Infrastructure-production system dynamics in national and regional systems

t.

512

A.P. Elhance

and method0

ad T.R. Laks

h&mama-p&rim

system

cal shortcomings of this research have been identified

empirical results of these st velopments in the neoclassical theory of tions and flexible accelerator formulaa multi-equation econometric tween market (variable) and model which makes a clear distinction citly incorporates costs of adjustments, and is based on a non-restrictive nal form which satisfies various theoretical requirements. The gate data from India for the nation and n estimated with a for six states, separately, for the period 1950-51 to 1978-79. Output from the estimations includes optimal paths and speeds of adjustments ‘or infrastructure inputs; market inputs’ own and cross-price elasticities and demand elasticities with respect to the level of output, infrastructure stocks and associated user costs; and production cost elasticities with respect to output and infrastructure stocks. In this paper, only the results relating to demand effects, cost effects and adjustment effects are presented and di~ussecl. A fuli discussion of all the results obtained, including all the plice and demand elasticities, is available in Elhance (i987).

Over the past three decades, in developed and developing countries alike, awareness of the failure of purely market-based h as well as of the persisting (and generally economic disparities. The earlier reliance on aspatial

0 attempts at regionalization of al, intersectorally balanced terms 0, governments (national, regional, are inc

Apart regions.

from di~iy

rising demands for industrial tures incurred for the produ

amenities as education, medica& entertainment, s facilities. While provision of these facilities (amenities) has an introit &nificance for the welfare of the regional population, a strong case can also be made for the economic impact of such amenities. It is argu region experiences a two-fold economic impact from in infrastructure. First, there is a demand effect - the education, housing, medicr;l, communication, etc., facilities on the welfare and, thus, on the productivity of regional popu!ation. Secondly, t supply effa - the attractiveness for modern industries of amenity- . and skilled population, and as a result more rapid development of .eading to increasin ted to be set into moti A cyclic process is thus welfare of the population development and enhan In the long run, the impact of infr%tructure creation should lead to extensive modifications in the relative prices, both of factors of production and final products. The expectation is that there wit! emerge a new general equilibrium of costs and prices at a higher level of in employment. Consequemtly, increasingly larger shltres of nation&, and local government budgets are now spent on regional social capital in most developed and developing countries. Such cost reduction and output expansion ments have been recently empirically captu estimations of cost functions and production sanctions. production functions of all total use must be equal to 0

514

A.P. Elhmce and lX.

ameter, etc.). Infrastructure is, thus, viewed as a stock [Ieven et al. ( 1970)]. of such empirical assessments are no

cation of a regional production unit ga~ng firm-level data) with market in with i~r~tructure stocks. Output el estimated and interpreted. Also, complementa~ti~ and substitutions between input factors are assessed. In some variations of this approach, efficiency parameters of the production function are related to the infrastructure investments migren (1985)]. ow useful are such results derived from a largely static, equilibria& shortterm framework in a context where infrastructure is viewed as providing a new structure of costs and prices? These studies rely on conventional economic concepts and a framework of production functions, output and Allen elasticities of substitution that, while not necessarily static, have been used in a static way. Yet infrastructure investments are viewed as facilitating economic transformation, in other words as a developmental mechanism. There is a crucial difference between being industrial units and becoming industrial units. The key notions arc dynamic change, and disequilibrium behavior. An appropriate analytical framework would integrate product;on and investment behavior, describe intertemporal patterns of industrial organization, and make explicit the general dynamic response patterns to change a notion of ‘adjustment costs’ provided a vehicle for such a theoretical formulation. Adjustment costs are the costs associated with increasing the supply of those resources whose production requires sign&ant periods of e: resources such as phisticated machines, transport capacity, skilled human capital, etc. adjustment costs - while initially analyzed as have been generalized by Treadway way (1969) views the firm as producing two sorts of able output and (2) relatively fixed, firm-specific pacity). The cost of production of the latter is the e is that an analytical treatment of the

tructure a~umulation.

dynamic infrastructurein section 3 integrates the folio

(2) Flexible accelerator literature. (3)

enter into the production and cost func

(4) Flexible functional forms. Quadratic functional specified and estimated econometrically to avoid unn restrictions ou model parameters and to generate testable hy~the~s. Two econometric models are fully easure of overall market (variab!e) inputs and an aggre odei Ik is specified with four m stock (S) wherea c (S,) and social (S,) infrastructures. measures of econ the data and details of the empirical development of this model. oat with urn Estimations of the econometric models are carri for likelihood and iterative Zellner techniques. Models I d II are estuna ode1 II for six states of the Indian Union.’ For the the nation, and and refers to onl system’ is limi I?rese”=nistudy, the ‘aroduction r---d state economies. registered manufacturing sector of the national structure stock indices comprise four types of economic and social O@infrastructures each. The time period covered in this study is t independence period 1950-S 1 to 19’78-79. rent e Section 5 of the paper reviews and interprets the in terms of i~~rastru~ture-produ~tio~

A.P.

PAKISTAN

Eihmee and 7IR.

.

2) -

LANKA

Fig. I

for optimizing behavior at al and mtional economies

A.P. Elhanceand 7X. La

nature of the infrastructures, sa firm within a regicn or a nation. Further, the re nal (national) gate single unit minimize the taneously, the State makes desired adjustments t s of the various infrastructures. The economic cost min multi-equation econometric models, and oreticai restrictions on parameters of the econometric models are elicit long-run elasticities. 3.1. Notation = time index (base t = 0). Xi(t) = the demand function for the variable input i (i= X, L, E9 econometric model). Sj(t) =the level of the jth quasi-fixed factor? C(r) =total costs faced (at time t) by the production system. r(t) =interest rate at time t (assumed constant). Q(t) = Q[Xi(t), SLt)j the production function of the producers. C,(t) =eost incurred for adjustment to the level of the jth quasi-fixed factor at time t. A(t) = PriR Of the itn vatiab%einput. =normalized yric;r:st the ith variable input. Pitt) M(t) = normalized restricted variable cost function. Xi(t) =the conditional demand function for variable input i, given the output Q(t) and the levels of quasi-fixed inputs, S&j. = represents a time-derivative uf K(E~,i.e., R(t) = dR/dl [a - 1 su~sc~pt &tj denotes the value for the year t- 1, a ’ (prime) denotes the first-order derivative and Udenotes the second-order derivative]. =short-run elasticities; i= j own price elasticity, i #i cross-prke elasti4 city. &. -long-run elasticities; i= j own price elasticity, i#_i cross-price elas#.I ticity. ES,‘I”L)=e~asticity with respect to quasi-fixed inpu S&L) =eta&icity with respect to the output level &iQ

t

3.2. Mode?

The overall objective of the firm is to involved in producing a future strc

A.P. El

ati ER. La&s-

infiostructure-podwtim system dyamics

sing the levels of variable inputs, X,(t), conditional of quasi-fixed factors, S,jt). tal cost of pareduction at time t is

cost of Ulustment function for the quasi-fi The present value of this cost stream is (2)

ere p(t)= the firm’s discount rate. The conditions for the minimization of T(0) w.r.t. Xi(t) and S#) are (9

aT(o)/iYx,(t)=o,

(3)

(ii)

aT(o)/as&)

(4)

= 0.

Given strict quasi-concavity of the production function, Q(t), in vakble inputs, Xi(t), the first-c :der condition (3) can be solved to obtain the cost . . ’ ‘ng short-run demand functions for the variable inputs. mese ctions are ‘conditional’ upon the levels of the output Q(t) and the inputs SAC) in the short run, and are expressed as Xi(t) to hem from ‘free’demand functions Xi(t)]. tituting these conditional demand functions into the function C(t) and solving the optimization problem (2) yields the nonnafized restrkit,J cost fi?lCtiOti

Pi(t~Ribi(zh

t)f =I

sjf99

Q(91,

(5)

i i=K,E,M.

el, we shall use pi=

the normudizedprice

fining the cost of adjustment functio

whprp ii. = ..I”_. nccet rmlrt-hncm -*w--:-fixed ..-. w-v 1, y~.“.Iuuu nrba y..rv nf Y. thr. ..SY yuao1

factor

j.

The short-run cost minimization behavior of the firm normalized restricted cost function, N(e), conditional on now be represented as

T(O)=Te+ CN(Pisj,Q,+C(~jaiSj+~j~j+ilj 0

i

Further substituting (r+ai)Qj/fiL=c(i, the normalized user cost for the factor Sj and aj/fiL=qj, i.e., the normalized asset urice for S_+,we obtain the Euler condition for minimizing r(O):

The steady-state solution for (9) is obtained Dreadway (1971, 19’74 2~

by setting Sj= Sj =0 in the steady state. Here, Sf is the optimal (or desired) level of the #h quasi-fixed factors such that the present value of the cost stream is minimized. t Solution of (10) with a quadratic specification for t yields function Mj(Sj) of the type si>

aj

+

c YijPi i

or

+

rjjs?

+

rjQ

=

tdjj(Si)

520

A.P. Ehance end TX. Lakshmman, hfm.muctwt?-pruduction

system dynamics

djustment paths for the quasi-fixed inputs Following Lucas (1967), this adjustment process is s

where B . ; a matrix of adjustment parameters. In contrast to the ad hoc specifications of the adjustment process the elements of B* mat * constant, they now depend on the exogenous variables, the technology and the cost of adjustment functions. If it can be assumed that the stock of the jth quasi-tixed factor demanded of the price and stocks of the other such factors [Lucas * can be represented as a diagonal matrix such that in the case of only two quasi-fixed factors, B* reduces to

Under the assumption of independence, the adjustment parameters /If? and represented as I% can

l-e= -(f)Cr- k2-4 - wmhM”(O)}fl*

(12)

In the following &velopment of econometric models, a quadratic approximation to the normalized restricted cost function N(t), is specified, with a - I subscript to represent quasi-fixity of infrastructure stocks, as N=L+p,K+p&+p,M

where k = number of quasiThe cost of adjustment functions by quadratic fun&ions sue M(G) = (WI 1(Q2 WS) = w~22(~2)2 ith these qua&&c specifications for demand equations for the variable inputs (i Ri=aNldpi=ai+Yiipi+CYijPjfCYiSk_, k i

+Y&*

The optimum level of the quasi-fixed inputs are St, such that s,*=gl/Ykk)

-ak-CYikPi-Y@Q-uk i

hence d&=&-s,_,

-~k-~YikPi-YQkQDUk i

The short-run lab

-Sk-

1

(19

*

demand equation is obtained from the identity

N=L +PKK+PM~+PEE

(W

as L=N-xp,i

i

(i=K, E, Ad).

Cross-equation parameters restrictions are Yij=Yji* qs. (141, WI,

(191, (211

(2)

s

. .

524

A.P. Ehnce

and TR. i_&hmaq

Infi4sructum-pmiUCth9n system dynamics

Table 2 Parameterestimates (Model I) (Nation, 195!&51to 1978-79).

Parameters

Estimated value 29.8734 7.0245 2.0019 18.4027 0.4346 -0.1329 - (a.024 -0.3201 2.9218 0.026 -0.4293 - 2.9283 0.029 Q623§ -4.4412 1.7051 O.C#O 0.103 -0.003 0.2624

Ratio d estimate to asymptotic standard error 2.0197 20.%29 1.4301 14.8017 1.1123b 0.0271b 3:OOll 31.0043 26785 0.904Sb 1.1014b 22; SO 21.8367 0.9!113b 3.9425 9.9463 54.2984 20143 21.5420 1.103b o.7404b

*IF sta&icx K-equation: 0.612is; ihI@&&: o.as;o; L 0.64X; ~f-eqwttioa: 0.5IIA No. sf observations: 28 - 1= 27 (1972-73 missing);No. of free parameters= 21. bstatistmliy non-signikant at 10%significance level.

GC@PibA:

Estimates of all parzctzs of the two models, I and II, have been obtained by estimating the four demand equations for market inputs. A total el I are estimated for the nation, and 27 nation and the six states, separately. Nearly a third of the estimated parameters are found to be statistically not significant at the loo/olevel of signific through a two-tailed t-test. Ail but one of the parameter estimates have tically valid signs. R2 statistics for ode1 I range from 0.5114 to 0.6530. For Model II, the el II is found to be better than ates for the nation for ti~cly~ are presented in tables 2 and 3 along with their

Table 3 Parameter

Parameters

YKK+&car YKJZ +

&E

YKM + 4~ YKQ

+ &Q

YKI Ym, YEE + &, YEM +&A# yEQ+&Q YEa YE2 YMM + &M YMQ -+ 6MQ YM, :‘.‘ki %Q+&?Q

YQl YQ2 Yll

estimates

( ode1 11) (Nation, 1950-51 to 1978-791.” .___ R - 3 of estimaie to asymptotic Estimated value standard error

53.2411 2.4257 2.0925 13.2578 0.4789 0.0633 - 164890 - 0.0633 - 0.6297 4.2678 0.0260 -0.4261 0.3057 -2.9405 1.9820 0,0380 0.7880 ct.4130 -6&X26 1.482 0.0275 0.0901 0.0607 -0.002 -0.091 0.1298 0.625

5.

1.1120b 11.9437 3.6780 1.2 2.1463 41.1143 21.8745 1A479

0.9874’ 2.7985 10.97&I l.2469b 1.9001 0.86@Ib 23.7579 33.0045 11.8927 0.9427b 61.0345 2. 0 4’J2gb Oktl5b 2.9701

Y22 ‘R2 statistics:Kequation: 0.7329; &equation: 0.8462; Mequation: 0.6310; L-equation: 0.3523. No. of free parameters: 27. %atistically non-significant at 10% level of sigttificance

detail elsewhere [Elhance (1987)]. In the interests of s only on the6 -. demand effects - cost effects, and - infrastructure stock adjustment effects. 6While we do not describe the price and substitution may be noted that capital and overall infrast~ct~rc are s level of individual Indian states, capital is a complementarywith social infrastructure.

526

A.P. Elhawe ad

TR. Lokslunaoran, Iqjkzstructure-production system dywnks

Table 4 OutDut

demand elasticities of i&astructure(197O-71).” I

Nation ahara!d.ltfa Tamil Nadu west Bengal Uttar Pradesh Biha.F Gissa

Q.903 0.678 0.860 1. 0.982 0.950 1.495

II

0.628 0.820 1.027 1.111 0.215 1.244 - 2.437b

*I - Economic infkastructure; II -I Welfareinfrastructure. bBasedon negative estimate for yz2.

5.1. Demand efsects

Elasticity estimates show that as the output increases, production systems respond mainly by larger-than-proportional increases in materials input, followed by increases in the labor input. These results also con&m the occurrence of ‘overshooting’ in the short run [Berndt et al. (1980)] followed by more complex responses, at least for the states. Relative fixity of capital vis-&is other variable inputs is reconfirmed by most national and state estimates. Energy responses to output increases fall between labor and capital responses in almost all cases. Out of 48 output-input elasticities calculated for the six states, only six yield negative values, refkcting substitution relationships among variable inputs. An interesting finding relates to changes in the output level and the resultant changes in the demands for economic and social infrastructure stocks. Table shows that increases in output level lead to only less-thanproportional creases in the demand for economic infrastructures. This result is obtained for the nation and for four of the six states - only for two are the increases either strictly proportional or larger-thanrtional. These results imply that economies of scale or positive exte~a~ties are obtainable in the Indian econo y as economic infrastructure els. For social infrastructure, results for aharashtra and Uttar Pradesh, exhibit sa which is based on a ree states show largerstructure. Estimates ter economies of scale for re, whereas, a converse

Table 5 Cost e!asticitk ode1 I ENS

+#Q

- 0.05

&NS, &NSz

- 0.03 -0.01

SR

LR

SR

L,R

0.87

0.

0.92

0.87

Table 6 Cost elasticities: States (1970-71). %I

&NC

8NQ

&Q

Maharashtra Tamil Nadu west 5eogal

- 0.24 -0.04 -0.17

-0.28 0.002 0.02

0.73 1.01 0.97

0.91 1.11 1.04

Uttar Pradesh Bihar Oka

-0.20 -0.47 -0.01’

-0.19 -0.21 0.33”

0.92 1.04 2.2Y

0.92 1.22 1.32”

‘Includes a theoretically invalid parameter value for y22.

5.2. Cost effects Yet another significant empirical finding relates to the elasticity of costs of production vis-&is output changes (EN& both in the short and long runs. For both lvIode1 aharashtra, West Pradesh - the short-run cost-output elasticities (.8&Q)are less tlnan LO (tab1 6). This implies that a i% rise in o production, thus exhibiting econo To our knowledge, this is the models which has clearly demon the Indian manufacturing sector in the post-in run also, economies of scale are

range between LO1 (short run in

528

A.P. Elhance and XR. L,ak~hmman,

Inghsttucture-pductio~ system dynamics Table 7

Adjustment coeffkients for infrastructurestocks (1970-71). ode11 Nation Maharashtra Tamil Nadu Uttar Pradesh Bihar Orissa

8” 0.192 -

ode1 I1 8: 0.181 0.213 0.093 0.196 0.102 0.094 0.109

fir 0.098 0.1% 0.110 0.315 0.286 0.077 a

“No e.%baie is reportedsince yz2 is negative.

or the nation, production cost-i ructure stock elasticities (table 5) ode1 I and ENsi and ENS2 II - show that a loo/, increase in the overall stock leads to a M”Jo decrease in production costq whereas 10% increases in economic and social infrastructure stocks, respectively, lead to only 0.3% and O.I% decrease in costs. These results lend support admittedly weak - to the hypothesis that availability of infrastructure stocks has a cost reduction effect on production systems. Further, the relative emphasis on economic infrastructure v&&is social irafrastructure would a developing economy. el II present a rather mixed picture (table 6). In all the states, cost-economir= infrastructure stock elasare negative and range from -0.01 to -0.47. These estimates, to the cost-reducing effect of economic infrastructure al level also, imply that cost savings are much higher level than at the national. Evidence on cost reduction re stocks is, howe mixed. In only three states are the elasticities (EEs) negative, ranging n -0.19 to -0.28. In the states, positive values are obtained indicating cost escalation structure growth.

hese coeflicients

e six states for economic

es for the nation s

(i) adjustments ably smaller (ii) adjustments adjust;ilents

to infrastructure st than the op for economtc for social i~r~tru~t~r~.

Thus, for a developing economy like India’s, evi lagging of infrastructure stock development vis-&is o and an emphasis on more directly productive economrc 1 vis indirectly productive social infrastructures would seem to s conceptual formulations by Hirschman ( 1958).’ Bihar also has the lowest adjustment coefficients and nearly the hi cost reduction impacts compared to the nation and other states for categories of infrastructures, suggesting that very positive returns can obtained by relative concentration of infrastructure development efforts in Bihar.

To summarize the technical and empirical contributions of this research, it has been demonstrated that (i) production-infrastructure interdependencies can be subjected to empirical analyses with the help of theoretically rigorous econometric models based on unrestricted functional forms, (ii) the demand, own-price and cross-price elasticities of vatiable inputs are affected by the availability (or Lradequacies) of infrastructure stocks, as are the variable

especially economic infrastructure stocks, (iv) there iz some evidence for t existence of scale economies in

aintained

assumpti

A.P. Ei

of

c4uldT.R.

in$usttructwe~o$wtion

systm dynamics

which have

ases introduced by aggrealyzed. In the case of of India would seem to ch an endeavor. Estimations can also be performed with time-series and cross-section pool data and these estimates compared

obtained with a

ility of economic znd social infrastructure stocks, and, consecomponents is another maintar ity of this separability assumption. If, as future is to empirically test the e +hr;n -4r;* a cCSqucncc oa &US* YLII~xWa the assumption is shown not to hold 1 test& then the theory needs to be developed to incorporate im%astructure interirical findings of this study have also pointed to the relative fixity of input visd-vis other variable inputs in the Indian economy. This yet another empirical exploration, that is to treat the capital stock pun along with the overall infrastructure stock, in to analyze their separate adjustment dynamics. This, too, is findings do point to certain policy-oriented concluthe rnain~n~ assu s, especially regarding iliiy, and the nature available &x this study, reluctant to draw out these conclusions at this stage.

gate agricultural productivity:International evidence* for U.S. manufacturing, 1947-1974 (EPRI, Palo Alto, 1982, The conttibution of infrastructure to regional

Gupta, S.P. and J.P. Si

Judge, GG, WE. Griffiths, R.C. Hill (Wiley, New York). KlL.H., 1968, Social amenities in area economic gmwth ark&). Lakshman-an, T.R. and Fu Chen Lo, 1970, A regional growth Puerto of municipal growth patterns and public investment (CONSAD Research Pittsburgh,PA). Leven, CL., J.B. Legler and P. Shapiro, 1970, An analytical frameworkfor regionald~v~~~p~e~~ policy (MIT Press,Cambridge, MA). Looney, R. and P. Fredericksen, 1981, The regional impact of infrastructure inves Mexico, Regional Studies 15, no. 4,28X296. Lucas, R, 1%7, Adjustauznt costs and the theory of supply, Journal of Political Economy, August, 331-334, hka., K., 1973,Rcgiouai proriuctisn functions and social overhead capital: An analysis of the Japanesecase, Regional Science and Urban Economics 3, no. 2,157-186. Mukhejee, M, J.L. Gayan and I. Roy, 1981, A quantitative study of inter-state variation in social development, The Journal of Income and Wealth5, no. 1. Nurske, A, 1957, Problems of capital formation in underdeveloped countries ( Oxford). Raza, M, S. Naqvi and J. Dhar, 1978.Sources of economic and social statistics of India (Eureka Publications, New Delhi). Rosenstein-Rodan, P.N, 1943, Problems of industrialisation of eastern and soutb-eastem Europe, Economic Journal 53. Saxonhouse, G.R., ‘,977, Productivity change and labor absorption in Japanese cotton spinning ?891-1935, Quarterly Journal of Economics 91. Treadway, A.B., 1969, On rational entrepreneurial behaviour and the demand for investment, Review of Economic Studies 36,227-239. Treadway, A.B., 1971, On the multivariate flexible accelerator, Econometrica 39.845-855. Tread.vay, A.B., 1974, The globally optimal flexible accelerator, Joumrr! of E~XK&Z Theory 7, 17-39. W&en, Rune, 1985, Productivity and infrastructure: An empirical study of S n the regional production milieu, in: Folke turing industries and their depe &., Eccrromic faces of the building sector Borje Johansson and T.R. Laks Council for Building Research, Stockholm).