1. Introduction

From a sectoral point of view, economic growth is initially linked to agricultural activities (^{Cameron and Neal, 2014}; ^{Brue and Grant, 2009, p. 35}). With the advent of industrial processes, the secondary sector progressively gained relevance. In that respect, economic growth is associated with growth rates in the secondary sector (especially in manufacturing). The positive relationship between productivity growth in the industrial sector and output growth in the same sector has been empirically demonstrated (^{Kaldor, 1984}). However, in the early 2000s, industrialized countries exhibited elevated growth in the tertiary sector, transforming themselves into service economies (^{Schettkat and Yocarini, 2005}; ^{Maroto-Sánchez and Rubalcaba, 2008}; ^{Maroto Sánchez, 2012}).

In developing economies, service activities are increasingly important in economic activity, suggesting a pattern of tertiarization (^{Bonet, 2007}; ^{Timmer et al., 2015}; ^{Aboal et al., 2015}). The expansion of services is also approached from the perspective of deindustrialization, understood as a process of continuous reduction of the manufacturing sector (^{Gemmell, 1982}; ^{Rowthorn and Ramaswamy, 1999}; ^{Tregenna, 2009}), which is generally accompanied by an increase in the contribution of services (^{Gemmell, 1982}; ^{Palma, 2005}). In the case of developing economies such as those in Latin America, the process is characterized as a type of premature deindustrialization. In other words, before reaching mature levels of industrialization, services tend to expand while manufacturing declines (^{Palma, 2005} and ²⁰¹⁹; ^{Rodrik, 2015}; ^{Camacho and Maldonado, 2018}).

As far as the economy of Ecuador is concerned, the services sector is becoming increasingly important in the sectoral structure due to its predominance in terms of Gross Value Added (GVA) and employment. According to data from the ^{World Bank (2023)}, in 2021, services as a percentage of GDP represented 53.4% and 51% as a percentage of total employment. Thus, the study of the services sector is considered relevant because the sector's significant importance in economic activity is based on low productivity levels, which have remained relatively stagnant since 2000. Together with improvements in agricultural productivity, this has contributed to a reduction in the productivity gap between the primary and services sectors while, at the same time, distancing it from the productivity of the secondary sector.

The productivity of the tertiary sector is an essential factor for encouraging economic growth, as demonstrated by ^{Triplett and Bosworth (2004)} for the U.S. economy where, after 1995, aggregate productivity growth was driven mainly by the productivity of service industries (labor productivity and total factor productivity), establishing it as one of the most dynamic and innovative sectors. Similarly, ^{Pugno (2006)} argues that health, education and cultural services drive economic growth by improving human capital. Business services also have a positive effect due to their ability to adopt and circulate information technologies (^{Oulton, 2001}). However, the optimistic view followed the pessimism that described services as a stagnant and non-progressive sector, slowing economic growth due to low productivity levels (^{Baumol, 1967}).

In this context, this research aims to analyze the relationship between service sector productivity and Ecuadorian economic growth from 1990-2018 using cointegration and causality econometric techniques. The main finding was that the tertiary sector and the commerce and transportation subsectors had a positive effect in the long run; however, in the short term, services as a whole have a negative influence, which can be explained by the significant deterioration in the productivity of the tertiary sector.

The paper is organized into five sections. Following the introduction, the second section reviews the theoretical and empirical framework regarding the main reasons for the expansion of tertiary activities, emphasizing papers that analyze the relationship between economic growth and service sector productivity. The third section describes the methodological strategy that follows the cointegration approach based on multivariate autoregressive distributed lag (ARDL) models and the causality of ^{Toda and Yamamoto (1995)}. In addition, the database and variables used are presented. The results and discussion are developed in the fourth section and, finally, in the fifth section, the main findings and some suggestions for future research are presented.

2. Literature review and contribution

Interest in economic activity has been shifting from the agricultural sector to the industrial sector and, recently, to services, thus configuring two processes of structural transformation. The first occurs as a result of the displacement of economic activities from the agricultural sector to the secondary sector due to the significant productivity rates that appeared in the industrial sector, specifically in manufacturing (^{Lewis, 1954}; ^{Kuznets, 1973}; ^{Kaldor, 1984}; ^{Chenery and Syrquin, 1975}). The second process occurs with the shift of activities towards the tertiary sector (^{Kuznets, 1973}; ^{Duarte and Restuccia, 2010}). Specifically, the empirical work of ^{Gemmell (1982)} states that by the 1960s, there were already signs of deindustrialization and that increased participation in services often accompanied this process. ^{Timmer et al. (2015)} argue that since the 1990s, the service sector of developing countries has expanded rapidly.

Several elements can explain the expansion of the service sector. The most cited element in specialized literature is the so-called cost disease, which provides a negative outlook on the performance of the tertiary sector. ^{Baumol (1967)} - using an unbalanced growth model - predicts that stagnant productivity levels in services hurt economic growth. Later, ^{Baumolet al.(1985)} assessed cost disease by including activities that combine inputs from the progressive sector (manufacturing) and the stagnant sector (services). They conclude by arguing that the cost problem in stagnant activities is more alarming than anticipated. However, using an unbalanced growth model, ^{Oulton (2001)} presents a more optimistic view of services, mentioning that Baumol's thesis is only valid when stagnant activities produce final goods. On the other hand, the aggregate productivity growth rate will increase with services producing intermediate goods (such as business and financial services) even when their productivity growth rate is slow.

According to ^{Ghavidel and Narenji Sheshkalany (2017)}, services with low levels of total factor productivity and technological progress are highly likely to suffer from cost disease. With that in mind, not all service activities suffer from it. In that respect, using an endogenous growth model, ^{Pugno (2006)} finds that activities such as health, education and cultural activities positively affect economic growth because they favor the training of human capital. In contrast, according to ^{Baumol (2012)}, services related to health, education and cultural activities suffer, in a generalized way, from cost disease. Furthermore, activities such as business services are widely recognized for their importance in driving economic growth due to their ability to adopt and circulate information technologies and, by contributing to innovation processes (^{Pugno, 2006}; ^{Wu and Baumol, 2012}; ^{Oulton, 2001}; ^{Greenhalgh and Gregory, 2001}).

Empirical evidence in developed countries suggests a negative relationship between the share of services as a whole (in terms of GVA and employment) and aggregate productivity growth; nevertheless, the conclusions may be conditional on how the service sector is defined and measured (^{Maroto-Sánchez, 2012} and ²⁰¹³). However, some papers provide more optimistic conclusions about the role of services in the economy. ^{Greenfield (2005)}, for example, suggests a re-examination of the service sector on a conceptual and empirical level because so-called cost disease may be a misdiagnosis. Meanwhile, ^{Triplett and Bosworth (2003)} assert that cost disease in service industries in the United States had been overcome.

Other determining factors for the expansion of services are:i)income growth (in line with Engel's Law), suggesting that the increase in income goes to the consumption of services with high income elasticity such as education, health, leisure, etcetera;ii)human capital, services are increasingly specialized, therefore, they require more highly skilled labor;iii)Information and Communication Technologies (ICT), which encourage the emergence of new services through innovation; and,iv)the continuous integration of services with the products of other economic sectors (^{Maroto-Sánchez, 2010} and ²⁰¹²; ^{Rubalcaba, 2015}; ^{Falvey and Gemmell, 1996}; ^{Howells, 2004}; ^{Messina, 2005}).

3. Methodology

The link between service sector productivity and economic growth is studied by implementing several ARDL models to test for a long-term relationship. The variables of interest correspond to the labor productivity of the main economic sectors (agriculture, industry and services) and the trade and transport service subsectors. They are constructed as the ratio between GVA and the number of people employed. Both VAB and employment are retrieved from the Economic Transformation Database (TE) of the University of Groningen (^{De Vries et al., 2021}). The remaining variables are: Gross Domestic Product (GDP) per capita, Gross Fixed Capital Formation (fbkf) and Trade Openness. They are taken from the freely available indicators of the ^{World Bank statistics (2023)}. Trade Openness is the ratio between the sum of exports and imports for the GDP. Data is collected annually from 1990 to 2018 and is transformed into logarithms. Table 1 summarizes the variables, denomination and database.

According to ^{Pesaran and Shin (1999)}, ARDL models have better properties in small sample sizes, as is the case of this research, and can be used when the variables are endogenous and I(0), I(1) or mixed. For ^{Jalil et al. (2016)}, the absence of serial correlation in the ARDL models makes endogeneity less of a problem. The characteristics of the approach make it advantageous compared to the methods of ^{Johansen and Juselius (1990)}, which conditions the series to be I(1), and the two-step method of ^{Engle and Granger (1987)}, which, in addition to requiring the variables to be I(1), presents problems of bias in small samples (^{Mah, 2000}) and is not suitable for testing cointegration between more than two series (^{Levendis, 2018, p. 360}).

The econometric equation for estimation is as follows:

Where Y_t is GDP per capita, p is the lag order ≥ 1 for the dependent variable and q is the lag order ≥ 0 of the independent variables. Based on equation 1, five multivariate models are estimated where the dependent variable (GDP per capita) is fixed in all models, as are the investment and trade openness control variables (fbkf). Meanwhile, the labor productivity variables of the economic sectors and subsectors vary for each model.

The long-term relationship is evaluated using the ^{Pesaran et al. (2001)} bounds test, which proposes the absence of a level relationship as the null hypothesis and is rejected when the F or TE statistic is located above the upper limit of the critical value. In this case, the inference is conclusive, so there is no need to know the integration order of the series. According to ^{Kripfganz and Schneider (2018)}, the validity of the test hinges on the assumptions of normality, absence of serial correlation, homoscedasticity and stability of the coefficients over time. The test is carried out based on the error correction model (ECM) represented in the following equation (2):

Where α=1-∑J=1Pϕi represents the adjustment speed coefficient and θ=∑j=0qβjα are the long-term ecoefficients. The MCE can also be estimated using the following reparameterization:

The MCE is estimated using equation (3) with the unrestricted and non-trended intercept. The critical values for the test are those proposed by ^{Kripfganz and Schneider (2020)}, which have the advantage of covering all possible sample sizes, lag lengths and number of variables in the long-term relationship. The choice of lag length is critical, so several strategies are used: i) Schwarz (BIC) and Akaike information criteria (AIC) are allowed to determine the optimal number of lags; ii) following ^{Ang (2010)} and ^{Jalil et al. (2016)}, two lags are imposed; andiii)following ^{Sankaran et al. (2019)} and ^{Mah (2000)}, the maximum length of lags is restricted to three and two, with AIC being allowed to select the optimal lag. The best model choice is based on the fulfillment of the assumptions described above.

The existence of a long-term relationship implies that causality exists but does not suggest its direction; hence, the ^{Toda and Yamamoto (1995)} causality test is implemented. The method consists of adding lags (K + d_max) and allows fitting a VAR model with the variables in levels and regardless of whether the series are stationary in differences or around a deterministic trend, I(d) or cointegrated (^{Levendis, 2018}). In that respect, five bivariate models are specified where the dependent variable for each model is GDP per capita and the explanatory variables are the labor productivity variables corresponding to each economic sector and subsector.

4. Results and discusión

In general, the labor productivity of the main economic sectors shown in Figure 1 indicates a growing trend in the agricultural sector. The secondary sector has remained at relatively high and stable levels, while the service sector indicates a declining performance which, since 2000, has remained stagnant since it has not been able to recover the productivity levels observed in 1990. Clearly, by the end of the study period, the deterioration of productivity in the tertiary sector widened the productivity gap with respect to the industrial sector, while it narrowed in relation to agricultural productivity.

Source: compiled by the authors

Figure 1 Labor productivity of the main economic sectors 

Before presenting the results, Table 2 shows some descriptive measures with the information on levels. Twenty-nine observations were used. The highest average productivity can be found in industry and the lowest in the agricultural sector. The productivity of the commerce subsector shows a higher standard deviation than that observed in the large economic sectors and transportation. Investment also indicates a high level of dispersion. The minimum level of productivity is concentrated in agriculture, and the maximum is in industry.

Although the approach used to test a long-term relationship does not strictly require unit root tests, it is important to rule out that the variables are I(2), so Table 3 presents the results of the Dickey-Fuller Augmented (DFA) and Phillips Perron (PP) tests. The AIC criterion provides the lag length for the DFA test, while the PP test uses the Newey-West lags. In general, it is observed that the series are not I(2); however, the trade productivity variable in two of the three specifications of the DFA and PP tests suggests that it is stationary on levels.

Table 4 presents the bounds test results, suggesting a long-term relationship exists in all models. Hence, tables 5 and 6 present the long-term, MCE and short-term coefficients, respectively.

The results suggest that, in the long run, the productivity of all sectors and subsectors, except for agricultural productivity, which is negatively related, indicates a positive effect on economic growth. All coefficients are statistically significant, and, specifically, transportation services exhibit the largest magnitude, revealing that a 1% improvement in transportation labor productivity translates into a 0.98% increase in GDP per capita. The MCE, for all models, falls within the expected range and with the appropriate sign (-1 and 0) and indicates the speed with which long-term distortions are adjusted in the current period. For example, in the case of the services sector, 69.1% of the long-term equilibrium distortion is corrected in the current period.

In the service sector, as a whole and by activity, the long-term results are consistent with the work of ^{Matuka and Asafo (2021)}, ^{Jalil et al. (2016)}, ^{Yousuf et al. (2019)}, confirming the importance of services in boosting economic growth. Specifically, the performance of traditional services such as trade and transportation is fundamental because they directly influence the competitiveness of other economic sectors (^{Pagés, 2010}; ^{Crespi and Vargas, 2015}). In other words, they are activities highly integrated into the sectoral structure of the economy, so their good performance is desirable to boost economic growth.

However, in the short term, services as a whole hurt economic growth, which can be explained by the significant deterioration of their productivity since 1990, approaching the productivity levels of the agricultural sector by 2018. Thus, the decreasing levels of productivity in the services sector can be explained by two factors:i)a significant component of informal employment, which is characterized by low productivity (^{Freije, 2002}; ^{Arias et al., 2020}; ^{Fajnzylber, 2008}): andii)low productivity of companies in the sector and poor allocation of resources, which, according to ^{Pagés (2010)}, explain much of the low overall productivity and low productivity of services in Latin America. Similarly, ^{Rubalcaba et al. (2016)} argue that the poor performance of services in Ecuador is based on the inefficient allocation of resources. Furthermore, the poor allocation of resources in Latin America can be explained by the low development of the financial market, tax evasion (especially in small and low-productivity firms), and evasion of social security obligations (^{Pagés, 2010}).

Concerning the other economic sectors, the findings presented in the agricultural sector may indicate that improving agricultural productivity is not enough, as suggested by ^{Gollin (2010)}, who argues that improving agricultural productivity is neither a necessary nor sufficient condition for increasing economic growth. The productivity of the agricultural sector is at its lowest (compared to the services and industrial sectors) and exhibits an upward trend between 1990 and 2018. Despite showing improvements, the agricultural share in GVA has barely increased from 9.23% (in 1990) to 11.23% (in 2018). The low productivity levels that characterize the sector result from significant inequalities in terms of land distribution and technical progress (^{Castillo, 2014}; ^{Liudmila et al., 2019}; ^{García Pascual, 2006}). In the short term, the coefficient is not statistically significant.

The secondary sector's direct relationship in the long and short term is as expected and in tune with the extensive literature, which suggests the importance of industrial development to boost economic growth (^{Lewis, 1954}; ^{Kaldor, 1984}; ^{Baumol, 1967}; ^{Rodrik, 2009}; ^{Szirmai, 2012}; ^{Szirmai and Verspagen, 2015}; ^{Attiah, 2019}). In Ecuador, the secondary sector presents the highest levels of labor productivity, but its contribution to GVA does not exceed 40%.

Table 7 presents the results in relation to the direction of causality. The service sector, as a whole, is led by GDP per capita, but not the other way around. As for the trade and transportation subsectors, causality is one-way and runs from trade to growth and from growth to transportation activities. Moreover, bidirectional causality exists between the agricultural sector and GDP per capita. Conversely, industry causes GDP per capita but not vice versa.

The direction of causality between services and GDP per capita supports the thesis that suggests that the increase in income levels contributes to the expansion of some service activities that have an income elasticity of demand greater than unity (^{Maroto-Sánchez, 2012}; ^{Rubalcaba, 2015}; ^{Falvey and Gemmell, 1996}). Furthermore, a tentative explanation is that the growing economy allows for greater resources to be available and invested in infrastructure for the transportation sector, which contributes to improving its productivity levels. Commercial activities represent important sources of employment and consumption and are essential for the functioning of other economic sectors; therefore, good performance of their productivity will boost economic growth.

5. Conclusions

This study examined the relationship between service sector labor productivity and economic growth using multiple multivariate ARDL models and the causality approach. The results indicated a long-term equilibrium relationship between the main economic sectors and service subsectors (transportation and trade) and GDP per capita.

Based on the bounds test, in the long-term, services with their corresponding subsectors and industries have a positive and statistically significant impact on economic growth, in contrast to agriculture, which is negatively affected. In the short term, the services sector as a whole presents an inverse relationship, while industry has a positive effect. The coefficient of agricultural productivity is not statistically significant. In this context, the relevance of the service sector and the trade and transportation subsectors in driving and boosting Ecuador's economic growth in the long term is confirmed. However, the continued deterioration of labor productivity in services as a whole negatively affects economic growth in the short term.

^{Toda and Yamamoto's (1995)} test revealed a bidirectional causality relationship between agricultural productivity and economic growth; several unidirectional causality relationships range from the industrial sector and trade to GDP per capita and from economic development to services and transportation. The expansion of transportation services with economic growth may be because a growing economy allows for allocating more resources that directly influence its productivity levels. On the other hand, commercial services are highly integrated into the productive structure, which drives economic growth.

The findings of this article can suggest some possibilities for future research. For example, the factors that explain the deterioration of productivity in the service sector (some already identified in this research) can be studied in depth from a microeconomic perspective at the company level. This would facilitate the identification of critical elements for a more accurate design of public policies for sectoral development.