1 Introduction

The primary source of economic growth between “perspiration growth” (input growth or factor accumulation growth) and “inspiration growth” [productivity gains or total factor productivity (TFP) growth] has been long debated in the empirical studies on East Asian economies (World Bank 1993; Krugman 1994; Young 1995; Aswicahyono and Hill 2002; Mahadevan 2007; van Leeuwen et al. 2015, 2017). As the pioneering arguments on the source of economic growth, Young (1995) and Krugman (1994) summarized that the “East Asian economic miracle” was the result of “perspiration” rather than “inspiration”. In accordance with the traditional Solow model, perspiration-dominant growth should predictably slow down as factor accumulation is subject to diminishing returns to scale (Solow 1957). However, inspiration growth can increase the maximum possible output, given factor accumulation through an upward shift of the production frontier.

Studies on the sources of economic growth also induced measurement studies on TFP (Kalirajan et al. 1996; Angeriz et al. 2006; Li et al. 2008; Isaksson 2009; Wei and Hao 2011; Machek and Hnilica 2012; Danquah et al. 2014; Beugelsdijk et al. 2018; Kataoka 2020). For example, Isaksson (2009) described the advantages and disadvantages of the three approaches—growth accounting, regression analysis, and frontier analysis—and concluded that none is perfect. Further, many studies (e.g., Aswicahyono and Hill 2002; Van der Eng 2010; Asian Productivity Organization 2019; Musyawwiri and Üngör 2019) have applied the conventional Solow growth accounting and regression analysis, which requires the restrictive assumptions of a single output, full utilization of the factors of production, and perfect competition. Both derive total factor productivity (TFP) growth as an exogenous residual, that is, as the difference between output and weighted input growth. The conventional growth accounting approach assumes constant returns to scale (CRS) and various returns to scale (VRS). While the income shares under CRS in several studies (e.g., Kataoka 2013; Mendez and Kataoka 2020) are fixed at the conventional 2/3 and 1/3 for labor and capital input, respectively, the TFP growth under VRS is calculated as the residual plus the scale effect. Regression analysis requires the specification of a particular functional form and offers a partial resolution, as it allows relaxing the CRS assumption for the estimation of income shares.

Further, frontier analysis approaches, such as non-parametric data envelopment analysis (DEA) and parametric stochastic frontier analysis (SFA), can apply the Malmquist TFP index to multiplicatively decompose TFP growth into two components (efficiency change and technological change, EC and TC, respectively) (Färe et al. 1994; Wei and Hao 2011). However, each approach has advantages and disadvantages as follows. On one hand, DEA does not require any functional form assumptions although it is deterministic, highly sensitive to outliers, and does not consider any random variations. On the other hand, SFA incorporates the error term, although it requires specific functional forms, distributional error term assumptions, and modifications for multiple input and output frontier estimations (Coelli et al. 2005). From Fan et al. (1996) pioneering work proposing a semi-parametric method that allows for statistical noise and requires no specific functional form of the production frontier, many new semi-parametric and non-parametric stochastic frontier techniques have been applied to narrow the gap between SFA and DEA (Gong 2017). Frontier analysis addresses the question of whether TFP stems from technological progress and/or efficiency gains. Production takes place inside the production frontier, and the distance between the production frontier and production indicates inefficiency. Equivalently, the farther below the frontier the production is, the larger the inefficiency becomes. For example, efficiency gains derive from the decrease in distance, while technological progress derives from the frontier shift. Efficiency cannot continue to improve without technological progress, since efficiency gains cannot recur once the frontier is reached (Margono et al. 2011).

Being an emerging East Asian economy, as a large insular and the world’s fourth most populous nation with a wide distribution of abundant natural resources, Indonesia consists of economically diverse provinces: the major urban agglomeration (Jakarta), resource-rich off-Java Provinces (Ache, Riau, East and South Kalimantan, and Papua), internationally popular tourist destinations (Bali and Yogyakarta), emerging business cluster provinces (West and East Java), and labor-intensive agricultural provinces (all remaining provinces) (Hill et al. 2008; Kataoka 2018). The nation is also beset by spatial output imbalances: nearly 60% of the national income is derived from the on-Java Provinces, which account for only 6% of the nation’s land, as shown by the choropleth map in Fig. 1.Footnote 1

Fig. 1
figure 1

Provincial distribution of gross regional domestic product (GRDP) in Indonesia, 1990

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To mitigate such economic imbalances, the government implemented several policy measures, such as administrative guidelines in the 5-year national development plans and integrated economic development zones, migration to sparsely populated off-Java Provinces, progressive inter-governmental fiscal transfers, and decentralization reforms (Kataoka 2020); however, the policy outcomes are still below target levels. As shown in Fig. 1, the annual average growth rates of the gross regional domestic product (GRDP) in the three most developed on-Java Provinces (East and West Java and Jakarta) exceeded the national growth rate of 4.8% during 1990–2015.

Since the World Bank (1993) conducted its multi-country analysis, many studies have examined Indonesia’s TFP growth at the national, sectoral, regional, and firm levels. However, there is no consensus on the empirical results because of the different choices of datasets and/or methods to process the estimates. For example, Van der Eng (2010) found inconsistencies between the Penn World Tables (PWT) and official data from Indonesia’s Statistical Agency in several existing studies. Additionally, physical capital data, which is essential for TFP estimation, has never been officially published. Among existing literature, Van der Eng (2010) used the GDP data from Indonesia’s Statistical Agency and estimated − 0.9% of annual average TFP growth rate in the national growth accounting TFP residuals for 1975–1997: − 9.7% for 1998–1999 and 1.7% for 2000–2008. On the other hand, Musyawwiri and Üngör (2019) used the PWT data and estimated the values as 0.6% for 1967–1996, − 10.7% for 1997–1999, 2.0% for 2000–2006, 0.8% for 2007–2009, and 2.4% for 2010–2014. The Asian Productivity Organization (2019) derived the values as 0.3% for 1970–1990, − 1.1% for 1990–2010, and − 1.5% for 2010–2017 from data obtained from the World Bank’s World Development Indicators (WDI). Differing from the aforementioned growth accounting studies, Grosskopf and Self (2006) used the DEA-based Malmquist productivity index and the WDI data for five Southeast Asian nations to estimate 0.7% TFP growth rate in Indonesia for 1960–1996.

At the regional level, several studies have measured TFP growth in Indonesia (Margono et al. 2011; Kataoka 2013, 2018, 2020; Mendez 2020; Mendez and Kataoka 2020; Purwono and Yasin 2020). For instance, Margono et al. (2011) conducted Translog SFA, incorporating labor and capital inputs with GRDP output, covering 26 provinces for 1993–2000, which considers the effects of the financial crisis of 1997–1998. They employed the approach of Kalirajan et al. (1996)Footnote 2 to additively decompose output growth into output growth due to input growth and output growth due to TFP growth and found negative TFP change due to efficiency deterioration. Although they applied the SFA approach, considering the effects of random shocks in production, their study ignored the role of human capital. Kataoka (2013) estimated provincial capital stock for 1987–2007 following Van der Eng’s (2010) approach and used the conventional growth accounting method to identify small positive mean provincial TFP growth, which varied significantly by province.

Kataoka (2018) used DEA to measure overall technical efficiency scores, which were multiplicatively expressed by pure technical (resource utilization efficiency) and scale efficiencies (resource allocation efficiency) for the 26 provinces over 1990–2010. He found considerable improvements in both multiplicative efficiency components. Mendez (2020) and Mendez and Kataoka (2020) used Kataoka’s (2018) DEA efficiency scores to examine the convergence club hypothesis, both graphically and numerically. Further, Kataoka (2020) applied the DEA-based Malmquist productivity index (MI) to measure provincial TFP growth, which consists of technological growth and efficiency improvement, over 1990–2015. He found that seven of the 26 provinces experienced negative TFP change due to technological regress, and it was barely offset by efficiency improvements. Only some on-Java Provinces, mainly Jakarta and West Java, were found to contribute to national technological progress. Purwono and Yasin (2020) used Cobb-Douglass and Translog-type SFA to measure the annual TFP growth of 29 provinces for 2002–2017. They found negative mean TFP change at a nearly zero level, where the negative growth rates were mostly exhibited by the less developed Eastern regions in Indonesia. Meanwhile, Jakarta never showed negative TFP growth rates during the observation period, which confirms the findings of Margono et al. (2011). However, except for Margono et al. (2011) study, no existing studies have examined the contributions of factor accumulation and TFP growth on national and provincial output growth.

To address this gap in the literature, the present study identifies the source of national and provincial output growth, measured by the GRDP, in Indonesia over 1990–2015, referring to Kalirajan et al. (1996) additive decomposition method. Our study contributes to the existing literature in at least three ways, as follows. First, as opposed to the existing SFA-based studies, we use the DEA approach, which has flexibility due to its free functional form, less restrictive assumptions, and multiplicative decomposability, for TFP measurement. In addition to the conventional DEA method, we apply the bootstrap technique to derive the bias-corrected efficiency score to cope with stochastic noises from unobserved production. Second, extending from Margono et al. (2011), our frontier analysis uses the long quinquennial balanced panel data of one output and three input variables, covering 26 contiguous Indonesian provinces over 1990–2015. Therefore, our analysis weighs more on the long-term growth path rather than short-term cyclical changes. Further, our dataset incorporates the input variables of human capital in addition to physical capital as the role of human capital is becoming more significant in Indonesia’s long-term economic growth. Lastly, our decomposition analysis quantifies the relationship between the sources of national and provincial output growth, by disaggregating the national output growth components to provincial ones.

2 Methods

2.1 Output growth decomposition

Following Kalirajan et al. (1996),Footnote 3 Fig. 2 illustrates how the output growth in province i from base year \({t}_{0}\) to target year \(t\) (t = 1,…, T) is additively decomposed. Let \({X}_{i}^{{t}_{0}}\left({X}_{i}^{t}\right)\) and \({Y}_{i}^{{t}_{0}}\left({Y}_{i}^{t}\right)\) be the actual values of a set of inputs, such as labor force, physical and human capital, and output in province i in year \({t}_{0}\) \(\left(t\right)\), respectively. Given the actual input and output in years \({t}_{0}\) and \(t\), we can derive the CRS frontiers for years \({t}_{0}\) and \(t\). Technological progress occurs and then the frontier shifts upward from year \({t}_{0}\) to \(t\). The output variable with double asterisks, \({Y}_{i}^{{t}_{0}**}\left({Y}_{i}^{t**}\right)\), is the projected output value in province i in year \({t}_{0}\) \(\left(t\right)\) on year \(t\)’s frontier, while the variable with a single asterisk, \({Y}_{i}^{{t}_{0}*}\left({Y}_{i}^{t*}\right)\), is the projected output value in year \({t}_{0}\) \(\left(t\right)\) on year \({t}_{0}\)’s frontier.

Fig. 2
figure 2

Graphical illustration of output growth due to input growth (DI), efficiency growth (DE), and technological growth (DT)

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Accordingly, the output growth in province i from years \({t}_{0}\) to \(t\), denoted as \({DY}_{it}\left(= {Y}_{i}^{t}-{Y}_{i}^{{t}_{0}}\right)\), is additively decomposed into three growth components. First, the vertical distance between \({Y}_{i}^{{t}_{0}}\) and \({Y}_{i}^{{t}_{0}*}\) (\({Y}_{i}^{t}\) and \({Y}_{i}^{t**}\)) indicates technically inefficient and efficient output gaps in year \({t}_{0}\) \(\left(t\right)\). The output growth due to efficiency growth, expressed as \({DE}_{it}=\left[\left({Y}_{i}^{{t}_{0}*}-{Y}_{i}^{{t}_{0}}\right)-\left({Y}_{i}^{t**}-{Y}_{i}^{t}\right)\right]=\left({DE1}_{it}-{DE2}_{it}\right)\), indicates how much province i decreased its inefficiency between two years. More intuitively, this infers how much province i moves closer to the frontier in the corresponding year. A positive (negative) value denotes an improving (deteriorating) efficiency. Second, the output growth due to technological progress is measured by the distance between two frontiers, given the same input values at \({X}_{i}^{{t}_{0}}\). This is expressed as \({DT}_{it}=\left({Y}_{i}^{{t}_{0}**}-{Y}_{i}^{{t}_{0}*}\right)\), and indicates that province i can produce more outputs at the unchanged input levels. Such progress is associated with the improvement of the quality of physical and human capital and other non-input factors, possibly induced by policy implementation. Third, output growth due to input growth is measured by the distance between two input levels, given the same technology along year \(t\)’s frontier. This is expressed as \({DI}_{it}=\left({Y}_{i}^{t**}-{Y}_{i}^{{t}_{0}**}\right)\) and means that a province can produce more outputs as input increases, without changing the technology level. Therefore, the decomposition can be mathematically expressed as

$$ \begin{aligned} DY_{it} & = \left[ {\left( {Y_{it}^{{t_{0} *}} - Y_{it}^{{t_{0} }} } \right) - \left( {Y_{it}^{t**} - Y_{it}^{t} } \right)} \right] + \left( {Y_{it}^{{t_{0} **}} - Y_{it}^{{t_{0} *}} } \right) + { }\left( {Y_{it}^{t**} - Y_{it}^{{t_{0} **}} } \right) \\ & = DE_{it} + DT_{it} + DI_{it} = DP_{it} + DI_{it} \\ \end{aligned} $$
(1)

where \({DP}_{it}\left(={DE}_{it}+ {DT}_{it}\right)\) denotes output growth due to productivity or TFP growth. We assume that a nation consists of n provinces (i = 1,…, n). Defining the corresponding national values as the variables without subscript i (i.e., \({DY}_{t}={\sum }_{i=1}^{n}{DY}_{it})\), we express the national output growth decomposition as

$$ DY_{t} = DE_{t} + DT_{t} + DI_{t} = { }DP_{t} + DI_{t} . $$
(2)

2.2 Data envelopment analysis (DEA) models

We use the DEA efficiency score to compute the four projected output values: \({Y}_{i}^{{t}_{0}*}\), \({Y}_{i}^{{t}_{0}**}\), \({Y}_{i}^{t*}\), and \({Y}_{i}^{t**}\). DEA derives the piecewise linear frontier assembled by the best practices observed in decision-making units (DMUs), which use multiple inputs to produce outputs, and assesses the relative efficiency of each DMU in a specific year (Coelli et al. 2005). The DEA efficiency score is the relative ratio of the distance from the origin to the DMU’s production over the distance from the origin to its frontier. This study treats province i as a DMU and uses an output-oriented model, considering the substantial provincial gaps in factor endowments in Indonesia.

In Fig. 2, \(\left({Y}_{i}^{{t}_{0}}/{Y}_{i}^{{t}_{0}*}\right)\) and \(\left({Y}_{i}^{t}/{Y}_{i}^{t**}\right)\) illustrate the output-oriented CRS DEA efficiency scores in years \({t}_{0}\) and \(t\), respectively. These two values are the ratios of the production points of DMUs measured by the same year’s frontier. By contrast, \(\left({Y}_{i}^{{t}_{0}}/{Y}_{i}^{{t}_{0}**}\right)\) and \(\left({Y}_{i}^{t}/{Y}_{i}^{t*}\right)\) are measured by the frontiers for different years. For example, \(\left({Y}_{i}^{{t}_{0}}/{Y}_{i}^{{t}_{0}**}\right)\) indicates the relative efficiency of the DMU in year \({t}_{0}\), measured by year \(t\)’s production frontier.

We obtain \(\left({Y}_{i0}^{{t}_{0}}/{Y}_{i0}^{{t}_{0}*}\right)\) in province i0, one of the n provinces of interest under evaluation, by the following linear programming (LP) problem:

$$ {\text{Max}}_{\theta ,z} \theta , $$

subject to

$$ \begin{aligned} & \mathop \sum \limits_{i = 1}^{n} z_{i} \cdot X_{i}^{{t_{0} }} \le X_{i0}^{{t_{0} }} , \\ & \mathop \sum \limits_{i = 1}^{n} z_{i} \cdot Y_{i}^{{t_{0} }} \ge \theta \cdot Y_{i0}^{{t_{0} }} , \\ & z_{i} \ge 0, \\ \end{aligned} $$
(3)

where θ and z are the decision variables for the model. \({\theta }^{-1}\) is equal to \(\left({Y}_{i0}^{{t}_{0}}/{Y}_{i0}^{{t}_{0}*}\right)\), which represents an efficiency score ranging between 0 and 1 (efficient: score = 1; inefficient: score < 1). We also obtain \(\left({Y}_{i0}^{{t}_{0}}/{Y}_{i0}^{{t}_{0}**}\right)\) using the following LP problem:

$$ {\text{Max}}_{\theta ,z} \theta , $$

subject to.

$$ \begin{aligned} & \mathop \sum \limits_{i = 1}^{n} z_{i} \cdot X_{i}^{t} \le X_{i0}^{{t_{0} }} , \\ & \mathop \sum \limits_{i = 1}^{n} z_{i} \cdot Y_{i}^{t} \ge \theta \cdot Y_{i0}^{{t_{0} }} , \\ & z_{i} \ge 0. \\ \end{aligned} $$
(4)

We obtain \(\left({Y}_{i0}^{t}/{Y}_{i0}^{t**}\right)\) and \(\left({Y}_{i0}^{t}/{Y}_{i0}^{t*}\right)\) using DEA models (3) and (4) with \({t}_{0}\) and \(t\) switched, respectively.Footnote 4

Note that, in \(\left({Y}_{i}^{{t}_{0}}/{Y}_{i}^{{t}_{0}**}\right)\) and \(\left({Y}_{i}^{t}/{Y}_{i}^{t*}\right)\), where the production points for one year are measured by a different year’s frontier, the \({\theta }^{-1}\) values should not be less than or equal to one simply because the data point could lie above the feasible production. This will most likely occur under the LP problem for \(\left({Y}_{i}^{t}/{Y}_{i}^{t*}\right)\), where production points from year \(t\) are compared in base year \({t}_{0}\)’s frontier. Technical progress occurs in case \(\left({Y}_{i}^{t}/{Y}_{i}^{t*}\right)\)>1. This could also possibly occur in the LP problem for \(\left({Y}_{i}^{{t}_{0}}/{Y}_{i}^{{t}_{0}**}\right)>1\) if technical regress has occurred, but it is less likely (Coelli et al. 2005).

In addition, we deal with stochastic noise in terms of performance measurement. The conventional DEA estimator is biased, as the frontier is defined only relative to the best-practice observations in the finite sample. As the “true” frontier might lie above the conventional frontier if more efficient provinces exist outside the sample data, upward biases are theoretically evident. The conventional efficiency score is upward biased when it shows a larger score value than the “true” efficiency score values (Enflo and Hjertstrand 2009; Moradi-Motlagh et al. 2015; Toma et al. 2017). To address this drawback, our study computes the DEA bias-corrected efficiency score by applying the bootstrapping procedure developed by Simar and Wilson (1998, 1999, 2000). In this study, we specify 2000 bootstrap replications. The bootstrap estimation procedure takes bias-corrected confidence intervals (CIs).

3 Data

We use output and three input variables (GRDP, labor force, physical capital, and human capital), covering the 26 contiguous Indonesian provinces over 1990–2015. All monetary values are in 2000 base-year constant prices. All provincial data are originally from the Statistical Yearbook of Indonesia (BPS 1992–2018), except for physical and human capital data, which BPS has not officially published. For physical and human capital value, we employ Kataoka’s (2020) provincial estimates.

The term “human capital” has been used in neoclassical economic studies since the early 1960s, such as Schultz (1961) and Becker (1964). Becker (1964) illustrates that human capital is commonly taken to include peoples’ knowledge and skills acquired by education and training. Similar to physical capital, additional investment in human capital yields additional output. Human capital, one of the primary factors of production, is durable but non-transferable. Schultz (1961) incorporated the role of human capital in economic development. Human capital investment improves performance, productivity, employment flexibility and security, employability, and utility (Rowley and Redding 2012). The evaluation method of human capital varies in empirical studies. We define the average education year of labor force, weighted by the provincial labor force’s share of educational attainment, as human capital.Footnote 5

In Indonesia, the regional proliferation associated with political reforms after the 1997–1998 crisis increased the number of provinces from 27 in 1997 to 34 in 2015. The eight additional provinces were established as new provinces, and one province East Timor became an independent nation.Footnote 6 However, no data were adjusted for these historical changes. To solve these modifiable areal unit problems, we aggregated new and existing province data in the corresponding years for the solution, following several previous studies (Margono et al. 2011; Kataoka 2013, 2018, 2020; Mendez 2020; Mendez and Kataoka 2020).

Table 1 presents the summary statistics for the input and output variables employed in this study in 1990 and 2015.Footnote 7 The Wilcoxon rank-sum test of mean equality confirms that the means of all variables increased over this period and their statistical significance. All variables show a right-skewed distribution as the mean values exceed the median ones. Additionally, the output variables increased the inequalities across provinces, as measured by the coefficient of variation, while the input variables decreased them. Observing the shares of on-Java and off-Java Provinces, on-Java Provinces increased their output shares despite a decrease in physical capital and labor force over 1990–2015. This finding provides insights into our key research question regarding the non-input factors contributing to output growth in on-Java Provinces.

Table 1 Descriptive statistics for the output and input variables
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4 Empirical results

This section briefly describes the DEA efficiency scores and then presents the additive decomposition component to explore the sources of the national/provincial output growth for 1990–2015. We show below the results derived from the conventional and bias-corrected efficiency measures.Footnote 8 The conventional and bias-corrected efficiency scores are computed using Stata with the command teradialbc developed by Badunenko and Mozharovskyi (2016).

4.1 DEA efficiency scores

Table 2 presents four DEA scores, \(\left({Y}_{i0}^{{t}_{0}}/{Y}_{i0}^{{t}_{0}*}\right)\), \(\left({Y}_{i0}^{{t}_{0}}/{Y}_{i0}^{{t}_{0}**}\right)\), \(\left({Y}_{i0}^{t}/{Y}_{i0}^{t*}\right)\), and \(\left({Y}_{i0}^{t}/{Y}_{i0}^{t**}\right)\), measured by the frontiers of years \({t}_{0}\) and \(t\) where \({t}_{0}=1990\) and \(t=2015\).The scores are, respectively, denoted as f11, f12, f21, and f22. The conventional efficiency scores in 1990 and 2015 (columns 1–4) show greater values than the bias-corrected values for all provinces (columns 5–8). This indicates that the conventional efficiency scores are overestimated and hold positive bias values, as the bias-corrected frontier theoretically lies above the conventional frontier. The 95% confidence intervals for the bias-corrected bootstrap measures are shown in columns 9 and 10 for columns 5 and 8, respectively. All provinces’ bias-corrected efficiency scores listed in columns 5 and 8 fall within the confidence interval, except for Aceh in 1990. The following findings are notable.

Table 2 Efficiency score, measured by the frontiers of years t0 and t (t0 = 1990 and t = 2015)
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First, observing the conventional efficiency scores shown in columns 1 and 4, there are six best-practice performing provinces with scores of 1 (Aceh, Riau, West Java, East Java, Jakarta, and East Kalimantan) in 1990 and five (Bengkulu, West Java, Jakarta, East Kalimantan, and Maluku) in 2015, respectively. Among these, West Java and Jakarta are consistently efficient in both years, indicating no efficiency improvement over the study period. As the bootstrap frontier lies above the conventional frontier, no provinces are efficient (columns 5 and 8). The mean and median values have largely increased for both measures, and the mean comparison test confirms the statistically significant difference in efficiency means between the two years. The provincial means exceed the median values for both measures in 1990 (columns 1 and 5), but this relationship between the mean and median values reverses in 2015 (columns 4 and 8). This indicates that the efficiency scores based on conventional and bootstrap measures shifted the positive skewness values to negative values and the coefficient of variation decreased. The provincial efficiency distribution thus changed from right to left skewed, the peak position shifted to the right along with the x-axis, and the efficiency difference across provinces declined. This is consistent with the findings of Kataoka (2018) and Mendez (2020) that Indonesia experienced efficiency convergence across provinces, with efficiency improvements over the analyzed period.

Second, observing the provincial outputs in 1990, as evaluated by the 2015 conventional and bootstrap frontier (columns 2 and 6), 10 and eight provinces showed scores equal to or above unity, respectively. This indicates that the corresponding projected output values on the 2015 frontier were lower than the actual output values in 1990. In other words, the 2015 frontier lies below the 1990 output of the corresponding 10 provinces, and those provinces failed the upward shift of the best-practice frontier in 2015. This change, indicating technological regress, is less likely to occur.

Third, observing the provincial outputs in 2015, evaluated by the 1990 conventional frontier (column 3), seven provinces show scores equal to or above unity. This indicates that only seven provinces could have produced more output than the 1990 best-practice output values, given the same input level in 1990. For the bootstrap measure (column 7), only three provinces—West and East Java and Jakarta—could have produced more than the 1990 best-practice output values. In other words, the majority of provinces failed to produce output above the 1990 best-practice levels. These observations that that majority of provinces have not experienced technological growth over 1990–2015 are less likely to occur. This finding provides insights into our key research question.

4.2 National-level analysis: Source of the national output growth

Figure 3 shows the national output growth decomposition, which consists of output growth due to input growth (DI), efficiency growth (DE), and technological growth (DT) for 1990–2015 (leftmost side bar graph) and its quinquennial sub-periods (the remaining bar graphs).Footnote 9 The sum of each sub-period growth component is equal to the growth for 1990–2015 and the values within parentheses present the periodic national output growth values. The figure shows several noteworthy observations.

Fig. 3
figure 3

Contributions to national output growth by component

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First, the national output value has not increased monotonically for any periods, although the national GDP has grown by 4.8% annually on average. The national output growth value (DY) declined for sub-period 1995–2000 compared to the previous sub-period (1990–1995) due to the 1997–1998 financial crisis and the subsequent recession. The output growth value did not recover to the level of sub-period 1990–1995 until sub-period 2005–2010.

Second, the national output growth is dominantly attributed to output growth due to input growth for 1990–2015 and the corresponding sub-periods. The bias-corrected results through the bootstrap measure confirm the findings of the conventional measures. This indicates that Indonesia experienced perspiration rather than inspiration growth over 1990–2015. This is consistent with Van der Eng (2010), Margono et al. (2011), and Kataoka (2013) in that output growth in Indonesia is mainly explained by factor accumulation.

Third, observing the leftmost bar graph for 1990–2015, TFP growth (DP), which is the sum of DE and DT, took negative values, and DT plays a greater role in determining DP for both conventional and bootstrap measures. Then, comparing DE and DT by sub-period, the conventional DT took negative values for 1990–2005 and positive values during 2005–2010 and after. The bias-corrected DT increased its negative values until 2000 and then decreased them. DE showed a reverse trend with DT in the conventional and bootstrap measures. This means that the main contribution to TFP growth varied by sub-period as Indonesia experienced a shift in the primary factors influencing TFP growth from efficiency improvement to technological growth from 1990 to 2015.

4.3 Provincial-level analysis: source of the national output growth

Next, we disaggregate the national output growth components into provincial components. Figure 4 presents the provincial output growth decomposition into two components: provincial input growth (DI) and TFP growth components (DP) for 1990–2015, while Fig. 5 presents the provincial TFP growth decomposition into two components: efficiency growth (DE) and technological growth components (DT). The sum of all provincial DIs and DPs is equal to the national output growth value of IDR 2,046 trillion for 1990–2015. The two figures show several interesting findings.

Fig. 4
figure 4

Contributions to provincial output growth by component, 1990–2015

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Fig. 5
figure 5

Contributions to provincial TFP growth by component, 1990–2015

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First, Fig. 4a and b shows that provincial output growth is dominantly attributed to output growth due to input growth (DI) for 1990–2015. This trend is the same across almost all provinces and is confirmed by both the conventional and bootstrap measures, indicating that all Indonesian provinces, except Maluku, experienced “perspiration growth” rather than “inspiration growth” during 1990–2015.

Second, the conventional measure shows that the national output growth for 1990–2015 is mainly attributed to output growth due to input growth (DI) in the four provinces of Jakarta and West, Central, and East Java, which account for over 60% of the national output growth (Fig. 4a). The factor accumulation in on-Java Provinces was the main driver of Indonesia’s GDP growth for 1990–2015. The results using the bootstrap measure shown in Fig. 4b confirm this finding.

Third, the majority of provinces show negative values of TFP growth component values (DP) under the conventional and bootstrap measures for 1990–2015 (Fig. 4a, b). The deterioration in TFP in most provinces contributed negatively to output growth. As an exception, the six provinces of Jambi, Bengkulu, West and East Java, Jakarta, and Maluku experienced positive TFP growth based on the conventional measure. Interestingly, in addition to developed on-Java Provinces, remote off-Java Provinces also experienced positive TFP growth for 1990–2015. Alternatively, according to the bootstrap measure, only the three provinces of Jambi, Bengkulu, and Maluku experienced positive TFP growth. This finding is inconsistent with Margono et al. (2011) result in that all provinces show negative values of TFP growth components from 1994 to 2000.

Fourth, focusing on the conventional TFP growth decomposition (Fig. 5a), 13 provinces have a positive DE, while four provinces have a positive DT. These latter four are Riau, the rich resource province located in the Singapore/Indonesia Special Economic Zone, and three major developed on-Java Provinces—Jakarta, West, and East Java. Jakarta and West Java experienced no efficiency improvements as they kept operating at their optimal levels in 1990 and 2015. These findings are consistent with Kataoka (2020), who found that these two provinces shifted their production frontier upward. Conversely, Fig. 5b indicates that 17 provinces have a positive DE, while no provinces have a positive DT. This bootstrap measure indicates that Indonesia’s provincial output growth due to TFP growth for 1990–2015 is mainly attributed to DE. This is a serious policy concern as productivity cannot grow sustainably without technological progress that raises the fully efficient production level, as efficiency gains cannot recur once production reaches this level.

Next, Fig. 6a and b shows that the number of provinces with positive DE values gradually decreased after 2000–2005, while those with positive DT values increased in the conventional measure after 2005–2010 and in the bootstrap measure after 2000–2005. This possibly suggests that the frontier has gradually shifted upward in the recent period; however, some of those provinces did not keep the pace and fell slightly behind the frontier. This implies that the nation experienced the transition from the efficiency growth to technological growth. After 2010, in addition to the on-Java Provinces, several remote off-Java Provinces show positive output growth values due to technological growth in both conventional and bootstrap measures.

Fig. 6
figure 6

Number of provinces with positive EC and DC values by sub-period

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Figure 7 displays the province-level DT in the most recent period (2010–2015) and indicates that 16 and 17 provinces have positive values for the conventional and bootstrap measures, respectively, and the majority of the provinces experienced technological progress. Those include not only large-scale on-Java Provinces (Jakarta and West, Central, and East Java) but also remote off-Java Provinces (Bengkulu, Jambi, Lampung, East Nusa Tenggara, and Maluku). Specifically, three major on-Java Provinces played significant roles on the technological progress and there is a large gap in DT across provinces. As positive signs for further economic growth, this could be represented by interregional technology spillovers from more advanced provinces. To achieve sustainable economic growth, the government should also select the adequate provinces for policy implementation toward innovation. On the other hand, three off-Java, resource-rich, higher-income provinces, North Sumatra, Riau, and East Kalimantan, had the lowest DT values. This finding also indicates that the mining sector contributed less to technological growth.

Fig. 7
figure 7

Output growth due to technological growth by province, 2010–2015

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5 Discussion: transforming from perspiration-dominant growth

Given its spatial output imbalance due to a large insular geography, the primary source of regional output growth at the national and provincial levels has been a significant topic of empirical research in Indonesia. Using Kalirajan et al. (1996) SFA-based decomposition method, Margono et al. (2011) found that all provinces experienced perspiration growth during 1994–2000 and negative TFP changes due to efficiency regress, and this effect was barely offset by technological progress. Our DEA-based study confirms Margono et al. (2011) finding of perspiration-dominant growth at the national and provincial levels during 1990–2015. The national output growth is majorly attributed to the factor accumulation growth of four on-Java Provinces: Jakarta and West, Central, and East Java. However, our TFP growth decomposition analysis presents inconsistent results compared with Margono et al. (2011), as the negative TFP change is mainly attributed to technological regress, and it is barely offset by efficiency improvement. Besides, six (four) provinces experienced positive TFP (technological) growth during the period based on the conventional measure. After 2010, in addition to the on-Java Provinces, several remote off-Java Provinces showed positive output growth due to technological growth in both conventional and bootstrap measures. Developed on-Java Provinces played a significant role in technological progress.

In the neoclassical model, factor accumulation and TFP growth determine economic growth. Factor accumulation exhibits diminishing returns and TFP growth is determined by technological progress and efficiency improvement. Technological progress is essential for sustainable TFP growth as efficiency gains cannot recur once production reaches the fully efficient level, which can be raised by technological growth. In short, the Indonesian economy is not expected to sustainably grow without technological progress. For further economic growth in Indonesia, policies promoting technological progress, such as deregulation, improvement in governance and financial access, technology transfers, and urban agglomeration, are crucial. In the context of urban agglomeration policy, the government should carefully select the target locations to facilitate technological progress.

Beyond the neoclassical view, factor accumulation, both physical and human capital investment, could be important for facilitating technological progress. For example, physical capital investment introduces new technologies to shift the frontier upward and rejuvenate industrial structures. More highly educated and skilled labor may facilitate innovation and the adoption of more advanced technologies. Moreover, the unified growth theory proposes that the driving force of the economic growth is transited from physical capital accumulation in the initial stage to the technological progress in the mature stage through human capital accumulation (Galor 2005). The developed provinces experienced sustained technological progress and factor accumulation in the economic growth stage. The key policy implementation, then, is related to ways of coordinating the policies promoting factor accumulation and TFP growth toward sustainable economic growth in the future.

6 Conclusions

Our growth decomposition analysis applies a non-parametric frontier analysis method based on conventional and bootstrap DEA method to examine the sources of the national/provincial output growth in Indonesia for 1990–2015. We found that the national and almost all provincial economies experienced “perspiration growth” (factor accumulation growth) rather than “inspiration growth” (TFP growth). The national output growth is dominantly attributed to the factor accumulation growth of four developed on-Java provinces. Moreover, most provinces show negative output growth due to TFP growth, mainly attributed to technological regress. Only six (four) provinces experienced positive TFP (technological) growth. After 2000, there has been a rise in technological growth from on-Java Provinces to remote off-Java Provinces.

We conducted the DEA-based decomposition analysis to explore the source of national and provincial output growth over a relatively long period. However, our work has several limitations and potential empirical extensions. First, our study ignores the bidirectional cause–effect relationship between factor accumulation and TFP growth. We assume that productivity growth factor as well as factor accumulation are exogenously determined in the output growth model. This rules out the assumptions that physical capital investment introduces new technologies and highly skilled labor is a key input to the innovation process. Second, our analysis disregards the effects of two physical capitals on output growth. Galor (2005) unified growth theory proposes the replacement of physical capital accumulation growth with human capital accumulation growth in the development process. Heterogeneity in the effects of physical and human capital on output growth could be explored in future studies. This would provide interesting policy discussions for possible solutions toward technological progress in Indonesia. Third, this study pretermits observations regarding the two major crises: the 1997–1998 Asia economic crisis and the 2007–2008 global economic crisis. This is simply because we focused on the long-term transition in output and influential factors, and not on the short-term cyclical changes.Footnote 10