Pollcy, Re"srch, and External Affairs
WORKING PAPERS
Public Economic
Country Economics Department
The World Bank
May 1991
WPS 689
Do Tax Policies
Stimulate Investment'-,
in Physical
and Research and Development
Capital?
-1 C,~~~~~~~~~~~~~~~~~~~~
Anwar Shah
and
John Baffes
Among tax policies designed to stimulate investments in Paki-
stan, the investment tax credit has not been cost-effective. But
allowing full expensing for research and development costs has
been.
uwPolicy.Rseavch. and Extana AConplcx didi tts PRE WoddngPipeps todisnninatethefindings of wozk in poess and
to encouage the exchange of ideas among Bank taff and all othera inted fit development ines. These papers ery the names of
the autos, reflect only thr iews, mnd should be used and cited accordingly. The findings, interpretations, and concions are the
authors' own. They should not be auhbuted to the Wodd Bank, its Board of Diretors, its nanaganent, or any of its mnember coutnies.
Poliy, R.aroh, and Ext4nl Affirs
Pbflb Ec6nomks
WPS 689
This paper - a product of the Public Economics Division, Country Economics Department -is pan of
a larger effort in PRE to evaluate tax incentives for industrial and technological development. Copies are
available free from the World Bank, 1818 H Street NW, Washington, X 20433. Please contact Ann
Bhalla, room N10-053, extension 37699 (25 pages, with tables).
Tax policy instruments are often used to stimu- and their implications for revenues foregono by
late private investment in developing counties. the government.
But researchers have not explf A'd how well such
policies have met stated policy objectives. The model results yield an objective, empiri-
cally derived cost-benefit ratio that is superior to
To evaluate the cost-effectiveness of tax standard cost-benefit analysis and King-Fullerton
incentives for industrial and technological type marginal effective tax rate analysis.
development, Shah and Baffes specify a dynamic,
prodfiction structure model with endogenous Shah and Baffes apply this model MMnpiri-
capacity utilization. cally for Pakistan. Yhe results suggest that the
invesment tax credit has not been effective at
Taxes and incentives are part of the user cost stimulating investments in Pakistan. The private
of capital, and thereby affect producer decisions investment stimulated has been less thanwthe
about choice of inputs, technology, and capital government revenues foregone.
accumulation.
Allowing full expensing for rsarch and
Empirical estimates of this model allow one development expenditures, on the other hand,
to infer both the impact of investtment incentives has been cost-effective.
The PRE Working Paper Series diuiinates the fiTndings of otod wnder way in di Banls Poliqy, Reseucl ad Exmtl
AffairsComplex. Anobjective,of theseries is togetthesefingsoutqly,ersentaifpisarelo wesuhmnffliypolishd.
The findings, iiterpretations, mid conclusions in thm papers do not necessarily epesat ofkid Bank poliy.
Ploduced by thec PRE Dissektin Center
Table of Contents
I. Introduction . . . . . . . . . . . . . . . . . . . . . . ...1
II. Corporate Tax Incentives in Pakistan . . . . . . . . . . . . . 2
111. The Model . . . . . . . . . . . . . . . . . *. . . . . . . ......... 3
L. Flexible Accelerator . . ......... . . . . ...... . 4
ii. Empirical Model . . . . . . . . . . .. . . . . . . 6
IV. Data, Estimation and Testing Procedures . . . . . . . . . . . . 7
V. Empirical Results . . . . . .. . . . . . . . . . . . . 9
VI. The Impact of Tax Policies on Investment in Physical
and Knowledge Cadital ................... . 14
VII. Policy Implications . .. . . . . . . . . . . . . 15
Endnotes . . . . . . . . . . . . . . . .. . 19
References . . . . . . . .... . . . . . . . . . .. .. 20
Appendix A: Derivation of Input Demands . . . . . . . . . . . . . 22
Appendix Bs Data Description and Construction of Variables . . . . 24
*This is one of a series of paper commissioned by the World 3ank Research Project
(RPO #675-10), An Evaluation of Tax Incentives for Industrial al. I Technological
Development". The project is directed by Anwar Shah of the Public Economics
Division, World Bank. We are grateful to Bela Balassa and Terean Baysan for
comments.
I. Introduction
Tax policy instruments are frequently used to stimulate private
Lnvestments in developing countries. The impact of such policies in meeting
stated policy objectives remains an unexplored area of research. This paper
specifies an empirical framework to evalute the cost effectiveness of incentive.
for industrial and technological development offered through the tax code. It
takes a first step in quantifying the impact of investment incentives in
stimulating additional investment and also draws implications of such measures
for government revenues. Its major point of departure from previous studies on
this subject for developing countries is that it models a dynamic production
structure with endogenous capacity utilization. Taxes and incentives enter into
the user cost of capital and thereby affect producer decisions as to the choice
of inputs, technology and capital accumulation. Empirical estimation of this
model allows one to infer the impact of investment incen*ives as well as revenue
foregone implications of such tax expenditures. Thus the model results yield an
empirically derived cost-benefit ratio which due to its objective nature is
superior to standard cost-benefit analysis and "king-Fullerton type marginal
effective tax rate analysis (for developed country applications see Shah (1986)
and Bernstein (1987)).
Pakistan has been chosen as a case study for an empirical examination
of the effectiveness of investment incentives in view of the policy emphasis on
these instruments and also because of excellent time series and cross section
industry level data. Section II describee in brief the regime of tax incentives
for industrial and technological development in Pakistan. Section III describes
the theoretical model aw well as presents an empirical specification. Section
IV describes the data and estimation and testing procedures. Section V presents
empirical results. Finally, Section VI carries out policy simulations and draws
ove-all policy implications from the analyses presented in this paper.
1
Thn *,aper concludes that the investment tax credit has not been an
effective instrument for stimulation of investment in Pakistan and that the
private investment stimulation offered by this measure, falls short of the
revenues foregone by the government. Full expensing allowed for R&D
expenditures, on the other hand, has been found to be a cost-offective instrument
of tax policy.
II. Corporate Tax Incentives in Pakistan
Pakistan has followed a stable corpe-ete tax rate regime since early
1960e. Corporate income tax rate at 30% and a super tax at 25% have been
maintained consistently during the last two decades. Only in the fiscal year
1989-90, was the super tax rate brought down to 15%. Foreign direct investment
receives tax treatmert equivalent to domestic investment. Louses are allowed to
be carried forward six years but no carryback of such louses is permitted. A
sales tax at 12.5% is payable on all domestically manufactured goods by the
producer and on imported goods by the importer. Currently (1989-90), import
duties at differential rates are imposed on imported machinery and equipment.
These rates vary from 20% to 50% if similar machinery was not manufactured in
Pakistan and a higher rate of 80% applies to imported machinery with domestic
substitutes. Businesses are further subject to a large number of miscellaneous
licensing fees and charges.
The regime of fiscal incentives through the corporate income tax has
experienced significant changes over time. From time to time, Pakistan has
relied upon a variety of fiscal incentives to stimulate investment. These
include accelerated capital consumption allowances for certain physical assets,
full expensing for R&D investments, tax rebates, regional and industry specific
tax holidays and investment tax credits. These are briefly discussed belows
Tax Holidays: Tax holiday for two years for specific industries (e.g.,
engineering goods) and specific regions (most of the country except major
metropolitan areas) was introduced in 1959-60. The holiday period was
subsequently raised to four years in 1960-61. These tax holidays were eliminated
2
in 1972-73 but reinstated again in 1974-75. Presently tax holidays for fivc
years are permitted to engineering goods, poultry farming and processing, dairy
farming, cattle or sheep breeding, fish farming, dates processing and manufacture
of .gricultural machinery industries and also to all industries in designated
areas of the country.
Investment tax credits: Industries are eligible for varying tax
credite according to location. A general tax credit for balancing,
modernization, and replacement of plant and equipment was introduced at 15% rate
in 1975-76 but its application was restricted to designated areas. Since 1976-
77, the credit was made available regardless of location and type of industry.
This credit was withdrawn in 1989-90 and reinstated again in 1990-91.
Tax rebates: Companies exporting goods manufactured in Pakitan are
entitled to a rebate of 55% of taxes attributable to such sales.
Accelerated Capital Consumption Allowances: Capital consumption
allowances follow accelerated schedules for machinery and equipmernt, transport
vehicles and housing for workers (25%), oil exploration equipment (100%), ship
building (20-30%), and structures (10%) on a declining balance method.
Expenditures relating to research and development, transfer and adaptation of
technologies and royalties are eligible for full expensing.
Of the incentives enumerated earlier, only the two genera:. _..centives,
namely, investment tax credit for physical investment and full expensing of ROD
expenditures are the subjects of investigation in this paper. Since these two
types of incentives are widely used in both the developed and the developing
world*, an evaluation of their impacts are expected to yield lessons of general
interest to policy makers in Pakistan and elsewhere. The following sections
present an empirical examination of this issue.
III. The Model
A flexible accelerator type dynamic factor demand model with endogenous
capacity utilization (see Epstein and Denny, 1983), as described in the following
section, is eminently suitable to examlne the impact of tax policies on
3
investment in a developing economy. The model employs a flexible and non-
restrlctive technology and capturee short run divergence of fixed factors from
th(tAr equilibrium values as well as the speed of such adjustments.1 The
theoretical und. pinnings and empirical form of this model is discussed in the
following:
L. A Flexible Accelerator Model
Consider that a typical firm in manufacturing industry faces the
following short-run cost function (C ( ))s
(1) C(K,I,W,Y) - min (W'Ss Y - F(3,K,I))
where S denotes the vector of perfectly adjustable factors, R denotes the vector
of quasi-fixed stocks, I denotes gross investment in those stocks, Y is the level
of output while W is the price vector associated with the perfectly adjustable
inputs. F(3SK,X) describes the technology and satisfies all classical
properties: twice continuously differentiable, increasing in (3, K) and
decreasingr in 1. The fact that it 4s decreasing in I reflects the assumption
that the quasi-fixed factors are subject to increasing internal costs of
adjustment (see Treadway (1970, 1974) and Mortensen (1973)). C(K,I,W,Y) is the
instantaneous cost functlon which satisfies: C x 0; C is increasing in (Y, I)
and decreasing in Kg C is convex in I and concave in W.
At any point in time the firm takes inuut prices, output, and state of
technology as given and minimizes the discounted sum of future costs over an
.&nfinite horizon. Specifically, the firm selects the investment path that
solves:
(2) V(K,Y,P) - Ninimum L (|0 (C(K,,W,Y) + P'K)dt: K - I - &8g; Kt|m no
where 8 is a diagonal matrix composed of the depreciation ratesl 81 is the
depreciation rate of the ith stocks P is the user cost (rental rate) vector
corresponding to Kg r is the real rate of discount, which is assumed to be
constant. We asgume static expectations with respect to output and prices, i.e.,
4
the current 'evel of output and prices will prevail forever. The rmainLng
notations are as followas (1) denotes transposLtion: ('1) denotes
Lnversions a dot over a functLon (e.g. K) denote. differentiation wlth respect
to time. Boldface-type letters represent vectors or matrices. FLnally,
subscripts of functions denote dLfferentiatLon (e.g. ;pdenotes
differentiation of V wlth respect to the vector P.
Note that the user cost of capital embodies the provLsLons in the tax
codes and is defined as follows (see Auerbach, 1990):
P - q (r + 8)(1 - 7 - 7z)( l-7) 1
where q - purchase price of capital
r - weLghted average real cost of debt and equlty finance
8 - economlc depreciation rate
7 - investment tax credit rate
Y - corporate tax rate
s - present value of depreciation allowances
0 - a profitabllity parameter.
V(K, Y,P) is the value function and is characterized by the following
set of propertLes (for notational convenience we suppress Lts arguments):2
V 2 0 i se concave ln Ps (r44)Vk - P - V0K C Ot Vi < 0S LV- Yyk O-
After defining the value function we can apply the following analogue
of Shophard's lemma (McLaren and Cooper, 1980)s
(3a) K (K,?,P) - Vpk (j - K),
(3b! * (K,Y,?) - -rn, + vKJCx.
Expressions (3a-3b) define the polLcy functionw or the optimal stock profiles for
both quasL-flxed (3a) and perfectly adjustable (3b) factors. Upon application
of a specLfic functLonal form, (3a-3b) will yleld the set of dynamic Lnput
demands.
5
ii. Empirical Model
In order to empirically implement the model we have to approximate (2)
by a functional form. We specify the following quedratic value function (Epstein
and Denny, 1983):
(4) V(K,y,P) = (1/2j [P'0 We] [W y +w [P IW] [
V7 ~ -1 ° 0
+ [P w [r"P &P
+ ~ we]L 0 r!i [:F
Bpp, ApkS Avku 5,,, B"PK, HPI and Fp denote appropriately dimensional matrix
parameters; B'pp = Bpp, S;, = s,,, and 'w - BP. Applying Shephard's lemma
analogue (3a) to the value function (4) results in:
(5a) K (K,Y,P) = (r - P )K + rk (p pP + w W) Y + Gp-
K'- K'(K*,Y,P) denoteo the levels of net investment, i.e., the dynamic factor
demands. Further, applying (3b) to (4) will yield the demands for the perfectly
adjustable inputs:
(5b) 3 (K,Y,P) = -r(3".W + BpW9)Y - rk,k(K - r1K) - Fp.
Equations (5a) and (5b) form the basis for estimation. Appendix A offers a
detailed description of the steps involved to arrive at (5a) and (5b).
Notice that an application of Euler equation to (2) will yield the
flexible accelerator adjustment paths for K.
(6) K ' K(r)(K - t(Y,P))
where X(r) is the matrix describing the adjustment mechanism and K(Y,P) denotes
the steady state levels of capital stocks. Then, we can express the
set of input demands defined in (5a) ln terms of (3) if w& eett
(7a) X(r) - r - Apk, and
(7b) K(Y,P) - -(r - Apk) (rApb(BD,P + OW)Y + p)'
where (7a-7b) express (Sa) in the flexible accelerator form.
6
IV. Data, XNttuation, asd TGstLng Procedure
Data in the current study cover the 1956-1985 time period for total
private sector manufacturing industries Ln Pakistan and were obtained from
various Pakistan government publicatLons. A total of five inputs were Lncluded
in ths study: three quasi-fixed (land and buildings, machinery and equpiment,
and R&D) and two perfectly adjustable (labor ond intermediate inputs). Basic
data on input shares and their growth rates are presented in Table 1. A detaLled
descriptlon of the data as well as the derivation of *.he rental rates of capital
used in the analysis is offered in Appendix B.
Since ,he model of the previous section was developed in a continuous
time framework, some modifications had to be made to render it estimable.
First, K was replaced by the discrete approxLmation (Kt - Kt..) and the system
of equations (5a-5b) was modified accordingly. Second, the time trend, which a
measure of output augmenting technical change, enters the equations as a discrete
approximation of the exponential function e -t. Finally, a disturbance error
term is additively appended to each equation. These disturbance terms reflect
random errors in optimization and are assumed to possess classical statistical
properties. While the introduction of such an error structure is an ad hoc
procedure, it shares the merit of keeping estimation straightforward, while
focusing on economic characteriutics of the model.
Since (5a) is a closed form solution for endogenous variables,
seemingly unrelateco regressions (SUR) were used to estimate the model. In
particular the nonlinear ITSUR procedure available in SAS was utilized to
simultaneolsly estimate the parameters of each equation.3 Because the
covariance matrix was iterated to convergence, the estimated parameters are
asymptotically equivalent to full informatin likelihood estimates (under the
assumptions of the error and model structure).
Price elasticities are calculated as enj - (aKj/8Pj)(Pj/Ki)r where Pj
refers to the rental rate of input j. Those expressions pertain to short-run
elasticities. To obtain the long-run elasticities we estimate the steady state
level of stocks, x. This results in the substitution of the matrix A pk
7
Table Is Average Growth Rates of Inputs and Input Shares in the Pakistani
Manufacturing Industry.
Period 1K 1(3 K4 Ks
Average Annual Growth Rates of Inputs (in percontages)
1956-65 12.7 11.2 11.5 6.2 8.4
1966-75 .1 3.6 4.2 4.2 8.0
1976-85 3.2 1.2 15.8 -0.2 13.4
Average Input Shares in Total Cost (in percentages)
1956-65 14.39 32.59 0.34 39.26 13.37
1966-75 13.67 38.02 0.41 35.13 12.78
1976-85 8.49 34.24 0.50 38.71 18.07
SOURCEs Calculated from data described in AppendIx B.
NOTES: Xi - land and buildings; K2 - machinery and equipment; K3 - R&D; K4 -
labor; K5 - intermediate inputs.
8
by the matrix (a - r) APk in (6). Long-run elasticlties are then derlved
in a straightforward fashion. Output as well as tax elasticitles are obtalned
in a similar manner.
V. Empirieal Results
Tables 2 and 3 report parameter entimatem regarding the quasi-fixed and
perfectly adjustable factors.4 Of these, adjustment coefficients are of special
interest. These coefficients give the speed of adjustment of the capital lnputs
to their respective long-run equllibrium levels. Specificallyt the land and
buildings coefficient (Ml,) is -0.18 which indicates that about 18% of the
adjustment process takea place within a year or alternatively it taku.. -ore than
five yerrs for the full adjuutm3nt to occur. On the contrary, the coefficient
associated with machinery and equipment (M22) indicates that the full adjustment
will occur in slightly lo.aa than two years. Finally, th6 R&D adjustment
coefficient (M33) indicates that 26% of the adjustment process will occur withln
a year. The relatively slow adjustment of R&D as opposed to machinery and
equipment is consistent with studies for Canada (Bernstein, 1986) and the US and
Japan (Nadiri and Prucha, 1989). Another r.uslt of interest is the cross-
adjustment cotiffcients of land and buildings and machinery and equipment with
R&D. Contrary to the above mentioned studiem, here we find that a deficient
stock of R&D induces substantial decrease in physical capital.
Table 4 reports short- and long-run prLce and output elasticitles. The
short-run response of capital use to own rental rate changes is very small and
negative as expected. Long-run responses on the other hand are substantially
larger and exceed unity for structures. Increases in output have a positive
long-run effect on all inputs wlth the elasticity exceeding unity for physical
assets and R&D capital.
Table 5 reports the corporate tax rate and investment tax credit
elasticitLes. As expected, corporate income tax rate increases adversely affect
9
Table 2: Reduced Porn Parameter 3stiaates -- guasi-FLxed Factors.
Parameter Estimate Parameter Estimate
M11 -0.1897 E23 1.6952
(0.77) (0.53)
M12 -0.0476 E31 -0.0003
(0.44) (0.08)
M13 10.2074 E32 -0.0028
(0.70) (0.47)
M21 -0.1012 E33 -0.0050
(0.23) (0.67)
M22 -0.5562 Gil -0.2756
(2.74) (0.87)
M23 60.1381 G12 0.3451
(2.29) (0.87)
M31 0.0059 021 -1.4481
(2.37) (2.42)
M32 -0.0003 G22 1.3963
(0.29) (1.95)
M33 -C.2634 G31 0.0062
(1.77) (1.76)
Ei -0.0900 G32 -0.0011
(0.24) (0.28)
E12 -0.1414 0.0379
(0.24) (2.30)
E13 0.1993 Hi -40.5454
(0.27) (1.01)
B21 0.5306 H2 -219.2600
(0.79) (2.71)
E22 -0.8115 H3 -0.3226
(0.77) (0.79)
NOTES Numbers in parenthesis denote absolute t-ratios. The subscripts denote:
1 - land and buildings; 2 - machinery and equipment; 3 - R&D; 4- labor; and 5 -
intermediate inputs.
10
TALE 3t Reduced Form Parameter Estimates -- Perfectly Adjustable Factors
Parameter Estimate Parameter Estimate
Rl -0.1362 Q23 0.3310
(0.45) (0.76)
R12 0.3479 Sit 0.1395
(0.75) (1.83)
R21 a 0.4364 812 0.0872
(2.87) (1.58)
R22 -0.5728 S13 4.3916
(2.43) (0.95)
Q11 0.1558 821 0.1188
(0.34) (3.09)
Q12 -1.2225 S22 0.0772
(0.27) (2.78)
Q¶3 0.2409 823 0.2250
(0.28) (0.10)
Q21 -0.1964 P1 1527.4000
(0.86 (16.17)
Q22 0.2508 F2 380.3700
(0.60) (7.99)
NOTES Numbers in parentheses denote absolute t-ratios. The subscripts are
defined in Table 2.
11
TAWLE 4t Short- and Long-Run Price and Output Blasticities--Calculated at
Sample means.
SR LR SR LR
e11 -0.083 -1.703 41 0.049 0.110
(0.075) (1.530) (0.045) (0.101)
812 -0.141 -0.214 842 -0.075 -0.074
(0.133) (0.202) (0.072) (0.071)
813 0.232 0.700 C43 0.095 0.096
(0.220) (0.664) (0.093) (0.094)
814 -0.410 -0.657 C44 -0.075 -0.180
(0.481) (0.770) (0.092) (0.221)
Ci5 0.429 3.010 845 0.146 0.130
(0.353) (2.481) (0.125) (0.111)
C21 0.148 -0.819 £51 -0.125 -0.165
* (0.126) (0.695) (0.058) (0.076)
C22 -0.244 -0.214 852 0.168 0.135
(0.217) (0.190) (0.082) (0.154)
C23 0.245 0.169 e5 0.258 -0.050
(0.221) (0.153) (0.116) (0.023)
824 -0.699 -0.422 65 0.423 0.828
; (0.819) (0.494) (0.274) (0.537)
825 0.532 2.390 855 -0.514 -0.811
(0.401) (1.806) (0.155) (0.246)
831 -0.007 -0.851 ,1* -0.049 1.693
(0.004) (0.489) (0.311) (2.156)
832 -0.064 0.150 42Q -0.206 1.614
(0.039i (0.090) (0.704) (1.999)
C33 -0.133 -0.163 no -0.011 1.287
(0.074) (0.091) (0.102) (1.133)
934 0.207 0.511 ,4 0.140 0.082
(0.147) (0.362) (0.099) (0.041)
en -0.033 1.268 1150 0.210 0.218
(0.013) (0.516) (0.276) (0.425)
MlO!3E SR and LR denote short- and long-run elasticLtLe.. The subscripts are
explained in Table 1. In addition: 7 m corporate rate and 7 - investment tax
credit. esj denotes the percentage change ln input L due to one percent change
in the rental rate of input j. '1fa denotes the percentage in lnput use i due to
one percent output change. Numbers Ln parenthesis denote standard errors.
12
2ABLE 5S Short- and Long-Run Tax glasticitles--Calculated at Sample Umns
SR LR
-0.031 -0.237 0.100
(0.028) (0.201) (0.110)
f2. -0.017 -0.142 eO 0.094
(0.014) (0.139) (0 077)
-0.006 -0.058 +st -0.044
(0.005 (0.029) (0.040)
* -0.002 -0.003 -0.041
(0.003) (0.003) (0.037)
-0.003 -0.011
(0.003) (0.008)
0.018 0.151
(0.018) (0.147)
52y 0.007 0.081
(0.008) (0.078)
* 0.005 0.054
(0.004) (0.033)
-0.001 0.002
(0.002) (0.002)
tsy 0.002 0.008
(0.002) (0.005)
NOTEBs SR and LR denote short- and long-run elasticities. The subscripts are
explained in Tables 1 and 4. e, denotes the percentage change in input use 1
due to one percent change in r. ti, denotes the percentage change in input use
i due to one percent change in 'y. e1, denotes the percentage change in the
rental rate of input i due to one percent change in T-. * denotes the
percentage change in rental the rate of input i due to one percent change in y.
Since y was introduced in 1976-77, the respective elasticity is the average of
9 observations only.
13
factor utilization in both areas whereas increases in investment tax credit have
the opposite effects. These effects as indicated by elasticity values are
uniformly small.
VI. The Impact of Taz Policies On Investsent in Physical and Knowledge Capital
The estimated model can be used to evaluate the investment impact of
alternate tax policy instruments per dollar of foregone revenues and using this
criterion to rank instruments in terms of their relative efficacy. For this
purpose, model parameters were used to simulate the impact of three policy
changes. First policy simulation assumes an increase in investment tax credit
from 15% to 30% and estimates the impact on factor demands for such a change for
three most recent years (see Table 6). A doubling of investment tax credit
expectedly leads to uneven changes in demand for various sectors with the
machinery and equipment receiving the most stimulus and R&D investment the least
augmentation. While this policy change results in a major increase in aggregate
investment, foregone revenues exceed the investment stimulus by a small margin.
Incremental benefit-cost ratio is estimated to equal 0.95 with such a policy
initiative.
Pakistan offers full expensing option for R&D investment. This measure
according to the calculations presented in Table 7 is seen to be a cost-effective
instrument for R&D investment stimulation. Incremental benefit-cost ratio is
estimated to be greater than one (1.49).
A third simulation assumes a corporate tax rate reduction from 55% to
30%. Such a tax reduction is estimated to have the greatest positive impact in
the short run for machinery and equipment and least for structures (see Table 8).
Foregone revenues associated with such a change are estimated to exceed changes
in aggregate investment by a significant margin. The incremental benefit-cost
ratio is calculated to be less than one (0.71).
14
VIz. Policy Implications
This paper examined the tax sensitivity of investment in physical and R&D
capital in Pakistan and found that while such investment was sensitive to various
tax measures, the elasticity values were without exception quite small. Further,
incremental benefit-cost ratio associated with changes in investment tax credit
and corporate tax rate was smaller than one. Full expensing option for R&D
investment was found to be cost effective. Pakistan currently follows a high tax
and low incentives regime in major metropolitan areas and a high tax and high
incentives regime in selected less developed areas. The analyses presented in
this paper suggests that fiscal incentives for investment were generally not cost
effective and therefore public policy emphasis should be on creating a stable low
tax regime.5 In terms of short run investment stimulation, investment tax credit
was found to be more efficient than the corporate tax rate reductions.
15
MuELs 6: Short-Run Effects of a Major Sncreass in Physical Ilvestmsat Tax
Credit*
Effects at Existina Outout Levels
p6rcent Cumulative 1983-85
(Million Ru2eesl
A. On Factor Demand s
Structures 8.8 4,484
Machinery and Equipment 15.7 25,201
A&D 4.9 241
B. Total Change in Investment 29,926
C. Foregone Revenues 31,416
D. Incremental Benefit-Cost Ratio (B + C) 0.95
NOTEs * Model calculations by assuming an increase in investment tax from 15%
to 30%.
16
TAJL 7: implications of Full UxpeunLsg Optiou for R&D Ivestment and
Oovezrnaat Revenues
1983-85
(cumulative thousands rupees)
A. R&D Investment Gains 443,130
B. Lose in Government Revenues 298,041
Benefit-Cost Ratio (A + 3) 1.49
17
Table Os Short-Run ffeocts of a Major Reduction in Corporate Incoas Tax Rate*
Effects at Exim:ina Outout Levels
P2rce" Cumulative 1983-85
(Million Rupees)
A. On Factor Demands
Structures 3.24 1,763
Machinery and Bquipment 13.66 21,671
R&D 3.96 192
B. Total Changes in Investment 23,832
C. Foregone Revenues 33,511
D. Incremental Benefit-Cost Ratio (B + C) 0.71
NOTBE * These calculations are based on model simulations assuming corporate tax
rate reduction from 55% to 30%.
18
ENDNOTES
1 Recent advances in dynamic duality (see Rpstein (1981), Epstein and Denny
(1983)) have facilitated empirical applications of such models, so that the
structure of the industry can be examined wlthout imposing severs restrictions
on the technology.
2. A complete characterization of the properties of the value function &s
well as the cost function can be found in Epstein and Denny (1983), whil- the
profit function can be found in Epstein (1981)).
3. Because of the nonlinear nature of the model and the large number of
parameters to be estimated, some simplifications were made. First, the model
was estimated in reduced form. We estimated expressions (All) and A12) as
described in Appendix A. Second, the two blocks of equations were estimated
separately, i e., we first estimated the three oquations corresponding to the
quasi-fixed factors and then the ones corresponding to the parfectly
adjustable factors. Finally, in order to account for heteroikedasticity, we
divided the stocks by the output, so the system was expressed in input/output
ratio form.
4. The results reported here are based on static expectations. In addition
we run the model by using first and second order autoregressive expectation
schemes regarding rental rates and output. Results regarding land and
buildings and machinery and equipment were fairly insensitive in terms of
adjustment rates and elasticities. On the contrary R&D showed a high degree
of sensitivity.
5. A referee has argued that this conclusion dose not strictly follow from
the model results.
19
Auerbach, A. "The Cost of Capital and Investment in Developing
Countrieu,"Working Papers Series 410, Public Economics Division, The World
Bank, April 1990.
Berndt, B. and C. Horrison. "Short Run Labour ProductivLty in a DynamicHodel."
Journal of Econometrics. 16(1981)0339-365.
BernsteLn J.I. Research and Dovelopment, Tax Inaentives, and the
Structure of Production and Financing. UnLversLty of Toronto Press,
Toronto, 1986.
Eloner, R. and I. Nadiri. "Investment Behavlor in Neoclassical Theory." Reviow
of Economics and Statiatics. 50(1968)t369-382.
Epstoen, L.G. and M.G.S. Denny. "The Multivarlate Flexible Accelerator
Model:Its Empirical RestrLctions and an Application to U.S.
Manufacturing." sconometrica. 51(1983):647-674.
Epstein, L.G. and A.J. Yatchew. "The Empirical Determination of Technology and
Expectations: A SimplifLed Procodure." Journal of Econometrics.
27(1985)t235-258.
Epstein, L.G. "Duality Theory and Functional Forms for Dynamic Factor Demands."
Review of Economic Studles. 48(1981)S81-95.
Government of Pakistan. Pederal Bureau of Statistics. Census of Manufacturing
Zndustries, Varlous Issues. Karachi.
Government of Pakistan. Finance Division. Economic Survey StatIstical
Supplements 1987-88. Islamabad.
Lucas, R. "Optimal Investment Policy and the Flexible Accelerator."
International Economic Review. 8(1967):78-85.
Meeose, R. "DynamLc Factor Demand Schedules for Labor and Capltal Under Rational
Expectations." Journal of Econometrics. 14(1980):141-158.
Mohnen, P.A., M.I. Nadirl, and I.R. Prucha. "R&D, Productlon Structure and
Rates of Return in the U.S., Japanese and German Manufacturlng Sectors:
A Non-separable Dynamic Factor Demand Model." European Economic Review.
30(1986):749-771.
Mortensen, D.T. "Generalized Costs of Adjustment and Dynamic Factor Demand
Theory." Econometrica. 41 (1973) t657-665.
McLaren, K. and R. Cooper. "Zntertemporal Duality: Application to the Theory
of the Firm." Econometrica. 48(1980):1755-1762.
Nadlri, M.I. and I.R. Prucha. "Comparison and Analysis of Productivlty Growth
and R&D Investment in the Electrlcal Machinery Industrles of the Unlted
States and Japan." Nimeo, New York University and University of Maryland,
January 1989.
Nadiri, I. and S. Rosen. "Interrelated Factor Demand FunctLons." American
Economic Review. 59(1969):457-471.
shah, Anwar (1986). Research and Development Investment, Industrial Structure,
Economic Performance and Tax PolLcLes. Finance Canada. Discussion Paper,
Ottawa, November.
20
Treadway, A.B. "Adjustment Costs and Variable Inputs in the Theory of
Competitive Firm." Journal of Economlo Thoory. 2(1970)t329-347.
Treadway, A.S. "The Globally Optimal Flexible Accelerator." Journal of
Economic Theory. 7(1974)tl7-39.
21
APPENDIX As DERIVATION OF INPUU DEMANDS
Rewrite the value function defined in (6) ass
(Al) V(K,Y,P) M (1/2)(P'B P + W'B' P + P'S W + W'BWW)Y + P'A>KS
+ W'Aw K + P r-1A 18 + W,r-lF
pk p p
and consider tgain the Shephard's lemma analogue regarding the quasi-fixed
inputs,
(A2) (K,Y.P) - Vpk(rVj - K)
Differentiating (Al) with respect to P and transposing the resulting
expression gives.
(A3) Vp . (BppP I BW W)Y + Ap+K ApkHp.
Differentiating VI with respect to R and inverting yields:
(A4) -1 A
Vpk Jpk
Substituting (A3) and (A4) into (A2) results in:
(A5) K (K,Y,P) - Apk(r((Bppp + BwoW)Y + ApkK + r ApkRP) - R).
Rearranging terms in (AB) yields the dynamic factor demands:
(A6) K (R,Y,P) (r - &pk)K + rApk(BppP + "WPW)Y + 3p.
The Shephard's lemma analogue regarding the perfectly adjustable inputs is
given bys
(A7) I (K,Y,P) = -rV% + V kK
Differentiating (Al) with respect to W and transposing the resulting
expression gives:
(AS) V4 - (B W + B P)Y + P'AK + ak +r + Fp.
v NW PMe pk vk p
Differentiating J. with respect to K yields
(A9) Vwk A wk.
substituting (AS) and (A9) into (A7) and rearranging terms results in the
22
input demands for the perfectly adjustable inputes
(AlO) 3* (K,,P) = -r(3.W + SpW)y - rk(K p p1.) - F .
To avoid nonlinearities in the estimation, we expressed (A6) and (AIO) in
reduced forms ass
(All) (K,?,P) UK + (NP + OW)Y + a and
p
(A12) 8* (K,?,?) (RW + QP)Y + S(K - r 1) - Fp.
where f - (r - ap) 3 rAmpopp, O a rA p f - -rB,,, R - -rS., and 8-
-rAw"
A descriptive exposition of the reduced form matrix parameters has as
followss
Ml 1 "12 "I]3 11 "12 2213 1 [I "12 [,
J W N 1 22 "23 , N B 1 22 "23 , O- 021 22 . 1F
[x1 "32 "33] 3 1 32 33,J 1 a32j .83
Rl a i12] rIi Q12 013] 2 1 12 8131 [t1
= 2 2 1 0 QI, a8W - , .
I L t22k 1 222 Q223 *21 S22 8W23. P L2
The structural form parameters of (All) and (A12) are then recovered from the
reduced form as Apk (r - 3), Bpp a (r - ) (r - M) lr LaG, B.
- -r n1, Rp"" -r 1R, and Akk 1 -r 18 where Ml, , 0, Q, R, and 8 are the
estimated reduced form matrix parameters.
23
APPENDIX Bs DATA DESCRIPTION AND CONSTRUCTION OF VARIABLES
Most of the data used in this study were obtained from various issues of
Census of Manufacturing Industries and the Economic Survey Statistical
Supplements 1987-88 and cover 1956-1985 period. The construction of variables
was done as followes
Land and Buildings: Quantity of land and buildings was constructed by
dividing stocks by the investment deflator. Stocks were constructed by
employing the perpetual inventory method, with depreciation rate set equal to
0.05. As a starting value of stocks we used the 1956 end-of-year book value
of land and buildings. The rental rate of land and buildings was calculated
by invoking the following formula (see Auerbach, 1990): Pt - qt(r+8)(1-y-
rz)((l--)0) 1, where: Pt - user cost (rental rate) of land and buildings; qt -
investment deflator; r - weighted average of thie real costs of debt and
equity finance where the weight is given by the shareholders, equity to total
capital employed ratio (constructed from data reported in various published
and unpublished sources; ranging between 0.047 and 0.110; 8 - depreciation
rate (set to 0.05); 7 -investment tax credit (introduced in 1977, 0.15); i -
corporate tax rate including super tax rate (equal to 0.55 as reported in
budget speeches); z - present value of investment allowances received by the
firm; e - profitability parameter (set to 0.90).
Machinery and Equipments Quantity and rental rate of machinery and
equipment were constructed analogously to that of land and buildings variables
except that the depreciation rate used is 0.10.
R&D: Quantity of RhD was constructed by dividing R&D stocks by the
price of R&D. R&D stocks were constructed using the perpetual inventory
method with the depreciation rate set qual to 0.10. R&D expenses were
obtained from United Nations (Industrial StatLstics Yearbook) and various
Government of Pakistan data sources. When data on R&D investment was not
available we used the royalties and other fees expenses. Rental rate of R&D
was calculated invoking the formula for rental rate described earlier and
setting z - 1.0 and a - 0.10.
24
Labors Quantity of labor was measured as the total number of days
worked durlng the year. The prLe- index was constructed by dlvidLng total
employmont cost during th year by number of days worked.
IntermedLate Inputst Intermediate inputs include electricity, petroleum
fuel, natural gas, and lmported and domestically pdoduced mlicellaneous
materials. Aggregate prle¢ and quantity indices were constructed from these
components by using the TornquLst approximation of DLvisia index.
Outputs Quantity of output was constructed by dividing total value of
output by the manufacturing output deflator.
25
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