Hayami and Ruttan (1971, 1985) check for any substantial differences between
aggregate production function estimates and micro production function estimates.
They estimate comparable production functions at the aggregate, per capita and
per farm levels. Comparing aggregate and per farm results, they conclude, “The
results from the two sets of data are not sufficiently different to lead to different
inferences regarding the agricultural production structures among countries”
(p. 899). These equations are juxtaposed in Table 2, along with other estimates
(including per hectare comparisons) by Evenson and Kislev (1975), Nguyen (1979),
and Yamada and Ruttan (1980). Judging by these estimates, Hayami and Ruttan’s
remarks made in 1971 still seem to be appropriate. The two latest studies by Kawagoe,
Hayami and Ruttan and by Lau and Yotopolous have not estimated aggregate
production functions; rather, these studies have deflated the production functions
by the number of farms for the purpose of allowing for scale economies
Table 3 lists some of the cross-sectional OLS estimates that use similar methodologies.
The range of the estimated elasticities is greatest for labor and land.
Labor has consistently displayed very low standard errors (high t-ratios), consistent
with the expectation of its importance in production. The variation in its estimated
coefficients may be partly due to the different years of estimation, improvements
in the quality of data, or different sample sizes. Land has continued to be one of
the most troubling coefficients estimated in these studies. For example, in the
Yamada and Ruttan (1980) study, the land coefficient was relatively small and
statistically insignificant. G. Edward Schuh, commenting in a conference meeting,
thought this problem to be a very serious error in the Yamada and Ruttan study,
given a priori considerations and the implications of its measurement and estimate.
Sometimes the land coefficient has even been negative (for example, Nguyen’s
1979 estimate), implying that a unit increase in land leads to a decrease in output
General education, despite numerous measurements, has continually displayed
high standard errors (low t-statistics). Studies by Evenson and Kislev (1975)
and Lau and Yotopolous drop general education from their final estimates. In the
two studies that have used research, both Evenson and Kislev and Antle notice the
tendency for fertilizer to become statistically insignificant when research is
included. Evenson and Kislev think that ferilizer probably is collinear with research, since fertilizer use increased with the Green Revolution. In the Kawagoe,
Hayami and Ruttan study, the dummy variable for LDCs are highly negative and
statistically significant (-0.29, -0.39, and -0.61 for 1960, 1970 and 1980, respectively),
implying that LDCs are substantially less productive than developed
countries.
Comparable OLS and PCR estimates by Antle and Kawagoe, Hayami and
Ruttan are shown in Table 4.2 Although the PCR estimator can be a restricted
estimator and therefore may involve some coefficient bias (in exchange for less
error variance), generally speaking the estimated coefficients have not been very
different when PCR has been used. Exceptions include for Kawagoe, Hayami and
Ruttan: livestock, 1960 (0.31 to 0.16); general education, 1970 and 1980 (0.32
to 0.21, and 0.51 to 0.35, respectively); and the LDC dummy variables, 1960 and
1980 (-0.29 to -0.14, and -0.61 to -0.30, respectively).
Comparable estimates of the pooled cross-sectional, time series data are
grouped together and are shown in Table 5. An important point is that most of the
time dummy variables have been negative (although statistically insignificant),
suggesting that productivity has worsened over time.
Antle; Kawagoe, Hayami and Ruttan; and Lau and Yotopolous have estimated
equations for subsample observations. Antle’s cross-sectional LDC results for 1965
(PCR) showed land (0.44) and infrastructure (0.27) to be relatively important in
explaining intercountry production variation (Table 4). In the Kawagoe, Hayami
and Ruttan study, the estimated coefficients (OLS) for LDCs, which were slightly
different from the overall sample, include general education (0.41) and the time
dummy variables (-0.22 and -0.43 for 1970 and 1980, respectively). The coefficients,
which were noticeably different in the DC subsample compared with the
overall sample, include labor (0.71), machinery (0.18), general education (-0.17),
and the time dummy variables (0.11 and 0.17 for 1970 and 1980, respectively).
Lau and Yotopolous’ first-difference equations are shown in Table 5 but are not
comparable, because they do not estimate the constant term. Wong’s (1986) estimates
for nine socialist countries, though not a subsample, are shown in Table 4.
Most of Wong’s coefficients seem reasonable, although it may be inappropriate to
compare such estimates with market-oriented economies, given the completely
different assumptions and incentive structure of socialist economies.
Of the ten cross-sectional OLS estimates shown in Table 3, nine of the ten
displayed returns in the range of 0.93 to 1.17 for the conventional inputs, indicating
constant returns to scale; when nonconventional inputs are included in the calculation,
all displayed increasing returns to scale. Since the PCR parameter estimates
are similar to the OLS estimates (Table 4), the same finding holds there too. Of
the pooled estimates shown in Table 5, two of the three estimates for the overall
sample also have similar results as above. For LDCs, Antle and Kawagoe, Hayami
and Ruttan estimate decreasing (0.80) and slightly increasing (1.04) returns to
scale with conventional inputs, respectively; with nonconventional inputs, both estimate increasing returns (1.04 and 1.61, respectively). For developed countries,
Kawagoe. Hayami and Ruttan calculate increasing returns to scale with both conventional
and nonconventional inputs (1.32 and 1.29, respectively). Wong’s (1986)
estimates for nine socialist countries show that diminishing returns to scale exist
with both conventional and nonconventional inputs (0.81 and 0.91, respectively,
PCR estimator).
F-tests have been conducted for the equality of coefficients between groups
of countries and also between time periods. For LDCs and DCs, Antle tests three
alternative specifications and rejects only one specification; he infers that the evidence
is inconclusive. Kawagoe, Hayami and Ruttan conduct F-tests under four
specifications, rejecting all four tests, and concluding that there are structural differences
in the production functions between the DCs and LDCs. For the equality
of coefficients over time, Nguyen (1 979) conducts three different F-tests (changing
input coefficients, changing intercept, and the two effects combined), cannot reject
any of them, and concludes that the intercountry production function is stable.
Kawagoe, Hayami and Ruttan conduct F-tests with four specifications, cannot
reject any of them, and also conclude that the production function is stable over
time
Some of the findings of Kawagoe, Hayami and Ruttan have recently come
under criticism. Moll has challenged the returns to scale for DCs, arguing that this
finding is not consistent with farm-level data in the developed countries. Kawagoe,
Hayami and Ruttan have responded to Moll by emphasizing the technological leaps
in DCs in recent decades, especially in relatively land-abundant countries that have
increased their use of tractor and mechanical technology. Lau and Yotopolous have
challenged specific coefficients: land (too low for all samples); general education
(too high in LDCs and negative in DCs); and time dummy variables (high negative
coefficients for LDCs, implying retrogression).