Centre for Business and Economic Research
IBA Working Paper No. 18-5
Are All Public Investments Equally Efficient? Experience from the Pakistan Economy.
Qazi Masood Ahmed, Syed Ammad Ali
August 2018
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Research Funding and Publication Committee
Dr. Farrukh Iqbal
Dr. Qazi Masood
Dr. Huma Baqai
Dr. Sayeed Ghani
Dr. Huma Amir
Dr. Junaid Alam
Dr. M. Ayaz
Dr. M. Nishat
Dr. Sajjad Haider
Dr. Shahid Qureshi
Dr. Shakeel Khoja
Dr. Zeenat Ismail
Disclaimer: The views expressed in this paper are those of the author/s and do not necessarily
reflect those of the Institute of Business Administration, Karachi and Centre for Business and
Economic Research.
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The Centre for Business and Economics Research (CBER) publishes its working paper series for
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Abstract:
This study using the VAR methodology explores the impact of aggregate public investment, physical
investment (infrastructure and energy) and social sector investment (education and health) on private
investment, output and employment. This study using disaggregated data from nine sectors of the
Pakistani economy indicates these public investments have crowding in effect in 49 cases, while in 21
cases there is crowding out, labor absorption effect in 34 cases, while in 36 cases labor substitutions
and finally positive output effect in 52 cases, while in 18 cases output effects are negative. Overall, these
results indicate that all seven types of public investments are growth stimulating through both
crowding-in and labor absorption effects. The physical public investment has stronger crowding-in
effects than social public investment but the reverse is true for employment effects. As far as output
effects are concerned, analysis of the sum across the sectors shows all the public investment have
positive output effects - highest for health investment followed by infrastructure, energy and then
education. The results of the study reiterate the importance of trickle-up theory and support its axioms
and also support Keynesian crowding-in argument of public investment.
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Synopsis:
The issue of effectiveness of public investment on growth is massively debated in economic literature
ever since Solow (1956) and then Aschauer (1989A,B) started working on it. In economics literature, the
production function approach is commonly applied for such analysis. This study incorporates the VAR
methodology; treating all variables as endogenous and also capturing the dynamic feedback effects of
public investment on private investment, output and employment. This study is among the very few
studies in Pakistan that estimates the long term elasticities and marginal productivities of public
investment.
The trickle-down and trickle-up impacts of growth are crucial to reduce the inequalities and social unrest
in the society. To make growth inclusive, public expenditure plays a vital role through different channels
– output, employment and private investment and the analysis on the effectiveness and the relative
efficacy of disaggregated public investments can provide a more useful insight to policy makers. This
paper makes an early attempt in Pakistan to see the impact of physical investment (infrastructure and
energy) and social sector investment (education and health) on these variables. This highlights the size
of the impact of public investment on sectoral output and also which type of public investment is more
beneficial in developing country like Pakistan? The relative strength of physical capital versus human
capital is important issue in development studies and this study adds new insights into this discussion.
This study using disaggregated data from nine sectors of the Pakistani economy indicates in which
sectors the public investment has crowded-in private investment and where it crowded-out private
investment. Where labor has been absorbed following public investment and where public investment
has replaced labor? And finally because of all these direct and indirect effects the public investment has
increased output or reduced output? These are useful information for the policy makers who faces
budgetary constraints.
The study period consists of 1964 to 2014 and covers nine sectors, i.e. Agriculture, Mining and
Quarrying, Manufacturing, Electricity & Gas Distribution, Construction, Transport Storage &
Communication including Railway & Post office, Finance & Insurance, Wholesale & Retail trade and
Services including Ownership of Dwellings and Public Administration & Defense including Community
sectors.
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The study gives output elasticities, private investment elasticities and employment elasticities w.r.t.
aggregate public investment, total physical investment, total social investment, health investment,
education investment, infrastructure investment and energy investment. The results provide evidence
that these public investments have crowding in effect in 49 cases, while in 21 cases there is crowding
out, these investments have labour absorption effect in 34 cases, while in 36 cases labour substitutions.
The results also provide evidence that these public investments have positive output effect in 52 cases,
while in 18 cases output has decreased. Overall, these results indicate that all seven types of public
investments are growth stimulating through both crowding-in and labor absorption effects. The physical
public investment has stronger crowding-in effects than social public investment but the reverse is true
for employment effects. As far as output effects are concerned, analysis of the sum across the sectors
shows all public investment have positive output effects - highest for health investment followed by
infrastructure, energy and then education. The results of the study reiterate the importance of trickle-up
theory and support its axioms and also support Keynesian crowding-in argument of public investment.
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Introduction:
The issue of the effectiveness of public investment on private investment and consequently on growth is
debated vastly in economic literature. On the one hand the classical school of thought believes that
increment in public spending reduces economic growth by crowding out private investment as higher
spending requires higher taxes at individual or corporate level which creates a distortion in the choice of
economic agents or increases interest rate if the expenditures are financed through borrowing.
Keynesians, on the other hand, consider government spending a key variable for economic growth.
Keynesians argues that government development expenditures on health, education and infrastructure
increases labour productivity and also reduces cost of business which motivates private investment.
Since the seminal empirical work by Solow (1956), the issue continues to be tackled from different
angles. Some have used the production function approach and others have used single equation method
as suggested by Aschauer (1989A,B), which captures only the direct effects of public investment on
growth. Periera (2000) gave another twist to this literature by capturing the indirect effects of public
investment on output through its effects on other inputs like private investment and employment.
Following the theoretical debate on effectiveness of public spending numerous empirical studies have
been carried out, which examine the role of government spending by using different estimation
techniques and different forms of public spending e.g. public spending on education, health, aggregate
capital formation, infrastructure, defense, general consumption and many more. Schultz (1961) in his
seminal study on human capital stressed the importance of human capital as a major determinant of
economic growth and afterwards many studies have examined the role of public investment in human
capital in the form of health and education on the economic growth. A cross country study conducted by
Biswajit and Mukhopadhyay (2012) explored the impact of public health and education expenditures on
economic growth through a VAR/VECM model for 12 countries which results make evident that both
types of spending have significant positive impact on economic growth; however the education
spending has more profound impact than health spending, on growth.
Khan (2005) analysed the impact of average years of schooling, literacy rate, school enrolment and life
expectancy at birth on economic growth using a cross-sectional regression for 72 low and middle
income countries, including Pakistan, The results show all the educational and health indicators have
significant positive effect on real per capita growth. Bose, N. et. al. (2007) examined the effect of public
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expenditures on growth using a panel of 30 developing countries using a huge data set of 72 variables
using different regression at aggregated and disaggregated level; they concluded that government
capital expenditures and the education expenditures have significant positive effect on growth.
Mittnik and Neumann (2001), Kamps (2005), Afonso and Aubyn (2008) analysed the impact of public
investment on output, private investment and employment through a VAR model and found positive
effect of public investment in majority of the cases. Yang (2006) analysed the impact of public and
private investment on growth in Japan and USA through OLS and GMM techniques, the results show
that the both types of investment have positive output effect. Pereira (2000) pioneer work investigated
the effects of aggregate public investment and infrastructure investment at disaggregated level by using
a VAR model for US and found that both at aggregated and disaggregated levels public investment have
positive effects on output and crowd in private investment. This study found marginal productivity 4.46
indicating one dollar investments will increase private output by $4.46 and found the highest rate of
return in electric, gas, transit system, airfield etc. which was 16.1%. Pereira (2001) estimated a VAR with
private gross domestic product, private investment, public investment and private employment for US
economy and both private and public investment are further disaggregated into high ways and streets,
electric and gas facilities, sewage and water supply, education and hospital building and development
structure. At aggregate level he found that public investment has a positive effect on private
investment, the marginal productivity was $4.5 and annual rate of return 7.8%. Fan, et. al. (2002)
estimated the marginal productivity and returns of different types of public spending including R&D,
irrigation, roads, education, electricity and telephone investment in rural China using the panel data of
different provinces from 1970 to 1997. The estimated results are based on simultaneous equations
model, evident that the education investment has the highest marginal productivity among all sort of
public investment.
Wang (2005) analyzed the impact of five different types of government expenditures, he found
significant crowding-out effect of expenditure on capital & infrastructure while expenditure on human
capital has significant crowding-in effect, however the remaining public expenditure have no significant
effect on private investment in Canada. Murty and Soumya (2006) in case of India using a
macroeconomic general equilibrium model investigated the effect of public investment in infrastructure
on growth and poverty from 1978-79 to 2002-03 and concluded that a 20% sustain increased in public
infrastructure investment finance through borrowing by commercial banks, will increase real growth by
1.8% and 0.7% decline in poverty. In other studies Marattin and Salotti (2014) in case of UK and
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Matthew (2011) in South Africa also estimated efficiency of different types of public spending through
SVEC/VAR.
Khan and Sasaki (2001) analyzed the impact of per worker public capital; at aggregated and
disaggregated level specifically in agriculture related public investment, public transport &
communication investment and public investment in financial-social welfare investment, on economic
growth at aggregate and seven different sectors, furthermore he also analyzed the impact of these
public investment on aggregate private investment in case of Pakistan, by using annual data series from
1964 to 1997 through standard production function approach. The estimated elasticities of public
investment at aggregated and disaggregated level, employment elasticity and private investment
elasticities all are positive at aggregate level as well as at sectoral level, however the output elasticities
w.r.t. to employment were negative in 4 out of 7 sectors, namely in energy sector, transport &
communication and services sectors. Akram, et. al.(2008), Abbas(2000), Abbas and Foreman (2007) and
Qadri and Waheed (2011) examined the growth effect of health and education by using school
enrollment at different level of schooling, health indicators e.g. life expectancy, population per bed and
health expenditure. The results of these studies stress that both health and education have significant
positive effect on growth, however the growth effect is much greater in case of health expenditure
compare to education. Hyder (2001) examined the effect of real public investment on private
investment and growth through a VEC model during 1964 to 2001 and found a complementary
relationship between public and private investment and positive growth effect.
Saeed et. al (2006) examined the effect of public investment at aggregate and disaggregate level in a
VAR model using the real variables i.e. public investment, employed labour force, GDP and private
investment. The study found in agriculture there is crowding in while in manufacturing crowding out and
at aggregate level it is inconclusive. Naqvi (2003) analyzed the impact of per worker aggregate public
and private capital in case of Pakistan through a VECM model over 1965 to 2000. The results evident
that in exogenous model the elasticity of private and public capital per workers were 0.25 and 0.23
respectively, while in endogenous model the long term elasticity of public investment is much higher
than private investment i.e. 0.49 and 0.29 respectively. In a most recent study Ammad & Ahmed (2014)
and Ahmed & Ammad (2014) analysed the impact of public investment in different sectors and in the
energy sector on sectoral economic growth, private investment and employment in Pakistan. They
found a strong crowding-in effect of public energy investment.
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The present study is an addition in this literature and few more aspects. It is one of the early attempts
where the effects of social and physical capital and their components infrastructure, energy, health and
education are analyzed in terms of their marginal productivities both at aggregate and sectoral levels.
This study tests the classical and Keynesian hypotheses of crowding-in and also the trickle-up effects of
public investment both at aggregate and sectoral growth in Pakistan; to test these hypotheses this study
estimates a) the relative effects of public investment in physical (infrastructure and energy) and social
(health and education) sectors on output by estimating through long term marginal productivity, b) the
complementarity or substitutability of public investment on the private investment to see the crowding-
in or out effect, and c) the sectoral effect of these pubic investment on employment in each sector by
estimating employment elasticities. All these effects of public investment will be traced on nine sectors
of the economy. This study used Vector Auto Regressive (VAR/VECM) technique to measure the effect of
public investment on output, private investment, and employment for which separate VAR models are
estimated for each sector and each type of public spending. This methodology allows measuring the
dynamic feedback effect among the variables.
The present study extends the empirical analysis (Ahmed & Ammad 2014) and explores other types of
public investments on output, private investment and employments in the nine sectors. In this paper we
give results in three sets. Set 1 the impact of aggregate public investment, total physical investment,
total social investment and their specific components i.e. infrastructure, energy, health and education
on total output, private investment and employments in the economy. Set 2 the impact of Aggregate
public investment, aggregate physical investment and aggregate social investment on output, private
investment and employments in the nine sectors of the Pakistan economy and Set 3 on the four
components of physical and social investment i.e. energy, infrastructure, health and education on the
sectoral output, private investment and the employment in the nine sectors. The results of this study,
the output elasticities, private investment elasticities and employment elasticities 70 each, provide the
answers to some of the important policy questions and also help in future policy making process by
indicating which of public investments is more beneficial for which sectors of the economy.
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Methodology:
This study is based on the methodology applied by Pereira (2000, 2001) where a Vector Auto Regressive
(VAR/VECM) technique is used for measuring the effect of public investment on output, private
investment, and employment at sectoral level. This methodology allows measuring the dynamic
feedback effect among the variables. Each VAR model consists of Public investment, Private investment,
Output and employment for each sector. The VAR models can be defined as
p
i
tittt XACX1
----------(1)
Where X is a vector of (4x1), C is the intercept vector also (4x1), A is the matrix of coefficient (4x4) and
is the vector of error term (4x1). The selection of the variables is proposed in such a way to cover the
policy aspects of public investment as discussed in previous empirical studies.
The linear form of the model is
Xt = ∆log lpub, ∆log lpriv , ∆log Y, ∆log Emp,----------(2)
Where lpub, lpriv, Y and Emp are real public investment, real private investment, real output and
employment respectively. The paper uses same order in the analysis i.e. public investment first and then
private investment, output and employment.
Dynamic Feedback Effects:
Measuring the effect of public investment on other variable, an impulse response function for each VAR
model needs to be generated. By definition an impulse response function measures the effect of a shock
in one endogenous variable to other variables in the model. The residual of the VAR are
contemporaneously correlated whereas for measuring the effect of shock in one variable on another
variable, the residual should be uncorrelated. The VAR model can be modified in such a way that
contemporaneous correlation between the residuals is diagonal which is called orthogonalization. To
attain these uncorrelated residual Choleski decomposition is used and the resulting accumulated
impulse response measures the cumulative response of all variables due to change in policy variable i.e.
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public investment. The outcome of accumulated impulse response function provides the accumulated
long term elasticity of the VAR model for a shock in policy variable.
Long Term Accumulated Marginal Productivity:
The long term accumulated marginal productivity of policy variable measures the unit change of the VAR
model variables due to one unit change in policy variable. This concept of marginal productivity is
different from the conventional concept. One of the main reason is that it is not based on the
assumption of ceteris paribus; here it refers to the total (dynamic) marginal product because it capture
all the dynamic feedback among the variables. The value of marginal productivity is obtained by
multiplying the accumulated long term elasticity with the ratio policy variable to the response variable.
i
i
IPUBIPub
Y
log
log
---------(3)
The above equation (3) is the long term elasticity, which is obtained directly through an accumulated
impulse response function, which measures the accumulated change in growth rate of different
variables. The numerator of this elasticity is accumulated change in output growth rate of the ith sector,
while the denominator accumulated change in growth rate of public investment in the ith sector.
The above elasticity can be transformed into long term marginal productivity by multiplying the
accumulated long term elasticity with the ratio of policy variable to the response variable
i
i
IPUBIPub
Y
IPub
YMP
------------------------ (4)
The long term accumulated marginal productivity of policy variable measures the unit change of the VAR
model variables due to an unexpected one unit change in the policy variable mentioned above.
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Data Description and VAR Specification:
Data Description:
This study is based on annual time series data from 1964 to 2014 for all nine sectors of the Pakistan’s
economy. However, the data on finance & insurance, manufacturing, energy and wholesale & retail
trade sectors start from 1981 as the data was not available earlier for employment and public
investment. The study employed three variables from each sector i.e. output, private investment and
employment. There are seven policy variables i.e. public investment at aggregate level; which is public
investment in all sectors plus general public investment, second total public physical investment; which
is the sum of electricity & gas distribution sector (energy) and transport, storage & communication
sector (infrastructure), third, the total public social investment; which is the sum of health development
expenditure and education development expenditures, fourth, public energy investment; which is the
investment in electricity & gas distribution sector, fifth, public infrastructure investment; which is the
public investment in transport, storage & communication sector, sixth, health investment; which is the
health development expenditures and seventh, education investment; which is the education
development expenditures. All data series were obtained from the State Bank of Pakistan Annual
Report, 50 Years of Pakistan Economy, and various issues of the Economic Survey of Pakistan, , except
development expenditures on education which were taken from poverty reduction strategy papers
(PRSP) and for few years’ data from SPDC annual review (2002-03). As far as the data on employment is
concerned it is worth mentioning here that in Pakistani economy the informal employment dominates.
The Informal sector accounts for 73.6% of non-agricultural total employment, while the sectoral
distribution shows that the highest informal employment exist in wholesale & retail trade ( 34.3%)
followed by manufacturing (21.5%), construction (16.8%), community, social & personal services (15.4%)
and transport (10.9%). The other category (comprising of mining & quarrying; electricity, gas & water
and finance, insurance, real estate & business services) accounts for about one percent. (Source: LFS
2013-14).
The study employed all the variables in real term, the entire dataset is converted into real variables
through the GDP deflator for 2005-06, however to generate the common base of 2005-06 deflator series
we had to use the standard splicing technique for combining different base year deflators’ series of
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1959-60, 1980-81, 1999-2000 and 2005-06, Finally natural logarithm and difference is applied on all the
series to convert them into growth rate form, the variable being used in this study.
Following the official division of the economy, the entire economy is divided into nine main sectors and
the average share of the study variables are presented in Table 1 & 2. Table 1 shows the average decade
wise trend, throughout the study period, of public investment in selected policy variables; the table
shows that public investment in physical capital is much higher than social capital investment. Table 2
shows last 10 years averages of private variables from 2004 to 2013, which shows that in terms of
output the highest share goes to agriculture followed by wholesale & retail trade, services and
manufacturing while the energy sector has lowest contribution in GDP. The private investment average
share trend shows that the highest share of private investment goes to services sector followed by
agriculture, manufacturing and transport & communication sectors respectively. The employment
history shows that the highest employment share belongs to agriculture followed by wholesale & retail
trade, manufacturing, services, construction, transport storage and communication, finance and
insurance, electricity and gas distribution, and then mining & quarrying. Furthermore, the graphical
trends of all the study variables are presented in appendix-C.
Table 1 Average Public Investment in Policy Variables
Table 1: Average Public Investment in Policy Variables (Million Rs.)
Years Aggregate Physical
Investment Infrastructure Energy
Social
Investment
Education
Development
Expenditures
Health
Development
Expenditures
1964-1973
2963.2 546.4 288 258.4 249.72 189.12 60.6
1974-1983
21360.3 5148.6 2104.1 3044.5 1691.6 1024.8 666.8
1984-1993
69795.3 28422.6 10294.6 18128 7011.48 4661.28 2350.2
1994-2003
177025.1 78492.3 40373.8 38118.5 18231.94 12693.14 5538.8
2004-2013
499819.1 122529.2 61209.6 61319.6 90581.57 69023.47 21558.1
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Table 2 Average Value of Last 10 years
Table 2: Average Value of Last 10 years (2004-2013)
Sector Output (Million Rs.)
Private Investment (Million Rs.)
Employment (Thousand)
Agriculture 2989397 372721 22423 Wholesale & Retail Trade 2468369 36851 7545 Services 2391546 405924 6728
Manufacturing 1789142 283305 6845
Infrastructure 1418818 214285 2712
Finance and Insurance 401802 28220 414
Mining & Quarrying 398838 27289 93 Construction 265098 13325 3287 Energy 235643 20372 324 Sum/Aggregate 12358653 1402291 50708
VAR Specification and Estimation: In order to estimate the demarcated model, all the variables are used in logarithmic growth rates; taking
first difference of original variables, while Augmented Dickey-Fuller (1979) and Philips Perron (1988)
tests are used to check the order of integration; the results of this unit root analysis, presented in Table
6 Appendix-A, shows that all the growth variables are stationary i.e. I(0). As mentioned in the literature,
the innovation in the growth rate of public investment variables will temporarily effect the growth of
other variables which by definition will translate into permanent effect on the level of these variables.
The selection of optimal VAR lags length is based on Schwarz Information Criterion (SC) and the Akaike
Information Criterion (AIC). For each model, lag selection was made on the basis of Schwarz Information
Criterion using different specifications up to four lags. The results1 reveal that in all cases one lag is
showing a minimum information criterion value; therefore, one lag is used in the VAR models.
Furthermore, other diagnostic tests were applied to address the issues of heteroskedasticity, serial
correlation, normality and parameter stability. The diagnostic results, presented in appendix-D, endorse
that all the models are free from heteroskedasticity and serial-correlation problems, except a few. The
assumption of normality is also tested in all the cases, however the results do not support the normality
assumptions in most of the cases, but we can discount this issue as Lutkepohl (1991) discussed that the
VAR parameters estimators do not depend on the normality assumption. Finally, for stability of the VAR
models AR inverse roots test is applied for all the models which shows, mentioned in appendix-E, that in
1 For the sake of brevity the information criteria results are not reported, but available on demand.
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all the VAR models parameters are stable i.e. lie inside the unit circle. For the sake of brevity the results
of diagnostic tests are not reported, but readily available on demand.
Sensitivity Analysis:
In order to test the robustness of the results we have carried out a sensitivity analysis. Since all the
marginal productivities are based on long term accumulated elasticities derived from impulse response
function so the sensitivity analysis is based on different simulations in the main model by removing one
or two variables to confirm the relationships established in the main model. To check the variation in
elasticities we performed seven different simulations i.e. one the initial or main model consist of all four
variables of the interest, in second case a three variables VAR model is estimated where public
investment, private investment and employment are used, in third case the estimated VAR based on
public investment, private investment and output, in fourth scenario the VAR based on public
investment, employment and output, in fifth case a two variable VAR consist on public investment and
private investment, in sixth case public investment and employment and in seventh case public
investment and output were incorporated in a VAR model. By applying all these simulations we
generated 280 elasticities for each type of variable i.e. private investment, employment and output. The
sensitivity results strongly validate the main model results in all the cases2. Furthermore, to verify the
sensitivity of impulse response results’ we compared the result of the main model with generalized
impulse response results; and found no significant differences between both results.
Empirical Results:
We presented here three set of results and analyses, Set 1 the impact of aggregate public investment,
total public physical investment, total public social investment and their four components i.e. health,
education, infrastructure and energy on total output, private investment and employments in the
economy (Table 3), Set 2 the impact of aggregate public investment, total physical investment and total
social investment on output, private investment and employments in the nine sectors of the economy
(Table 4) and Set 3 on the four components of physical and social investment i.e. energy, infrastructure,
health and education on the output, private investment and the employment in the nine sectors (Table
5).
2 Due to limited space, as we have total 1120 elasticity coefficients, the results are not reported; however available
on demand.
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Table 3 Impact of Different Public Investments on Aggregate Economy (MPs)
Table 3 Impact of Different Public Investments on Aggregate Economy(MPs)
Type of Public Investment Output Private Investment
Employment
Aggregate Public Investment 0.301 0.148 463
Physical Investment 0.635 0.619 -480 Social Investment 0.901 0.364 3463
Energy Investment 0.289 0.279 -431
Infrastructure Investment 2.089 1.686 -1,563
Health Investment 2.315 0.778 18,065
Education Investment 1.368 0.447 3,186
Set 1- Aggregate Analyses of Public Investment:
Table 3 shows that all seven public investments have a positive impact on private investment in Pakistan
which shows crowding-in phenomena in Pakistan. These results also reveal that the crowding-in
coefficients for total physical investment are much higher than the social investment i.e. the marginal
productivity of physical investment (0.619) is much higher compared to marginal productivity of social
investment (0.364)). This implies government efforts to increase private investment will be more
successful if the government investment concentrates more on physical investment. Furthermore all the
components of physical and social investments show crowding-in effect on private investment and
among them the highest marginal productivity is registered for infrastructure (1.686) followed by health
(0.778), education (0.447) and lowest marginal productivity is registered for energy investment (0.289).
Table 3 also analyzes the impact of these public investments on total employment. The impact of
aggregate public investment on total employment in the economy is positive - one million rupee
aggregate public investment will generate 463 jobs through the direct effect of public investment and
the indirect effect through the changes in private investment on employment. Table 3 shows the
relative impact of social investment on employment is much higher than the physical investment. This
further shows the impact of the components of social investment i.e. health and education investments
the employment effects are positive and much higher than the components of physical investment i.e.
infrastructure and energy investment which are negative.
Table 3 further shows in all seven cases the impact of public investments on output is positive. This is
the result of direct effects of public investment on output and indirect effect of public investment on
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output through private investment and employment. The results show the impact of social investment
on output is higher than physical investment, but their components show the highest impact on output
comes from health investment followed by infrastructure, education and energy investment. This Table
shows that in terms of marginal productivity the impact of aggregate public investment on output is
0.301 and further shows that the impact is higher for social investment (0.901) than physical investment
(0.635). Table 3 also shows the impact of component of these investment, the highest impact on output
comes from health investment (2.315) followed by infrastructure (2.089), education (1.368) and energy
investment (0.289).
We can recapitulate this section by saying that the aggregate public investment, total physical and
social investments and their components has positive and larger effect on output in Pakistan economy,
we also conclude that all types of public investment has crowding-in phenomena in Pakistan and in case
of aggregate and social investment the impact on employment are also positive. We can further
conclude the impact of social investment is higher than physical investment on output because of their
significant impact on employment. It is also concluded that physical investment has more significant
crowding-in effects while social investment has more significant employment effects. Our analysis
further shows the impact of health investment on output is highest because of its very high impact on
employment but the infrastructure investment has also very high positive impact on output because of
its significant crowding-in effect on private investment. Similarly the education investment effect on
output is positive because of much larger effect on employment and the energy investment also has
positive output effect because of its crowding-in effect.
Set 2 - Sectoral Analysis of Public Investments:
The results of our next empirical analysis are given in Table 4. This is based on the impact of aggregate
public investment, total public physical investment and total social public investment on the sectoral
output, private investment and employment in all nine sectors of Pakistan’s economy. In column 1 we
divided these sectors in two parts i.e. first, major commodity producing sector, and second services
sector and other sectors. In commodity producing sector we have agriculture and manufacturing sectors
whereas the remaining seven sectors are service related sectors, except a very small mining & quarrying
sector. These latter seven sectors are place in descending order according to their share in GDP, as
mentioned in table 2.
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The top four sectors, two from commodity sectors i.e. agriculture and manufacturing sectors and two
from services sectors i.e. whole sale and retail trade and services including community services, public
administration, defense, ownership of dwelling; covers almost 80% of the total economy. The other five
sectors are relatively small and constitute 20% of the total economy, therefore our analysis is divided
into two categories the first covers first four sectors referred as bigger sectors separately from the
analysis on other five sectors which referred to smaller sectors.
First we analyzed the impact of aggregate public investment, total physical public investment and total
social public investment on private investment in nine sectors of the economy. All bigger sectors shows
crowding in phenomenon in all the cases. For smaller sectors, the results are mixed showing both the
crowding-in and crowding-out phenomena i.e. in 5 out of 15 cases there is crowding-in and in remaining
cases crowding out is observed (Table 4 columns 5-7). The last row of columns 5-7 in Table 4 shows the
sum of across the sectors, reveals crowding-in of all types of public investments and the marginal
product is equal to, 0.196, 0.603 and 0.7698 for aggregate public investment, public physical investment
and public social investment respectively.
The impact of these public investments on employment shows that in bigger sectors the results are
predominantly negative only in 4 out of 12 cases there is a positive employment effect; in three out of
four positive cases, total social public investment has positive employment effect in agriculture sector,
wholesale & retail trade and services sectors. However the majority of bigger sectors show negative
employment effects i.e. replacement effect of aggregate public investment on labor and the impact of
physical capital investment are negative in 7 of 8 cases. For smaller sectors, the results are mixed and
half (8 of 15) of the cases in smaller sectors show the replacement of labor effect of public investment.
The last row of table-4(column 8-10) shows only in social public investment the sum of across the
sectors the impact is positive whereas in aggregate public investment and physical investments the sum
of across the sectors impacts is negative. The results on employment are not consistent to economic
intuition but also not unpredictable in Pakistani economy as the informal employment dominates in
Pakistan. Under such dominating informal employment the results are sometime counter intuitive
especially in case of physical investment.
19
Table 4 Sectoral Analysis: Impact of Aggregate, Physical and Social Investment (MPs) on Sectoral Economy
Impact of Aggregate, Physical and Social Investment(MPs) on Sectoral Economy
Output Private Investment Employment
Sector Aggregate
Public Investment
Physical Capital
Investment
Social Capital
Investment
Aggregate Public
Investment
Physical Capital
Investment
Social Capital
Investment
Aggregate Public
Investment
Physical Capital
Investment
Social Capital Investment
Agriculture -0.006 0.072 -0.121 0.079 0.187 0.2384 206 -382 3045
Manufacturing 0.079 0.322 0.583 0.078 0.349 0.1263 -69 -913 -1008
Wholesale & Retail Trade 0.36 1.228 0.881 0.001 0.004 0.0151 -192 -987 1494
Services (Community Services +Public Administration & Defense +Ownership of Dwellings)
0.119 0.139 0.228 0.059 0.251 0.1459 -326 -1199 498
Transport, Storage and Communication
0.046 0.224 -0.173 -0.0003 -0.084 0.2061 -31 135 -234
Finance and Insurance 0.057 0.161 0.31 -0.011 -0.039 -0.0125 8 172 173
Mining & Quarrying 0.106 0.095 -0.023 -0.003 -0.014 -0.0258 -55 -183 -126
Construction 0.045 0.082 0.23 0.003 0.011 0.0078 -11 -110 -487
Electricity and Gas Distribution -0.046 -0.216 -0.073 -0.011 -0.062 0.0684 36 150 282
Sum Across the sectors 0.76 2.108 1.842 0.196 0.603 0.7698 -435 -3317 3636
20
Table 5 Results of Disaggregated Social and Physical Investment on Sectoral Private Variables in terms of Marginal Productivities (MPs)
Results of Disaggregated Social and Physical Investment on Sectoral Private Variables in terms of Marginal Productivities(MPs)
Sectors
Output Private Investment Employment
Energy Investment
Infrastructure Investment
Health Investment
Education Investment
Energy Investment
Infrastructure Investment
Health Investment
Education Investment
Energy Investment
Infrastructure Investment
Health Investment
Education Investment
Agriculture -0.093 0.487 -0.392 -0.098 0.333 0.252 0.660 0.290 913 -1,675 7,272 4,189
Manufacturing 0.044 0.614 -1.120 0.870 0.310 0.644 -0.299 0.217 -1,588 -1,569 3,904 -1,945
Wholesale & Retail Trade 2.113 1.493 2.247 0.939 0.001 0.002 0.004 0.022 -574 -2,388 6,105 1,298
Services (Community+Public Administration & Defense +Ownership of Dwellings) 0.542 -0.013 1.868 0.155 0.274 0.566 0.414 0.155 -4,497 1,385 7,324 -185
Transport, Storage &Communication 0.130 0.804 0.288 -0.287 -0.284 0.034 0.416 0.290 150 132 384 -541
Finance and Insurance 0.127 0.304 0.921 0.310 -0.092 -0.035 0.145 -0.025 -359 784 298 212
Mining & Quarrying 0.346 -0.140 0.242 -0.035 -0.019 -0.030 0.043 -0.047 -323 -214 -808 -99
Construction 0.085 0.129 0.901 0.265 -0.002 0.033 0.044 0.012 -283 -212 297 -774
Electricity and Gas Distribution -0.316 -0.533 -1.641 0.154 -0.122 -0.120 0.212 0.033 133 312 1,892 75
Sum Across the sectors 2.978 3.145 3.314 2.271 0.399 1.346 1.639 0.947 -6,427 -3,446 26,669 2,229
21
The effect of these three public investments on output is positive, except in a few cases. For example, in
bigger sectors only the agriculture sector and in smaller sector only the electricity & gas distribution
sector have negative impact of aggregate public investment. For the physical public investment all
sectors, except the smallest electricity & gas distribution sector, shows positive impact on output. The
impact of social capital investment on output all big sectors, except agriculture, show positive output
effect, but in case of smaller sectors, the results are mixed and only the finance & insurance and
construction sectors show positive output effect of social public investment.
At sectoral level, the coefficients of marginal productivities show very encouraging results and in all
bigger sectors, except the agriculture sector, the impact of public investments has significantly
increasing outputs. The impact of aggregate public investment in bigger sector is highest in case of
whole sale & retail trade sector followed by services & public administration and manufacturing,
whereas in smaller sectors the highest impact is in mining & quarrying, finance & insurance, transport &
communication and construction. The marginal productivity of physical capital investment in terms of
output is highest among the bigger sectors in whole sale & retail trade sector followed by manufacturing
whereas in smaller sectors the impact are in descending order as follows transport & communication,
finance & insurance, mining & quarrying and construction sectors. Similarly the marginal productivity of
social investment shows the highest effects in bigger sectors are in whole sale & retail trade sector
followed by manufacturing and services & public administration, while for smaller sectors the highest
impact is in finance & insurance and construction. This analysis clearly shows the bigger sectors are the
most important beneficiary of these public investments and their positive impacts outweigh negative
impacts on few smaller sectors. The sum of across the sectors output effects given in the last row of
table 4 (columns 2-4) in each case positive and confirm that public investment stimulates growth.
The other interesting aspect of this analysis is the inter-comparison effects of physical and social capital
investment on output, private investment and employment. Such effects on output shows that the
social capital has larger effect i.e. in five sectors including manufacturing, services from bigger sectors,
and finance & insurance, construction and electricity & gas distribution from smaller sectors, while in
remaining four sector the effect of physical capital dominate. Similarly, in terms of private investment
the social public investment also dominates. It has larger effect in 5 including two bigger sectors
agriculture and wholesale & retail trade sectors while physical investment has larger private investment
effect in 4 sectors including two bigger sectors manufacturing and services & public administration.
22
Finally in terms of employment the social public investment also has larger employment effect than the
physical investment; i.e. in 5 sectors the employment effect is positive and larger, including the three
bigger sectors, while physical investment has positive larger effect only in transport & Communication
sector. As far as the sum across the sectors are concerned, for output the impact is highest for physical
capital investment i.e. 2.108 compared to social capital investment which is 1.84. For private investment
the impact of public social capital investment is higher (0.7698) compared to physical capital investment
(0.60), finally the sum of across the sector employment effects is concerned the impact is higher for
social capital investment.
In conclusion the overall results are again very encouraging and show the aggregate public investment,
physical investment and social investment on private investment, employment and output are positive
in most of the cases. The positive impact of physical capital investment on output mainly comes from
crowding-in phenomenon of private investment, whereas in case of social capital investment the impact
on output mainly comes from the labor absorption phenomenon. However in few cases the results are
contradictory to the theoretical wisdom, as in the case of agriculture sector the effect of aggregate
public investment is negative on output but it is positive on private investment and employment, while
in case of transport & storage and mining & quarrying sectors aggregate public investment has positive
output effect but it has negative effect on private investment and employment, the same situation is
also found for mining and quarrying sector in case of physical investment.
Set 3- Component Analysis of Sectoral Analysis:
In the previous section we discussed the impact of physical and social investments now we discuss the
impacts of their components. Table 5 is based on the impact of the components of total physical
investment i.e. infrastructure and energy and total social investment i.e. health and education on
sectoral private investment, employment and output in the nine sectors of Pakistan’s economy.
The results show that in 15 out of sixteen cases the public investment has crowding-in effect in four
bigger sectors, only exception is health investment on manufacturing sector. In smaller sectors the
results are mix - half of the sectors show crowding-in while remaining half shows crowding-out effect.
The results show overall the crowding-in phenomena are very pervasive at sectoral level in Pakistan.
Sum across the sectors analysis (last row of columns 6-9 of Table 5) shows in all four cases the sum is
positive and highest in health followed by infrastructure, education and energy.
23
On employment, the components of public investments have mixed effects (Table 5) - in bigger sectors 6
out of 8 cases of health and education investment have positive employment effect, while in case of
energy and infrastructure investment just 2 out of 8 are positive in bigger sectors. Smaller sectors have a
mix effect where 11 out of 20 have positive employment effect and it is more vehement in case of
health and infrastructure investment. Sum across the sectors analysis (last row of columns 10-13 of
Table 5) shows public investment on health has highest employment effect followed by education. This
whole analysis of employment clearly indicates the public investment on health and education has
significant effects on employment generation compared to physical investment.
As far as output is concerned, the sum across the sectors analysis (last row of columns 2-5 of Table 5)
shows all public investment have positive effects and the positive effect is highest for health investment
followed by infrastructure, energy and then education. This analysis also shows in bigger sectors only in
the agriculture sector the output effect are mostly negative whereas in other three sectors most of the
outputs are positive. In the smaller sectors, only in the electricity & gas distribution and mining &
quarrying the most of the outputs are negative and in remaining sectors the output effects are positive.
Finally the comparative analyses shows that health has highest output effects in four sectors, education
and infrastructure has highest output effects in two sectors each and energy investment in one sector.
This clearly supports the argument of trickle-up approach of development.
The results of table 5 also have some outliers especially in case of agriculture sector the energy, health
and education investment have negative output effect but positive private investment and employment
effect in each cases, in the same way in services and electricity & gas distribution sectors infrastructure
and health investment have the same relation with negative output, but positive private investment and
employment effects respectively. Another set of outliers is found in case of energy investment; where it
has positive output effect but private investment and employment both are negative in finance &
insurance, mining & quarrying and construction sectors. Finally we can conclude the results from three
sets by saying that public investment has very positive effects on output, private investment and
employment. The results gives mixed results on the relative strength of physical public investment and
social public investment and their components analyses are also backing such results.
Another dimension of the result is the comparison of the sum of estimated sectoral MPs with directly
estimated aggregate public investment effects from VAR models for private investment, output and
24
employment specified for the aggregate of the economy. The following chart gives a comparison of the
results of table 3 and the last row of table 5
Table 5A Comparison of aggregate and sectoral sum
Sector
Output Private Investment Employment
Sum Across the sectors
Aggregate Public Investment
Sum Across the sectors
Aggregate Public Investment
Sum Across the sectors
Aggregate Public Investment
Energy Investment 2.978 0.289 0.399 0.279 -6,427 -431
Infrastructure Investment
3.145 2.089 1.346 1.686 -3,446 -1563
Health Investment 3.314 2.315 1.639 0.778 26,669 18065
Education Investment 2.271 1.368 0.947 0.447 2,229 3186
This provides insight as to whether both are close to each other or not. From this, we can glean
additional information on where the impact is potentially an outlier and creating problems. Our
analysis is based on the comparison in terms of their relative effects on output, private investment and
employment. In general results shows both are close in many cases but apart in few cases. For example
in case of output the two impacts are close to each other in case of education, infrastructure and health
but quite distant in case of energy investment. In case of private investment the impact are closer in all
four cases but more closer in case of energy and infrastructure. In case of employment effects the both
values are close in case of health and education but far away in case of energy and infrastructure.
25
Conclusions and Policy Implications:
Our study provides empirical evidences of the effectiveness of public investment on private investment,
output and employment. In the literature, the production function approach is commonly applied for
such an analysis. This study incorporates the VAR methodology; treating all variables as endogenous and
also allows capturing the dynamic feedback effect of public investment on private investment,
employment, and output.
The results of the aggregate public investment are similar to the previous study (Ahmed and Ammad
2014) and therefore the policy implications of both studies are very similar. The present study covers
more disaggregate public investments and provide some additional results which are more useful for
the policy makers in understanding the role of the government policy for public investment as strategy
to boost private investment in the country. The overwhelming results illuminate an important lesson
that the public investment attracted private investment in Pakistan in past and therefore to attract
private investment in future the government of Pakistan should increase public investment. This lesson
can also be learned from the experience of several developing countries particularly India. In India, in
last twenty years despite high fiscal deficit very high public investment was made which led to very high
economic growth. Similarly in 60s and 80s in Pakistan, very high public investment financed by high
budget deficit had led to high economic growth in Pakistan. Even the 70s experience of Pakistan
economy was also very unique. Although in 70s, very high but specific nature of public investment
(predominantly to build large public entities) did not attract high private investment but benefited
Pakistan economy in different ways. Initially due to high employment elasticities the public investment
absorbed large number of workers in 70s (Majid 2000) and subsequently it contributed to high
economic growth of 1980s once the large entities completed their gestation periods and start
productions in 80s.
The study gives output elasticities, private investment elasticities and employment elasticities w.r.t.
aggregate public investment, total physical investment, total social investment, health investment,
education investment, infrastructure investment and energy investment. The results provide evidence
that these public investments have crowding in effect in 49 cases, while in 21 cases there is crowding
out, these investments have labour absorption effect in 34 cases, while in 36 cases labour substitutions.
The results also provide evidence that these public investments have positive output effect in 52 cases,
while in 18 cases output has decreased. Overall, these results indicate that all seven different measures
26
of public investments are growth stimulating through both crowding-in and labor absorption effects.
These results support the finding of earlier studies Hyder (2001), Mittnik and Neumann (2001), Kamps
(2005), and Afonso and Aubyn (2008). The physical public investment has stronger crowding-in effects
than social public investment but the reverse is true for employment effects. As far as output effects are
concerned, analysis of the sum across the sectors shows all public investment have positive output
effects - highest for health investment followed by infrastructure, energy and then education. The
results of the study reiterate the importance of trickle-up theory and support its axioms and also
support Keynesian crowding-in argument of public investment.
The issue of development priorities is also addressed in this paper. This paper provides guidance to the
government about the relative efficacy of physical investment and their components infrastructure and
energy against the public social investment and their components like health and education. This study
provides empirical evidences that both physical investment and social investments have a positive
impact on the economy whereas physical investment has more intense effects on private investment
and the social investment has more vehement effects on employment. The sectoral analysis further
indicates that the impact on output is larger for physical investment compare to social investment
however in component analysis the impact of each component on output is positive but shows less
variation among them. The issue of development priorities is further explored in this study where the
sum across the sectors analysis shows public investment on health has highest crowding-in effect and
output effect followed by infrastructure. The sum across the sectors analysis further shows public
investment on health and education has the highest employment effect. This whole analysis of
employment clearly indicates the public investment on health and education has significant effects on
employment generation compare to physical investment. As far as output effects are concerned, the
sum across the sectors analysis shows all public investment have positive effects and positive effect is
highest for health investment followed by infrastructure, energy and then education.
Overall, these results indicate that public investment is growth stimulating through both crowding-in
and labor absorption effects of each type of public investment. The physical public investment has
stronger crowding-in effects than social public investment but the reverse is true for the employment
effects. The results also show that aggregate effects of social public investment on output are stronger
than physical investment as also mentioned by Wang (2005). The results of the study reiterate the
importance of trickle-up approach and support its axioms.
27
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29
Appendix A: Unit Root Results
Table 3 Unit Root Results
Unit Root Results
Variable
Augmented Dickey-Fuller test statistic Phillips-Perron test statistic
Level First Difference Level First Difference
Without
Trend
Trend and
Intercept
Without
Trend
Trend and
Intercept
Without
Trend
Trend and
Intercept
Without
Trend
Trend and
Intercept
Prob.* Prob.* Prob.* Prob.* Prob.* Prob.* Prob.* Prob.*
LAgr_GDP 0.9916 0.4334 0 0 0.9992 0.5576 0 0
LAgr_Iprv 0.9658 0.3391 0 0 0.9754 0.316 0 0
LAgr_Emp 0.9715 0.1749 0 0 0.9951 0.1797 0 0
LMing_GDP 0.9242 0.5565 0 0 0.9242 0.5235 0 0
LMing_Iprv 0.8834 0.6336 0 0 0.894 0.6451 0 0
LMing_Emp 0.0297 0.0683 0 0 0.0268 0.0595 0 0
LMfg_GDP 0.737 0.3189 0 0.0002 0.6906 0.3641 0 0
LMfg_Iprv 0.1669 0.9559 0.001 0.0011 0.1669 0.9559 0.001 0.0011
LMfg_Emp 0.9724 0.819 0 0 0.9752 0.8172 0 0
LConst_GDP 0.3573 0.5324 0 0 0.1911 0.6918 0 0
LConst_Iprv 0.4766 0.1334 0 0 0.6022 0.1299 0 0
LConst_Emp 0.0791 0 0 0 0.0311 0 0 0
LElec_GDP 0.5762 0.6589 0.0009 0.0034 0.5909 0.6074 0.0009 0.0099
LElec_Iprv 0.0576 0.0924 0.0028 0.0165 0.0567 0.0924 0.0022 0.0156
LElec_Emp 0.1757 0.1777 0.0001 0.0006 0.1755 0.1631 0.0001 0.0006
LTranp_GDP 0.6483 0.2775 0 0 0.6449 0.1689 0 0
LTranp_Iprv 0.8443 0.1801 0 0.0002 0.8888 0.4941 0 0.0002
LTranp_Emp 0.7908 0 0 0 0.0329 0 0.0001 0
LFinc_GDP 0.422 0.8109 0 0.0001 0.3846 0.8156 0 0.0001
LFinc_Iprv 0.4466 0.5965 0 0.0001 0.4415 0.5677 0 0.0001
30
LFinc_Emp 0.2601 0.524 0 0 0.2813 0.5071 0 0
LSrv_GDP 0.856 0.0633 0 0 0.7925 0.0525 0 0
LSrv_Iprv 0.9284 0.3481 0 0 0.9309 0.3481 0 0
LSrv_Emp 0.771 0.0021 0 0 0.8792 0.0018 0 0
LAgg_GDP 0.8852 0.2307 0 0 0.8422 0.2062 0 0
LAgg_Iprv 0.9633 0.325 0 0 0.9591 0.3051 0 0
LAgg_Emp 0.993 0.535 0 0 0.993 0.4834 0 0
Ledu 0.589 0.2433 0 0 0.5733 0.2433 0 0
LTrade_GDP 0.8808 0.3997 0.0001 0.0007 0.8878 0.4091 0 0
LTrade_Iprv 0.8248 0.567 0 0.0002 0.821 0.5298 0 0.0002
LTrade_Emp 0.8557 0.0002 0 0 0.9064 0.0002 0 0
LHealth 0.2318 0.6749 0 0 0.2321 0.6252 0 0
Linfra_Pub 0.4105 0.5324 0 0 0.49 0.5921 0 0
Lenergy_Pub 0.2924 0.6059 0 0 0.3204 0.7134 0 0
LHUMAN_CAPITAL 0.5706 0.5025 0 0 0.48 0.508 0 0
Lagg_Ipub 0.4075 0.8248 0 0.0002 0.3208 0.8355 0 0.0001 LPhy_Capital 0.3661 0.7408 0 0.0007 0.1695 0.8063 0 0
LAgr is representing the log of agriculture sector, Lming is representing the log of mining sector, LMfg is representing the log of manufacturing
sector, Lconst is representing the log of construction sector, Lelec is representing the log of electric and gas sector, LTranp is representing the log
of transport & communication sector, LFinc is representing the log of finance & insurance sector, LSrv is representing the log of services sector,
LTrade is representing the log of wholesale & retail trade sector, LAgg is representing the log of Aggregate economy, Lhealth is representing
development expenditures on health, Linfra_pub is log of public investment in Infrastructure, Lenergy_pub is log of public energy investment,
Lhuman-Capital is log of human capital investment and Lphy_capital is the log of physical capital investment.
EMP is representing the employment, IPub is representing the public investment, Iprv is representing the private investment and GDP is the gross
domestic product
31
Appendix B: Estimated long Term Elasticities
Table 4 Impact of Public Aggregate, Public Physical and Public Social Investment (Elasticities) on Sectoral Economy and Aggregate Economy
Impact of Public Aggregate, Public Physical and Public Social Investment(Elasticities) on Sectoral Economy and Aggregate Economy
Output Private Investment Employment
Sector Aggregate
Public Investment
Physical Capital
Investment
Social Capital
Investment
Aggregate Public
Investment
Physical Capital
Investment
Social Capital
Investment
Aggregate Public
Investment
Physical Capital
Investment
Social Capital
Investment
Agriculture -0.00104 0.002955 -0.00367 0.105633 0.061492 0.05795 0.004581 -0.00209 0.012301
Manufacturing 1981 0.021971 0.022084 0.029531 0.138258 0.151081 0.040374 -0.00506 -0.01635 -0.01333
Wholesale & Retail Trade 1981 0.072983 0.060946 0.032325 0.008779 0.01315 0.037172 -0.0127 -0.01604 0.017933
Services (Community Services +Public Administration & Defense +Ownership of Dwellings)
0.024776 0.007117 0.008639 0.072528 0.07579 0.032572 -0.02424 -0.02184 0.006699
Transport, Storage and Communication
0.016364 0.019338 -0.01105 -0.00071 -0.04823 0.087144 -0.00569 0.006101 -0.00782
Finance and Insurance 1981 0.070408 0.049148 0.069855 -0.18993 -0.16957 -0.04032 0.009821 0.050813 0.037939
Mining & Quarrying 0.132259 0.029255 -0.00519 -0.0479 -0.06388 -0.08585 -0.29628 -0.24154 -0.12281
Construction 0.085466 0.037839 0.078569 0.130416 0.102738 0.053112 -0.00167 -0.0041 -0.01342
Electricity and Gas Distribution 1981
-0.0971 -0.1122 -0.02805 -0.25893 -0.37119 0.3044 0.055121 0.056851 0.078665
Aggregate Economy 0.012189 0.006295 0.006601 0.052635 0.054115 0.023492 0.004567 -0.00116 0.006185
32
Table 5 Results of Disaggregated Social and Physical Investment on Sectoral Private Variables Elasticities
Results of Disaggregated Social and Physical Investment on Sectoral Private Variables Elasticities
Output Private Investment Employment
Sectors Energy
Invesment Infrastructure
Investment Health
Invesment Education
Investment Energy
Invesment Infrastructure
Investment Health
Invesment Education
Investment Energy
Invesment Infrastructure
Investment Health
Invesment Education
Investment
Agriculture -0.0019 0.0100 -0.0028 -0.0023 0.0548 0.0414 0.0382 0.0536 0.0025 -0.0046 0.0070 0.0129
Manufacturing 0.0015 0.0210 -0.0135 0.0336 0.0670 0.1391 -0.0228 0.0528 -0.0142 -0.0140 0.0123 -0.0196
Wholesale & Retail Trade
0.0525 0.0370 0.0196 0.0263 0.0020 0.0030 0.0021 0.0412 -0.0047 -0.0194 0.0174 0.0119
Services (Community Services +Public Administration & Defense +Ownership of Dwellings)
0.0139 -0.0003 0.0168 0.0045 0.0413 0.0853 0.0220 0.0264 -0.0410 0.0126 0.0235 -0.0019
Transport, Storage and Communication
0.0056 0.0347 0.0044 -0.0140 -0.0811 0.0098 0.0418 0.0934 0.0034 0.0030 0.0031 -0.0138
Finance and Insurance
0.0194 0.0462 0.0494 0.0533 -0.2010 -0.0761 0.1108 -0.0617 -0.0533 0.1159 0.0156 0.0355
Mining & Quarrying
0.0531 -0.0215 0.0131 -0.0061 -0.0427 -0.0665 0.0340 -0.1189 -0.2129 -0.1409 -0.1876 -0.0737
Construction 0.0197 0.0298 0.0733 0.0689 -0.0085 0.1517 0.0718 0.0636 -0.0053 -0.0040 0.0019 -0.0163
Electricity and Gas Distribution
-0.0821 -0.1385 -0.1501 0.0450 -0.3661 -0.3620 0.2247 0.1120 0.0251 0.0589 0.1258 0.0159
Aggregate Economy
0.0014 0.0103 0.0040 0.0076 0.0122 0.0736 0.0120 0.0220 -0.0005 -0.0019 0.0077 0.0043
33
Appendix C: Data Trends
Figure 1 Data Trends Aggregate Data Trends
Log of Real Aggregate Output
Log of Real Aggregate Private Investment
Log of Real Aggregate Employment
Log of Real Construction Output
Log of Real Construction Private Investment Log of Real Construction Employment
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGG_GDP
10.8
11.2
11.6
12.0
12.4
12.8
13.2
13.6
14.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGG_IPRV
9.6
9.8
10.0
10.2
10.4
10.6
10.8
11.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGG_EMP
10.0
10.4
10.8
11.2
11.6
12.0
12.4
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LCONST_GDP
4
5
6
7
8
9
10
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LCONST_IPRV
5.2
5.6
6.0
6.4
6.8
7.2
7.6
8.0
8.4
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LCONST_EMP
34
Construction Sector Data Trends
Energy Sector Data Trends
Manufacturing Sector Data Trends
Log of Real Energy Output
Log of Real Energy Private Investment
Log of Real Energy Employment
Log of Real Manufacturing Output
Log of Real Manufacturing Private Investment
Log of Real Manufacturing Employment
10.4
10.8
11.2
11.6
12.0
12.4
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10
LELEC_GDP
7.2
7.6
8.0
8.4
8.8
9.2
9.6
10.0
10.4
10.8
11.2
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10
LELEC_IPRV
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10
LELEC_EMP
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LMFG_GDP
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LMFG_IPRV
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LMFG_EMP
35
Mining Sector Data Trends
Services Sector Data Trends
Log of Real Mining Output
Log of Real Mining Private Investment
Log of Real Mining Employment
Log of Real Services Output
Log of Real Services Private Investment
Log of Real Services Employment
8
9
10
11
12
13
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LMING_GDP
5
6
7
8
9
10
11
12
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LMING_IPRV
1
2
3
4
5
6
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LMING_EMP
11.6
12.0
12.4
12.8
13.2
13.6
14.0
14.4
14.8
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LSRV_GDP
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LSRV_IPRV
7.00
7.25
7.50
7.75
8.00
8.25
8.50
8.75
9.00
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LSRV_EMP
36
Transport & Communication Sector Data Trend
Finance & Insurance Sector Data Trends
Log of Real Transport & Comm. Output
Log of Real Transport & Comm. Private Investment
Log of Real Transport & Comm. Employment
Log of Real Finance Output
Log of Real Finance Private Investment
Log of Real Finance Employment
10.4
10.8
11.2
11.6
12.0
12.4
12.8
13.2
13.6
14.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LTRANP_GDP
8.8
9.2
9.6
10.0
10.4
10.8
11.2
11.6
12.0
12.4
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LTRANP_IPRV
5.6
6.0
6.4
6.8
7.2
7.6
8.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LTRANP_EMP
10.4
10.8
11.2
11.6
12.0
12.4
12.8
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12
LFINC_GDP
5
6
7
8
9
10
11
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12
LFINC_IPRV
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12
LFINC_EMP
37
Wholesale & Retail Trade Sector Data Trends
Agriculture Data Trends
Log of Real Agricultural Output
Log of Real Agricultural Private Investment
Log of Real Agricultural Employment
Log of Real Agricultural Output
Log of Real Agricultural Private Investment
Log of Real Agricultural Employment
12.4
12.8
13.2
13.6
14.0
14.4
14.8
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12
LTRADE_GDP
7.5
8.0
8.5
9.0
9.5
10.0
10.5
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12
LTRADE_IPRV
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12
LTRADE_EMP
12.4
12.8
13.2
13.6
14.0
14.4
14.8
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGR_GDP
8.8
9.2
9.6
10.0
10.4
10.8
11.2
11.6
12.0
12.4
12.8
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGR_IPRV
9.0
9.2
9.4
9.6
9.8
10.0
10.2
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGR_EMP
38
Public Sector Variables Data Trends
Log of Real Pubic Investment in Energy
Log of Real Public Education Investment
Log of Real Pubic Investment in Infrastructure
Log of Real Pubic Investment in Health
8.0
8.4
8.8
9.2
9.6
10.0
10.4
10.8
11.2
11.6
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LENERGY_IPUB
7.6
8.0
8.4
8.8
9.2
9.6
10.0
10.4
10.8
11.2
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LEDU_DEV
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LINFRA_IPUB
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LHEALTH_DEV
39
Log of Real Pubic Investment in Physical Capital
Log of Real Public Human Capital Investment
Log of Real Pubic Aggregate Investment
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LPHY_IPUB
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LHUMAN_CAPITAL
11.00
11.25
11.50
11.75
12.00
12.25
12.50
12.75
13.00
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
LAGG_IPUB
40
Appendix D: Diagnostic Test
Table 6 Diagnostic Test
Table 7 Diagnostic Test: Dynamic impacts of Aggregate Public Spending Model
Sectors/Model Numbers of lags in
VAR
Autocorrelation test
Normality test
Heteroskedasticity Test
(p-value)1 (p-value)2 (p-value)3
Agriculture 1 0.1483 0 0.5184 Mining & Quarrying 1 0.1636 0 0.838 Manufacturing 1 0.0173 0.1329 0.2812 Construction 1 0.0174 0 0.1583 Electricity and Gas Distribution 1 0.0642 0.8227 0.3938 Transport, Storage and
Communication 1
0.2991 0.0002 0.4701 Wholesale & Retail Trade 1 0.3716 0.0071 0.1176 Finance and Insurance 1 0.6402 0 0.0573 Services 1 0.0135 0 0.2369
Aggregate Pakistan 1 0.4175 0 0.451
1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
Table 8 Diagnostic Test: Dynamic impacts of Education Public Spending Model
Sectors/Model Numbers of lags in
VAR
Autocorrelation test
Normality test
Heteroskedasticity Test
(p-value)1 (p-value)2 (p-value)3
Agriculture 1 0.1023 0 0.3772 Mining & Quarrying 1 0.9175 0 0.4444 Manufacturing 1 0.0518 0 0.4613 Construction 1 0.3327 0 0.0545 Electricity and Gas
Distribution 1 0.0009 0.0001 0.8536
Transport, Storage and
Communication 1 0.5262 0 0.1317
Wholesale & Retail Trade 1 0.0586 0 0.4272 Finance and Insurance 1 0.8815 0 0.6616 Services 1 0.0748 0 0.6628 Aggregate Pakistan 1 0.7412 0 0.7854 1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
41
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
Table 9 Diagnostic Test: Dynamic impacts of Public Energy Spending Model
Sectors/Model Numbers of lags in
VAR
Autocorrelation test
Normality test
Heteroskedasticity Test
(p-value)1 (p-value)2 (p-value)3
Agriculture 1 0.7669 0 0.6353 Mining & Quarrying 1 0.1481 0 0.8725 Manufacturing 1 0.4121 0.0019 0.8139 Construction 1 0.0915 0 0.2022 Electricity and Gas
Distribution 1 0.0016 0 0.9088
Transport, Storage and
Communication 1
0.9179 0 0.8225 Wholesale & Retail
Trade 1 0.2894 0.0006 0.77
Finance and Insurance 1 0.3913 0 0.5012 Services 1 0.0064 0 0.674 Aggregate Pakistan 1 0.3245 0 0.4423 1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
Table 10 Diagnostic Test: Dynamic impacts of Health Investment Model
Sectors/Model Numbers of lags in
VAR
Autocorrelation test
Normality test
Heteroskedasticity Test
(p-value)1 (p-
value)2 (p-value)3
Agriculture 1 0.159 0 0.8413 Mining & Quarrying 1 0.6209 0 0.9698 Manufacturing 1 0.1754 0 0.4956 Construction 1 0.0516 0 0.0004 Electricity and Gas
Distribution 1 0.224 0.7579 0.7182
Transport, Storage and
Communication 1
0.2461 0 0.0766 Wholesale & Retail Trade 1 0.1803 0 0.5173 Finance and Insurance 1 0.7434 0 0.3801 Services 1 0.0117 0 0.419 Aggregate Pakistan 1 0.4858 0 0.3546 1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
42
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
Table 11 Diagnostic Test: Dynamic impacts of Social(Health + Education) Investment Model
Sectors/Model Numbers of lags in
VAR
Autocorrelation test
Normality test
Heteroskedasticity Test
(p-value)1 (p-value)2 (p-value)3
Agriculture 1 0.3462 0 0.4358 Mining & Quarrying 1 0.8884 0 0.5203 Manufacturing 1 0.1254 0 0.3097 Construction 1 0.1546 0 0.0908 Electricity and Gas Distribution 1 0.0253 0.0001 0.7796 Transport, Storage and
Communication 1 0.8144 0.0001 0.0533
Wholesale & Retail Trade 1 0.2536 0 0.4208 Finance and Insurance 1 0.5977 0 0.8615 Services 1 0.0396 0 0.3802 Aggregate Pakistan 1 0.4209 0 0.7826 1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
Table 12 Diagnostic Test: Dynamic impacts of Infrastructure Investment Model
Sectors/Model Numbers of lags in
VAR
Autocorrelation test
Normality test
Heteroskedasticity Test
(p-value)1 (p-value)2 (p-value)3
Agriculture 1 0.0902 0 0.7157 Mining & Quarrying 1 0.6174 0 0.9911 Manufacturing 1 0.104 0 0.9352 Construction 1 0.3457 0 0.6332 Electricity and Gas Distribution 1 0.2426 0.3343 0.7335 Transport, Storage and
Communication 1
0.6899 0 0.4479 Wholesale & Retail Trade 1 0.5729 0 0.7188 Finance and Insurance 1 0.5954 0.0152 0.2733 Services 1 0.3009 0 0.7228 Aggregate Pakistan 1 0.7081 0 0.9389 1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
43
Table 13 Diagnostic Test: Dynamic impacts of Physical Capital ( Infrastructure and Energy) Investment Model
Sectors/Model Numbers of lags in VAR
Autocorrelation test
Normality test Heteroskedasticity
Test
(p-value)1 (p-value)2 (p-value)3
Agriculture 1 0.6554 0 0.6145 Mining & Quarrying 1 0.6425 0 0.8781 Manufacturing 1 0.0824 0.0287 0.9562 Construction 1 0.1198 0 0.1578 Electricity and Gas Distribution 1 0.006 0.6782 0.7577 Transport, Storage and
Communication 1 0.9422 0 0.7612
Wholesale & Retail Trade 1 0.3664 0.0033 0.4618 Finance and Insurance 1 0.5593 0 0.1984 Services 1 0.0311 0 0.644 Aggregate Pakistan 1 0.4297 0 0.4627 1: Based on VAR residula serial correlation LM test with null no serial correlation
2: Multivariate Jarque-Bera residual normality test. For the null hypothesis of normality
3: VAR Residual Heteroskedasticity Tests. For null hypothesis of no Heteroskedasticity
44
Appendix E: AR Roots Graphs
AR Roots Results of Aggregate Investment Models
Figure 2 AR Roots Graphs
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
45
AR Roots Results of Public Education Investment Models
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
46
AR Roots Results of Public Energy Investment Models
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
47
AR Roots Results of Public Health Investment Models
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
48
AR Roots Results of Public Social Capital (Health and Education) Investment Models
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
49
AR Roots Results of Public Infrastructure Investment Models
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
50
AR Roots Results of Public Physical Capital (Infrastructure and Energy) Investment Models
Agriculture Sector Model Mining Sector Model Manufacturing Sector Model Construction Sector Model Electricity Sector Model
Finance Sector Model Service Sector Model Wholesale & Retail Model Aggregate Sector Model Transport Sector Model
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial