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UNIVERSITY OF
ILLINOIS LIBRARY
AT URSANA-CHAMPAIGN
BOOKSTACKS

Digitized by the Internet Archive
In 2011 with funding from
University of Illinois Urbana-Champaign

http://www.archive.org/details/inducedinnovatio36yeun

y.

Faculty Working Papers

College of Commerce and Business Administration

University of Illinois at Urbana-Champaign

No. 36

FACULTY WORKING PAPERS
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign

December 23, 1971

Induced Innovation: A Ces-Type
Meta=Production Function

Patrick Yeung
University of Illinois

Terry Roe
University of Minnesota

iails A (ued et hecuint
e Hes 3 brie aie Tc shana gl

iy

INDUCED INNOVATION: A CES-TYPE
META-PRODUCTION FUNCTION

1. INTROOUCTION

The Hicksian version of the Induced innovation hypothesis [5]
focuses the cause of technological change on changes In relative input
scarcitlies. Recent developments of the Induced Innovation hypothesis
Include the introduction of the concept of a ‘meta-production function"
(see Hayami and Ruttan [3]). {it is the purpose of this study to develop
@ meta-production function by adapting the currently popular CES pro-
duction function, and to present a more direct empirical test of the
validity of the Hicksian Hadbeed innovation hypothesis.

A brief review of the development of the Hicksian hypothesis Is
given in Section ti. The C&S-type meta-production function and its
properties will be developed in Section bit. Using historical aggregate
statistical data for agricultura! production in Japan, 1880 through

1940, the empirical analysis is presented in Section IV.
fi. HICKSIAN INDUCED INNOVATION: A BRIEF REVIEW

The induced innovation hypothesis was initially postulated by Sir
John Hicks in 1932 [5]. Since then, the hypothesis has developed along

various lines (see, for instance, W. Fellner [2] and C. Kennedy [6].

Assistant professor, Department of Economics, University of Illinois,
and assistant professor, Department of Agricultural and Applied Economics,
University of Minnesota, respectively. The authors are indebted to Vernon
Ruttan, William Griffiths and William Wade for suggestions and comments
on an earlier draft. The research on which this paper is based was partially
supported. by the University of Minnesota Economic Development Center.

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1 "tegen enna! avaid hanna haha ™ els

. ah suri te ie ue

in what follows, we shall stick to the spirit of Hicks' origina! ver-
slon of the hypothesis.

According to the hypothesis, technological changes frequently occur
In response to the Inelastic supply of certain productive Inputs. This
situation can be depicted in the manner of Syed Ahmad's graphical elabora-
tlon [1] (Figure 1).

Suppose the initial input price situation for a two-factor case Is
represented by the relative price line PoPor and the efficient production
of Q, of the output Is shown by the tangency point b. (An autonomous
neutral technological improvement would be shown by a shift of the isoquant
Q, to Q,, with the new tangency point b still lying along the same factor-
intensity ray OR as point a.) Let Factor 2 become relatively more ex-
pensive, so that the relative prices are now represented by PyP,- The
traditional substitution effect would shift the point of tangency along
&% from b to c. |

Suppose induced innovation is now introduced into the analysis.

When the relative factor price change forces a departure of the equilibrit
point from the Initial point b, then a concommitant shift of the Iso-

_ quant Q, to Q,' occurs, so that the new tangency point becomes d instead
of c. This concommitant adjustment of the isoquant reflects a non-
neutral technological change which is biased against Factor 2 (Factor 2
saving) and blased towards Factor | (Factor | using). In this situation,
costs have decreased from p;p, to Py ‘Py’ The locus of efficient points
such as b and d gives rise to an envelope curve uu which Ahmad called
an “Innovation possibility curve." The entire set of uu curves describes

* a dynamic production function.

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Factor 2

Figure I:

Factor }

Depiction of Blased Technological Change Induced by” the
inelastic Supply of Factor 2.

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A similar kind of dynamic production function was given the name
of “meta-production functlon'' by Y. Hayami and V. W. Ruttan [3]. Study-
ing the cases of agricultural production in the United States and Japan,
Hayam! and Ruttan concluded that changes in input mixes represent a pro-
cess of a dynamic factor substitution which accompanies changes in the
production surface induced by changes In relative factor prices. In
the course of economic development, with demand for farm product in-
creasing, the price of a less elastic factor tends to rise relative to
the prices of more elastic ones. Prices of machinery and fertilizer
tend to decline relative to the prices of land or labor, as the case
may be. Under such conditions, technological innovation has been directed
toward relaxing the constraints imposed by the relatively inelastic
supplies of primary factors of production. Mechanical Innovations are
seen to be Induced toward labor-saving, and biochemical innovations as
Induced toward land-augmentation.

An explicit form of meta-productlion function was postulated by
Hayami and Ruttan In [4]. There, they presented a rather general model
of agricultural development for thirty-eight developed and under-developed
countries involving such explanatory variables as land and livestock to
serve as proxies for internal resource accumulation, machinery and
fertilizer to reflect technical inputs, and general and technical educa-
tlon in agriculture as an approximate measure for human capital. A critical.
assumption in thelr approach is that technical possibilities available
to agricultural producers tn different countries are subsumed under the

' same potential or meta-production function.

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Though the meta-production function specified by Hayami and Ruttan
may be used to test the induced Innovation hypothesis, a more direct
test of the hypothesis may be devised within Ahmad's simpler framework.

This will be the task of aeons ttl and fv.
ttt. A CES=TYPE raebisutievn FUNCTION
A dynamic two-factor production of the general form
Y= F(K, Ls; t)
can be explicitly specified to be of the CES form:
(1) Ve = [a(K, eFt)“P + B(L, edt) “Pl /p

where Y, K, & and t represent output, capital, labor and time respectively;
a and § are traditionally referred to as the distribution parameters, é
and X the rates of factor augmentation over time, andp the substitution
parameter (sce, for example, Y. Kotowltz (7) A specific feature of this
approach Is that the factors are expressed in effictency units.

There are, however, certain weaknesses implicit In this approach.
First, the rates of factor augmentation are assumed to be fixed over time.
There is no a priori reason why this should be true. Second, the ques-
tion of whether the technological change indicated is Induced or autono:
mous is ignored, the source of innovation being left unspecified.

To reduce these weaknesses, Equation (1) can be improved upon by
postulating that the Innovation Is Induced by relative Input price changes,

such as in Ahmad's framework. Specifically, in dealing with agricul tural

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output (Q), stipulating the primary factors to be land (A) and labor (L),

a meta-production function may be written as
(2) Q, = fala, eFFe)-P + w(t, erFey Py“!

where 1, represents an index of Felacine factor prices of labor and land.
Like Equation (1), it Is homogeneous in the Inputs. The essential differ-
_ gence between Equation (2) and Equation (1) lies in the replacement of
Gare t with the labor-land index I,. tn thls case, factor augmentation
We assumed explicitly to be induced by changes in I,- Even though con-
‘stant factor-augmentation parameters, 6 and \, are still postulated, the
rates of factor augmentation need not be constrained to be constant over
time.1/

In both Equation (1) and Equation (2), it can be observed that if 6
and \ are equal and different from zero, then technological change is
neutral. When $ is different from A, the innovation [Is non-neutral In
character. Furthermore, in Equation (2) if 5 exceeds A, the case is
land-saving (iabor-using) and if A exceeds 5, the case is labor-saving
(land-using).

To make Equation (2) operational, let us define the relative f-ctor

price Index to be

(3) = O/O.,

'/ they would not be constant over time If and when [, Is not perfectly
correlated with t.

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where F) is the relative prices of labor and land in the t-th year and
t, represents the base year.

Assuming that factors are paid according to their marginal productiv-

ities,

l+p
(4) r= - 2 a(2} eel
and

(s) wera lah? riot

Dividing Equation (5) by Equation (4) yields:
(6) x = S(Al MP (nado!
Taking lagarithms and re-arranging terms,

Lp Rag e aneree
(6a) inft} ein B+ Lin + Giese |

a

from which we can obtain the elasticity of factor substitution oa,

(7) gs p+ thle se 1 + 10-8) or),

I+

altiel>

Since our CES-type production function is dynamic, this elasticity is

mot constant over time, but changes with fea Therefore, as the dynamic

UVrote that as I approaches zero, the adjustment term [1 + (A-5)pL]
approaches. the constant elasticity value 4 of static conditions. This
+,

occurs Irrespective of whether (A-5) is expressed in absolute terms.
-However, from the description of Figure |, it is evident that the adjust-
ment factor is positive, regardless in which direction the innovation is
biased. Therefore, the (A-6) term should be replaced by its absolute value.

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(variable) elasticity is associated with the concept of meta-production
function, it may be referred to as the 'meta-elasticity of factor sub-

stitution."
iV. EMPIRICAL ANALYSIS

The specification of the functional form of the me ta-production
function developed In the preceding section offers a direct test of the
Hicks-Ahmad version of the induced innovation hypothesis. Specifically,
it Is shown that positive verification of this hypothesis is obtalned by
rejecting the null hypothesis that 6 Is different from \ at the tra-

ditional levels of significance.

Statistical Model
The estimation of the unknown parameters of (2) is obtained by con-

verting equations (4) and (5) to In form as follows:

1G) eed ble | Se

(4a) in(s] fa aa re rt

and

(Sa) infff = = Line hein ws eg,
+p

Since the coefficient I/(l+o) is common to both variables r and w these

equations were combined to yield the following estimating equdtion
(8) Q’=xXBtu

where

‘pelt uberq~a2am Yo sqatine oad “ait betalsores al sdltieale ‘si sf task
due yo298? Yo estolaenle-aieatt ert es on bevioter vy iat a ne!

e- t ; | . ba a
irae | 2heyJAMN ete wt oe er

oe

‘nol s2uborq~63.6m orl? 20 mo? fenol 29002 anid 0 rotanal oe.
oil) Yord29) i201ib @ zretto noliasz gnibessrg edt ot berolevel 13
vieHFas¥ 29092 .alesisogyd noldevonat baoubal. om 40 nolaray t A
ye bontasdo al zhaeisoqys eis 40 aolseatthoaw ott la0q sans nat

gts. ad 18 ‘ pant dnsno¥? 1b al d darl9 stendoay ttn ot 9
6 Dies seoneoldingie. Ao > eleva f

i 5

ate

praia gual ae og al

oe Cs

XS he sabe koe
sf + wat wi Maier! Oe 9 al 7
sean? w bre 4 “aside tyiv: sig ot some at Aoi anol Vac

; neared bi: oe e
dotsbics Rai seaises ed tot oils biaty 64 bentémoa
~~ mith -) 7 " Yt ie Be
they be aah we Sd

Rast Pe. 4 aii Pa a Are af .
; a x ; { Phe 7h dak iid at

my in he aa eens ah Het hpe=y hp ; nae i

Lt oy arte ce
mare en ee

In (YA) ¢, 1 0 In rte I, 0
Q' =IIn (a/A) a alt 0 In r I 0
In (yu) a | In wen on Te,
In (Y/L)¢, 0 i In Wen 0 pte
a,
b, lip In e
wea the
by lic In 8
1
B b, itp
&p
by, jas
b pas
5 l+p

and u is a 2(,+1) component vector of disturbances which are assumed to
be randomly, !og normally and independently distributed with a zero mean
and a constant variance. This formulation allows for the restricted
estimation of (I/itp) by ordinary least squares and therefore the deriva-
tion of unique estimates of the parameters of (2).

in the case of Japan, it has been observed that for the period 1880
to 1940 Japanese cockcetuucel production increased as wages secularly
declined relative to land vaiues. Under these circumstances, the in-
duced Innovation hypothesis suggests that technological progress was

_ blased against (in favor of) land (labor). Therefore the null hypothesis

he b
1 le
i NV eo
me. Da
Pane
Vey Vue gy ae;
| deel -_ Ye
i
if \
i UPR i
fi)
iW
ty Hi f
Mane Ma i 4 '
"4

03 bomveee a6 Ao trlw asonedwwi el Yo r08 900, snenoqio9 eae
| “neem ores s is iw berudisa pie vfeaebasgabnt bas Viesion no! ah
| botolyaeo3 ott sot ewot le neliafumor elit “sone tiey 1na3 4909) &
“evived. ory sotsredi bos eoiaupe enol, Wonibre xe (arth) To mols
(8) Yo svshamoneg mts to ieedholoae supioa Bt

086 adi wets ds teas bovanade noed aan 40 ight
“ylreluaae eognw 1“ aeaoronl mo inaubore eta

kon

sal ott “(#eanng amudy lo ae

Pr a wre
wvitaler

en aT ‘
“eon exenyorg, {91 potondses ttt woengove theniat! fol ‘boos

. ) bea Air Lo
| stents cay Hun ods medersdt ae baw! Bs isd eninge ‘haaed
ha ‘hie es Rs :

id

Is that 6 Is not different from \ and the alternative hypothesis [fs that
6 is larger then dA.

This test Is predicated on the prior test that only 6 is different
from zero and of the appropriate sign since reliable estimates of a and
6 are generally difficult to obtain. in other words, testing the hypo-
thesis that the model of form (2) is a “suffictent"' explanation of the

data.

Data

Time series observations on agricultural output, land and labor in-
puts, their prices and a discussion of its derivation are available from
(4) for Japan for the perlod 1880 to 1960. However, only the data for
the period 1880 to 1940 were used because of data and structural dis-
continuities during the war and postwar periods.

All observations are quin-quennial. Observations on land and labor
are measured at every five years beginning with 1880. Prices (rents and
wages) are measured as the average of five years ending the year spec’
fied. This Is to take into account the effect of expectation and adjusi-~
ment jag on technological adoption.

The apriorl selection of the "best'' measures of agricultural output,
and the land and tabor Inputs, Is difficult in the case of this model
when various measures appear to contain a similar level of accuracy. There
fore, the two data series which are used as measures of agricdhtural out~
put are gross agricuitural output net of Intermediate goods supplied wi thi:

agriculture (al! commodities) and gross output (al! crops) Table 1. The

v Vy , a ee
a: He

cide

“on ats Cuamenaal neisa, ne nlaste of sn wt

a0?) eteb avid (ino svevonast .o2¢! @ oaat ateg as 203 aaah 9
: rel tuvudourde bing aah, Yo. seusoad bacw oye fet og oa8t by Fv
vtbornag and #9 leu ton ant ent id zolt

aa nak,
rae

3 seiel bie bast cv ) anoitevneedd: | -Inbunaup-wtup ave enotvovierde | an
| bine atnen): geolyt’ 0881 nel ontnntead ine ‘owt reve: tet que
“) htaaeelinany old golbris a7eoy BHT Yo! per ere alt em vowwesen |
i sapatig bee. Nob eIIAQXs sie toed te ong eer onal, sist all ii iat
' Ad in he Ave - ynolagaba Inc igotaetona: 7 he: in
steatwe lavottualive Yo sowesem pana peta: Yo notsooton:| Ine nq ; |

- Aoki eli Ae pews tt? | nt ‘efoai) tp a eosiget ode bre. | ne om bn

gn ait yoawone to. tind vetiate ® aston oF, resage rovwewee qual f

| “100 Faws (u9 (age rer soueode a beaw one: Hake solves + 208 tft
aint iw bmi bqywe aboon oi ntbger tint Ne toh. auqaia, i * ui
| adh eho KGOT (ager: ante oaro axore nek (awa th

TABLE 1

JAPANESE AGRICULTURAL OUTPUT, LAND AND LABOR INPUTS
AND THEIR PRICES FOR THE PERIOD 1880 To 1940

Year Agricultural Production (Q) _
A commod t= A

tiles

(VAR. 1)
1880 100
1885 113
1890 = 126
1895-131
i900 «149
1905 = 165
1910 = 188
1915214
1920 232
1925-231
1930 8=6249
1935 263
1940 =. 264

Source: Y. Hayami and V.W. Ruttan,

crops
(VAR. 2)

0=100
100

Land (A)

Paddy

field

(VAR. 3)
000*s ha.

2801

2824

2858

2877

2905

2936

3007

3072

3136

3199

3274
3296
3276

Arable
land
(VAR. 4)
000"s ha.
4748
4814
4922
5034
5200
5300
5573
5778
5997
5914
5961
6103

6121

Perspective (Baltimore: John Hopkins, forthcoming,

Labor (L)
oraie wetted
(VAR.5) (VAR. 6)

000's 000's
14655 7842
14481 7766
14279 7677
14485 7651
W421 7680
14069 7617
14020 7606
13942 7585
13939 7593
13941 7586
13944 7579
13750 6972
13549 6365

Agricultural Development - An Internationa]
9 e

7 A

ie De, vue
nL i }
rr | ‘
7 LF
| -
ie

1 f '
7, i
wat af

eran hes tuene ae ee
trum Aoshs-3 SIMA aWAL ruarud aanirr asain Beata
19 OPEL OF, tied OO1Aa" BHT AQT: ARMAS, adeaid ha

ome

‘alt ihe “9 tes 1 ng

TABLE | (continued)

JAPANESE AGRICULTURAL OUTPUT, LAND AND LABOR {INPUTS
AND THEIR PRICES FOR THE PERIOD 1880 To 1940

re Rel.Fac.Price Index
Land Price (r) Farm Wage (w) (14109
Average Value Arable land aily wage aie (ustng (using

of arable land price index rate varlables variables
9 and 7) 10 and 8)

WAR. 7) (VAR. 8) (VAR.9) (VAR. 10) (VAR.11) = (VAR. 12)
yen/ha. 934=36=100 yen/day 934-36=100

343 10.5 0.22 18.3 100.000 100.000
a 12.4 0.16 21.4 66.878 99.027
Aba 14.6 0.17 19.3 59.695 75.852
615 21.7 0.19 25.9 48,167 68.486
917 | 31.5 0.31 40.3 52.706 73.410
998 34.5 0.31 4k 9 48,429 74.677
1586 46.9 0.41 49.5 40.304 60.561
1613 63.0 0.46 61.9 kk 463 56.378
3882 109.7 1.39 127.3 55.825 66.586
3711 140.3 1.65 172.9 69.321 70.713
3388 132.4 ‘Ete 156.5 51.540 67.825
2783 97.4 0.91 96.9 _ 50.980 57.262

4709 134.1 1.90 154.2 62.907 67.490

4 i (
ni
' i
’ ny
ap’
ih
i yi

sh

; Baie eae sunt”

zruas oh ‘ana WAS TusTue ‘hae 8 in 32 ai
bya or Ses tip a eae eae ‘ait one he

fdéixev, enideliny
Siow ol §(\ ban &
t | CIT ARV

pene |

“900.001” 000.0 |
Tease 008 ee ae
SRS RRR AR) ea
a ee ee
te meee | ee ee ae
SO eae aa ee a
abe Heh eA
BNE ‘gale TE Cea
Sey a Te Se: a 0
lei | orsete eect a
ached ie a eta iN
Sate R02 AR HA
TAS) ee Se

13

two measures of land are hectars of paddy fields and hectars of arable
land, while the two measures for labor are all workers and male works
(Table 1).

Two different measures are also used to measure land prices and farm
wages (Table 1). The average value of arable land prices are the welghted
average of the prices of paddy flelds and upland fields where the areas
of each are used as weights. The arable land price index is the simple
average of paddy field price index and the upland field price index. The
two measures of farm wages ne the wage of daily contract workers and
the index of male daily contract workers.

From the information in Table 1, elght estimations of Equation (8)
can be obtained. The first four estimations are based on four dependent
variable transformations each regressed on the independent variables
7, 9 and It (Table 1). The second four estimations are based on the same
four dependent variable transformations each regressed on the independent
variables 8, 10 and 12 (Table 2). The four dependent variable trans-

formations are

Q\=

In(Var.t/Var. 3) lin (Var.2/Var.3)] [in(var.1/Var.4) In (Var.2/Var.4)
In(Var.1/Var.5)} |

9 Q32 ® Qa,"
In(Var.2/Var.5) In(Var.i/Var.6) In(Var.2/Var.6,

x ra} |

sldare " 26320 be iat ‘hag Ng ernie |
ahvew ofek bra suntan. ie me tial ii eae on

+
~

pays - = bie moive boat orweyon <a bore

ae ie 006 at erste blot? inet i, abies aque at sly ‘
| _algate ony zi xobal oahg nef gideve oat beorbataral sa |
de oat oxabat aii biol natu ona ns rsiont aang bli? vbbeg " cate
eae eyaihow souy3n09 te bie ee ld, ane -sogel amet Yo a
mi levasrow | aaerin hah oem Yo )
@ nolseupa: Ro cootsantzes aapto af aldst ta pobemotal ot 07

nd Aqpbraga awa? ne brand avn spolFeatheo, wot ant aot sbantes oo

ie

side tiey Thabangobr | erty hed baeesr gor 90 nat zemadanens |
omne bry no boved ove. anolreataes quo? broaee sat aT ‘oiger), Hh be 8
© snabogat ay a) vocasge, dons tivo! omnotenand ‘eldpivev aa tar
wane? gidetrey inabieyah yuo} ett AS. steer) ‘gt bom oF Be

st Tes. sei ill ae fiesiovns.saval ‘o be!
os a le TaVNT-vOV) AN Ay Mesra\toravdan , ys ecm

14

V. EMPIRICAL FINDINGS

The results from fitting the statistical model (8) to the data pre-
sented In Table | appears in Table 2. The statistical model seems to fit
the data reasonably well and the coefficient estimates are generally
consistent in sign. However, sign changes did occur in the estimates of by
based on the dependent variable Q;' regressed on the independent varlables
7, 9 and 11 and with the estimate of b, based on the dependent variable
Q,' regressed on the variables 8, 10 and 12. Variance estimates of the
coefficients b;, 53, and b3 are less than twice their corresponding
coefficient magnitudes with four exceptions. These exceptions are the
variance estimates of b) based on the dependent variables Q,' and Q,'
regressed on variables 7, 9 and Il, the variance estimate of bj based
on the dependent variable Q;" regressed on variables 8, 10 and 12 and
the variance of bz based on the dependent variable Q,' regressed on vari-
ables 8, 10 and !2of Table i. in all cases, the variance estimates of
by are large while the variance estimates of bs are small.

The parameter estimates of the economic model (2) and their vartance
are derived from the estimated statistical model (Table 3). The deriva-
tion of the parameter estimates is straightforward. The estimated para-
meter variance is based on the large sample property relationships of
the asymptotic distribution of a function of sample moments [(@&}.

The estimated distribution parameters a and 8 are of the cprrect sign

in all cases although the estimated variance of these parameters are

et

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ig

large. {tt follows from the relationship for estimating thelr varlance
that this estimate is sensitive to the magnitude and signs of the inter-
cepts by and bo .l/ Therefore, if the assumptions which guarantee con-
sistent estimates of b; and by are not strictly valid, the variance of
a and 8 may be overestimated.

Of primary importance here, are the estimates of the parameters 5,

XA and p. The estimates of the factor augmentation parameters 6 and X are
of the same sign with one exception. in al! cases, the value of 6 exceeds
the value of A even though the estimated variance of 6 is large.

The estimates of the substitution parameter p are of the correct
sign and strongly different from zero in ail cases. Thus, It seems
reasonable to conclude that model (2) is a “sufficfent"’ explanation of
the data. We therefore proceed with testing the induced innovation
hypothesis.

To test the hypothesis that 6 Is not different from A, it is necess-
ary to estimate their covariance since only the covariance of &4, bs is

given directty.4/ The carrying out of this test suggests that this

are seer teenies

the relationship for estimating the variance of 6 and X appears
In footnote a of Table 3. {t should be noted that each of these equations
contain a remainder term which approaches zere as sample size increases.
2/ the estimate cf the covariance of 6\ is based on Thiel [8] and is
of the form:

bi bs) bi 1
Cov. (64) = = Van ba - aren| (Cov (bat
; aaa ren lias | TF el ees

1 bh 1 bs
-j— Cov, (b2b,) - | —— Cov. (b
reat id “tw tes ne aa ops

th 2

— enerme oti eoglagmee | xt in

‘iy ey hal iar i dike
yb worenarng ons a2 go ee) ods | bs «O70 donved vo@n!
Aber ms ier, i ce vy, f 4 ry Pie iw, iy oe 0 Mh Wil rik
? PDS lls be hee aP
ne k bas eS ed onenag soya: hamgue eiom ‘nda No) ‘eatemlian
= 4) ah “w tod ane, Ae
‘ebgeoke s 0 onlay, ea: naan Ie ab _-naliqeone ona da twes
ay | eet a ny Yo panglaey baseaiaae oe
oa 7 ; Me ot ae !
"amor a one he ‘ab hes nied see
at e a?) Xo sonal ave sana he Sante Agee 2
zidd Jars etemeaue, geo, ai. Re, suo apa 8 co

ereaqqe r bre 4 te withjaad ny eat eh 9
eooliaups seers Jo rage 2 art baion of vtyore tte
sehanencnt whe beaut “8 Piss Todaaeveae "2 ayes,

hypothesis is strongly rejected in all cases. We therefore accept the
hypothesis that 6 Is different from A. This is consistent with the in-
duced [innovation hypothesis that for the circumstances observed in Japan
from 1880 to 1940 technological progress was blased against (in favor of)
land (labor) and therefore confirms the conclusions drawn by Hayami and
Ruttan [3].

The mean meta-elasticity of factor substitution estimates were derived
for the years 1880 to 1890, 1880 to 1940 and 1930 to 1940 (Table 4).
With one exception, the elasticity estimates are less than unity and,
in all cases, decline over the period 1880 to 1940. This implies that
the estimated production function is bounded, i.e., the function reaches
a finite maximum as one factor increases while the other is held constant.
This also implies that the adoption of technology in Japanese agriculture
over this period has decreased the marginal rate of substitution of labor
for land. l/ in other words, the development of biological innovations
of a yleld-increasing type in Japan have increased the difficulty of
effictentiy substituting a growing supply of labor for land.

it was pointed out earlier that the essential difference between
the meta-production function in equation (2) and the traditional formula-
tion of a comparable CES-type dynamic production function lies tn replac-

ing t with I,- in so doing, the factor-augmentation parameters are not

'/this result is substantiated by Wolkowitzs [9] findings in the
estimation of alternative homothetic production functions that '"Glven
that biased technical change enters ... so as to decrease the marginal
rate of technical substitution, it will in turn decrease the elasticity
of substitution."

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Atl noizsupe 342

20

constrained to be constant over time when I, Is not perfectly correlated
with ¢.

For purposes of comparison I. was replaced In the estimating equa-
tion by t, t=t,,t1,t2,---, for the years 1880, 1885, 1890, .... The

results of this analysis are briefly presented In the next section.

Relationships Between I, and t

The results from fitting (8) to the data Iflsted in Table | when t Is
substituted for I, is presented in Table 5 and Table 6.

While a large portion of the variation [tn the dependent variable is
explained, multi-collinearity between t and In r, and between t and In w
exceeded 0.9 in all cases. Also, the likelihood of serial correlation
appears to be higher In this model. in all but one case, the variance
estimates of the b3 coefficient is large. However, the estimates of the
remaining coefficients are generally consistent in sign with small vari-
ances.

The problem of estimating the distribution parameters a and 6 appears
to be more severe in this case than in the previous model. The estimates
of the substitution parameter p vary considerably in magnitude and the
corresponding variance estimates are’ large in all but one case. There=-
fore, it is concluded that model (1) is not a “sufficient! explanation
of the data and we do not proceed with testing the hypothesis Involving
the difference (6 - 4). However, for the single case where p Is signifi-
cantly different from zero, the difference (6 - A) Is found not to be

significantly different from zero.

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23

This analysis suggests that the meta-production function postulated
in (2) ts superior to the functlon specified in (1) in explaining agri-
cultural production in Japan for the years 1880 to 1940 as well as in

providing for a direct test of the Induced Innovation hypothesis.
{V. CONCLUSION

A dynamic CES-type function and its properties is developed which
incorporates the*Hicksian induced Innovation hypothesis Into a meta-
production function. Essentially, a relative input-price index is
used as the shift varfable of this function which Is postulated within
a two-dimensional input space. This study uses only a partial equi-
librium dopcoseh in that changes in the relative price index are assumed
to be exogenously determined.

Using historical data for Japanese agricultural production, it
was found that the hypothesis that biased technological progress of a
land-saving type was induced by the relative secular Increase in land
values was found to be statistically warranted.

A variable meta-clasticity of substitution is derived In Equation :
(7). tts estimated magnitudes are less than unity and generally decline
over the years 1880 to 1940, suggesting that the development of bio-
logical innovations of a yield-increasing type in Japan have increased

the difficulty of substituting a growing supply of labor for~land.

zs

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(1)

{2}

[3]

(4)

{5}
(6)

(7)

(8)

{9}

24
REFERENCES

Syed Ahmad, "On the Theory of tnduced Inventlon,'' Economic Journal,
vol. 76 (June, 1968), pp. 344-57.

William Fellner, ‘Two Propositions in the Theory of Induced Inno-
vations,"' Economic Journal, vol. 71 (June, 1961), pp. 305-8.

Yujiro Hayami and Vernon W. Ruttan, "Factor Prices and Technical
Change in Agricultural Development: The United States and

Japan, 1880-1960,'' Journal of Political Economy, vol. 74
(November, 1970). M

Yujiro Hayami and Vernon W. Ruttan, Agricultural Development = An
international Perspective (BaltTmore: Johns Hopkins, forth-
coming, 9 e

J. R. Hicks, The Theory of Wages (London: Macmillan, 1932).

Charles Kennedy, "Induced Bias in Innovation and the Theory of
Distribution,'* Economic Journal, vol. 74 (September, 1964),
pp. 541-47.

Yehuda Kotowitz, "On the Estimation of a Non-neutral CES Production
Function,'' Canadian Journal of Economics, vol. 1 (May, 1968),
pp. 429-39.

Henri Thiel, Principals of Econometrics, John Wiley & Sons, Inc.,
1971, pp. e

Benjamin Wolkowitz, Estimation of Alternative Homothetic Production
Functions, Paper presented at the Annual Western Economic
“Assoclation Heeting, 1971.

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