS1809 Institutions in Transition: Reliability Aymo Brunetti August 1997 M. Geller
of Rules and Economic Performance Gregory Kisunko 31393
in Former Socialist Countries Beatrice Weder
WPS1810 Inspections and Emissions in India: Sheoli Pargal August 1997 E. Krapf
Puzzling Survey Evidence about Muthukumara Mani 80513
Mainul Huq
WPS1811 Agricultural Development: issues, Yair Mundlak August 1997 P. Kokila
Evidence, and Consequences Donald F. Larson 33716
Al Crego
WPS1812 Managing Guarantee programs in Michael Klein August 1997 S. Vivas
Support of !nfrastructure Investment 82809
WPS1813 Tackling Healtn Transition in China Shaikh !. Hossain August 1997 C. Anbiah
81275
WPS1814 Making Education in China Equitable Shaikh i. Hossain August 1997 C. Anbiah
and Efficient 81275
Policy Research Working Paper Series
Contact
Title Author Date for paper
WPS1815 Unfair Trade? Empirical Evidence in Jacques Morisset August 1997 N. Busjeet
World Commodity Markets Over 33997
the Past 25 Years
WPS1816 Returns to Regionalism: An Raquel Fernandez August 1997 J. Ngaine
Evaluation of Nontraditional Gains 37947
from Regional Trade Agreements
WPS1 817 Should Core Labor Standards Be Keith E. Maskus August 1997 J. Ngaine
-Imposed through International Trade 37947
Policy?
WPS1818 What Affects the Russian Regional Lev Freinkman August 1997 N. Campos
Governments' Propensity to Michael Haney 38541
Subsidize?
WPS1819 The Argentine Pension Reform and Dimitri Vittas August 1997 P. Infante
Its Relevance for Eastern Europe 37642
WPS1 820 Private Pension Funds in Argentina's Dimitri Vittas August 1997 P. Infante
New Integrated Pension System 37642
WPS1821 The 'IPO-Plus": A New Approach to Itzhak Goldberg August 1997 1. Goldberg
Privatization Gregory Jedrzejczak 36289
Michael Fuchs
WPS1 822 Intergovernmental Fiscal Transfers Jun Ma September 1997 C. ima
in Nine Countries: Lessons for 35856
Developing Countries
WPS1823 Antidumping in Law and Practice Raj Krishna September 1997 A. Bobbio
81518
WPS1824 Winners and Losers from Utility Omar Chisari September 1997 T. Malone
Privatization in Argentina: Lessons Antonio Estache 37198
from a General Equilibrium Model Carlos Romero
WPSI 825 Current Accounts in Debtor and Aart Kraay September 1997 R. Martin
Creditor Countries Jaume Ventura 39026
WPS1826 Standards and Conformity Sherry M. Stephenson September 1997 M. Patena
Assessment as Nontariff 39515
Barriers to Trade