1. Introduction.

Set along the lines initiated by seminal papers on the effects of fiscal policy that look for a connection between public capital spending and aggregate output, a vast “infrastructure and growth” literature evolved in the last 25 years seeking to understand the links between capital accumulation in (either value or physical measures of) infrastructure and growth and welfare. Most of the empirical research devoted to this issue (as surveyed for instance by Égert et al., 2009 or Estache and Garsous, 2012) follows an aggregate production function econometric approach differentiating infrastructure within capital services and estimating the output-elasticity of infrastructure capital. Influential papers such as Aschauer (1989) and De Long and Summers (1991) opened up research in this direction pointing to the needed discrimination of the contributions to growth of private and public capital and of equipment versus plant. Elias (1966) implemented this approach for Latin American countries. More recently Ramey (2020) offered a solid elaboration on the interplay between infrastructure and aggregate output, separating short- and long-run effects.

In this paper, we adopt a different framework to explore the nexus between infrastructure and growth that departs from the usual approach to the topic on two accounts. First, instead of searching for the effects of different types of capital stock of infrastructure on growth, we study productivity shocks from infrastructure-related sectors into productivity growth. Second, instead of focusing on aggregate growth we study a sectoral model where productivity shocks contribute, bottom-up, directly and also indirectly through their impact on other sectors. We posit a production function relationship at sectoral level in order to infer the transmission of productivity shocks in infrastructure. Our departure from stocks to flows in our modelling strategy is important because it addresses a different, less studied, transmission channel and so it shifts the focus of attention from the “hardware” of infrastructure -represented by capital- to the “software”, represented by productivity. Attention to software rather than hardware has been the motivation of some studies (eg, Cavallo et al., 2020) on the requirements to improve the performance of infrastructure services beyond capital investment, to close the so-called infrastructure gap that have come under several critical reviews (see for example Gardner and Henry, 2023). For this task, we propose a simple analytical framework to move into an econometric modelling based on the data set from the Groningen Growth and Development Centre (GGDC) (Timmer and de Vries, 2007; Timmer et al., 2015). on a global data set on annual labor productivity for 10 sectors in 25 countries across 4 decades.

Related literature. With a data set different from what we use, the methodology of growth accounting, as developed by Jorgenson (1972) and others, also starts from an aggregate production function setting and, using the national accounts framework, decomposes contributions to growth into input accumulation and total factor productivity. These approaches can go into sectors of the economy insofar as national accounts data allows. Along this line, KLEMS productivity models that decompose primary inputs (capital and labor) along with energy, materials and services, have been applied in different regions. The case of Europe (EU KLEMS, Timmer et al., 2007) and more recently of Latin America and the Caribbean (LAC) region (LA KLEMS, Hofman, Mas et al., 2017, Hofman, Aravena y Friedman, 2017) are examples of such empirical research that involves collective efforts across countries. The potential sectoral extension of the KLEMS data set is a clear advantage over data set used by more aggregative approaches, such as those represented in the aggregate production function econometric approach. In principle, growth accounting could accommodate infrastructure inside its framework, by measuring infrastructure capital by sector and looking at its contribution to sectoral and aggregate growth. With the exception of Mas (2009) we have not found much explicit efforts in data building and measurements, within KLEMS models, to pinpoint the contribution of sectoral infrastructure to productivity growth. This would be a very promising methodological line given the versatility of the KLEMS approach to disaggregate by sectors. Nevertheless, such an approach should cope with difficulties related to the construction of databases, particularly related to the measurement of capital. Limitations in the national accounts frameworks in several countries posses challenges for the development of this line of analysis (an exception for Latin America is Mexico, see Navajas et al., 2021). We also relate to the existing applied econometrics literature which has made useful contributions to point the need to support infrastructure investment programs, to close development gaps and avoid underinvestment in critical infrastructure. Among this literature, a significant proportion of papers have devoted the analysis to the effects of infrastructure capital on growth (to quote a non exhaustive selection, for example, Calderón and Servén, 2016; Égert et al., 2009; and Estache and Garsous, 2012) or on aggregate output (Calderón et al., 2015). While the main result that infrastructure capital spurs growth is robust, there is no full agreement on which infrastructure sector matters most for growth, with results that may depend on the methodology employed. Parametrically speaking, these effects come usually (although not exclusively) in the form of an estimated output-elasticity to infrastructure sector -or sub-sector- capital or investment. However, the precise contribution of infrastructure to growth might not only be sector specific or even country specific but may also be conditional on the development stage (or even perhaps some growth episodes) of countries. Estache and Garsous (2012) raised the issue that the effects, for a given country, will depend on time, development stage and type of infrastructure. Their review of (mostly econometric) results give energy infrastructure (electricity) a leading role as having the most robust effect across countries. They argue that infrastructure is a sure bet contributor to growth in general, but particularly for low income countries. In reviewing different econometric methodologies and studies, Égert et al. (2009) find that telecoms and energy are clear contributors to growth, but they do not find similar effects for railroads or roads. However, other methodologies provide different results. For example, road infrastructure appears as a major contributor of productivity growth in Fernald´s (1999) account of the U.S. experience, following a productivity measurement approach. Also, in one of the few papers which includes infrastructure in a growth accounting framework, Mas (2009) finds road infrastructure, among several types of capital infrastructure (excluding energy), as the main contributor to growth in Spain (1985-2004), explaining about 52% of the contribution of infrastructure capital to growth, with total infrastructure having an effect equivalent to that of total factor productivity (TFP) for the whole sample. Beyond these contributions, there is no complete agreement from existing papers on which infrastructure sector matters most for growth, there is no –to our knowledge- even available empirical results on the sectoral impact of infrastructure (on which sectors).

Structure of the paper. In section 2 below we start writing down our econometric framework for studying, across economies and sectors, the effects of labor productivity in infrastructure-related sectors and of control variables among which capital-labor ratio proxies for infrastructure sectors are included. This allows obtaining effects from labor productivity and capital productivity in infrastructure sectors on other sectors. For each sector we evaluate a time series-cross section (TSCS) panel similar to Ahumada and Cornejo (2015), using an automatic selection procedure for estimation (Doornik, 2009; Hendry & Doorni, 2009) and taking account of cointegration, cross-dependence of residuals and exogeneity. We show how this approach can be extended to the study the case of single economies.

Section 3 describes our data, based on the Groningen Growth and Development Centre (GGDC) data set (Timmer and de Vries, 2007; Trimmer et al., 2015). Due to problems with the dataset in African economies we restrict our study to a sample of 25 economies (8 from LAC, 9 from OECD and 8 from Asia) between 1971 and 2014, due to the availability of control variables and the possibility of extending the sample beyond the GGDC dataset subject to national accounts data. The three infrastructure related sectors above are Utilities (Electricity, Gas and Water), Transport (Transport, Comunications and Storage) and Construction. Controls include different forms of capital that we use as proxies for capital in the infrastructure related sectors, measures of international trade openness, human capital and a political index.

Econometric results are presented in section 4. We are able to find acceptable empirical models in all sectors that report effects of (infrastructure-related sectors) labor productivity, capital (to labor) intensity, capital productivity and control variables, among which trade intensity emerges as a robust determinant of productivity (see for example Alcalá and Ciccone, 2004) in some tradable and non-tradable subsectors. We find transport (for OECD countries) and utilities (for countries outside OECD) labor productivity as being relevant in explaining long run agricultural labor productivity across counties. Both utilities and transport have only short run effects on manufacturing, while long run effects in this sector come from construction productivity. Transport, through its capital stock per worker, and utilities´ capital productivity have long term effects on labor productivity in mining. As for the service sectors, we find that construction productivity has significant effects (with a unitary elasticity) on the long term productivity of domestic trade and also on financial services productivity. There are also short run effects of transport on the two service sectors; from the capital stock per worker in the financial case and labor productivity in the trade sector. Elasticities of both labor productivity and capital stock effects, both long and short run, are computed for all these effects.

To assess the quantitative importance of the effects, in section 5 we translate the estimated long run effects of infrastructure-related productivity shocks into aggregate productivity growth in a straightforward manner. For this we assume an increase in the labor productivity growth rate in infrastructure-related sectors of a given country or region towards a given benchmark. This has a direct impact on the economy-wide labor productivity growth rate, but also an indirect effect through sectoral labor productivity growth rate and (given the employment share of the sectors). Given that long run impacts of infrastructure-related productivity shocks are localized in few sectors (which happen to be low productivity ones, such as agriculture, financial services and domestic trade) one may a priori expect that the quantitative aggregate magnitude of long term impacts is not particularly large in aggregate terms, although significant at a sectoral level. However, aggregation of effects due to “shocks of convergence” towards OECD or World average productivity growth in infrastructure related sectors tell otherwise. Computing shocks in labor productivity in utilities, transport and construction, such that these infrastructure related sectors productivity growth in LAC converge to the OECD or World average productivity growth rates of our sample we find a significant impact in economy wide labor productivity growth rates, that may increase by 75% the size of the average (across countries) economy-wide labor productivity growth rate (of 0.6% per year) observed for LAC during the period. Shocks in utility and transport on agriculture explain one-third of the effect while two-thirds come explained by shocks in construction productivity on financial services and domestic trade.

2. Econometric modeling

To study the effects of infrastructure on productivity growth we use an econometric approach to answer which kind of infrastructure productivity is relevant on which sectorial labor productivity. As mentioned in previous section, a great part of the literature on infrastructure and growth has an underlying framework where capital infrastructure enters into the production function process of the economy at an aggregate level, but distinguishing among several forms of capital infrastructure. Thus, beyond capital infrastructure effects, there is less effort to capture productivity spillovers stemming from infrastructure productivity towards the economy, not to mention other disaggregated sectors. On the other hand, historical evidence documents the fact that infrastructure act as a catalytic to spur and diffuse sectoral innovations (Murphy, 2020). To capture the interactions from a richer set of channels we submit a production process where a total productivity parameter of the infrastructure sector j, denoted by Aj enters the sectoral production function of sector s. Equations (1) to (3) shows this formulation where y denotes output, K and L capital and labor and A are efficiency parameters.

\(y_s=A_sK_s^{\propto_s}L_s^{1-\propto_s}A_j^{\beta_j} \left(1\right)\)s= other sectors

\(y_j=A_jK_j^{\propto_j}L_j^{1-\propto_j} (2)\)j= infrastructure sectors

Rearranging terms we write

\[\frac{y_s}{L_s}=A_s\left(\frac{K_s}{L_s}\right)^{\propto_s}\left(\frac{y_j}{L_j}\right)^{\beta_j}\left(\frac{K_j}{L_j}\right)^{-\beta_j\propto_j} \left(1^'\right)\]

\[log\frac{y_s}{L_s}=logA_s+\propto_slog\left(\frac{K_s}{L_s}\right)+\beta_jlog\left(\frac{y_j}{L_j}\right)-\beta_j\alpha_jlog\left(\frac{K_j}{L_j}\right) \left(3\right)\]

This framework accommodates the channels from infrastructure related sectors productivity shocks into other sectors and is also consistent with the usual channel operating through infrastructure capital. In fact, infrastructure can have an impact on other sectors through its capital stock, the productivity of capital or the productivity of labor. In the case where \(\propto_s\approx0\) then labor productivity shocks in the infrastructure sector capture shocks in the productivity parameter As, while in the case where \(\propto_s\approx1\) infrastructure capital productivity is main the driver that impact upon sectoral labor productivity. Given this formulation we use an econometric approach that, controlling for other factors and dealing with exogeneity and interdependencies, selects among those alternative channels, extracts elasticities from different (which) infrastructure related productivity improvements towards different (on which) sectoral productivity improvements.

Given that one of the aims of the research project was to respond to the query on how to obtain long run elasticity estimates –at world or global levels- from productivity growth in infrastructure related sectors on sectoral productivity growth, we developed a sample that covers OECD, Asia and LAC across more than four decades. Our panel data base with N= 25 countries and T= 44 years allow us to model a dynamic Time Series–Cross Section (TSCS) model to disentangle long run and short run effects (taken into account the possibility of integrated data) from the OLS estimations of a kind of a fixed-effect model, similarly as in Ahumada and Cornejo (2015). Pooling of countries across the world gives us a reference frame in which we can test country or region heterogeneities. In particular, we will use these estimates to compare with LAC´s ones.

Initially we started with unrestricted models of labor productivity (output per worker in logs, \(y\)) for a given sector “s”( agricultural, manufacturing, etc.) using, in each case, as explanatory variables the labor productivity of the three “j” infrastructure sectors (\(y_{utl}, y_{con}, y_{tsc}\)) along our proxies for the capital per worker of the same infrastructure sectors (\(k_{utl}, k_{con},k_{tsc}\)) so as to distinguish productivity from stock of capital effects. We also included, in the unrestricted model as control variables, (\(x\)) two different measures of trade openness (exports plus imports of each country as fraction of the GDP and also as a fraction of the sample's total exports plus imports) along with a human capital index, a political index and the total and machinery capital stock per worker. For the same unrestricted models, in order to evaluate country heterogeneity, we started including fixed effects through 25 dummy variables (one for each country) and also, when necessary, time effects (years) and outliers (impulse dummies for a specific country-year observation). The Appendix describes the data and sources in detail.

To handle such large information set, an automatic algorithm (Autometrics , see Doornik, 2009 and Hendry and Doornik, 2014) helped us to select the relevant variables. It uses a tree search to discard paths rejected as reductions of the initial unrestricted model based on ordered squared t-statistics, given a p-value provided by the researcher.

We can note that including unrestrictedly country dummies (instead of country demeaning the data as in the usual fixed effect estimation) we can evaluate intercept country heterogeneity by observing the dummies selected by the algorithm, given the main economic determinants. Other heterogeneities associated with elasticity differences can be evaluated as well after estimation by including multiplicative dummies of the effects detected and testing their significances. We perform this analysis for LAC, at this stage.

Given the time behavior of the data we take into account the possibility of unit roots and evaluate cointegration according to the following approach. The unrestricted models of labor productivity are formulated for their log differences and the explanatory variables expressed in log levels and log differences (as in Bardsen for time series, Westerlund (2007) and Smith and Fuertes (2010) for panel data).

Therefore, the starting unrestricted models have the following form for a given economy “s” sector,

\[\Delta y_{s,it}=\alpha_i+\gamma_t+\delta_s y_{s,it-1}+\beta_{s,utl} y_{utl, it-1}+\beta_{s,con} y_{con, it-1}+\beta_{s,tsc} y_{tsc, it-1} + \phi_{s,utl} \Delta y_{utl, it}+ \phi_{s,con} \Delta y_{con, it} + \phi_{s,tsc} \Delta y_{tsc, it} + \theta_{s,utl} k_{utl, it-1} +\theta_{s,con} k_{con, it-1}+\theta_{s,tsc} k_{tsc, it-1} +\lambda_{s,utl} \Delta k_{utl, it}+ \lambda_{s,con} \Delta k_{con, it}\lambda_{s,tsc} \Delta k_{tsc, it} ´ +x_{it-1}´ ϕ_s+\Delta x_{it}´ \tau_s+\varepsilon_{s,it} i=1, ..,N ; t=1,…,T (4)\]

where “i” indicates each country and “t” each year of the panel for sector “s”. In the first row we have the coefficient of the country and time effects and the long run effects of labor productivities given by (as \(\delta_s\) is expected to be significantly negative under cointegration) by the negative value of \(\frac{ \beta_{s,utl}}{\delta_s}\frac{, \beta_{s,con}}{\delta_s}\frac{, \beta_{s,tsc}}{\delta_s}\) , that is the long run infrastructure sector elasticity, respectively. The next row indicates the impact effects of changes in infrastructure productivities. Similarly, the third and four rows includes parameters for the long run and short run effects of capital per worker of the infrastructure and the last row for the control variables in the vector \(x´\) respectively. All variables are in logs (except the political index).

From the log functional form in equation (4) we can also obtain the effects of infrastructure sector capital productivities, as well. In this case the estimates should not reject the hypothesis that \(\beta_{s,j=}- \theta_{s,j}\) for j = utl, tsc, con because when they hold the corresponding effects becomes\(\beta_{s,j} y_{j, it-1}- \theta_{s,j} k_{j, it-1}= \beta_{s,j} (ln\) (Y/L) - \(ln\) (K/L) = \(\beta_{s,j} (ln\) (Y/K). Therefore the estimates of \(\beta_{s,j}\) is the elasticity with respect to capital productivity of the j infrastructure sector.

It is important to note that equation (4), nesting levels and differences, allows us to have variables which enter the model either in the long run or short run, or both.

The advantage of estimating this type of model is that it can be easily reparametrized as an error correction (EC) model which includes growth rates and deviations from the log run relationship. For example, when there is only a long run effect of a j infrastructure sector say, construction on a given s sector productivity, the restricted Equation (1) would have the next EC representation,

\(\Delta y_{s,it}=\alpha_{si}-\delta_s [y_{s,it-1}-\beta_{s,con}^* y_{con, it-1}]+ \phi_{s,con} \Delta y_{con, it}\)\(+\varepsilon_{sit}\) (5)

where\(\beta_{s,con}^*=\frac{\beta_{s,con}}{ \delta_s}\)

If the variables were first order integrated, we can test whether or not this long run relationship is a cointegration vector evaluating the significance of the t-statistic of the lagged explained variable (of the estimated coefficient of \(\delta_s\)). Although the distribution of this statistic is non-standard when there is no cointegration, the critical values derived from the response function in the Monte Carlo study of Ericsson and MacKinnon (2002) can be used to test cointegration.

Since our main interest is to evaluate for the long run effects of infrastructure productivity during the automatic selection we kept fixed (an option of Autometrics) the log levels of productivity, apart from the constant term and only dropping the non-significant ones after estimation.

We also initially assumed: i) there is no cross-dependence of the (country) residuals ii) there is no effects among the different economic sectors at world level and iii) the explanatory variables are all exogenous. To evaluate these assumptions for the selected models we performed the following post estimation checks.

With respect to i), we calculate Driscoll-Kraay standard errors and compare significance according to them. We also report heteroscedasticity consistent standard errors trying to separate changes in significance due to heteroscedasticity from cross dependence. If we observe that using these SE, the t-statistics are not different from the OLS, then there would not be misspecification due to cross dependence or heteroscedasticity.

To analyze ii) we test long run sectors interdependence from augmenting the selected model from equation (4) for a given sector by the other sectors lagged levels and testing their significance. The augmented equation could be considered as one of a VEC (Vector Error Correction) for the different sectors’ productivities while the productivities and capital for the related infrastructure sectors as external variables of this system.

Regarding iii), we re-estimate the models by instrumental variables in cases when infrastructure (log differences) variables enter contemporaneously into the selected models. Our main identification assumption is that capital per worker of the infrastructure sectors are exogenous and therefore can be used as valid instruments, as detailed in the different cases. For long run effects we check if they are significant in the inverted (one of the VEC) reduced form equations, when modelling the different sectors. If it were significant we have not structural effects but those of the reduced form.

We can note (see Hendry, 2007) in the case of variables with unit roots representation we can have different sources of no exogeneity. To see it in the simple case of the conditional model of equation (5) which assumes cointegration of the labor productivity of the sector with that of the infrastructure, the marginal model for construction could be,

\(\Delta y_{con,it}=\rho[ y_{s,it-1}-\beta_{s,con}^* y_{con, it-1}]+ \omega_{con} \Delta y_{s, it-1}+\varepsilon_{con,it}\) (6)

While \(\omega_{con}\) is associated with Granger- Causality from the “s” sector on construction, it is neither necessary nor sufficient to be zero for a valid conditional model to obtain consistent estimates of the parameters in (5). For weak exogeneity, \(\rho=0\)is needed, that is the EC term does not enter the marginal model. Given that we started with a conditional model then, \(\rho=0\) requires that the effect of \(y_{s,it-1}\)should be not significant in (3). Therefore, no level of the sector “s” enters into each equation of infrastructure sector which has effects on sector “s”. This evaluation is often called LR exogeneity. However, the contemporaneous effect of \(\Delta y_{con, it}\) can be associated, apart from the long run effect, to\(E[\varepsilon_{con,it.}. \varepsilon_{s,it}]\neq0\). Thus, we use IVE to have consistent estimates from a single equation like (5).

3. Data

Our panel database is based on the Groningen Growth and Development Centre (GGDC) data set (Timmer and de Vries, 2007; Timmer et al., 2015). The GGDC 10-sector database provides value added data expressed in local currencies, using 2005 as base year for constant-price measures. In order to make comparisons between countries regarding labor productivity and following Rodrik et al. (2017), we converted value added data from local currencies to purchasing power parity (PPP) international dollars by use of the conversion factors provided by the International Comparison Program (ICP) initiative led by the World Bank, in particular the 2005 update.

Several warnings have been issued regarding the accuracy of the 2005 ICP, especially since the 2011 ICP revealed major corrections on PPP conversion factors. Papers dealing or mentioning this controversy include Deaton and Aten (2017), Pinkovskiy and Sala-i-Martin (2016), Feenstra et al. (2016) addressing the updates undertaken on the Penn World Table (PWT) 9.0, and Johnson et al. (2013). In general, findings conclude that these distorted estimates are more frequent and severe in African country data, where newer versions of the ICP and broad databases as the PWT have explicitly addressed the problem with constantly updating the corresponding conversion factors. This is the main reason behind our decision to exclude African countries from our dataset. The GGDC 10-sector database provides data for 13 countries from Sub-Saharan Africa, Middle East & North Africa that we have not taken into consideration in light of the data issues related (many of which manifested themselves in preliminary cross-section comparisons of labor productivity across countries and across sectors after adjusting for PPP exchange rates). As of today, these data limitations extend themselves to other datasets: another problem we would have eventually encountered concerns data availability for the trade estimates we use (in particular, for Ethiopia, Tanzania, Zambia & Mauritius as shown in World Bank Open Data for trade estimates).

Labor productivity at the sectoral level (one-digit level of the International Standard Industrial Classification, ISIC) is expressed both in levels and as a gap (i.e. relative to the average for the economy) and includes a set of control variables (5 measures of capital stock per worker; and other 12 controls), for a sample of 25 countries (8 from LAC, 9 OECD (non LAN, non Asia) and 8 from Asia) and 44 years (1971-2014). Table 1 summarizes the glossary of our dataset definition, while Figure 1 shows the coverage in terms of countries, time span for labor productivity measures and for control variables. Light blue in Figure 1 indicates available data across countries and controls. Light red indicates years, countries or variables where data is not available. Following a detailed work, that included extending (splicing) by related (national accounts) measures, the GGDC productivity measurement to 2014, we ended up with a sample from 1971 to 2014 for the above mentioned 25 countries.

Using the database of Penn World Tables (PWT) in combination with de GGDC database on sectoral employment we constructed a proxy for capital stock per worker in the construction sector using the capital stock for “Structures” in the PWT database relative to employment in the construction sector. In a similar fashion we do the same for the transport sector (using the capital stock of “Transport Equipment” reported in PWT data and employment in the transport sector in the GGDC data). In the case of utilities we use as a proxy for capital Total Installed Power Capacity from EIA database and employment in the utility sector from GGDC.

4. Econometric results

4.1 Agriculture

In the model of shown in Table 2 for agriculture, 5 out of 25 country effects were retained, which show very similar coefficients and can therefore be constrained to only one coefficient. These countries are Colombia, India, Mexico, Peru and Philippines, all with lower productivity in the agricultural sector. The only significant control with the expected sign is the change of trade shares.

In this estimated model agriculture labor productivity receives long run effects from transport productivity but only for OECD countries, and from utilities for the rest of countries in the sample. Furthermore, the selected model has labor productivity and stock of capital per worker in the construction sector as determinants. The values and signs of the estimates for the impact of construction sector coefficients allow us to rewrite the model, as shown in section 2, separating the effects of capital productivity (and the capital per worker, if significant) for this infrastructure sector. Indeed, our estimates can give us information not only about the effects of infrastructure labor productivity and capital stock per worker but also about “capital productivity” when it is relevant as it is in the agriculture sector case.

Assuming a conditional model, the results indicate a long run relation :

\(Ly_agr = constants + 1.21 OECDELy_tsc + 0.55 NO OECDELy_utl + 0.99 (Ly-Lk)_con (7)\)

These estimates indicate that in the long run a 1% increase in the labor productivity of transport increases labor in agricultural sector in 1.2% for OECD countries, anything else constant, while a 1% rise in the labor productivity of utilities increases 0.5% in countries not belonging to the OECD. Finally, a 1% increase in capital productivity of construction means about 1% increase in agriculture productivity for all the countries. To evaluate residual cross section (country) correlation, we present in Table 2 Driscoll-Kraay (DK) standard errors. Significant effects are maintained and are very similar to those using standard SE. The model has no contemporaneous effects of infrastructure productivities and also no long run effects from other (than infrastructure) sectors on agricultural labor productivity are detected.

4.2 Mining

For the mining sector results in Table 3 shows that 3 of 25 countries have different effects. Two are more productive countries (Denmark and Netherlands) which show similar coefficients and were constrained to only one, and one less productive (Singapore).

In the estimated model we found a long run effects of the capital stock per worker in transport. Results also show an effect from utilities, both from labor productivity and from its capital stock. The values and signs of their estimates indicate that the relevant explanatory variable in the mining sector equation is capital productivity in utilities. Moreover, for this variable there were also interaction effects with the financial sector (with the expected sign). Assuming a conditional model, the results indicate a long run relation :

Ly_min = constants + 0.65 Lk_tsc + 0.05 (Ly-Lk)_utl* Ly_fin (8)

These estimates indicate that in the long run a 1% rise in the capital stock of transport increases labor productivity in mining by 0.65 % anything else constant while the effect of capital productivity of utilities is dependent on the level of the financial sector productivity. We have the same similar significant effects for the main economic drivers using the Driscoll-Kraay standard errors to take into account possible cross dependences. Regarding exogeneity, the model has no contemporaneous effects of infrastructures productivities and also no long run effects from other sectors on labor productivity of utilities are detected allowing us a structural interpretation of this model.

4.3 Manufacturing

For the manufacturing sector results are presented in Table 4. We found no different country fixed effects, after controlling by the explanatory variables of this model. The model also includes 5 impulse dummies for outliers and time effects for 2009-2010 after the global crisis, representing a negative productivity shock of about 4%. The model of manufacturing productivity detected significant effects of controls (two measures of trade openness and an index of human capital) and the (contemporaneous) short term or impacts effects from all the infrastructure related productivity sectors. In the long run, effects come from construction productivity as well as from trade openesss (the ratio of trade to GDP) and from an index of human capital (hc). No effects from our measure of the machinery stock per worker of manufacturing was significant.

Assuming a conditional model, the results indicate a long run relation :

Ly_man = constants + 0.42 Ly_const + 0.35 Ltrade_gdp + 1.98 lhc (9)

Regarding infrastructure estimates in the long run a 1% rise in construction productivity increases manufacturing labor productivity in 0.4 % anything else constant. Significant effects of the explanatory variables remains when using the Driscoll-Kraay standard errors to take into account possible cross dependences. Since the model has contemporaneous effects of infrastructures productivities we perform instrumental variable estimation (IVE) of the model allowing for the variations of utilities, construction and transport (utl, const and tsc) as endogeneous, as shown in Table 5. We assume the capital of the three infrastructure related sector as exogeneous and thus we include their log levels and log differences as instrument (the specification test do not reject the null of their validity).

We can note that comparing with OLS estimates the IVE are similar for construction (about 0.13 vs. 012), higher for transport (0.39 vs. 0.27) and somewhat lower for utilities (0.03 vs. 0.05), although in the last case may need additional instruments. Given these results only transport labor productivity may be not exogenous regarding short run infrastructure effects and consider their IV estimates.

4.4 Finance, insurance and real estate

As shown in Table 6 below, in the case of financial services we found country fixed effects for China (above the sample average) and for Italy (below the sample). The selected model includes (contemporaneous) impacts from the variation of the capital stock per worker in transport as well as the change in the capital productivity in construction. This sector productivity is the only one which has is a long run effect on financial services labor productivity.

Assuming a conditional model, the results indicate a long run relation

Ly_fire = constants + 1.04 Ly_const (10)

In the long run a 1% rise in construction labor productivity increases financial services labor productivity about 1 %, everything else constant. Significant effects of the explanatory variables remains when using the Driscoll-Kraay standard errors to take into account possible cross dependences.

Since the model has contemporaneous effects of capital productivity in the construction sector we performed instrumental variable estimation (IVE) using the log levels and log differences of capital stock in the construction sector as instrument (the specification test do not reject the null of their validity).

Table 7 reports the IVE. Results indicate that the effect of capital productivity of construction on financial sector productivity is only slightly lower (from 0.20 in OLS estimates to 0.17).

4.5 Trade, restaurants and hotels

Table 8 shows the results for the domestic trade sector. It has country fixed effects for China, Singapore and Japan (relative more productive than the rest of countries) and Colombia (less productive). As control variables we found effects of trade share in the short run and the index of human capital in the long run. The selected model in this sector includes (contemporaneous) impacts from the variation of labor productivity in transport. The effect of construction productivity enters the model as the change in both the capital and labor productivity and in log level.

Assuming a conditional model, the results indicate a long run relation :

Ly_trh = constants + 0.97 Ly_const (11)

In the long run a 1% rise in construction productivity increases domestic trade sector productivity about 1 %, anything else constant. Significant effects of the explanatory variables remains when using the Driscoll-Kraay standard errors to take into account possible cross dependences.

Since the model has contemporaneous effects of infrastructures productivities we performed instrumental variable estimation (IVE) of the model allowing for the variations of construction and transport productivities as endogeneous, as shown in Table 9. We assume the capital of these infrastructure sectors as exogeneous and thus we include their log levels and log differences as instrument (the specification test do not reject the null of their validity but at 5%).

Comparing OLS estimates the IVE are similar for construction (about 0.10 vs 0.13) , higher for transport ( 0.33 vs 0.48) . Given these results only transport productivity may be not exogenous regarding short run infrastructure effects and consider their IVE estimates.

4.6 Summing up results

Main results from previous estimations are shown in the Table 10 in the form of long run elasticities coefficients, while Figure 2 depicts all the effects found.

Figure 2: Long-run impact labor productivity elasticities: which on which sectors?

Source: Table 10

• Elasticity estimates show that the effect of infrastructure is not uniform.

• utilities (energy infrastructure and water) labor productivity shocks have effects on agriculture (outside the OECD), mining (only when interacting with financial services) and manufacturing (only in the short run).

• Transport labor productivityshocks have effects on agricultural sector (for OECD countries), and on domestic trade services (only in the short run).

• Construction labor productivityand capital shocks have effects on all the sectors we studied but enter the model in different ways (short and or long run; labor or capital productivities).

• The effects of the infrastructure capital stocks should be taken into account when modeling infrastructure sectors as drivers of other sectors.

•  From the sensitivity analysis, we observe that results are similar when residual cross dependence (through countries) is considered and we found no long run effects from other sectors.

• From the sensitivity analysis too, there are several contemporaneous effects of the infrastructure sectors that require instrumental variable estimation. It was performed using the capital stock per worker in the infrastructure sectors as instruments. Results are in general robust to this procedure.

5. Relative magnitude of effects: an example for the LAC region

Productivity improvements in infrastructure related sectors “j” affects aggregate productivity performance through direct (own) and indirect effects. Expression (12) decomposes all the effects needed to compute or simulate effects.

\[\Delta log⁡\left(\frac{y}{l}\right)_=\sum_{j} \alpha_j\Delta log\left(\frac{y}{l}\right)_j+\sum_{i} \alpha_i\left(\eta_{\frac{y}{l}_i,\frac{y}{l}_j}\Delta log\left(\frac{y}{l}\right)_j+\eta_{\frac{y}{l}_i,\frac{y}{k}_j}\ log\left(\frac{y}{k}\right)_j+\eta_{\frac{y}{l}_i,\frac{k}{l}_j}\Delta log\left(\frac{k}{l}\right)_j\right) (12)\]

where i=1,…7 are other sectors, j=utl, tsc, con are infrastructure related sectors and α are labor share ratios. Expression (12) decomposes the final effect on aggregate productivity growth in a “direct or own” effect (the first term on the RHS) and an “indirect” effect that depends on the infrastructure-related sector (j) elasticity (defined for labor productivity y/l, capital productivity y/k and capital-labor k/l) of the sectoral (i) labor productivity, and the rate of growth (or, for simulation purposes, the convergence to a benchmark of the rates of growth) of y/l, y/k and k/l in the infrastructure related sector j. Employment shares αi and αj also drive the magnitude of effects.

Expression (12) is easy to compute given the set of relevant elasticities taken from Table 10, the labor shares and assuming an increase in annual rates of growth of productivities in the infrastructure related sectors. We have computed an example for the LAC region assuming a shock to the labor productivity growth rate of the infrastructure-related sectors equivalent to close the gap between the regional mean and the best performer of the region (in each sector). LAC best performers are Brazil for utilities, Chile for transport and Peru for construction with annual growth rates of 5.3%, 3.0% and 0.5% respectively while average rates for LAC for these sectors are 2.1%, 1.4% and -0.5%. This means that simulated shocks are given by the difference between these values (3.2%, 1.6% and 1%) and direct effects come from these shocks multiplied by the shares of the three sectors in total employment in LAC (which are 0.6% for utilities, 6.5% for transport, communication and storage and 8% for construction). Results are shown in Table 11.

This generates an increase on the growth rate of aggregate labor productivity equivalent to 0.96% per year which represents an increase of 168% of the annual rate for LAC in our sample. Only 20% of this effect comes from the direct effect given by the increase in productivity in infrastructure while almost 80% come from the effect through others sectors productivity. Construction is responsible for more than 60% of the total (direct plus indirect) effect while utilities (energy infrastructure) explain 28% and transport less than 11%. Our results, for this LAC exercise in particular, are in accordance with previous ones that emphasize the role of energy infrastructure over transport. However, our estimation allows us to distinguish between the two in another important dimension. While energy infrastructure operates through indirect effects on the agriculture sector, transport does so only directly, ie through the productivity growth of the transport sector. Construction affects productivity growth through its direct effect but also and mainly indirectly through its effect on domestic trade and financial services.

6. Final remarks and extensions

That infrastructure matters for growth is an established result both in theory and empirical studies (cf. Calderón and Serven, 2016, survey in the New Palgrave Dictionary). On the other hand, several sectoral professionals and top executives at development banks have informally complained that these results are too aggregative and fly at ten thousand miles from their ground based needs to establish priorities or evaluate infrastructure strategies by countries. Indeed, although papers on infrastructure and growth have produced empirical results that account for the importance of aggregate or different types of infrastructure investment on aggregate growth there is no complete agreement on which infrastructure sector matters most for growth, with results that may depend on the methodology employed. This may be unavoidable insofar specificities across countries and development stage may create these discrepancies, although differences in data and methods are also responsible for these disparities. However, the literature is silent on the empirical sectoral impact of infrastructure. So it is not only which infrastructure matter most for growth, but also which infrastructure for which sector seem to spur growth. The logical reaction to this knowledge gap is to look for more disaggregated dataset and methodologies that can address the sectoral effects of infrastructure. For example, Izquierdo et al. (2018) made a preliminary conjecture pointing towards combining growth accounting datasets and panel dynamic econometrics to study productivity shocks effects in infrastructure related sectors on others sectors and on aggregate productivity and growth. They rapidly found that data limitations are a clear drawback at this stage, so data buildup should be taken seriously and promoted. Another problem is that methodologies should be flexible enough to address country cases providing more country specific results that can dialog with infrastructure policy in practice.

In this paper we have made an effort in this direction by using an available dataset on sectoral labor productivity across countries and implementing a dynamic panel econometric approach. To our knowledge neither this dataset nor the chosen econometric approach has been previously combined to address the performance of infrastructure related-sectors in terms of their contribution to productivity growth. With new data and new methods we have been able to gain new insights. We are able to decompose direct (which infrastructure sector) and indirect (on which sector) effects of infrastructure sector productivity improvements on aggregate productivity. We found that the latter dominates the former. Energy infrastructure dominates transport infrastructure (except for a group of OECD countries in our sample) insofar as productivity growth is concerned, which is a result previously found in some review papers. However, we were able to capture another dimension concerning the channels for productivity growth. In our results, energy infrastructure effects are mainly indirect and affecting agriculture sector productivity while transport infrastructure effects operate mainly directly. Finally the construction sector has the largest effects on productivity growth both direct and indirect (through the domestic trade and financial services sectors). Another insight is whether infrastructure productivity shocks increase productivity gaps or disparities across sectors. Our results do not seem to support that hypothesis. Despite the fact that infrastructure sectors such as energy and transport are relatively high labor productivity sectors (and that construction has low productivity) the indirect effects concentrate in three sectors (agriculture, domestic trade and financial services) that are relatively low productivity.

Our results do have a number of qualifications regarding data and methods which we take as a positive aspect to motivate improving this line of research. First, a two digit sectorial database is still too-aggregated to fully address the complain stated at the beginning of this section. Thus, more measurement efforts are needed so that more disaggregated but still consistent data is available. Even with this aggregation level we believe we could benefit from the spread of the KLEMS methodology across regions, which would allow to implement a model that studies TFP shocks within a consistent growth accounting framework. These steps using KLEMS within our framework have been achieved in research done both at the country specific level expanding considerably the scope of sectors (for Mexico in Navajas et al., 2021) or at a global level to study infrastructure productivity interactions with global shocks (Ahumada et al., 2022). Secondly, the econometric approach can move towards a global panel that exploits more interactions across sectors and countries. Doing so while explaining country specificities at a level useful for policy dialogue seems a promising avenue.

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Contribución de los/as autores/as

1. Administración del proyecto, 2. Adquisición de fondos, 3. Análisis formal, 4. Conceptualización, 5. Curaduría de datos, 6. Escritura - borrador original, 7. Escritura - revisión y edición, 8. Investigación, 9. Metodología, 10. Recursos, 11. Software, 12. Supervisión, 13. Validación, 14. Visualización.

Appendix A

Sectoral productivity performance

Labor productivity growth highly correlates with per capita GDP growth in our sample (See Figure A.1). Economies that perform well in terms of output per worker have a higher performance too in terms of GDP per capita. This is not surprising since a production function approach, as a representation of growth accounting, would indicate an equation where output per worker would be determined by capital per worker and total factor productivity, for any measurement adjustment done to reflect varieties or quality of capital and labor. This is also true at a sector level, including the infrastructure related sectors.

Figure A.2 is an introductory descriptive representation of the performance of labor productivity across sectors and countries in our sample. Actually, it tells us a lot about features we need to understand to evaluate our data. Sectoral labor productivity performance has 3 distinct sector (Construction, domestic trade and social services) that are clear underperformers for the groups of “best performers”, the World and certainly LAC. Two other sectors (government and financial services) are clearly part of underperformers both at the world panel level and in LAC.

Figure A.1. Labor Productivity (Y-Axis) & Value Added per Capita (X-Axis) Annual Growth Rates (%) for period 1971-2014

Figure A.2. Annual sectoral labor productivity growth rates: World, Best Performers & LAC 1971-2014 (%)

Infrastructure related sectors such as Utilities and Transport stand along the most dynamic sectors such as Mining and Manufacturing. Agriculture displays a dynamic performance in terms of productivity growth across the period. All the service sectors and construction emerge in this introductory picture as low growth productivity sectors. They are also low productivity in levels or static terms at the end of the sample period. Figure A.3 shows productivity levels (and therefore gaps) across sectors and regions and best performing countries. LAC display a 10-25% gap against the world average depending on the sector; this gap being larger for low productivity sectors. Against the best performer the gap is about the double in size.

Figure A.3. Labor productivities (in logs) for best sectoral performer, world average & LAC average (2014)

Agriculture stands as a peculiar sector which is low productivity in static terms, but displays dynamism across the sample. This has not been enough to change its positioning below the economy-wide or average labor productivity from the beginning to the end of the sample period. Looking at the relative position (or gap) against the economy-wide labor productivity level (i.e. within a given economy), we can define a ratio which may be higher or lower than 1 at the beginning and at the end of the sample period. This allow us to make a classification of sectors and countries or regions as “structural overperformers” (if the ratio is >1 both in 1971 and 2014), “structural underperformers” (if it is <1 in both years), “dynamic growers” (if it is <1 in 1971 and >1 in 2014) and “dynamic laggards” (if it is >1 in 1971 and <1 in 2014). Table A.1 shows this classification for our group of countries and the world, while Table A.2 does the same for all sectors in the 25 countries of our sample.

Agriculture stands as a structural underperformer in this classification, except for the case of Argentina, Denmark (actually the best world performer in Figure A.1) and France, where the growth rate of labor productivity has been relatively high. At the world level only two sectors in one region (Manufacturing and Transport in the OECD) have reversed their low-productivity status in 1971, surely as a consequence of trade competition and reforms. There are also visible differences, on averages, in the service sectors in Asia and LAC, that become less marked or uniform across countries. The Service sectors and Construction were in general either structural underperformers or dynamic laggards, with some exceptions.

Cross plots of labor productivity gaps (relative to the economy wide) are show in panel Figures A.4 to A.7

Figure A.4. World Average: Plots of sectoral labor productivity gaps 1971-2014

Figure A.5. OECD-average sectoral labor productivity gaps (1971-2014)

Figure A.6. Asia-average sectoral labor productivity gaps (1971–2014)