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CENTREFOR THESTUDY OFLIVING
STANDARDS

Public Infrastructure and Productivity:
Updating the Canadian Case

Matan I. Sirota

September 2022
CSLS Research Report 2022-04

Public Infrastructure and Productivity: Updating theCanadian Case
Abstract
This report revisits the public capital hypothesis in Canada using a classical model with updated
estimation techniques. Provincial panel data spanning 1998-2020 are leveraged to determine theeffect of public infrastructure on business sector output and productivity. Several specifications(levels and first-differences) of the Cobb-Douglas production function are estimated using OLS
and FGLS techniques that account for heteroskedasticity, autocorrelation, cross-sectional
dependence, and province-specific effects. I find output and productivity elasticities for
aggregated public infrastructure to be predominantly insignificant from zero. A detailed
disaggregation of public infrastructure by asset type and function also yields largely insignificant
results.

2

Public Infrastructure and Productivity: Updating theCanadian Case
Table of Contents
Abstract................................................................................................................................................... ii
Table of Contents……………………………………………………………………………...……………ii
Executive Summary………………………………………………………………………………………..iii
Introduction............................................................................................................................................. 1
Literature Review .................................................................................................................................... 3
International ........................................................................................................................................ 3
United States .................................................................................................................................... 3
Europe .............................................................................................................................................. 7
Canada ................................................................................................................................................ 9
Framework and Estimation Methods...................................................................................................... 13
Data ...................................................................................................................................................... 16
Results .................................................................................................................................................. 18
Aggregated Public Infrastructure Analysis .......................................................................................... 18
Unconstrained Production Function ................................................................................................... 18
CRTS Production Function................................................................................................................ 21
First-Difference Form........................................................................................................................ 23
Disaggregated Public Infrastructure Analysis ...................................................................................... 25
Public Infrastructure Stock by Asset Type ......................................................................................... 25
Public Infrastructure Stock by Asset Function ................................................................................... 27
Core vs. Non-Core Public Infrastructure ............................................................................................ 29
Discussion ......................................................................................................................................... 29
Conclusion ............................................................................................................................................ 31
References............................................................................................................................................. 33
Appendix .............................................................................................................................................. 37
Literature Review Summary .............................................................................................................. 37
Infrastructure Asset Types and Functions ........................................................................................... 39
Aggregated Specification Without Unemployment Rate ..................................................................... 43
Public Infrastructure by Asset Type, First-Difference Form ............................................................... 44
Public Infrastructure by Aseet Function, First-Difference Form.......................................................... 45
Core Infrastructure, First-Difference Form ......................................................................................... 46ii

Executive Summary
This report estimates the impact of public infrastructure on output and productivity in Canada using the aggregated production function framework. Panel data
covering the ten provinces during the 1997–2020 period is leveraged. The dataset
also includes disaggregated measures of public infrastructure—by asset type andfunction—allowing us to examine which types of infrastructure are most (andleast) productive within the production function framework. Various model specifications and estimation techniques are employed to ensure results are robust.
Beginning with the aggregated analysis, the Cobb-Douglas production function
is first estimated in levels through three standard specifications: unconstrainedelasticities, constant returns to scale (CRTS) on private inputs, and CRTS on all
inputs. To remedy nonstationarity present in the data, I also estimate the modelin unconstrained, first-difference form. Both OLS (pooled and fixed effects) and
FGLS (random effects) estimation techniques are employed for all specifications.
Under all three returns-to-scale assumptions, output/productivity elasticities withrespect to public infrastructure are positive and statistically significant for thepooled OLS estimations (i.e. no fixed effects or solely time fixed effects), ranging from 0.038 to 0.123. Controlling for province-specific effects through fixed
effects, a negative and insignificant relationship is found (−0.058 to −0.128). The
FGLS coefficients are largely insignificant as well. The change in elasticities seen
between the pooled and fixed effects estimations resembles that in previous literature, which has also found fixed effects to reduce the impact of public infrastructure
on productivity. The first-difference form, also in line with the literature, yields
an insignificant and negative elasticity (-0.138).
The disaggregated analysis is separated into three sections: asset type, asset function, and core vs. non-core. The first two levels of disaggregation generate estimates that largely follow those in the aggregated analysis: many remain statistically insignificant in levels regardless of the estimation technique being used,and essentially all asset types and functions are insignificant in the first-difference
specification. In levels, institutional buildings and communication networks have asignificant, robust, and positive elasticities. Commercial buildings and transportation machinery and equipment, on the other hand, have a significant, robust, andnegative effect on production. The aforementioned infrastructure assets turn insignificant in the first-difference specification with the exception of transportation
machinery and equipment.
In terms of asset function, health and housing and community amenities are estimated to have a positive impact on output, while public transit equipment,
environmental protection, and public order and safety are deemed negative underthe production function framework in levels. When first-differencing, only public
transit equipment retains its robust statistical significance.
Finally, I group fuel and energy, transport, housing, environmental protection, andcommunication asset functions to create a measure of core infrastructure, while thesum of all other functions is considered non-core. Core infrastructure’s elasticity
is estimated to be insignificant under all estimation techniques, while non-core
infrastructure is highly significant and positive in levels. This contradicts muchof the literature, which generally finds core infrastructure to be productive. Thismay be driven by the inclusion of environmental protection and exclusion of healthinfrastructure from the measure of core infrastructure. The estimate offered bythis report suggest that the impact of public infrastructure on output/productivity
is largely insignificant from zero. The methodology employed, however, presents
a significant caveat that should not be neglected. While the standard production
function may be capable of providing rough estimates of the contributions of public
infrastructure towards private sector productivity, its aggregated nature, and theextensive set of assumptions that should be satisfied to justify its use, largely
prevent its results from having policy implications. In other words, the resultspresented in this report are ”obtained within a very narrow framework” (GarciaMilà et al., 1996). The widespread statistical insignificance found in this paper only
emphasizes the need for micro-oriented, cost-benefit analysis of new infrastructure
projects.

Public Infrastructure and Productivity: Updating
the Canadian Case1
1

Introduction

Canadian infrastructure has seen a rise in attention and over the last few years.
In 2016, the Liberal government announced the Investing in Canada Plan (ICP),
which committed over $180 billion towards infrastructure over 12 years (Infrastructure Canada, 2018). ICP led to the creation of the Canada Infrastructure
Bank a year later, a crown corporation equipped with $35 billion over 11 years
and the purpose of investing and attracting private-sector investment for revenuegenerating infrastructure projects. Infrastructure Canada examined the challenges
and opportunities facing the nation’s infrastructure in the 2018 report titled Investing in Canada: Canada’s Long-Term Infrastructure Plan (Infrastructure Canada,2018). In 2021, the department initiated an assessment of national infrastructure by engaging with various jurisdictions, groups, and experts (Infrastructure
Canada, 2021).
Another development that motivates this paper is the declining labour productivity
growth rates in Canada (Greenspon et al., 2021; Sharpe & Ashwell, 2021; Williams,
2021). Just as slowdowns in labour productivity motivated the seminal work of
Aschauer (1989a), declining rates in Canada similarly raise questions regarding therole of public infrastructure in stimulating and supporting Canadian productivity.
Finally, with the exception of Jacques-Arvisais and Lapointe (2022), I did not finda paper published in the last decade that specifically contributes to the Canadianliterature through econometric analysis. The availability of more recent and disaggregated data, and the fact that marginal benefits derived from various infrastructure assets decrease as their network solidifies, warrant an updated examinationof the infrastructure-productivity relationship in Canada.
Empirical investigation of the relationship between public infrastructure and private productivity rose to prominence over three decades ago. Initial studies largely
relied on national time-series and aggregated measures of public capital to estimate
its effect on production and productivity. These studies often found output elasticities with respect to public capital that are implausibly large (e.g. Aschauer, 1989a,
1989b; Ford & Poret, 1991; Munnell, 1990b). Criticism of these findings naturally
1This study was undertaken at the Centre for the Study of Living Standards (CSLS) as part of
the Directed Research Program run by the Department of Economics at the University of Ottawa.
The research was supervised by CSLS Executive Director Dr. Andrew Sharpe. The author is amathematics and economics student at the University of Ottawa. Email: msiro087@uottawa.ca

1followed, with subsequent papers attributing the large elasticities to several issues(e.g. Aaron, 1990; Gramlich, 1994; Tatom, 1991). First, data at the national levelis likely to be nonstationary, meaning standard estimation techniques, namely the
production function in levels, are likely to produce results that reflect spurious
correlation rather than a direct causal relationship. Furthermore, even if theseresults reflected causality between infrastructure and productivity, it may not be
driven by the former. The simple production function assumes public capital stock
is strictly exogenous, such that it is the source of causality, but periods of higher
output and, therefore, tax revenues, can lead to increased public investment as
well. The production function approach is also prone to various forms of simultaneous and omitted variable bias. The wide range of estimates reported for public
capital in the early literature indicates that results were unreliable from the more
pragmatic perspective of policy makers.
This study contributes to Infrastructure Canada’s national infrastructure assessment by providing an updated econometric analysis of provincial data spanning
the 1998–2020 period. It employs the standard Cobb-Douglas production function
to retain comparability with the vast literature, while also correcting for some of
the issues associated with this classical model. As with many papers following Aschauer (1989a), this study benefits from the use of panel data, which offers greater
variation than its time-series counterpart and facilitates the use of various estimation techniques, enabling more exhaustive robustness checks of results. Morespecifically, I estimate a Cobb-Douglas production function in both levels anddifferences while accounting for autocorrelation, heteroskedasticity, cross-sectional
dependence, as well as fixed and random effects.
Leveraging Statistics Canada’s Infrastructure Economic Accounts, which offer disaggregated measures of public infrastructure, this study also reports elasticity
estimates for 11 types of infrastructure assets as well as 9 asset functions. Thislevel of disaggregation is unprecedented in the literature employing production
functions, and can provide more comprehensive insights into the productivity ofvarious infrastructure assets.
My results overwhelmingly suggest that public infrastructure has little to no effecton business sector output within the production function framework.
Section 2 reviews the literature by region. Section 3 presents the theoretical framework, model specifications, and estimation methods used throughout the study.
Section 4 describes the data used. Section 5 presents and discusses the results.
Finally, Section 6 concludes.

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2

Literature Review

Since the work of Aschauer (1989a), researchers have eagerly undertaken the challenge of solving the public infrastructure-private productivity puzzle. Many formsof data, measures of public capital, model specifications, and econometric techniques have been proposed over the last three decades (see Pereira and Andraz,
2013; Romp and de Haan, 2007, for comprehensive surveys of the literature).
Given the methodology and nature of the data used in this paper (see sections 3
and 4), I focus my review of international studies primarily on those leveraging
regional panel data and a Cobb-Douglas production function. Since variations ineconometric techniques have shown to influence results significantly, this approach
maintains focus on the most relevant and comparable results to this study. The
limited Canadian literature, however, is surveyed regardless of the methodology
employed. Appendix A provides a summary table of the literature employing
regional panel data and a Cobb-Douglas production function.

2.1

International

2.1.1

United States

Aschauer (1989a) sparked great debate about the relationship between public infrastructure and production. Employing Cobb-Douglas production for the 1949–
1985 period, he concluded that public capital stock (net federal, state, and local
capital stocks of nonmilitary equipment and structures) played an important rolein explaining the U.S. productivity slowdown in the 1970s. A 1% increase in theratio of public to private capital stock resulted in a 0.39% increase in output perunit of private capital. This estimate was also robust to different subsamples oftime (elasticities range from 0.38% to 0.56%). Furthermore, he found that a 1%
increase in public capital stock increased total factor productivity by 0.34-0.39%.
Aschauer used capacity utilization rate in manufacturing as a control for businesscycle fluctuations.
Later, Aschauer (1989b) investigated the relationship between public investment
and productivity growth in G7 countries, as data deficiency prevented capital stockfrom being used instead. These new measures of public capital and productivity
were accompanied by capacity utilization as control, and their elasticities estimatedusing a production function with OLS. Aschauer found that a 1% increase inpublic nonmilitary net investment relative to GDP (lagged one year) increases
productivity growth (GDP/person employed) by 0.44%, a result that is robust
to oil shocks. He also concludes that, keeping tax revenues fixed, governments
can raise productivity by “altering the composition of government spending awayfrom public consumption and toward public nonmilitary capital accumulation.”3

He also provided evidence against the reverse causation argument that is often
posed against the use of a production function.
Munnell (1990b) set to confirm Aschauer’s (1989a) results using the same CobbDouglas framework, albeit with larger emphasis on the various returns-to-scaleassumptions that can be made. Moreover, rather than setting output relative to
private capital as Aschauer did, Munnell elected to subtract labour from output toestablish a measure of labour productivity as the independent variable. Capacity
utilization rate in manufacturing is once again used as a control variable. She
found that a 1% increase in public nonmilitary capital stock raises private nonfarm
business sector output per hour (productivity) by 0.31%-0.37%. She also examines
core infrastructure, which includes highways, mass transit, airports, electrical andgas facilities, water supply facilities, and sewers (two-thirds of public capital at
the time), while excluding other buildings such as offices, police and fire stations,courthouses, garages, passenger terminals, as well as structures for conservationand development. For this measure of public capital stock, she finds that a 1%
increase in the ratio of core infrastructure to labour hours raises productivity by
0.39%. Munnell concluded that insufficient public capital investment at the time
may have slowed labour productivity growth by 0.1–0.2 percentage points.
Munnell (1990a) examined the impact of public capital stock on productivity andeconomic activity at the state and regional levels from 1970 to 1986. Lack of state
data, however, necessitated a method to divide national data. She leveraged annual
state investment data to obtain a series of state public capital stock and various
measures of state activity in different private sectors. Employing a Cobb-Douglas
production function and state unemployment rate as a control variable, Munnell
estimated an output elasticity for public capital of 0.15%. Separating public capital
into components, she also finds that majority of public capital’s impact on grossstate product comes from highways and water and sewer systems, while otherstate and local public capital (primarily consisting of buildings such as schools
and hospitals) have very little effect. Combining states into four regions, Munnell
find positive but varying elasticities for public capital (0.07 for the Northeast, 0.12
for the North Central, 0.36 for the South, and 0.08 for the West).
Expanding on Munnell (1990a), Eisner (1991) used the same state panel to produce different results. Munnell use observation vectors consisting of deviations
from the means of public and private capital stock, labour, and output series forall states and years, thereby combining cross-section and time-series variance andcovariance. Eisner, however, employs observation vectors of the “differences foreach state from the mean of all its own observations”; effectively incorporatingstate fixed effects. In this model, Eisner finds a small, negative, and insignificant
elasticity for public capital, a result that contradicts the significantly positive coef4

ficient reported by Munnell. Under the assumption of constant returns on private
inputs, the coefficient returns to positive and significant territory, which Eisnerconjectures may be due to public capital proxying for private capital (with which
it is correlated). When accounting for time effects instead, elasticity of public
capital becomes positive, significant, and similar in magnitude to Munnell andCook’s finding (0.165). In the first-difference regression, Eisner finds statisticallyinsignificant and slightly negative elasticities for private and public capital (-0.32
and -0.007, respectively), as well as a large and highly significant output elasticity
for labour (0.831). He therefore concludes that states with more public capital in
one year do not produce more during that same year. He rationalizes this conclusion through the possible lagged effect that public infrastructure has on output
as well as the fact that many of the benefits derived from public capital are notincluded in conventional measures of output such as GDP.
Using data for the 48 contiguous states from 1969 to 1983 and a Cobb-Douglas
production function, Garcia-Milà and McGuire (1992) investigate the effect of
highways (measured as highway capital per square mile) and education (measured
as total state and local expenditures for K-12 and post-secondary education) on
gross state product. They include time dummies to control for time-specific effects
and the business cycle. To account for state-differences, however, they include thepopulation and a measure of the average industrial mix of each state instead ofstate dummies to preserve the long-run relationship between the factors of production. Garcia-Milà and McGuire find highly significant elasticities for all fivefactors, with labour featuring an unconventional output elasticity of 0.356, highways estimated at 0.045, and education reporting a large coefficient of 0.165.
Evans and Karras (1994) similarly use a 48-state panel for the 1970–1986 period
while controlling for the state unemployment rate. Devoting special attention to
the error structure, they adjust for first-order autocorrelation, estimating five specifications: (a) OLS on levels, (b) OLS on levels with time and state fixed effects,(c) OLS on levels with time and state fixed effects and a first-order autoregressive
error term, (d) OLS on differences with time fixed effects, and (e) OLS on differences with time fixed effects and a first-order autoregressive error term. Whenintroducing fixed effects in (b), they find that the elasticities of public capital (comprised of highways capital, water and sewers capital, and other capital) and current
government services (comprised of educational services, highway services, healthand hospital services, police and fire services, sewer and sanitation services) turnfrom significantly positive (0.096 and 0.045, respectively) to insignificant (-0.048
and 0.044). (c) returns the coefficients to statistical significance while maintaining
the same signs from (b) (-0.11 and 0.064). It is worth noting that in (c) labour
input is extremely large and significant (0.935) while private capital is small and5insignificant (0.002). Specifications involving differences are fairly similar, with(d) and (e) estimating a very large output elasticity for labour, a negative andinsignificant elasticity for public capital, and a positive and significant elasticity
for government services. Even when disaggregating public capital and government
services, or using data exclusively for the manufacturing industry, Evans and Karras do not find any significant and positive effect for public capital on output. The
labour and private capital elasticities, which contradict their respective shares ofincome in all specifications, suggest that the estimates may be biased.
Holtz-Eakin (1994) reconciles the results reported in previous studies by effectively
covering conceptual issues and reporting a diverse set of specifications in an effort
to correct for them. Using a panel dataset of the 48 contiguous states spanning
the 1969–1986 period (no control variable is used), Holtz-Eakin begins with asimple OLS estimation of the Cobb-Douglas production function including time
fixed effects. As expected, this estimation yields a significant and large elasticity
of 0.203 for public capital. Once state fixed effects are incorporated, the effectremains significant but turns negative (-0.0517). Imposing constant returns on
private inputs has negligible effect on this elasticity. Turning to a GLS estimationin which the state effects are treated as random and time fixed effects are retained,
Holtz-Eakin reports an insignificant effect of public capital when the function
is both unconstrained (0.0077) and under constant returns restriction (0.0212).
Finally, he estimates the function in first-difference form while retaining time fixed
effects (as well as “long”-difference form). He finds the elasticity of labour to bemuch larger (0.911), the elasticity of private capital to be much smaller (0.106),
and the elasticity of public capital to be negative and not significantly different
from zero. Aggregating the state data to the regional level is not found to affectthe estimates, “[...] suggesting that the use of regional data does not permit one tocapture additional spillovers of any substantial magnitude” (Holtz-Eakin, 1994).
Holtz-Eakin and Schwartz (1995) focus on the spatial nature of public infrastructure by including a measure of “effective” state highway capital in the CobbDouglas production function. This measure essentially accounts for the likely
spillover effect induced by the stock of highways in neighbouring states. Usingstate data from 1969 to 1986 and specifications in levels as well as long-difference
form (to control for state-specific effects without damaging the long-run relationship between variables), they find spillover productivity from neighbouring highways to be negligible. Holtz-Eakin and Schwartz conclude that “spillovers amongstates do not appear to be at the heart of recent findings of a large productivity
impact from public capital.”
Using state-level data from 1970 to 1986, Baltagi and Pinnoi (1995) employ a
Cobb-Douglas production function in levels and various differencing forms (unem6

ployment rate is included as control). The pooled OLS estimation, which excludes
state fixed effects, reports significant elasticities for both aggregated (0.16) anddisaggregated public capital, similarly to Munnell (1990a). Once state-specificeffects are implemented, the impact of aggregated public capital becomes small,
negative, and insignificant (-0.03). When disaggregated by highways and streets,water and sewer facilities, and other public buildings and structures, elasticities
are estimated significantly at 0.08, 0.08, and -0.11, respectively. Treating state
effects as random through an FGLS estimation, Baltagi and Pinnoi find little difference in elasticities compared to those in the within estimator. Focusing on thefirst-difference regression, they find similar elasticities for private inputs to thosein previous papers, with an insignificant and low coefficient for private capitaland a large, highly significant one for labour. Output elasticity with respect toaggregated public capital, however, remains positive and significant (0.12). Whendisaggregated, only water and sewer facilities have a significant effect (0.05).
Garcia-Milà et al. (1996) expand on the approach taken by Holtz-Eakin (1994),
systematically testing for the most appropriate Cobb-Douglas specification while
using disaggregated public capital. The dataset employed spans 1970 to 1983
for the 48 contiguous states. Garcia-Milà et al. begin with an OLS specification
involving only time fixed effects, finding significant and positive elasticities forhighways as well as water and sewers (0.37 and 0.069, respectively), althoughother public capital is not significantly different from zero. Upon incorporatingstate-specific effects, whether they are treated as random through GLS or fixedwith OLS, the coefficients on highways and water and sewers are fairly small,positive, and significant while those on other public capital are small, negative,
and significant. Finding serial correlation in the data, Garcia-Milà et al. then turnto the first-difference forms of the three specifications reported for levels. Theyuse a Hausman and Taylor as well as a Chow test to determine that, even in firstdifferences, the third specification with time and state fixed effects is preferred.
Regardless, the elasticities for all three types of public capital assets are estimatedas slightly negative and insignificant in the three specifications. As in previous
studies, first-differencing causes labour to exhibit very high elasticities. While thecoefficients for private capital deviate from other studies, Garcia-Milà et al. findthat they resemble private capital’s accepted income share.
2.1.2

EuropeDe la Fuente et al. (1995) analyze data for 17 Spanish regions through three
years; 1981, 1986, and 1990. They employ a Cobb-Douglas production functionthat exhibits constant returns on all factors, accounts for stock of human capital(measured by average schooling of employed workers) and regional land area, and7

includes time fixed effects. They find a statistically significant elasticity for public
capital of 0.21.
Mas et al. (1996) also investigate Spanish data for 17 regions, albeit spanninga much larger period from 1964 to 1991. Employing a time trend and region
fixed effects, they report unconstrained and constant returns specifications (bothon private and all inputs) that estimate a significant productivity elasticity withrespect to public capital of around 0.07. Separating public capital into productive
stock (roads, water infrastructures, ports and urban structures) and social stock(health and education), Mas et al. find the former to be significant and positive andthe latter to be insignificant and negative. They also test for the spillover effect of
productive public capital by including the productive stock of neighbouring regions
to each region. This specification yields a higher elasticity for productive public
capital, leading the authors to accept the spillover effect hypothesis.
Picci (1999) examines 20 Italian regions from 1970 to 1995. He employs a similar
method to Munnell (1990a) for apportioning national data of public investment toeach region. In the Cobb-Douglas OLS specification with only time fixed effects,
Picci reports a significant output elasticity for public capital of -0.248. This elasticity turns positive (0.358) with the addition of regional fixed effects, a change that
contradicts previous literature from the U.S. which has largely found the inclusionof state fixed effects to diminish the magnitude and significance of public capital.
Peculiarity is also observed for the private input estimates, where output elasticities of labour and private capital are 1.08 and 0.133, respectively. Under constantreturns assumptions, the elasticity for public capital remains virtually the sameas in the unconstrained specification. A random effects estimation reports a much
lower positive elasticity (0.072), but is rejected by a Hausman test, which favours
the fixed effects model. Turning to a first-difference specification that preserves
time fixed effects, Picci finds a significant coefficient for public capital that is lower
compared to the specifications in levels, but is still much higher than those foundby U.S. studies employing first-differences.
Focusing on Germany’s manufacturing sector, Stephan (2003) employs a CobbDouglas production function and panel data consisting of the 11 West German
Bundesländer from 1970 to 1996. After testing for serial correlation, groupwise
heteroskedasticity, cross-sectional correlation, and non-stationarity, he estimatesvarious specifications (levels and first-differences) while controlling for capacity utilization. Among these specifications are first-differenced OLS with panel-corrected
standard errors (PCSE), and FGLS with PCSE, region fixed effects, and an AR(1)error structure. Stephan reports very large and significant output elasticities for
public capital that range from 0.385 to 0.651. Elasticities for labour (0.256–0.498)
are estimated to be lower than their income share (0.55).
8

2.2

CanadaAdding Canada to the literature, Wylie (1996) first employs a translog production function to determine the effect of infrastructure capital stock provided by
the “service sector” (represents services such as transportation, telephone systems,
electric power systems, trade, finance, insurance and real estate services, schools,
universities and hospitals, commercial services, and services of the federal, provincial, and municipal governments) on the Canadian goods-producing sector (defined
as manufacturing, agriculture, forestry, fisheries, mines, quarries and oil wells, andconstruction). Second, he follows Aschauer (1989a) to estimate the effect of infrastructure stock per hour worked on real output per hour worked in the goods sector
for the 1946–1991 period. Wylie incorporates a time trend as well as the unemployment rate in his Cobb-Douglas production function which he estimates using
OLS. He finds a significant productivity elasticity of 0.517 with respect to total
infrastructure stock per hour worked. When limiting infrastructure stock to public infrastructure, its productivity elasticity is stable and significant between 0.407
and 0.436. Both coefficients mentioned are larger than that of direct goods-sector
capital stock per hour worked, which ranges between 0.244 and 0.344 dependingon the infrastructure variable being analyzed. Wylie concludes that his findings
support Aschauer (1989a) and Munnell (1990b).
Khanam (1996) focuses on the effect of highway infrastructure capital and output
in the Canadian goods-producing sector (includes agriculture, forestry, fisheries,
mines, quarries and oil wells, manufacturing, construction and other utilities) between 1961 and 1994. She begins with a discussion of the primary causes of thediverging results observed in the early literature: “The degree of aggregation, useof different estimation techniques, errors in model specification, use of different
functional forms, and errors in variable measurements”. Addressing the degreeof aggregation, she notes the spurious correlation that can emerge from nonstationarity in national time-series data and leverages both pooled provincial data as
well as first-differences to mitigate this issue. To deal with the obstacle of varying functional forms, both Cobb-Douglas and translog production functions are
employed to test robustness. Following Holtz-Eakin (1994), she employs various
specifications, some with time and province-specific fixed effects, to broaden theestimations. Highway and private capital stocks variables are inputted with one
period lag.
Khanam finds statistically significant output elasticities with respect to highway
capital stock for the GLS (no time or province effects) and OLS (with time andprovince effects) specifications of 0.12 and 0.14, respectively. In the first-difference
form, only the OLS with no time or province effects specification offers significant
output elasticity with respect to highway capital stock (0.17). The marginal prod9

uct of highway capital stock derived from the Cobb-Douglas production function
is similar to that of private capital stock (and thus more “sensible” and “reasonable”) with the first-difference, time fixed effect as well as first-difference, time andprovince fixed effects specifications. Khanam also provides the output elasticities
of highway capital stock across provinces, finding, with a few exception, that theelasticities have a positive and diminishing contribution to provincial goods sector
output.
Harchaoui and Tarkhani (2003) estimate industry demand and cost functions
for the 1961–2000 period, allowing them to decompose multifactor productivity
growth, calculate the marginal benefits of public capital for each industry, anddetermine the effects of public capital on demand for labour, capital and intermediate inputs. The measure of aggregate public capital stock used is a chain Fisher
index of engineering construction of the federal, provincial, and municipal administrations. The average cost elasticity with respect to public capital stock for the
37 industries (cover 71% of the Canadian business sector), as determined by thetranslog cost function, is -0.062. All industries have the expected negative sign,and the most intense users of public capital boast larger magnitudes (e.g. transportation and construction). The average output elasticity with respect to public
capital (derived from the cost elasticity) is 0.066, with industries such as transportation and construction once again exhibiting the largest magnitudes. They
also find that a $1 increase in the net public capital stock generates approximately
17 cents of cost-saving producer benefits per year.
Paul et al. (2004) employ a translog cost function to investigate the effect of public
infrastructure on productivity in 12 Canadian manufacturing industries (coverabout two-thirds of total manufacturing sector output) from 1961 to 1995. The
stock of public infrastructure capital is measured as end-of-year stock of highways,
airports, roads, bridges, marine facilities, pipelines, sewage and water systems.
Both public and private capital stock are lagged one period to reflect beginningof-year stock. They find that for most manufacturing industries the cost elasticities
with respect to public capital stock lie between -0.1 and -0.4 and are statisticallysignificant, indicating that public capital reduces costs.
Brox and Fader (2005) also examine the Canadian manufacturing sector for asimilar time period (1961–1997), although employing a Constant Elasticity andSubstitution-Translog (CES-TL) cost model. The stock of public infrastructure
comes from two sources that have been combined. They find a large and statistically significant estimate for manufacturing cost elasticity with respect to public
infrastructure stock of -0.476. They note that this finding is larger than the results found by Nadiri and Mamuneas (1994) who use a translog cost function with
U.S. data to discover cost elasticities ranging from -0.11 to -0.21. Though not10mentioned in the paper, it is also larger than the wider range of cost elasticities
reported by Paul et al. (2004) for Canadian manufacturing industries within avery similar period of analysis. Brox and Fader also conclude that public capital is a substitute for private capital and that the former’s services enhance theproductivity of the latter.
Brox (2006) uses the same CES-TL cost model to investigate public infrastructurein the automotive sector (described as automobile assembly manufacturing industries) for the 1971–2004 period. He finds a significant cost elasticity of -0.677 withrespect to public capital stock.
Macdonald (2008) employs a Cobb-Douglas production and cost functions to investigate public capital’s role in productivity within Canada’s business sector from1981 to 2005. He leverages provincial panel data with the production function, andindustry panel data with the cost function. Macdonald notes the lack of consensus
regarding which CRTS assumption is most valid, and so elects to estimate bothconstant and increasing returns specifications. Only results using constant returns
are reported as they fit the data more reasonably. To avoid spurious results causedby trends over time, he uses first-difference form.
Macdonald also recognizes the need to control for fixed effects and contemporaneous shocks; however, he does so differently than Khanam (1996) by employing two
system estimators. The first (FGLS1) is a generalized least squares estimator thattreats each province as a separate equation; however, the output elasticities withrespect to the three inputs are constrained to be equal across provinces. The second estimator (FGLS2) modifies the first to account for residual serial correlation.
Furthermore, MacDonald has two specifications for each of the three estimation
techniques used (OLS, FGLS1, FGLS2), one with MFP and another where MFP
is constrained to zero. This yields interesting results as the productivity growthelasticity with respect to growth in public capital stock is only statistically significant for specifications with MFP = 0, indicating that either the vast majority of
the MFP effect can be attributed to public capital, or, much more sensibly, theimpact of public capital is difficult to disentangle from overall productivity growth.
MacDonald relates his findings to that of Harchaoui and Tarkhani (2003), notingthat MFP growth and public capital growth were discovered to be related and thatapproximately 12% of MFP growth is accounted for by public capital using cost
data. Evidently, with the data used in his production function, MacDonald was
not able to disentangle the two. When MFP = 0, elasticities were between 0.31
and 0.41. MacDonald concludes that the inability to disentangle MFP and public
capital is a data problem rather than an econometric one, and is also present inother panel data studies.

11Given the issue with the production function approach, Macdonald turns his attention to a Cobb-Douglas cost function. In this function, Macdonald uses a
combination of “roads and vehicles, which allows the impact of public capital tobe approximated as proportional to the input share of transportation services.” Hefinds varying cost elasticities for public infrastructure that depend on the specification and weight of the dependent variable. For the business sector, cost elasticities
appear to range from -0.08 to -0.15. For the manufacturing sector, the range is-0.14 to -0.27. This range is fairly similar to that found by Nadiri and Mamuneas(1994) for U.S. manufacturing and Paul et al. (2004) for Canadian manufacturing.
Macdonald recognizes that “the way public capital is measured here influences
the results. Only industries that pay for transportation services, which tend to
be goods-producing industries, appear to be making use of public infrastructure.
Service industries also make use of public infrastructure, however, they benefit
from the density of urban environments and agglomeration effects, which are notcaptured in transportation costs.”
Much more recently, Jacques-Arvisais and Lapointe (2022) examined the relationship between transportation infrastructure, output, and productivity in Canada’s
business sector from 1997 to 2018. They estimate an unconstrained Cobb-Douglas
production function in both levels and differences, including a time trend andthe provincial unemployment rate. After testing for heteroskedasticity, serial correlation, and cross-sectional dependence, they settle for the following estimation
techniques for the function in levels: (a) OLS with no province fixed effects, (b)OLS with province fixed effects, (c) FGLS, (d) Prais-Winston FGLS, (e) PraisWinston FGLS with province-specific effects. All five estimate a small, negative,
and significant output elasticity for roads infrastructure. Other transportation infrastructure has mixed effects, with (a), (c), and (d) finding a small, positive, andsignificant coefficients while the rest are insignificant. Marine engineering infrastructure is largely insignificant. These findings are echoed in the first-differenced
specification, which turns the small and negative (positive) output elasticity withrespect to roads infrastructure (other transportation infrastructure) insignificant.
Using an alternative panel covering the 2009–2018 period and featuring more specific categories of transportation infrastructure (roads, railway lines, seaports, andairports), Jacques-Arvisais and Lapointe find mostly insignificant output elasticities in both level and differenced forms, confirming the results from the original
dataset.

12

3

Framework and Estimation Methods

Similarly to the early literature, the analysis performed in this paper is based ona Cobb-Douglas production function that incorporates public infrastructure stock
as an independent factor of production:
Y = T F P · K αK L αL P αP
where Y is value added, T F P is total factor productivity, , K is private capital, L
is labour input, and P is public infrastructure. Log-transforming the production
function yieldsln(Y ) = ln(T F P ) + αK ln(K) + αL ln(L) + αP ln(P )Thus, the following unconstrained production function can be estimated using
provincial panel data:ln(Yit ) = β + αK ln(Kit ) + αL ln(Lit ) + αP ln(Pit ) + αUE ln(UE it ) + ϵit
where i indexes province, t indexes time, UE is the provincial unemployment rate
added to control for the business cycle, and αj represents the output elasticity
with respect to factor of production j.
Proper treatment of the error term, such that the likelihood of obtaining spurious results is reduced, is thoroughly discussed in the literature (e.g. Evans andKarras, 1994; Holtz-Eakin, 1994). As noted by Beck and Katz (1995), “[panel]data often allow for temporally and spatially correlated errors, as well as for heteroskedasticity.” This idea was confirmed specifically for the literature testing the
public capital hypothesis by Kelejian and Robinson (1997). Therefore, I test for
the aforementioned properties.
Autocorrelation: I first apply the test proposed by Wooldridge (2002) for firstorder autocorrelation in the error term using the xtserial command created by
Drukker (2003). The Bias-corrected Born and Breitung (2016) Q(p)-test is also
run using the xtqptest command created by Wursten (2018). Both tests are
significant at the 5% level and, therefore, reject the null hypothesis of no serial
correlation.
Groupwise heteroskedasticity: Using the xttest3 command, I find a highly significant modified Wald statistic for both OLS with fixed effects and FGLS estimations,indicating the presence of heteroskedasticity in both. This follows intuition as theprovinces vary greatly in size, economic conditions, etc...
Cross-sectional dependence: Given that my panel data consists of N = 10 and
T = 23, I run a Breusch-Pagan LM test using xttest2 which is applicable for13panels with T > N (Baltagi, 2021, p. 412). The null hypothesis of cross-sectional
independence is strongly rejected for all tested OLS and FGLS estimations.
Fixed Effects vs. Random Effects: Hausman and cluster-robust overidentification
tests are employed using hausman and xtoverid (Schaffer & Stillman, 2016). Bothindicate that a fixed effects specification is superior to one with random effects. I
also run xttest1, which tests for random province-specific effects, autocorrelation,
as well as joint random effects and autocorrelation. The p-values for all tests arewell below 0.01, thus, the null hypotheses of no serial correlation and no random
province effects are rejected. Similarly to Baltagi and Pinnoi (1995) and Picci(1999), the possibility that province effects are random motivates the use of FGLS
estimations along with OLS.
Stationarity: I check for stationarity in the dependent and independent variables
using various tests that allow for cross-sectional dependence, among them Hadri(2000) and Breitung and Das (2005). The null hypothesis of Hadri (2000) thatall panels are stationary is rejected in favour of the the alternative that at least
some of the panels contain unit roots. The null hypothesis that all panels contain
unit roots cannot be rejected through Breitung and Das (2005). This confirms theneed for estimation of the data in first-difference form as well.
Testing for the above properties has become a dependable practice in the literature employing panel data and Cobb-Douglas production functions (e.g. JacquesArvisais and Lapointe, 2022; Stephan, 2003). This development has not only
induced the use of estimation techniques that better reflect the data, but also
more exhaustive reporting of results through a range of estimation techniques. As
discussed below, this study maintains that approach.
For the aggregated public infrastructure analysis in section 5.1, I employ four
specifications of the Cobb-Douglas production function: unconstrained elasticities,
CRTS on private inputs, CRTS on all inputs, and first-difference form.
Imposing CRTS on private inputs only implies that αK + αL = 1, generating thefollowing specification:ln(Yit ) − ln(Lit ) = β + αK [ln(Kit ) − ln(Lit )] + αP ln(Pit ) + αUE ln(UE it ) + ϵit
Thus, the new dependent variable becomes productivity instead of output (output
per hour worked). Under CRTS on all inputs, the constraint on the elasticities is
αK + αL + αP = 1, resulting inln(Yit ) − ln(Lit ) = β + αK [ln(Kit ) − ln(Lit )] + αP [ln(Pit ) − ln(Lit )] + αUE ln(UE it ) + ϵit
The first three specifications are in levels and estimated using the following techniques: (1) OLS with no fixed effects (FE) and Driscoll and Kraay (1998) standard
14

errors (DKSE), (2) OLS with time FE and DKSE, (3) OLS with both time andprovince FE and DKSE, (4) FGLS with time FE, heteroskedastic and correlated
panels, and a common AR(1) coefficient for the error term, (5) FGLS with timeFE, heteroskedastic and correlated panels, and panel-specific AR(1) coefficientsfor the error term, (6) Prais-Winston FGLS with time FE, panel-corrected standard errors (PCSE), and a common AR(1) coefficient for the error term, and (7)Prais-Winston FGLS with time FE, panel-corrected standard errors (PCSE), andpanel-specific AR(1) coefficients for the error term.
(1)–(3) are estimated using the xtscc command in Stata (Hoechle, 2007). This
regression assumes an error structure that is heteroskedastic, autocorrelated up tosome lag (in this case the default is 2), and possibly correlated between provinces.
DKSE are robust to cross-sectional and temporal dependence as T becomes large.
These are all appropriate corrections given the outcomes of the previous tests.
(4)–(5) are estimated using xtgls with the panels(corr) option as well as corr(ar1)or corr(psar1). These options specify an heteroskedastic error structure withcross-sectional correlation and an AR(1) process that is either common or panelspecific. This method is feasible only when T is larger than N , as is the case here,
but Beck and Katz (1995) show that the standard errors produced by this method
tend to be underestimated.
To mitigate the problem above, (6)–(7) are estimated using xtpcse, as recommended by Beck and Katz (1995), and either the corr(ar1) or corr(psar1)
options. Similarly to xtgls, this regression assumes a heteroskedastic error structure with cross-sectional correlation and an AR(1) process that is either common
or panel-specific. The distinction lies in the Prais-Winston estimation and PCSEs.
Finally, given the results from the unit root tests, I estimate the production function in first-difference form:∆ ln(Y ) = β + αK ∆ ln(Kit ) + αL ∆ ln(Lit ) + αP ∆ ln(Pit ) + αUE ∆ ln(UE it ) + ϵit
Since first-differencing the variables effectively omits the province FE, this specification is estimated using the following: (1) OLS with DKSE, (2) OLS with DKSE
and time FE, (3) OLS with heteroskedastic PCSE, (4) OLS with heteroskedastic
PCSE and time FE, (5) FGLS with heteroskedastic and cross-sectionally correlated errors, and (6) FGLS with time FE as well as heteroskedastic and crosssectionally correlated errors. AR(p) error processes were not added to (1)–(6) as
first-differencing drastically mitigates autocorrelation (demonstrated by the AR(1)coefficients being very small when incorporated into the differenced estimations).
While estimates for (1)–(2) are expected to be similar to (3)–(4) as both are produced using OLS and standard errors that are robust to similar panel properties,
15

I nevertheless report both to ensure results in first-difference form are insensitive
to varying estimation techniques.

4

Data

Panel data is constructed from various Statistics Canada databases. The panel
covers the business sector of each province from 1998 to 2020. Statistics Canada
defines the business sector as all business establishments belonging to the North
American Industry Classification System (NAICS) codes 11–81, with the exceptionof owner occupied dwellings industry.
Real gross provincial product (chained 2012 dollars) and hours worked are obtained
from Statistics Canada’s productivity accounts (table: 36-10-0480-01).
Private capital stock (geometric end-year net stock, chained 2012 dollars) is extracted from the Investment and Capital Stock Statistics account within the Canadian System of Macroeconomic Accounts (table: 36-10-0096-01). Since Statistics
Canada does not provide business sector estimates for fixed non-residential capitalstock, private capital stock is estimated by subtracting the values of the ‘nonprofit institutions serving households’ industry and government sector from thetotal of all industries. Based on the industries available in the dataset, this adjustment should yield a solid approximation of private capital owned by businessestablishments belonging to NAICS codes 11–81.
Public infrastructure stock (geometric end-year net stock, constant 2012 dollars) is
acquired from the Infrastructure Economic Account within the Canadian System
of Macroeconomic Accounts (table: 36-10-0608-01). The data allows for various
disaggregations of infrastructure stock, including by purchasing industry, asset
type, and asset function. I extract public infrastructure stock by specifying the
public sector as the purchasing industry. This sector is comprised of the following
categories: federal government (excluding health services and defense), provincial government (excluding health and educational services), municipal (excluding
educational services), aboriginal, educational services, hospitals, nursing and residential care facilities, defence services, and government business enterprise. I alsoacquire public infrastructure stock data disaggregated by asset type and function.
The classifications of each, as well as the composition of infrastructure assets by
their function, are provided in Appendix B. Since estimates of public infrastructure stock are year-end, I lag them by one period such that each year possesses themonetary value of public infrastructure stock from which benefits can be derived(after accounting for the creation of new stock and the depreciation of used stockin the previous year).

16

Statistics Canada defines infrastructure as “the physical structures and systems
that support the production of goods and services and their delivery to and consumption by governments, businesses and citizens” and notes that it “represents
a set of assets that are used by other factors of production (labour and capital)in the production, distribution or consumption of goods and services” (Statistics
Canada, 2018). This definition suggests that fixed non-residential capital stock
and infrastructure stock (particularly when the latter is specified to be purchasedby the public sector while the former belongs to the business sector) are mutually
exclusive, thereby mitigating this source of measurement error.
The annual unemployment rate of each province is obtained from the Labour Force
Survey (table: 14-10-0020-01).
Canada’s three territories are excluded from the analysis for several reasons. First,
data for 1997 and 1998 is not available. Second, the Labour Force Survey tablefrom which the unemployment rate is extracted does not provide the rate for the
territories. Third, given that Statistics Canada provides estimates in the millions
for public infrastructure stock, three public infrastructure assets are reported aszero for the territories in at least some years (oil and gas engineering construction,other machinery and equipment, transportation machinery and equipment). Thus,
the logarithm of several territorial observations does not exist. Fourth, the Canadian literature also excludes the territories (e.g. Jacques-Arvisais and Lapointe,2022; Khanam, 1996); thus, this decision retains comparability. Finally, given theinherent difficulty in measuring public infrastructure, I judge that it is best to
avoid the territories’ data as it is likely susceptible to even greater measurement
error.
Table 1: Descriptive statistics, millions of dollars or hours
Variable
Real Value Added
Labour Hours
Private Capital
Public Infrastructure

Minimum

Mean

MaximumStandard Deviation

2445.9
80.9
2112
1012

120689.2
2315.7133593.5
39907.2

555370.810302.3
603920180077140902.8
2793.3149727.1
44572.1

17

5

Results

5.1

Aggregated Public Infrastructure Analysis

5.1.1

Unconstrained Production Function

Table 1 shows the unconstrained production function estimated without public
infrastructure as an independent factor of production. The income shares of bothprivate factors, as implied by their output elasticities, are fairly consistent throughthe seven estimations, with (3) being a notable exception. Kelejian and Robinson(1997) propose that high elasticities for labour input suggest that the variable“may be, at least partially, a proxy for some omitted factors”. The average labour
share (measured by Statistics Canada as total compensation divided by nominal
value added) between 1997 and 2018 is around 58% (Statistics Canada, n.d.-a).
Sharpe and Ashwell (2021) also state that the labour share has “steadily [been]around 50–60% in Canada, with the other 40–50% going to capital.”
While elasticities for private capital and labour appear to be largely in-line witheconomic theory, it is also observed that the effect of unemployment on output
is estimated to be slightly positive in columns (1)–(3). This peculiarity, however,is negligible. First, (1) and (2) do not account for province-specific effects and,
therefore, provide estimates that should not be considered particularly reliable.
Second, the coefficients are small and highly insignificant.
Adding public infrastructure to the production function results in some changes
to table 1. As can be seen in table 2, elasticities for private capital decreaseslightly (but retain their statistical significance) for all but one estimation—(3).
This suggests that public infrastructure may be a substitute for private capital,or that the former is simply proxying for the latter. Elasticities for hours worked
also decrease slightly with the inclusion of public infrastructure (curiously, theexceptions are (5) and (7), which are the only estimations to employ panel-specificAR(1) processes).
Time and province fixed effects are highly significant in all applicable estimations,indicating their importance. Similarly, the AR(1) coefficients in the error terms
for estimations (4)-(7) are very large. For example, the common AR(1) coefficients for (5) and (7) are 0.968 and 0.957, respectively, confirming the presence ofautocorrelation and the need to correct for it.
When failing to account for province-specific effects, the output elasticities withrespect to public infrastructure are positive and significant at least at the 5% level.
Specifically, a one percent increase in public infrastructure increases business sector
output by about 0.10–0.12 percent. Once province fixed effects are included, the18Table 2: Unconstrained production function results, levels, public infrastructure
omittedOLS
Real Value Added

FGLS

Prais-Winston FGLS

(1)

(2)

(3)

(4)

(5)

(6)

(7)

PrivateCapital0.511***(0.028)0.509***(0.033)0.044(0.053)0.353***(0.036)0.510***(0.028)0.401***(0.055)0.424***(0.063)

Hours
Worked

0.523***(0.029)0.528***(0.034)0.827***(0.101)0.685***(0.038)0.499***(0.031)0.621***(0.064)

0.526***(0.075)

Unemployment
Rate

0.027
(0.032)0.047(0.037)0.010(0.036)-0.031**(0.013)-0.040***(0.011)-0.045**(0.020)-0.051**(0.020)Constant

1.088***(0.156)

0.928***(0.209)6.228***(1.576)

1.666***(0.332)1.655***(0.264)

1.849***(0.406)3.243***(0.808)Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.994
230

0.995
230

—
230

—
230

—
230

1.000
230

1.000
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

elasticity becomes negative and insignificant. When employing random effects
through FGLS estimations, the coefficients remain insignificant but turn small
and positive. Thus, the output elasticities with respect to public infrastructure
estimated here follow a similar development to that found in the literature (e.g.
Baltagi & Pinnoi, 1995; Evans & Karras, 1994; Holtz-Eakin, 1994). Overall, thestatistically insignificant estimates for public infrastructure in columns (3)–(7)suggest that it has minimal impact on business sector output within the CobbDouglas production function framework.
Appendix C provides the same estimations as table 2 while omitting the unemployment rate. Results are robust to the exclusion of unemployment rate as acontrol variable.

19

Table 3: Unconstrained production function results, levels, aggregated public infrastructure
OLS
Real Value Added

FGLS

Prais-Winston FGLS

(1)

(2)

(3)

(4)

(5)

(6)

(7)

PrivateCapital

0.481***(0.028)0.478***(0.030)0.097*(0.056)

0.323***(0.039)0.472***(0.023)0.386***(0.054)0.411***(0.054)

Hours
Worked

0.455***(0.040)0.438***(0.064)0.808***(0.086)0.650***(0.048)0.534***(0.037)0.601***(0.088)0.559***(0.091)

PublicInfrastructure

0.101***(0.018)0.123**(0.044)-0.115(0.080)0.070(0.047)0.025(0.039)0.038(0.086)0.014(0.090)

Unemployment
Rate

0.018
(0.031)

0.039(0.037)0.025(0.034)-0.033**(0.014)-0.041***(0.010)-0.047**(0.021)-0.052**(0.021)

Constant

0.903***(0.185)0.667**(0.313)

7.976***(2.316)1.506***(0.375)1.313***(0.230)1.755***(0.438)2.589***(0.735)Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.994
230

0.995
230

—
230

—
230

—
230

1.000
230

1.000
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

20

5.1.2

CRTS Production Function

This section presents regression results under both constant returns on all inputs
and constant returns on private inputs assumptions.
Both tables 3 and 4 maintain the narrative that public infrastructure has little
to no effect on productivity. The only exceptions to this claim are estimations(4) and (5) in table 3, which produce significant productivity elasticities for public
infrastructure (0.044 and 0.025). However, since the elasticities are small, and theirsignificance is not supported by the more conservative Prais-Winston estimations,
I do not consider this a significant deviation from the overall message. My findings
under CRTS assumptions are similar to Holtz-Eakin (1994) in that they do notchange much from the unconstrained form.
Table 4: CRTS on private inputs production function results, levels, aggregatedpublic infrastructure
OLS
Output per Hour Worked

(1)

(2)

FGLS

Prais-Winston FGLS

(3)

(4)

(5)

(6)

(7)

Private Capital
Per Hour Worked

0.500*** 0.499***(0.030)(0.035)0.099(0.059)0.338***(0.036)

0.483***(0.024)0.395***(0.055)0.438***(0.065)

PublicInfrastructure

0.038***(0.002)0.040***(0.003)-0.128(0.086)0.044***(0.015)0.025**(0.011)

0.025(0.019)-0.024(0.035)

Unemployment
Rate

0.029
(0.032)0.050(0.040)0.031(0.034)-0.033**(0.013)-0.038***(0.010)-0.047**(0.020)-0.046**(0.020)Constant

0.946*** 0.770***(0.164)(0.248)6.296***(1.876)1.483***(0.352)

1.348***(0.255)1.740***(0.426)2.703***(0.853)Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.867
230

0.877
230

—
230

—
230

—
230

0.981
230

0.989
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

21

Table 5: CRTS on all inputs production function results, levels, aggregated public
infrastructure
OLS
Output per Hour Worked

(1)

(2)

FGLS

Prais-Winston FGLS

(3)

(4)

(5)

(6)

(7)

Private Capital
Per Hour Worked

0.482*** 0.480***(0.027)(0.028)0.063(0.053)0.362***(0.037)

0.482***(0.025)0.392***(0.052)0.435***(0.048)Public Infrastructure
Per Hour Worked

0.087***(0.017)

0.098**(0.042)-0.058(0.061)

0.003(0.043)0.005(0.039)0.023(0.085)0.032(0.091)

Unemployment
Rate-0.050(0.034)-0.040(0.038)0.026(0.037)-0.029**(0.012)-0.051***(0.011)-0.051**(0.021)-0.061***(0.021)

Constant

1.825*** 1.715***(0.183)(0.267)3.605***(0.148)2.408***(0.140)1.992***(0.113)2.288***(0.247)2.151***(0.242)Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.850
230

0.858
230

—
230

—
230

—
230

0.980
230

0.989
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

22

5.1.3First-Difference Form

Turning to the first-difference form of the production function, table 5 presents
estimates that once again indicate little to no impact of public infrastructure on
private output. While all the elasticities for public infrastructure have turned
negative, they remain small-to-moderate in magnitude and statistically insignificant from zero. The exception is estimation (5), which does not include time
fixed effects and suggests that a one percent increase in public infrastructure decreases output by 0.11 percent. While the vast majority of time fixed effects are
insignificant for (2) and (4), they are highly significant in (6), suggesting that thestandout negative and significant elasticity reported in (5) may be attributed tothe omission of time fixed effects.
These minor changes to the elasticities align with the literature, which has largely
found output elasticities with respect to public capital to decrease in magnitude,
turn negative, and/or lose their statistical significance once first-differences areused (e.g. Baltagi & Pinnoi, 1995; Evans & Karras, 1994; Garcia-Milà et al., 1996;
Holtz-Eakin, 1994). The changes in the elasticities of private inputs, namely private capital becoming small and insignificant while labour input retains its highsignificance, are also in-line with the literature. Unlike private capital, the unemployment rate demonstrates much more sensible behaviour in the first-difference
form, exhibiting a negative and significant coefficient in all estimations. While it
may tempting to interpret this as an indication that first-difference form is themore appropriate specification, the literature also notes some of its weaknesses,
such as potentially eliminating the long-run relationship between the variables.

23

Table 6: First-difference production function results, levels, aggregated public
infrastructure
OLS
Real Value Added

FGLS

(1)

(2)

(3)

(4)

(5)

(6)

PrivateCapital

0.064(0.078)0.074(0.085)0.064(0.097)0.074(0.092)0.074(0.049)0.057(0.053)

Hours
Worked

0.388***(0.072)0.385***(0.104)0.388***(0.096)

0.385***(0.122)0.407***(0.046)

0.402***(0.061)

PublicInfrastructure-0.138(0.081)-0.069(0.078)-0.138(0.101)-0.069(0.111)-0.108**(0.043)-0.012(0.054)

Unemployment
Rate-0.080***(0.019)-0.046**(0.017)-0.080***(0.020)-0.046**(0.019)-0.054***(0.009)-0.032***(0.011)

Constant

0.019***(0.004)0.012(0.014)0.019***(0.004)0.036***(0.008)0.018***(0.002)0.037***(0.002)Time FE

—

✓

—

✓

—

✓

0.454
220

0.586
220

0.454
220

0.586
220

—
220

—
220

2

R
N

Standard errors in parentheses. (In)dependent variables are in logarithmic form and differenced.
* p < 0.10, ** p < 0.05, *** p < 0.01

24

5.2

Disaggregated Public Infrastructure Analysis

The next three subsections summarize the noteworthy findings from my disaggregated analysis; however, I reserve my discussion of the results to the fourth
subsection. Under the production function framework, results must already beinterpreted with caution (see Section 6 for elaboration), but this theme becomeseven more important when attempting to interpret the elasticities for disaggregated measures of public infrastructure.
5.2.1

Public Infrastructure Stock by Asset TypeI begin my analysis of disaggregated public infrastructure with asset types. As abalanced panel is required for some of the estimation techniques employed in thispaper, oil and gas engineering construction assets were omitted from the analysis
in this subsection because there are many zeroes in the series for Prince Edward
Island, Newfoundland and Labrador, and New Brunswick.
Similarly to tables 1 and 2, output elasticities for private capital and labour accurately reflect their factors’ respective income share in the FGLS estimations. With
regards to output elasticities of public infrastructure assets, institutional buildings,
communications networks, and arguably waterworks infrastructure have at least
moderately robust, positive estimates, although none are estimated precisely in
the OLS estimation with time and province FE. Moreover, the significant elasticities for communications networks and waterworks infrastructure are small, ranging
from 0.01 to 0.06. Institutional buildings, which consist of educational institutions
and hospitals (among other buildings) showcase more noteworthy elasticities between 0.12 and 0.16. Commercial buildings and transportation machinery andequipment, on the other hand, show robust, negative coefficients between −0.03
and −0.05. It should be noted that the relevant elasticities for commercial buildings tend to only be significant at the 10% level.
Appendix D presents the results for the first-difference specification. Essentially all
public infrastructure assets have an effect on business sector output that is insignificant from zero. The only exception is transportation machinery and equipment
which possesses a small, negative elasticity that is robust to all estimations.

25

Table 7: Unconstrained production function results, levels, public infrastructureby asset
OLS
Real Value Added

FGLS

Prais-Winston FGLS

(1)

(2)

(3)

(4)

(5)

(6)

(7)

PrivateCapital0.502***(0.027)0.485***(0.018)0.121**(0.045)0.411***(0.021)0.401***(0.018)0.438***(0.028)0.421***(0.029)Hours
Worked

0.388***(0.036)

0.386***(0.047)0.639***(0.074)0.540***(0.052)0.516***(0.043)0.521***(0.080)0.520***(0.079)Commercial
Buildings-0.081***(0.020)-0.130***(0.024)-0.048*(0.028)-0.045**(0.019)-0.010(0.016)-0.053*(0.030)-0.022(0.030)Institutional
Buildings

0.364***(0.027)0.303***(0.047)-0.040(0.058)0.158***(0.045)0.152***(0.036)0.144**(0.068)0.124**(0.061)MarineEngineering

0.123***(0.021)0.147***(0.024)-0.014(0.028)0.036*(0.022)0.021(0.016)0.077***(0.030)0.049*(0.028)Transportation
Engineering

0.205***(0.048)0.119*(0.069)0.009(0.109)-0.022(0.032)-0.024(0.024)0.009(0.052)-0.025(0.050)

Waterworks
Infrastructure

0.013(0.023)0.049*(0.026)-0.006(0.020)0.049***(0.016)

0.062***(0.014)0.045*(0.025)0.064***(0.023)

SewageInfrastructure-0.281*** -0.175***(0.028)(0.040)-0.024(0.066)-0.057(0.040)-0.092***(0.031)-0.076(0.063)-0.079(0.059)Communications
Networks

0.056***(0.012)0.062***(0.007)0.020(0.012)0.022***(0.006)0.018***(0.004)0.032***(0.008)0.023***(0.008)

Electric
Power-0.008(0.008)-0.025***(0.008)-0.026***(0.006)-0.010*(0.005)-0.007(0.005)-0.012(0.008)-0.009(0.008)Other Engineering
Construction-0.114***(0.037)-0.047(0.035)-0.029(0.022)0.006(0.018)0.019(0.012)-0.016(0.026)0.001(0.023)

Other Machineryand Equipment

0.041***(0.008)0.041***(0.005)-0.012(0.010)0.013**(0.005)0.007(0.005)0.022***(0.008)0.013(0.008)Transportation Mach. -0.046***and equipment(0.010)-0.058***(0.008)-0.053***(0.009)-0.030***(0.009)-0.030***(0.006)-0.044*** -0.038***(0.013)(0.012)

Unemployment
Rate-0.062***(0.022)-0.056**(0.026)-0.013(0.034)-0.042**(0.016)-0.059***(0.012)-0.045*(0.023)-0.061***(0.022)

Constant-2.093*** -1.753***(0.323)(0.392)

12.697***(3.076)0.629*(0.332)

1.573***(0.286)0.180(0.447)1.282***(0.460)Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.998
230

0.999
230

—
230

—
230

—
230

1.000
230

1.000
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

5.2.2Public Infrastructure Stock by Asset Function

Next, I analyze the impact of public infrastructure by asset function. The output
elasticities for private capital are lower than expected, while those for hours worked
are higher. These under-and-over-estimations of income shares suggest the results
are biased. Moreover, the coefficients for the unemployment rate exhibit very
odd behaviour that does not match previous findings. For estimations (1) and(2) the elasticities for unemployment are not only positive, but large and highly
significant. Additionally, previous tables have shown that FGLS estimations tend
to produce negative and significant coefficients, as would be expected, but in table
7 they are mostly insignificant. Given these factors, the results in table 7 should
be interpreted with additional caution.
Health and housing exhibit very robust and positive output elasticities, suggestingthese functions drive the positive contributions from public infrastructure to business sector output within the production function framework. On the other hand,public transit, environmental protection, and public order functions are estimatedto have a negative effect on output.
Appendix E presents the results for the first-difference specification. Similarly tothe analysis by asset type, essentially all infrastructure functions are estimated tohave elasticities that are insignificant from zero with only one exception—public
transit equipment.

27

Table 8: Unconstrained production function results, levels, public infrastructure
by function
OLS
Real Value Added

FGLS

Prais-Winston FGLS

(1)

(2)

(3)

(4)

(5)

(6)

(7)

PrivateCapital0.462***(0.027)0.455***(0.018)0.153***(0.054)0.371***(0.022)0.353***(0.017)0.376***(0.025)0.358***(0.023)

Hours
Worked

0.859***(0.049)0.882***(0.067)0.753***(0.056)0.660***(0.047)0.732***(0.045)0.721***(0.082)0.762***(0.078)

Health0.240***(0.016)

0.242***(0.020)0.034(0.035)0.105***(0.024)0.098***(0.020)0.128***(0.038)0.091***(0.035)

Education-0.150***(0.045)-0.213***(0.063)-0.162**(0.070)0.035(0.047)-0.024(0.044)-0.050(0.070)-0.067(0.069)Fuel andEnergy0.002(0.005)-0.009(0.006)-0.026***(0.008)-0.008(0.006)0.001(0.004)-0.003(0.008)-0.003(0.007)

Housing andCommunity Amenities

0.104***(0.016)0.140***(0.026)

0.041**(0.019)0.057***(0.018)0.076***(0.013)0.086***(0.023)0.097***(0.021)

Transport-0.094***(0.032)-0.119**(0.055)0.002(0.095)-0.025(0.025)-0.027(0.029)-0.045(0.050)-0.036(0.057)

Public Transit
Equipment-0.024*(0.012)-0.021(0.014)-0.029***(0.008)-0.034***(0.009)-0.032***(0.006)-0.032*** -0.031***(0.011)(0.011)

Environmental
Protection-0.349***(0.032)-0.276***(0.049)-0.012(0.064)-0.095**(0.041)-0.107***(0.032)-0.136**(0.063)-0.116**(0.054)

Communication

0.025***(0.008)0.031***(0.006)-0.001(0.009)0.014***(0.005)0.004(0.004)0.018**(0.007)0.010(0.007)

Recreation, Culture
and Religion

0.013(0.035)-0.012(0.027)-0.095***(0.022)0.012(0.026)0.030(0.020)0.030(0.034)0.040(0.035)

Public Orderand Safety-0.035*(0.018)-0.044***(0.015)-0.078**(0.028)-0.041***(0.013)-0.081***(0.009)-0.060*** -0.090***(0.015)(0.014)

Unemployment
Rate

0.147***(0.016)

0.192***(0.029)0.040(0.037)-0.036**(0.014)-0.014(0.013)0.004(0.024)-0.006(0.023)

Constant

1.027***(0.324)

0.941***(0.271)

11.695***(2.242)

1.279***(0.256)

1.898***(0.225)1.684***(0.369)2.098***(0.401)Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.998
230

0.998
230

—
230

—
230

—
230

1.000
230

1.000
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

5.2.3

Core vs. Non-Core Public Infrastructure

Following studies such as Munnell (1990b), Mas et al. (1996), and Picci (1999),
I also estimate the elasticities of public infrastructure by core and non-core functions. I define core infrastructure as the sum of stock classified under the following
functions: Fuel and energy, transport, housing (as it is comprised of waterworks
assets), environmental protection, and communication. All other functions are
considered non-core. The results in table 8 are striking. Core infrastructure isestimated to have output elasticities that are insignificant from zero using all estimation techniques, while non-core infrastructure is highly significant and positive.
This finding contradicts Picci (1999) and Mas et al. (1996). Non-core infrastructure supposedly being more productive than its core counterpart may be driven
by the inclusion of environmental protection in the latter as well as the exclusionof health infrastructure. Health is one of the few functions with a significant andpositive effect individually, and environmental protection has a robust, negative
effect, as shown in table 7.
Appendix F provides the results for the first-difference specification, in which bothcore and non-core public infrastructure are reported as having insignificant elasticities. An asset-based definition of core infrastructure was also estimated: the sumof marine engineering, transportation engineering, waterworks, sewage, communications networks, electric power, and oil and gas. As expected, this definition yields
similar results to the definition by asset function and is therefore not reported.
5.2.4

Discussion

Several papers have disaggregated public infrastructure by asset type in the past,
but never to the extent presented in this section, where as many as 11 infrastructure
assets are estimated within the same equation. Majority of assets and functions
have been found to be statistically insignificant in levels, while essentially all canbe considered insignificant when estimated in first-differences.
Researchers employing disaggregated measures of public capital have offered various explanations for the insignificance or even negative effect exhibited by some
types of infrastructure on output within the production function framework. For
example, when discussing their insignificant elasticity for public buildings, such as
schools and hospitals, Munnell (1990a) states the following:
The results suggest that the stock of buildings devoted to, say, education may not be the best indicator of the quality of educational services;teachers’ salaries, for example, might be a measure. Moreover, even if
physical capital were a good measure of service quality, in a highly mobile society the state that provides the educational or health services
29

Table 9: Unconstrained production function results, levels, core vs. non-core infrastructure, function definition
OLS
Real Value Added

(1)

(2)

FGLS

Prais-Winston FGLS

(3)

(4)

(5)

(6)

(7)

PrivateCapital0.448*** 0.427***(0.026)(0.030)0.067(0.075)0.371***(0.030)0.467***(0.024)

0.396***(0.045)0.446***(0.047)

Hours
Worked

0.358*** 0.257*** 0.854***(0.038)(0.077)(0.098)0.554***(0.045)0.479***(0.038)0.511***(0.082)0.454***(0.083)

Core Public
Infrastructure-0.005(0.018)0.006(0.023)-0.041(0.064)-0.013(0.028)-0.034(0.029)-0.016(0.059)-0.046(0.069)Non-core Public
Infrastructure

0.238*** 0.357***(0.021)(0.060)-0.095(0.065)0.124***(0.040)0.130***(0.035)0.136*(0.076)

0.155**(0.072)

Unemployment
Rate

0.035
(0.031)

0.066(0.043)0.029(0.035)-0.035***(0.011)-0.041***(0.010)-0.051**(0.021)-0.059***(0.020)Constant

0.764***(0.184)0.347(0.338)8.124***(2.266)1.474***(0.236)1.030***(0.239)1.558***(0.310)1.797***(0.507)

Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.995
230

0.995
230

—
230

—
230

—
230

1.000
230

1.000
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

may not be the one that reaps the benefits.
The claim that monetary measures of public infrastructure assets do not fullyreflect said assets’ impact on a aggregated productivity is certainly reasonable,
and helps explains to at least some degree any counter-intuitive findings derived
from the production function approach.
Building on the aforementioned notion, the benefits obtained from many infrastructure assets may also not be accounted for in the measure of value added. For
instance, Gramlich (1994) notes that “many of the benefits of highway investment
will involve the time saving of private individuals, which will generally not bereflected in national output.” He also asserts that the capital stock representing
education buildings and hospitals “should not have much short term impact on30

the supply of aggregate output as it is now measured”. Garcia-Milà and McGuire(1992), who focus on the effects of highways and education on productivity, also
touch on this issue. They propose that while it is possible that other public capitaland services are productive, their impact may not be as direct, meaning estimatesof ‘secondary’ infrastructure assets are unreliable at best, or misleading at worst.
Separating public infrastructure into its core and non-core components is designed
to show a more reliable estimate of the effect of infrastructure on productivity.
This study, unlike previous ones, finds no evidence that core infrastructure isindeed productive. In fact, my service-oriented measure of non-core infrastructure
is found to have a significant and positive effect in levels, though this peculiarity
disappears in the first-difference specification.
All in all, while some findings may suggest that some asset types and functions havean insignificant or even negative effect on business sector output, they are likely
induced by the nature of the production function framework and the data, which
poses a significant challenge towards capturing the true effects. This effectively
feeds into my conclusion.

6

Conclusion

This paper evaluates the effect of public infrastructure on Canadian business sector
output during the 1998–2020 period. Various specifications of the Cobb-Douglas
production function are estimated while correcting for heteroskedasticity, autocorrelation, and cross-sectional dependence. The relationship between public infrastructure and productivity has been found to be predominantly insignificant fromzero. There is, however, a significant caveat that must be taken into account whenusing the Cobb-Douglas production function to estimate the impact of public infrastructure. This caveat, as touched on in the introduction of this paper, hasbeen discussed in several papers employing the same methodology:
It would be wrong to conclude from this analysis that the large stockof public capital provides no benefits. The regression analysis indicates only that the productivity benefits in excess of direct provisionof amenities are negligible. [...] Instead, the main message is thatthe use of aggregate data do not reveal sufficiently large linkages between public sector capital and private production activities to support the contention that government capital spillovers are the source ofeconomy-wide variations in private productivity. (Holtz-Eakin, 1994)
The conclusion that public capital does not contribute to private output is obtained here within a very narrow framework [...] It is clear
31

that this approach does not exhaust all possible methods for examining the linkage between public infrastructure and productivity. [...]
we have not demonstrated that public infrastructure is unproductive.
Instead, we have found that within the aggregate production function
framework, there is no evidence of a positive linkage between public
capital and private output. (Garcia-Milà et al., 1996)
After all, government roads as such do not produce anything, and toinclude infrastructure or public capital as a separate input in a production function neglects the usually complex links. (Romp & Haan,
2007)
The underlying theme is that while the simple production function may be capable of providing rough estimates of the contributions of public infrastructure
towards private sector productivity, its aggregated nature, and the extensive setof assumptions that should be satisfied to justify its use, largely prevent its results from having policy implications. Even under ideal econometric conditions,
it can only deliver results convincingly with robust and statistically significant
estimates—a requirement that has not been met in this study.
The widespread statistical insignificance found in this paper emphasizes the needfor micro-oriented cost-benefit analysis of new infrastructure projects. Spillover
effects, province-specific needs, and many other factors must be taken into consideration before making investment decisions. The aggregated framework of the
production function, and the data that it entails, mean the model can never fully
take these factors into account, regardless of how many econometric tools are
deployed to accommodate its use. An alternative approach to the production
function that accommodates aggregated data is the VAR model, which does not
impose any assumptions on the direction of causality between public infrastructure and value added, and takes lagged values into account. A disadvantage ofthis methodology, however, is its atheoretical nature making its results difficult toverify and compare.
The availability of recent and disaggregated data warranted an update to the
Canadian literature on the public capital hypothesis. Revisiting the standard
production function approach allowed the findings of this paper to be compared toliterature that extends back over three decades. Ultimately, my findings resembled
those in the more recent literature by failing to show a linkage between public
infrastructure and private output/productivity.

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35

Stephan, A. (2003). Assessing the contribution of public capital to private production: Evidence from the German manufacturing sector. International
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Tatom, J. A. (1991). Public capital and private sector performance. Review, 3–15.
Williams, D. M. (2021). Pay and Productivity in Canada: Growing Together, Only
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Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data
(6th ed.). MIT Press.
Wursten, J. (2018). Testing for Serial Correlation in Fixed-effects Panel Models.
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Wylie, P. J. (1996). Infrastructure and Canadian Economic Growth 1946-1991.
The Canadian Journal of Economics, 29, S350–S355.

36

A

Literature Review Summary
Table A1: Summary of the literature employing regional panel data and a Cobb-Douglas production function
Public Capital Elasticities

Paper

RegionPeriodMunnell (1990a)

US, 48 states 1970–1986

Eisner (1991)

Munnell (1990a)

Garcia-Milà and McGuire (1992)

US, 48 states

1969–1983

Evans and Karras (1994)

US, 48 states

1970–1986

Holtz-Eakin (1994)
Baltagi and Pinnoi (1995)

US, 48 states 1969–1986
US, 48 states 1970–1986* Indicates statistical significance at the 5% level.
† Includes specifications with only time or region fixed effects.

†

Measure of Public Capital

OLS (No FE)

OLS (FE)

GLSFirst-Difference

AggregatedHighways & streets
Water & sewers
Other
AggregatedHighways & streets
Water & sewers
Other
Highways
Education
Aggregated capital
Highway capital
Water and sewer capital
Other capital
Aggregated services
Educational services
Highway services
Health & hospital services
Police & fire services
Sewer & sanitation services
Aggregated government capital
AggregatedHighways & streets
Water & sewers
Other

0.06*–0.15*
0.06*
0.12*
0.01
-0.026–0.165*
0.064*–0.077*
0.079*–0.116*-0.115*–0.011
—

—

—

—

—

—

-0.007–0.305*——

0.096*

0.044–0.045*
0.072*–0.165*-0.110*–-0.048

0.045*

0.044–0.064*

0.203*-0.03–0.39*
0.06*–0.16*
0.08*–0.19*-0.11*–0.09-0.056*–-0.052*—

0.008*–0.021*
0.004
0.06*
0.08*
-0.098*-0.063–-0.029-0.0620.011-0.061*0.035*–0.064*
0.057*
0.03
0.009-0.0070.004-0.102
0.12*
0.07
0.05*
0.01

Public Capital Elasticities
Paper

RegionPeriodMeasure of Public Capital

Garcia-Milà et al. (1996)

US, 48 states

1970–1983

De la Fuente et al. (1995)
Mas et al. (1996)

Spain, 17 regions
Spain, 17 regions

1981, 1986, 1990
1964–1991

Picci (1999)

Italy, 20 regions

1970–1995

Highways
Water & sewers
Other
AggregatedAggregated“Productive”“Social”
AggregatedCore
Non-core
AggregatedHighways
AggregatedRoads
Other transport
MarineStephan (2003)
Germany, 11 regions 1970–1996
Khanam (1996)
Canada, 10 provinces 1961–1994
Macdonald (2008)
Canada, 10 provinces 1981–2005
Jacques-Arvisais and Lapointe (2022) Canada, 10 provinces 1997–2018* Indicates statistical significance at the 5% level.
† Includes specifications with only time or region fixed effects.

OLS (No FE)
0.37*
0.069*-0.01——-0.248*—0.1—-0.201*0.101*-0.025*†

OLS (FE)

GLS

0.127*
0.12*
0.064*
0.043*-0.071*-0.048*0.21*—
0.065*–0.071*—
0.083*–0.063*-0.025–-0.021
0.358*
0.072*
0.501*-0.052*0.651*
0.385*–0.547*
0.14
0.12
—
—
-0.082-0.064–-0.086-0.0030.04–0.053*-0.025-0.044–0.02

First-Difference-0.058–-0.007-0.029–-0.002-0.056–-0.022——

0.184*

0.09–0.17*-0.06–0.02-0.074–-0.027
0.027–0.032-0.039–-0.008

B

Infrastructure Asset Types and Functions
Table B1: Classifications of Infrastructure Asset Types
Commercial Buildings• Sports facilities with spectator capacity• Indoor recreational facilities• Student residences• Airports and other passenger terminal• Communications building

Institutional buildings• Schools, colleges, universities and other educationalbuildings• Hospitals• Nursing homes, homes for the aged
• Religious centres and memorial sites• Museums• Historical sites• Libraries• Public security facilities

Marine engineering infrastructure• Seaports• Marinas and harbours• Canals and waterways• Other marine infrastructure

Transportation engineering infrastructure• Highway and road structures and networks• Bridges• Tunnels• Railway lines• Runways

Waterworks infrastructure• Water filtration plants• Other water infrastructure

Sewage infrastructure• Sewage treatment plants• Other sewage infrastructure

Communications networks• Cables and lines (except optical fibre)• Optical fibre cables• Transmission support structures• Other communication construction infrastructure

Electric power infrastructure• Wind and solar power plants• Steam production plants• Nuclear production plants• Hydraulic production plants• Power transmission networks• Power distribution networks• Other electric power construction

Oil and gas engineering construction• Pipelines

39

Other engineering construction• Waste disposal facilities• Outdoor recreational facilities• Pollution abatement and control

Other machinery and equipment• Turbines, turbine generators, and turbine generator
sets• Nuclear reactor steam supply systems• Water treatment equipment• Power and distribution transformers

Transportationequipment• Buses• Locomotives, railway rolling stock, and rapid transit
equipmentmachineryandSource: Statistics Canada, n.d.-b

Table B2: Classifications of Infrastructure Asset Functions
Health• Medical products, appliances andequipment• Outpatient services• Hospital services• Public health services• R&D health• Health n.e.c.

Education• Pre-primary and primary education• Secondary education• Post-secondary non-tertiary education• Tertiary education• Education not definable by level• Subsidiary services to education• R&D education• Education n.e.c

Fuel and energy• N/A

Housing and community amenities• Housing development• Community development• Water supply• Street lighting• R&D housing and community amenities• Housing and community amenities
n.e.c.

Transport• N/A

Public transit equipment

• N/A

40

Environmental protection• Waste management• Waste water management• Pollution abatement• Protection of biodiversity and landscape• R&D environmental protection• Environmental protection n.e.cCommunication• N/A

Recreation, culture, and religion• Recreational and sporting services• Cultural services• Broadcasting and publishing services• Religious and other community services• R&D recreation, culture and religion• Recreation, culture and religion
n.e.c.

Public order and safety• Police services• Fire-protection services• Law courts• Prisons• R&D public order and safety• Public order and safety n.e.c.

n.e.c.: “not elsewhere classified”
Source: OECD, 2021

41

Figure B1: Composition of infrastructure assets by their functions

42

C

Aggregated Specification Without Unemployment Rate

Table C1: Unconstrained production function results, levels, unemployment rateomittedOLS
Real Value Added

FGLS

Prais-Winston FGLS

(1)

(2)

(3)

(4)

(5)

(6)

(7)

PrivateCapital0.478***(0.026)0.473***(0.025)0.102*(0.051)0.314***(0.038)0.444***(0.026)

0.372***(0.060)0.397***(0.059)Hours
Worked

0.452*** 0.433***(0.041)(0.066)

0.791***(0.076)

0.679***(0.042)0.555***(0.035)0.641***(0.086)

0.598***(0.087)

PublicInfrastructure

0.103***(0.020)-0.104(0.077)0.054(0.044)0.028(0.037)0.016(0.085)-0.012(0.088)Constant

0.990*** 0.859*** 7.989***(0.085)(0.136)(2.317)1.410***(0.400)1.407***(0.266)

1.669***(0.499)2.668***(0.818)0.128**(0.047)

Time FE
Province FE
Common AR(1)Panel-Specific AR(1)

—
—
N/A
N/A

✓
—
N/A
N/A

✓
✓
N/A
N/A

✓
—
✓
—

✓
—
—
✓

✓
—
✓
—

✓
—
—
✓

R2
N

0.994
230

0.995
230

—
230

—
230

—
230

0.999
230

1.000
230

Standard errors in parentheses. (In)dependent variables are in logarithmic form.
* p < 0.10, ** p < 0.05, *** p < 0.01

43

D

Public Infrastructure by Asset Type, First-Difference Form

Table D1: First-difference production function results, public infrastructure byasset type
OLS
Real Value Added

FGLS

(1)

(2)

(3)

(4)

(5)

(6)

PrivateCapital

0.054(0.089)0.048(0.093)0.054(0.109)0.048(0.102)0.076(0.052)0.053(0.060)

Hours
Worked

0.407***(0.063)0.401***(0.111)0.407***(0.092)0.401***(0.122)0.384***(0.045)0.391***(0.069)Commercial
Buildings

0.011(0.039)0.018(0.034)0.011(0.031)0.018(0.030)0.007(0.016)-0.008(0.019)Institutional
Buildings-0.093(0.105)-0.144(0.101)-0.093(0.097)-0.144(0.092)-0.063(0.045)-0.075(0.054)

MarineEngineering

0.013(0.037)0.048(0.051)

0.013(0.032)0.048(0.032)0.007(0.016)-0.005(0.027)

Transportation
Engineering-0.059(0.038)0.023(0.062)-0.059(0.050)0.023(0.056)-0.021(0.024)-0.007(0.035)

Waterworks
Infrastructure-0.004(0.035)-0.007(0.037)-0.004(0.024)-0.007(0.026)0.012(0.015)0.031*(0.018)SewageInfrastructure

0.011(0.088)0.041(0.104)0.011(0.069)0.041(0.063)-0.031(0.034)-0.017(0.040)Communications
Networks

0.010(0.011)0.009(0.010)0.010(0.008)0.009(0.008)0.008*(0.004)0.007(0.005)

Electric
Power-0.010**(0.005)-0.012***(0.004)-0.010(0.008)-0.012(0.008)-0.010**(0.004)-0.012**(0.006)

Other Engineering
Construction-0.016(0.025)-0.011(0.021)-0.016(0.023)-0.011(0.022)-0.016(0.011)0.000(0.015)

Other Machineryand Equipment-0.009(0.011)-0.005(0.009)-0.009(0.014)-0.005(0.012)-0.008(0.007)-0.005(0.008)Transportation Mach.
and Equipment-0.043**(0.017)-0.027**(0.011)-0.043***(0.013)-0.027**(0.012)-0.032***(0.006)-0.022***(0.007)

Unemployment
Rate-0.074***(0.018)-0.051***(0.015)-0.074***(0.018)-0.051***(0.018)-0.058***(0.010)-0.050***(0.012)

Constant

0.025***(0.005)0.040***(0.006)0.025***(0.004)0.040***(0.009)0.020***(0.002)0.039***(0.003)Time FE

—

✓

—

✓

—

✓

R2
N

0.498
220

0.612
220

0.498
220

0.612
220

—
220

—
220

Standard errors in parentheses. (In)dependent variables are in logarithmic form and differenced.
* p < 0.10, ** p < 0.05, *** p < 0.01

44

E

Public Infrastructure by Asset Function, First-Difference Form

Table E1: First-difference production function results, public infrastructure byfunction
OLS
Real Value Added

FGLS

(1)

(2)

(3)

(4)

(5)

(6)

PrivateCapital

0.047(0.081)

0.051(0.094)0.047(0.103)0.051(0.097)0.042(0.053)0.066(0.060)

Hours
Worked

0.413***(0.062)0.419***(0.108)0.413***(0.092)0.419***(0.122)0.403***(0.048)0.383***(0.066)

Health-0.003(0.060)-0.027(0.054)-0.003(0.049)-0.027(0.044)-0.006(0.022)-0.016(0.028)

Education-0.086(0.054)-0.107(0.064)-0.086(0.089)-0.107(0.080)-0.067(0.042)-0.081*(0.047)

Fuel andEnergy-0.011**(0.005)-0.013***(0.005)-0.011(0.009)-0.013(0.008)-0.007(0.005)-0.010*(0.006)

Housing andCommunity Amenities-0.010(0.030)0.006(0.030)-0.010(0.023)0.006(0.026)0.021(0.015)0.030*(0.018)Transport-0.075(0.045)0.011(0.061)-0.075(0.051)

0.011(0.057)-0.038(0.026)

0.002(0.035)

Public Transit
Equipment-0.041**(0.018)-0.026*(0.013)-0.041***(0.012)-0.026**(0.012)-0.029*** -0.023***(0.006)(0.007)

Environmental
Protection

0.019(0.080)0.037(0.100)0.019(0.067)0.037(0.061)-0.019(0.036)-0.001(0.044)

Communication

0.005(0.013)0.005(0.011)

0.005(0.009)0.005(0.009)0.002(0.004)0.004(0.005)

Recreation, Culture
and Religion

0.009(0.039)0.011(0.036)0.009(0.034)0.011(0.034)-0.011(0.019)-0.007(0.023)Public Orderand Safety-0.047(0.031)-0.078**(0.034)-0.047(0.031)-0.078**(0.032)-0.013(0.016)-0.027(0.018)

Unemployment
Rate-0.071*** -0.046*** -0.071***(0.019)(0.015)(0.018)-0.046**(0.019)-0.053***(0.010)-0.038***(0.012)

Constant

0.025***(0.005)0.042***(0.006)0.025***(0.004)0.042***(0.009)0.020***(0.002)0.039***(0.003)Time FE

—

✓

—

✓

—

✓

0.499
220

0.616
220

0.499
220

0.616
220

—
220

—
220

2

R
N

Standard errors in parentheses. (In)dependent variables are in logarithmic form and differenced.
* p < 0.10, ** p < 0.05, *** p < 0.01

45

FCore Infrastructure, First-Difference Form

Table F1: First-difference production function results, public infrastructure byfunction
OLS
Real Value Added

FGLS

(1)

(2)

(3)

(4)

(5)

(6)

PrivateCapital

0.054(0.083)0.056(0.089)0.054(0.099)0.056(0.093)0.065(0.049)0.048(0.053)

Hours
Worked

0.397***(0.070)0.394***(0.106)

0.397***(0.096)

0.394***(0.121)0.409***(0.047)0.405***(0.061)

Core Public
Infrastructure-0.071(0.061)-0.016(0.057)-0.071(0.074)-0.016(0.077)-0.060**(0.030)0.001(0.037)

Non-Core Public
Infrastructure-0.111(0.104)-0.105(0.102)-0.111(0.101)-0.105(0.094)-0.066(0.044)-0.057(0.052)

Unemployment
Rate-0.079***(0.019)-0.045**(0.017)-0.079***(0.020)-0.045**(0.019)-0.053*** -0.033***(0.010)(0.011)

Constant

0.020***(0.004)0.037***(0.004)0.020***(0.004)0.037***(0.008)0.018***(0.002)0.038***(0.002)Time FE

—

✓

—

✓

—

✓

0.455
220

0.588
220

0.455
220

0.588
220

—
220

—
220

2

R
N

Standard errors in parentheses. (In)dependent variables are in logarithmic form and differenced.
* p < 0.10, ** p < 0.05, *** p < 0.01

46