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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IBA Working Paper Series

The Centre for Business and Economics Research (CBER) publishes its working paper series for

the main purpose of disseminating preliminary research results, conference proceedings and

unpublished work. This stimulates discussion and generates critical feedback from experts in the

field. The work could later be published in reputed journals and presented at conferences abroad.

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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