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The Productivity of Public Capital in Developing Countries

Florence Arestoff, University of Paris IX Dauphine

Christophe Hurlin, University of Orleans

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PART I

ESTIMATES OF GOVERNMENT NET CAPITAL STOCKS FOR 26 DEVELOPING COUNTRIES, 1970-2002

PART II

THRESHOLD EFFECTS IN THE PRODUCTIVITY OF PUBLIC CAPITAL IN DEVELOPING COUNTRIES

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PART I: ESTIMATES OF GOVERNMENT NET CAPITAL STOCKS FOR 26 DEVELOPING COUNTRIES, 1970-2002

INTRODUCTION

A departure in the empirical research…

The empirical research devoted to OECD countries generally focuses on the notion of “public capital” or “public spending”:

Hulten and Peterson (1984), Aschauer (1989), Ram and Ramsey (1989), Lynde and Richmond (1992), Evans and Karras (1994), Holtz-Eakin (1994), Sturm and De Haan (1995), Garcia-Mila, McGuire and Porter (1996), Otto and Voss (1998) and Fernald (1999)

The empirical studies devoted to Developing Countries generally emphasizes the notion of “infrastructures”:

World Bank (1994), Canning (1999), Canning and Pedroni (1999), Canning and Bennathan (2000), Easterly and Serven (2004).

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One Explanation: the lack of homogeneous data on public capital stocks for developing countries:

“There are few good estimates of the productivity of public capital [for developing countries] and what are few there are of limited comparability'' .

(Pritchett, 1996, page 36)

In this study, we propose various estimates of internationally comparable Government Net Capital Stocks for a panel of 26 developing countries over the period 1970-2000.

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PUBLIC CAPITAL STOCKS AND THE USE

OF THE PERPETUAL INVENTORY METHOD (PIM)

The PIM consists in cumulating historical series of past investments and in deducting assets which were retired.

The PIM has been used in order to estimate public capital stocks in Sturm and De Haan (1995) for the Netherlands, Berndt and Hansson (1992) for Sweden, Ford and Poret (1991) for France and Japan and by Kamps (2004) for 22 OECD countries

Pritchett (1996) argued that this method based on monetary value of investments cannot be directly adopted in the case of developing countries.

For various reasons, in many developing countries, one dollar's worth of public investment spending does not necessarily create one dollar's worth of public capital.

The use of the PIM leads to overvalue the public capital stocks

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CONTENTS

SECTION 2: ESTIMATES OF NET CAPITAL STOCKS BASED ON THE PIM

The assumptions on the depreciation pattern

The choice of initial stocks

SECTION 3: PUBLIC INVESTMENTS AND EFFICIENCY

The aim is to evaluate the capacity of public investments to generate capital

For that, we estimate an efficiency function by non parametric methods

We propose other estimates of net public capital stocks based only on the “efficient” component of public investments

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SECTION 2. THE BENCHMARK CASE: THE PIM

Net Capital Stocks = Value of assets held by government at the price of new assets minus the cumulative value of depreciation

The PIM requires three ingredients:

Internationally comparable times series on gross investment

Capital expenditure for central government only (WDI)

An evaluation of the initial net capital stocks

Jacob, Sharma and Grawbowski (1997) or Kamps (2004)

The time profile of the depreciation rates

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THE DEPRECIATION PROFILE

We consider a geometric pattern for the depreciation of public capital. The geometric pattern was used by Kamps (2004a) for OECD countries, Sturm and De

Haan (1995) for the Netherlands, Berndt and Hansson (1992) for Sweden, Ford and Poret (1991) for France and Japan and by the BEA (1999,2003) for the United States.

We consider a time varying depreciation rate For a given asset, the depreciation rate is assumed to be constant over time

However, as the relative importance of the different kinds of assets changes with time, so the average depreciation rate defined on the total stock does.

We use the decomposition of public investments proposed by Calderon, Easterly and Serven (2004) for nine Latin American countries over 1980-1998 as a benchmark .

Results: The estimated depreciation rates for the aggregated stock ranges from 2.5% to 2.7% given the methods used and is slightly decreasing since 1980.

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RESULTS

We observe a decrease of the average ratio of public capital stock to GDP mainly during the 90’s, but also a great heterogeneity of the situations.

This decrease occurs at least one decade after the corresponding decline observed for OECD countries (Strum, 1998)

This importance of this decrease is globally similar to that observed for OECD countries (Kamps, 2004)

The estimated average ratio of public capital stock to GDP is similar, even slightly superior, to the ratio observed on OECD samples (55.3% in 19990).

CONCLUSION: It is an illustration of the drawbacks of the use of the PIM based on monetary flows of investments

These estimates are relatively robust to the assumptions made on the depreciation patterns and on the initial stocks

The measurement errors on the public capital stocks in developing countries mainly comes from the overvaluation of the amounts of public investments which are actually used in creating capital

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SECTION 3. PUBLIC INVESTMENTS AND EFFICIENCY

The same investment flows in different countries may have very different effectiveness in actually producing capital due to

Differences in the efficiency of the public sector

Differences in the price of capital.

Consequence: Monetary public investment may be a very poor proxy of the amount of public capital actually produced

“One of the deep difficulties of development may well be that even when public capital is productive it may be difficult to create this capital in the public sector ''

(Pritchett, 1996, page 1)

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Here, we propose a Non Parametric approach in order to evaluate the inefficiency of public investments in creating capital.

The idea that a dollar's worth of public investment spending often does not create a dollar's worth of capital can be expressed as follows:

where f(.) denotes the efficiency function of public investments to generate new capital.

If f(.)=I, the PIM is valid

The distance |f(I)-I| reflects the inefficiency of public investments in creating capital

00011 fIIfIfKK ttttt

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For this purpose, three elements are required:

1. A series a public investments

2. The depreciation rates (or its time profile)

3. The public capital net stocks actually available in the countries.

IDEA: Estimate the efficiency function by comparing the changes in the physical measures of the capital to the monetary investments flows

We consider three physical measures of stocks (Canning, 1998): Electricity-generating capacity in million of kilowatts, the number of telephone lines, roads length or paved roads length in kilometers

We consider the public investments in three sectors: Electricity, telecommunication, road (Calderon, Easterly and Serven, 2004)

We consider periods in which the private investments in the reference sectors are negligible comparing to the public investments in two countries (Colombia and Mexico).

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PROBLEM: the efficiency function relates on the one hand the monetary flows of investments and on the other hand the nominal increases in public capital stocks

IDEA: We consider the valuations which are the most in favor of the PIM

Let Xit the physical measure of the capital in to the sector j and vit the monetary value of one physical unit of fixed capital:

We assume that the underlying prices follow a geometric process in order to take into account the increase in the costs of infrastructures:

Parameters and v are chosen by minimizing the distance from the PIM in order to get the valuations the closer as possible to the valuations compatible with the PIM, i.e. for which

jtjtjt XvK

tttt IfKKK 1~

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tjt vv 1

jttj IK 1,~

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The corresponding program is then defined by:

Given these parameter estimates, we then compute the increases in the monetary values of the infrastructure stocks

Finally, the efficiency function Is estimated by a LOESS regression, (Cleveland and Devlin, 1988)

A local polynomial is estimated for every reference point, using the points located in the neighborhood of this reference point. The dimension of the neighborhood is determined by a smoothing parameter defined by the ratio of the number of points included in the neighborhood to the total number of observations.

jttj

T

tjt

tj

t

v

IKts

IvvT

ArgMinv

1,

2

1

1

,

~..

1111

ˆ,ˆ

tjt

jtjt

tj XvXvK ,1,1

1, ˆ1ˆ1ˆ1ˆˆ~

tjjtj IfK ,1,ˆˆ~

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Figure 15. Non-Parametric Estimated Efficiency Function of Public Investmentsin Streets and Highways . United States, 1951-1992 (US $ million, Historical Cost)

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Figure 17. Non-Parametric Estimated Efficiency Function of TotalPublic Investments. Colombia, 1980-1994 (US$ million, current prices)

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For these two countries, the estimated efficiency function is a straight line

The relative efficiency, defined as the ratio of the ''productive'' investments to the total investments, is constant.

The estimated (linear-OLS) efficiency parameter is equal to 0.38 for Colombia and 0.40 for Mexico.

“A variety of calculations suggest that in a typical developing country less than 50 cents of capital were created for each public dollar invested''.

(Pritchet, 1996)

By using a linear efficiency function, we propose new estimates of the net capital stocks

For each country, we consider three values: =0.2 =0.4 =0.6

1 tt IIf

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0

10

20

30

40

50

70 75 80 85 90 95 00

Alpha = 0.2 Alpha = 0.4 Alpha = 0.6

Colombia

10

20

30

40

50

60

70

70 75 80 85 90 95 00

Alpha = 0.2 Alpha = 0.4 Alpha = 0.6

Indonesia

Figure 20. Real Government Net Capital Stocks in 26 Developing Countries1970-2002 (As a percentage of Real GDP)

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CONCLUSION - PART I

The decrease of the average capital public to output ratio in developing countries is observed in the 1990’s, i.e. at least two decades after the similar decrease observed in most of OECD countries.

If the PIM based on the totality of public investments is used to estimate the stocks, the average capital public to output ratio in developing countries is quite similar to that reported for OECD countries.

The main measurement errors on the stocks are not due to the choice of depreciation rates or to the choice of initial stocks (standard drawbacks of the PIM)

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'‘It would be naive to believe that everything called infrastructure spending in the fiscal accounts is necessarily productive or that such spending should be the only -or even the main- indicator of public infrastructure performance''

(Calderon, Easterly and Serven, 2004, page 3).

In order to assess the macroeconomic link between PUBLIC CAPITAL and GROWTH, POVERTY or PRODUCTIVITY:

Data on stocks are required: the effects of public investments are not independent of the level of stock and the composition of stocks (part II)

These data must be internationally comparable

In order to estimates these stocks and because the composition of stock matters, data on public SECTORAL investments are required

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PART II 

THRESHOLD EFFECTS IN THE PRODUCTIVITY OF PUBLIC CAPITAL IN DEVELOPING COUNTRIES

Objective : Identifying, Testing and Estimating the threshold effects in the productivity of public capital and infrastructures in developing countries

‘Our conclusion - that roads were exceptionally productive before 1973 but not exceptionally productive at the margin - is consistent with simple network argument. In particular, building an interstate network might be very productive; building a second network may not'‘

(Fernald, 1999, page 621)

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The relationship between the output and the level of public capital stock (or infrastructure stock) is non linear

→ THRESHOLD EFFECTS

Policy Implications:

Public investments or infrastructure investments do not offer a “continuing route to prosperity” (Fernald, 1999)

A massive investment in the building of one network can offer a one-time boost to the level of productivity of private capital and output rather than a continuing growth in productivity and output

This one-time boost to the level productivity may require a minimum level of investments.

The Threshold Effects may justify a specialisation of the public investments or the infrastructure investments in small number of priority sectors

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Technical Implications:

Network effects implies the use of Threshold Regression Model

Threshold regression models specify that individual observations can be divided into classes based on the value of an observed variable'',

(Hansen, 1999, page 346).

We propose to estimate various threshold specifications of infrastructure or public capital stock augmented production functions.

Problem: The estimation of Threshold models requires an important time dimension which is not available in the context of developing countries and even in the context of OECD countries.

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Panel Threshold Regression (PTR) model Hansen (1999)

The individual observations are divided into classes according to an observable variable

Transition Mechanism: If the threshold variable is below a certain value, called the threshold parameter, the productivity is defined by one model, and it is defined by another model if the threshold variable exceeds the threshold parameter

Panel Smooth Threshold Regression (PSTR) model Gonzalez, Teräsvirta and Van Dijk (2004) and Fok, Van Dijk and Franses (2004)

On the one hand the PSTR can be thought of as a regime-switching model that allows for a small number of extreme regimes associated with the extreme value of a transition function and where the transition from one regime to the other is smooth.

On the other hand, the PSTR model can be said to allow for ''a continuum'' of regimes, each associated with a different value of the transition function.

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CONTENTS

Section 1: Threshold Effects in the Productivity of Infrastructures

Section 2: Threshold Effects in the Productivity of Public Capital

Section 3: Panel Smooth Transition Regressions: Toward Heterogeneous Individual Estimates of the Productivity of Public Capital

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SECTION 1: THRESHOLD EFFECTS IN THE PRODUCTIVITY OF INFRASTRUCTURES

Infrastructure augmented Production Function (Calderon and Serven, 2004)

where y = output, k = capital stock, h = human capital and x = infrastructure. All variables are in log per worker terms.

Infrastructure appears twice, once its own but also as a part of aggregate capital k

“In this case the parameter captures the extent to which the productivity of infrastructure exceeds (if >0) or falls short (if <0) the productivity of non infrastructure capital.''

(Calderon and Serven, 2004, page 98)

TtNivxhkay ititititiit ,..,1,..,1

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Panel Threshold Regression with Two Regimes

This model can be rewritten as:

Generalizations with three or four regimes:

itqitqitiit ititWWay I'I' 21

sinon0

1I''

it

qititititjjjj

qsixhkW

it

itititititi

itititititiit qifxhka

qifxhkay

222

111

itqitqitqitiit itititWWWay 2211I'I'I' 321

itqitqitqitqitiit ititititWWWWay 332211I'I'I'I' 4321

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SPECIFICATION OF THE PTR MODELS

Testing the linearity hypothesis by a Likelihood Ratio Test (F1 Statistic)

The threshold parameter is not identified under H0 (Hansen, 1996): Necessity to use Bootstrap simulations to compute the critical values of F1

Testing the number of regimes (Statistics F2 and F3)

The choice of the threshold variable

The stock of infrastructure per worker

The lagged level of GDP per worker

Data: Canning and Bennathan (2000) or Calderon and Serven (2004)

The number of telephones, the electricity generating capacity expressed in kilowatts, the length of paved roads and the railways line length, both expressed in kilometres

2221110210 :: HH

1, tiit yq

itit xq

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SECTION 2: THRESHOLD EFFECTS IN THE PRODUCTIVITY OF PUBLIC CAPITAL

We now consider the threshold effects in the productivity of public capital

where kg denotes the log of the public capital stock per worker.

Threshold variables

The stock of public capital per worker

The level of infrastructure per worker (road, telephone, railways, electricity)

The lagged level of GDP per worker

itititititi

itititititiit qifkghka

qifkghkay

222

111

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SECTION 3: PANEL SMOOTH TRANSITION REGRESSION (PSTR) MODELS

A PSTR model with two extreme regimes

where = slope parameter of the transition and c = vector of location parameters

The marginal productivity of public capital is defined by a “continuum” of regimes given the level of the threshold variable qit.

The elasticity of output with respect to public capital varies smoothly with time between 0 and 0+ 1 and is different across countries

→ IT ALLOWS EVALUATING THE SMOOTH INFLUENCE OF Q ON THE ELASTICITY

ititititititititiit cqgkghkkghkay ,;111000

m

m

zzitit ccccqcqg

..,0exp1,; 21

1

1

1,;0,;10

cqgwithcqgkg

yitit

it

it

0.0826

0.0828

0.0830

0.0832

0.0834

0.0836

0.0838

0.0840

0.0842

74 76 78 80 82 84 86 88 90 92 94

MEXICO

0.08

0.09

0.10

0.11

0.12

0.13

74 76 78 80 82 84 86 88 90 92 94

THAILAND

Estimated Public Capital Elasticity with PSTR model Threshold = number of Kilowatts per worker

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CONCLUSION - PART II

The relationship between the output and public capital stocks or between the output and infrastructures stocks is non linear (threshold effects)

This conclusion is robust to changes in the panel model used, in the testing procedure applied and to changes in the composition of the panel sample.

The threshold effects in the productivity of infrastructures could be interpreted as network effects

Profile low –high –low or high – low of the elasticities with the level of stock Policy implication: sectoral specialization of the public investments in

infrastructure in developing countries

Strong threshold effects in the productivity of the public capital stocks in developing countries

Policy implication: The public capital is more productive in the countries in which the main infrastructure networks are the less developed.

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Our approach based on threshold models globally consists in assuming that the productivity of investments depends on the environment

Technically, this environment is described by the threshold variables used in the transition functions

In this study, we limit our analysis to the threshold effects related to the stocks (network effects)

Extensions: the environment considered must be extended to many other dimensions which could affect the productivity of investments in infrastructure

Economic variables (level and quality of private capital, human capital..)

Variables of political environment and governance, institutional arrangements etc.

Variables on the sectoral composition of investments

THRESHOLD MODEL would allow evaluating the influence of these variables on the productivity of infrastructure and/or public capital.