Xiao Jiang and Chau Nguyen

A Revisit to the Forgotten Debate after Half-Century: Balanced Versus Unbalanced Growth

November 2018 Working Paper 17/2018 Department of Economics The New School for Social Research

The views expressed herein are those of the author(s) and do not necessarily reflect the views of the New School for Social Research. © 2018 by Xiao Jiang and Chau Nguyen. All rights reserved. Short sections of text may be quoted without explicit permission provided that full credit is given to the source.

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A Revisit to the Forgotten Debate after Half-Century: Balanced Versus Unbalanced Growth

Xiao Jiang (Corresponding Author)

jiangx@denison.edu Denison University Granville, OH, USA

Chau Nguyen

chau.nguyen@lmh.ox.ac.uk Oxford University

Oxford, UK

Abstract

The debate between balanced and unbalanced growth doctrines has generated much heat since the publication of Rosenstein-Rodan’s seminal work in 1943 but vanished in early 1980s. This paper intends to empirically revisit the forgotten debate by first compiling a harmonized international dataset that contains sectorial value-added data for up to 175 countries over 45 years. This dataset enables us to construct the index of sectorial imbalance for each country, which further allows us to update the key empirical tests for the balanced and unbalance growth hypotheses that appeared in the literature. Moreover, we also conduct cross-country growth regression analysis to systematically examine the effects of sectorial balance (or imbalance) on growth. Overall, we have found empirical support for the balanced growth hypothesis. JEL Classification: O40; O25; C12; B29. Keywords: Growth, Sectorial Balance, Development, Cross-country regression

1. Introduction It has been 75 years since the publication of Rosenstein-Rodan’s seminal work in development economics - Problems of Industrialisation of Eastern and South-Eastern Europe (1943). It was from this work, written during World War Two amidst concerns about the reconstruction and industrialization of Eastern and South-Eastern Europe, that the balanced growth doctrine originated. In simple terms, the balanced growth doctrine argues that a country’s overall growth depends on its ability to stimulate growth across many sectors simultaneously, for reasons to be discussed in details in section 2. While the balanced growth doctrine attracted many followers (most notably Nurske (1953) and Lewis (1955)) during its time, there also emerged the polar opposite of this doctrine - the unbalanced growth doctrine, which argues that a country’s growth depends on its ability to stimulate growth in a few key strategic sectors, and the rapid growth in these particular

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sectors will lead the entire economy to grow at a faster pace. The notable followers of this doctrine include Hirschman (1953) and Streeten (1959).

Series of efforts have been made in 1970s to empirically test the balanced and unbalanced growth doctrines, thus those doctrines became testable hypotheses during this period. Essentially, the hypotheses are tested by calculating the cross-country correlation coefficient between the degrees of dispersion of cross-sector growth rates and the aggregate growth rates. A statistically significant and positive correlation coefficient, for example, would provide support for the unbalanced growth hypothesis, and vice versa for the balanced growth hypothesis. The results of such empirical tests are unfortunately inconclusive, and the correlation coefficient sign tends to switch with different measures of sectorial imbalance as well as samples that are used in the analysis. The balanced and unbalanced growth debate mysteriously vanished in the 1980s, and by now it seems to be completely forgotten by the vast majority of development economists. The only reference one can find is an entry in The New Palgrave Dictionary of Economics.

We argue that the balanced and unbalanced growth debate is still relevant in today’s world, both for economists and policy-makers. In a world with extremely uneven development, low-income and developing countries have been struggling to find robust methods to achieve faster growth. After having numerous “determinants of growth” explored and debated in growth literature (Mankiw, 1995; Barro, 1991, 1996; Durlauf et al., 2008), perhaps we shall revisit the forgotten debate, and examine the simple and old question of whether sectorial growth balance (or imbalance) is associated with greater long-run aggregate growth or not. The answer to this question will also shed light on the policy debate of whether government should have ‘general’ or ‘selective’ industrial policies. In this paper, we intend to empirically revisit the balance and unbalanced growth debate by using more recent and complete international data. By merging four different international databases (the Eora Multi-region Input-Output Table, the World Development Indicators, The Penn World Table, and UNStats), we obtain a harmonized international dataset that contains data for up to 175 countries over 45 years; and for each country and period, net output (or value-added) data is available for 7 sectors, which is crucial in constructing the index for sectorial imbalance.

The paper has the following structure. Section 2 reviews both the theoretical and empirical aspects of the literature on balanced and unbalanced growth. Section 3 replicates the empirical tests for balanced and unbalanced growth hypotheses that appeared in the literature with our new and comprehensive international dataset. Section 4 goes a step further by conducting a cross-country growth regression analysis based on the Solow growth model, in which the index of sectorial imbalance is treated as the non-Solow determinant of growth. Section 5 concludes the paper with policy implications.

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2. Balanced and Unbalanced Growth Doctrines and Hypotheses 2.1 Balanced Growth Doctrine Rosenstein-Rodan in his 1943 articles first proposed the argument for balanced growth. Written in the midst of World War II, Rosenstein-Rodan was concerned about the reconstruction of Eastern Europe. The crux of his argument lies in his insight that industrial sectors are complementary amongst each other. While the expansion of a single sector (or small set of sectors) might not be profitable, simultaneous expansion of all (or large number of) sectors might make those sectors that were originally non-profitable profitable via endogenous market creation and economies of scale. (Rosenstein-Rodan, 1943). Essentially, Rosenstein-Rodan’s argument for balanced growth is rooted in the concept of positive externality of demand spillover effects. Thus, according to this theory, a country’s ability to grow depends on its ability to mobilize large amount of resources to undertake large-scale investments simultaneously in all (or a large number of) complementary industries in order to “jump start” the economy. This is also called the ‘big push’ theory in development economics. (Rosenstein-Rodan, 1961)

Nurske (1953) saw domestic market limitation being a major obstacle for low-income countries’ growth, especially the ones with difficulty of expanding their exports in the international market. In line with Rosenstein-Rodan (1943), Nurske proposes balanced growth with “an all-around increase in productivity” as a method that developing nations could adopt to overcome such an obstacle. In fact, Nath (1962) has insightfully pointed out that Nurske (1953) and Rosenstein-Rodan (1943) would have the same argument if one considers that sectoral complementarity and demand spillover effects are effective ways of expanding the domestic market.

Lewis (1955) supports the balanced growth hypothesis, keeping an eye on international trade. He sees that unbalanced growth will result in the instability of relative prices and the deterioration of the terms of trade in sectors that are expanding rapidly, which in turn will drag down the overall growth of the country. Thus, only when there is balanced growth, the relative prices and terms of trade of various industries will remain constant as the economy grows. However, Lewis (1955) is also careful in arguing against the exclusive dependence of a country’s development on international trade, because such growth path also depends on international terms of trade, which, for small developing nations, are often beyond their controls. Thus, ultimately Lewis’s argument might need to resonate with Nurske (1953)’s proposal of expanding domestic market via balanced growth.

The balanced growth hypothesis was later formalized into a macroeconomic model by Murphy et al. (1989). In their model, the simultaneous industrialization of many sectors generates rapid growth via the cumulative causation, with economies of scale pushing up productivity and wage, and higher wage resulting in higher demand for goods and services produced in these sectors, which in turn fuels further growth. The mechanism modeled there is exactly the ‘big-push’ in Rosenstein-Rodan (1961).

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2.2 Unbalanced Growth Doctrine The two major constructive criticisms toward the balanced growth hypothesis are offered by Hirschman (1953) and Streeten (1959). Hirschman (1953) argues that, first of all, on a practical level the balanced growth doctrine is simply not applicable for developing countries due to their lack of resources. In his own words: “if a country were ready to apply the doctrine of balanced growth, then it would not be underdeveloped in the first place” (Hirschman, pp. 53-54) Rather than balanced growth, he proposes the unbalanced growth strategy with countries allocating their limited resources to a few strategic sectors - sectors with strong backward and forward linkages. Backward linkage indicates a sector’s ability to generate demand for the rest of the economy, and forward linkage on the other hand indicates a sector’s ability to generate inputs supply for the rest of the economy, both are given by the existing input-output structure of the economy. Thus, sectors with stronger linkages with the rest of economy should have some sort of developmental priority because their growth will effectively induced demand and/or supply-led growth for the rest of the economy. The strength of Hirschman’s argument also lies in its practicality, because in principle policy-makers can identify those strategic sectors by calculating each sector’s linkages based on the country’s input-output tables.

Streeteen (1959) sees economic imbalance in both consumption and production as necessary path towards income and output growth. He does not disagree with Rosenstein-Rodan (1943) about the existence of complementarities amongst industries. However, he took a step further by arguing that, in spite of those undesirable properties with unbalanced growth in a static setting, in a growing and enterprising society, sectoral imbalance creates the incentive to invest in consumer goods that are lagging behind and lines of production that are experiencing bottlenecks. Thus, his argument for unbalanced growth is an interesting one – it is the constant efforts of trying to overcome imbalance that fuels the overall growth of the economy. In other words, imbalance is a kind of “necessary evil” for economic growth. It is the process to correct the imbalance instead of the imbalance itself, that would induce growth. 2.3 Empirical Assessments The debate over balanced and unbalanced growth doctrines has also generated a series of efforts to empirically test them in the 1960s and 1970s. Swamy (1967) proposed a simple test for balanced (and unbalanced) growth hypothesis by first constructing the index of sectorial imbalance for each country over a period of time, and then calculating the cross-country correlation coefficient between the imbalance indices and the aggregate growth rates. A statistically positive correlation coefficient would support the unbalanced growth hypothesis, and vice versa for the balanced growth hypothesis. Swamy (1967) used the conventional standard deviation as well as the absolute differences between sectoral and average growth rates in his calculation of the index of imbalance. Based on his dataset that contains aggregate and sectoral growth rates for 45 countries, 6 sectors, and over 12 years (1948-1960), he found strong support for the unbalanced growth hypothesis.

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Yotopoulos and Lau (1970) agree with the overall method Swamy (1967) used. However, they proposed two modifications to Swamy’s index of sectorial imbalance. First, they used the aggregate growth rate-weighted relative standard deviation (or the Pearson coefficient of variation) as the index of imbalance to provide better comparison among countries. Second, they introduced relative sectoral sizes and sector-specific income elasticties as the weights for their index. The first weight obviously takes into account the difference in sizes of various sectors in an economy, whereas the second weight controls for the difference in sectors’ output responsiveness towards income changes, in light of Nurkse (1953)’s argument. Yotopoulos and Lau (1970)’s data covers the same sectors and periods as Swamy’s (1967), but the total number of countries was increased to 64. Their correlation coefficients indicate support for the balanced growth hypothesis.

Later in 1973, Yotopoulos and Nugent conducted an empirical test specifically for Hirschman (1953)’s version of unbalanced growth. Their method relies on the construction of what they call the Hirschman Compliance Index (HCI), which is the rank correlation coefficient between a country’s sectoral growth rates and backward input-output linkages across sectors. A country’s HCI is bonded between -1 and 1, and positive and high HCI indicates that the country’s sectoral growth pattern is more consistent with Hirschman’s notion of unbalanced growth with high linkage sectors growing at a faster rate than the low linkage ones, and vice versa for a HCI that is negative and low valued. The authors would then calculate the correlation coefficient between HCI and the aggregate growth rates across countries, and a statistically significant and positive correlation would imply that countries that better complied with Hirschman’s unbalanced growth doctrine are more likely to experience higher aggregate growth, henceforth the support for unbalanced growth hypothesis a la Hirschman. They conducted their analysis based on a panel of 39 countries, each with six sectors for a 10-year period (1950-1960), and found no empirical support for Hirschman’s unbalanced growth hypothesis. However, it is worth emphasizing that since their test is constructed specifically for Hirschman’s version of unbalanced growth hypothesis, the failure of passing the test does not automatically imply support for balanced growth hypothesis. The unbalanced growth hypothesis might still hold but not in a way as it is specified in Hirschman (1953). 2.4 The Disappearance of the Debate The balanced versus unbalanced growth debate started fading away along with the entire High Development Economics in the 1980s, and by now one can hardly find any reference to this debate in the development literature. Temple (2008) writes: ‘[T]he balanced growth hypothesis is currently at the margins of development thinking and policy advice. The ideas are still interesting, however, and their neglect is partly due to the accidents of intellectual history’. (Temple, 2008, pp. 3) A discussion of those “accidents” in intellectual history that caused the marginalization and disappearance of this line of thought is beyond the scope of this paper; however some interesting insights can be found in Krugman (1995).

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Temple (2008) points out another limitation with the balance growth hypothesis: ‘The ideas are difficult to test empirically’ (Temple, 2008, pp. 3). We believe this particular difficulty mainly comes from the (lack of) availability of quality data rather than the methodology. Methodologically, the research question is a simple one: what is the relationship between the degree of sectoral imbalance and aggregate growth? However, to answer this question in an empirically sound way, one needs to have access to sufficient amount of cross-country multi-sector time-series data on growth rates. However, this data was very difficult to obtain until very recently. The data limitation is also revealed in the earlier attempts of testing the balanced growth hypothesis as reviewed in section 2.3; all three authors had data on a small number of countries over very short spans of time.

While the “accidents” in intellectual history of development economics cannot be undone, the data limitation problem has been improving significantly since the 1980s. With the increasing availability of large international databases such as the Eora Multi-region Input-Output Table (MRIO), World Development Indicator (WDI), Penn World Tables (PWT), and the UN National Accounts Main Aggregates Database (UNNA), we can now empirically revisit the old ideas with new data. It is to our surprise that this has not been done by others yet. It appears that those “accidents” in intellectual history ensured that the balanced and unbalanced growth debate remains forgotten, despite rapid improvements in the data front. 3. Old Tests with New Data

Both Swamy (1967) and Yotopoulos & Lau (1970) tested the balanced versus unbalanced growth hypotheses by looking into the statistical relationship between the degree of dispersion of sectoral growth rates and the aggregate growth rate. A positive significant correlation coefficient would provide support for the unbalanced growth hypothesis, and vice versa for the balanced growth hypothesis. The authors conducted their analyses for the periods of 1948-1953, 1954-1958, and 1950-1960. Swamy (1967) found evidence supporting the unbalanced growth hypothesis, whereas Yotopoulos and Lau (1970) found evidence to the contrary. As such, the authors are firmly situated in opposite spectrum of the debate.

As the first step in our effort to empirically revisiting the debate, we update Swamy (1967)’s and Yotopoulos & Lau (1970)’s tests using a more up-to-date and comprehensive dataset. Our data comes from the raw input-output tables in the Eora multi-region input-output table (MRIO) database, which cover 177 countries from the year 1970 to 2015. In order to calculate the index of imbalance, which captures the degree of dispersion in sectorial growth, we extracted all components of value-added for each sector from the input-output tables, and then deflated them into real terms using the UN implicit price deflators. Finally, we calculated the 5-year overall growth rates based on the deflated data. The next question is how to measure the degree of dispersion using the data on sectorial value-added growth rates in hand. Swamy (1967) and Yotopoulos and Lau (1970) have two different measures for sectorial imbalance, and they are discussed and replicated below.

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3.1 Swamy’s Index of Imbalance

The most straightforward way of measuring sectorial imbalance is to use the standard deviation of sectorial growth rates. However, Swamy (1967) pointed out that squaring the differences between actual and expected (average) growth rate in the conventional standard deviation formula might result in biased calculations if there existed extreme outliers. Therefore, he instead proposes absolute deviation (absolute values of differences between actual and expected growth) as the measure of sectorial imbalance as below.

𝑣𝑣𝑠𝑠 = ∑ |𝑔𝑔𝑖𝑖−𝑔𝑔𝚤𝚤�𝑛𝑛𝑖𝑖=1 |

𝑁𝑁 (1)

In equation (1), vs is the index of imbalance by Swamy (1967), 𝑔𝑔𝑖𝑖 stands for real value-added growth rate of the 𝑖𝑖𝑡𝑡ℎsector, and 𝑔𝑔𝚤𝚤� stands for expected (average) value-added growth rates of all sectors.

Using the Eora dataset, we replicated Swamy’s 1967 study by calculating the correlation coefficients across various periods. The results are presented in Table 1 below. Table 1 shows that our results are consistent with Swamy’s results (as shown in table 2 below). For seven out of nine periods examined, there is a statistically significant and positive correlation between the index of imbalance and aggregate value-added (net output) growth rates. The two periods without a statistically significant correlation coefficient are 2001-2005 and 2006-2010, however their coefficients are still positive.

Table 1 Correlation Coefficients Using Swamy’s index of imbalance

1971-75 1976-80 1981-85 1986-90 1991-95 1996-2000 2001-05 2006-10 2011-15

Index of Imbalance 0.454*** 0.992*** 0.350*** 0.786*** 0.960*** 0.148* 0.124 0.103 0.871***

(No. of observations) 175 175 175 175 175 175 175 175 175 Note. *, ** and *** denote significant levels of 10, 5 and 1 percent respectively.

Source: Authors’ own calculations Table 2 Swamy’s Original Results

1948-53 1954-58 1950-60

Index of Imbalance 0.512 0.356 0.214

(No. of observations) 36 42 45 Note. All results are significant at the 5% level Source: Swamy (1967)

3.2. Yotopoulos and Lau’s Index of Imbalance

Yotopoulos & Lau (1970) propose using the Pearson coefficient of variation instead of the conventional standard deviation in order to take into account of the varying growth rates across different economies. The basic formula is:

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𝑣𝑣𝑦𝑦𝑦𝑦 = �∑ (𝑔𝑔𝑖𝑖−𝐺𝐺)2𝑛𝑛𝑖𝑖=1

𝑁𝑁/𝐺𝐺 (2)

where G stands for the overall value-added growth rate for the period under consideration. Noticing that by dividing the standard deviation by 𝐺𝐺, this becomes a relative measure of dispersion of sectorial growth, as the differences in countries’ average growth rates is taken into account.

Yotopoulos & Lau (1970) also introduce sectoral sizes as the weights to their basic formula in order to better reflect the country’s economic structure. Furthermore, they also use sector specific income elasticities as another weight in their formula in order to capture different sectors’ abilities of changing demand in response to economic growth (a change in income). Therefore, the most comprehensive version of their weighted index of imbalance can be expressed by equation (3) below

𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦 = �∑ 𝑤𝑤𝑖𝑖(𝑔𝑔𝑖𝑖 − 𝐸𝐸𝑖𝑖𝐺𝐺)2𝑛𝑛𝑖𝑖=1 /𝐺𝐺 (3)

Where 𝑤𝑤𝑖𝑖 stands for the sector 𝑖𝑖’s sectoral weight and 𝐸𝐸𝑖𝑖 stands for the income elasticity of the 𝑖𝑖𝑡𝑡ℎ sector.1 Yotopoulos & Lau (1970) also have a version of the index that only incorporates sectorial weights; the corresponding formula would be equation (3) without the term 𝐸𝐸𝑖𝑖.

The correlation coefficients based on all three versions of the index of imbalance in Yotopoulos & Lau (1970) are reported in Table 3 below. The coefficients are all statistically insignificant. Moreover, all of the correlation coefficients have positive sign (in contrast with the authors’ original results in the 70s, as shown in Table 4). The magnitudes of the coefficients are also quite close to zero, which suggests the lack of correlation between Yotopoulos & Lau’s index of imbalance and overall growth. Table 3. Correlation Coefficients Using Yotopoulos & Lau’s Index of Imbalance

1971-75 1976-80 1981-85 1986-90 1991-95 1996-2000 2001-05 2006-10 2011-15

vl 0.022 0.112 -0.023 0.012 0.044 0.059 0.029 0.094 -0.007

(No. of observations) 168 168 171 170 170 174 173 172 168

vlw (weighted by sector) 0.033 0.126 -0.036 0.012 0.040 0.065 0.049 0.075 -0.007

(No. of observations) 168 168 171 170 170 174 173 172 168

vle (Comprehensive) 0.033 0.129* -0.035 0.012 0.041 0.066 0.053 0.075 -0.007

(No. of observations) 168 168 171 170 170 174 173 172 168 Note. *, ** and *** denote significant levels of 10, 5 and 1 percent respectively.

Source: Authors’ own calculations 1The elasticities of the sectors, Ei, are calculated according to a method specified by Yotopoulos and Lau. Elasticities were derived through the cross- sectional regression model: ln(Vi) = a + bln(y) + εi, where Vi is the sectoral value added per capita for sector i, and y is GDP per capita, for the year 2010 (Yotopoulos & Lau used the model on data in 1960). The coefficient of ln(y), b, is our income elasticity of demand estimation. The income elasticities of the 7 sectors are presented in Appendix B.

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Table 4. Yotopoulos and Lau’s Original Results 1948-53 1954-58 1950-60

vl -0.423* -0.481** -0.382**

(No. of observations) 19 64 55

vlw (weighted) -0.426* -0.428** -0.382**

(No. of observations) 19 64 55 vle (weights and elasticities) -0.476** -0.423** -0.308**

(No. of observations) 19 64 55 Note. *, ** and *** denote significant levels of 10, 5 and 1 percent respectively.

Source: Yotopoulos & Lau (1970) 3.3 Relative versus Absolute Standard Deviation The major difference between the Yotopoulos & Lau’s index and Swamy’s index is the usage of coefficient of variation in the former versus absolute deviation in the latter. A reasonable suspicion would be that the usage of coefficient of variation by dividing the deviations by overall value-added growth rate 𝐺𝐺 is the main cause for the different results we observed above. To verify this, we recalculated Yotopoulos & Lau’s index without dividing the deviation by overall growth. The results are shown in Table 5 below. Table 5. Correlation Coefficient with Yotopoulos & Lau’s Index without Dividing Overall Growth

1971-75 1976-80 1981-85 1986-90 1991-95 1996-2000 2001-05 2006-10 2011-15

vle (weights and elasticities) 0.033 0.129* 0.300*** 0.906*** 0.312*** 0.563*** 0.274*** 0.246*** 0.867***

(No. of observations) 168 168 171 170 170 174 173 172 168

Source: Authors’ own calculations Table 5 confirms our earlier suspicion that when relative variation is taken out of the consideration by not including the 𝐺𝐺 in the Yotopoulos & Lau’s formula, the results become consistent with the Swamy (1967). Therefore, we can say that if we stick with absolute deviation (Swamy’s version) or standard deviation (Yotopoulos & Lau’s version without dividing by 𝐺𝐺), the correlation analysis will deliver statistically significant results supporting the unbalanced growth hypothesis. On the other hand, if we use the original Yotopoulos & Lau’s coefficient of variation as the index of imbalance, our results become inconclusive. While it is tempting to use the Swamy version for simplicity, we are more convinced by Yotopoulos and Lau’s argument that the varying rates of growth of different countries should be controlled for in order to properly isolate the effects of balanced/unbalanced growth on the overall growth of the economy. Since the result of correlation analysis based on Yotopoulos & Lau’s version of the index of imbalance is inconclusive, we propose an alternative test – cross-country growth regression model - to systematically assess the impacts of sectoral imbalance on growth while controlling for a standard set of growth determinants. The methodology and results are discussed in details in the next section.

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4. Balanced Growth in Cross-Country Growth Regression While calculating correlation coefficient is a straightforward way of assessing the direct relationship between the degree of sectorial (im)balance and aggregate growth, the results are unfortunately non-robust and inconclusive as shown in section 3. As such, in this section, we adopt an alternative approach to empirically test the hypotheses which involves modeling growth systematically and estimating the effects of sectoral (im)balance on growth, while controlling for other key factors affecting growth. This is done by running a set of cross-country growth regressions with the degree of sectoral imbalanced as an independent variable that determines growth. 4.1 The Canonical Model While there exists a number of growth regression models, as an initial effort of revisiting the balanced and unbalanced growth debate, this paper sticks with the most well-known canonical growth model – the Solow model.

Solow predicted that the rates of saving and population growth determined the steady-state level of income per capita. Thus the basic Solow growth regression is: ln�𝑦𝑦𝑖𝑖,𝑡𝑡� − ln�𝑦𝑦𝑖𝑖,0� = 𝛽𝛽0 + 𝛽𝛽1 ln( 𝑠𝑠𝑖𝑖) + 𝛽𝛽2 ln(𝑛𝑛𝑖𝑖 + 𝑔𝑔𝑖𝑖 + 𝛿𝛿𝑖𝑖) + 𝜀𝜀𝑖𝑖 (4) where 𝑦𝑦𝑖𝑖,𝑡𝑡 is real GDP per worker of country 𝑖𝑖 at time 𝑡𝑡 𝛿𝛿𝑖𝑖 is capital depreciation rate of country 𝑖𝑖 𝑛𝑛𝑖𝑖 is labor growth rate of country 𝑖𝑖 𝑔𝑔𝑖𝑖 is technology growth rate of country 𝑖𝑖 𝑠𝑠𝑖𝑖 is savings rate of country 𝑖𝑖

However, Mankiw et al. (1992) noted that even though the original Solow Model predicted the directions of effects of savings and population growth correctly, the magnitudes of effects were overestimated (1992). To better take into account the importance of the accumulation of human capital, they incorporated school enrollment rate in the Solow growth regression resulting the augmented model below: ln�𝑦𝑦𝑖𝑖,𝑡𝑡� − ln�𝑦𝑦𝑖𝑖,0� = 𝛽𝛽0 + 𝛽𝛽1 ln( 𝑠𝑠𝑖𝑖) + 𝛽𝛽2 ln(𝑛𝑛𝑖𝑖 + 𝑔𝑔𝑖𝑖 + 𝛿𝛿𝑖𝑖) + 𝛽𝛽3 ln(𝑠𝑠𝑠𝑠ℎ𝑖𝑖) + 𝜀𝜀𝑖𝑖 (5) with the addition of 𝑠𝑠𝑠𝑠ℎ𝑖𝑖 being the secondary school enrollment rate (Mankiw et.al., 1992). Thus in equation (5) both the accumulation of human capital (as measured by school enrollment rate) and the accumulation of physical capital (as measured by saving rate) determine the country’s growth.

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4.2 Barro Regressions Equation (5) can be viewed as the baseline cross-country growth regression model. Barro (1991) extended this regression into a set of extended Solow growth regressions to study the effects of a set of potential growth determinants on country’s growth, and these regressions are known as Barro Regressions. Equation (6) below is a generic representation of Barro’s regression. 𝑔𝑔𝑖𝑖 = 𝛼𝛼 ln�𝑦𝑦𝑖𝑖,0� + 𝛽𝛽𝑋𝑋𝑖𝑖 + 𝜃𝜃𝑍𝑍𝑖𝑖 + 𝜀𝜀𝑖𝑖, (6) where 𝑦𝑦𝑖𝑖,0 is country 𝑖𝑖’s initial level of per worker real GDP,2 𝑋𝑋𝑖𝑖 contains all the augmented Solow variables as in the right-hand side of equation (5), and most importantly 𝑍𝑍𝑖𝑖 represents those growth determinants that lie outside of Solow’s original model. Barro (1991, 1996) investigated the effects of government expenditure, political instability, economic system, market distortions, and geographical regions on economic growth by letting 𝑍𝑍𝑖𝑖 be the proxy for each of those non-Solow variables. More recently, Ulasan (2012) used various measures of trade openness as the 𝑍𝑍𝑖𝑖 to study the effect of trade openness on growth. Since the central question of present paper is whether sectoral balance (or imbalance) does or does not lead to faster growth, we can answer this question by applying the Barro regression with 𝑍𝑍𝑖𝑖 serving as the proxy for sectoral imbalance. Nevertheless, before diving into the results, we shall discuss a few typical shortcomings of this type of (cross-country growth) regressions.

Mankiw (1995) points out three common problems that cross-country growth regressions tend to have: simultaneity problem, multicollinearity problem and degree of freedom problem. The simultaneity problem arises when the independent variables are not really independent, but instead jointly determined with the dependent variable. When this happens, one cannot establish a causal relationship between the dependent and independent variables. It is indeed quite easy to conceive simultaneity problem in Solow type of cross-country growth regressions. However, while the problem might prevent us from firmly establishing the causal relationship between the dependent and independent variables, it does not prevent us from validating hypotheses by looking for certain correlations between the dependent and independent variables, which is exactly what we intend to do this present paper. Multicollinearity problem is also likely to occur in cross-country growth regressions because the independent variables might move together due to country-specific factors. Severe multicollinearity problem will make estimations highly sensitive to minor changes, and sometime it can cause the coefficient to switch sign, which is problematic for our research question. Therefore, it is essential that we report Variance Inflating Factor (VIF) for each estimation to get a sense of the severity of the multicollinearity problem. Degree of freedom problem arises because one can easily find more number of independent variables that affect growth than the number of countries in the world; hence the “true” growth model is simply not estimable using cross-country regression because it does not have enough degree of freedom. However,

2 By including the initial level of per worker real GDP, it controls for the potential effect of convergence on growth.

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this is not as problematic as it sounds for the purpose of the present paper, because we are not looking to estimate the “true” growth model, but rather just the relationship between sectoral imbalance and overall growth. Finally, Brock and Durlauf (2001) raised another problem with cross-country growth regressions; namely, their error terms are likely to be non-exchangeable across countries because country-specific characteristics that drive growth are embodied in those error terms. In statistics, this is also called the violation of “exchangeability”. With the violation of exchangeability, model uncertainty is not appropriately incorporated into the analysis, so the regression might be difficult to interpret. 3 Unless we abandon the method of cross-country growth regression analysis entirely, non-exchangeability is a problem we have to live with. 4.3 Data, Sample, and the Regression Following Barro (1991, 1996) and Ulasan (2012), we isolate the influence of the degree of sectoral imbalance on growth by including the index of imbalance as the key independent variable 𝑍𝑍 in equation (6). Hence, explicitly our regression model becomes 𝑔𝑔𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 ln�𝑦𝑦𝑖𝑖,0� + 𝛽𝛽2 ln( 𝑠𝑠𝑖𝑖) + 𝛽𝛽3 ln(𝑛𝑛𝑖𝑖 + 𝑔𝑔𝑖𝑖 + 𝛿𝛿𝑖𝑖) + 𝛽𝛽4 ln(ℎ𝑠𝑠𝑖𝑖) + 𝛽𝛽5ln (𝑣𝑣𝑖𝑖) + 𝜀𝜀𝑖𝑖 (7) where 𝑣𝑣𝑖𝑖 is the index of imbalance, representing the degree of dispersion of sectoral growth rates from overall growth rates as discussed in section 3.

Section 3 surveyed four versions of sectorial imbalance index based on Swamy (1967) and Yotopoulos and Lau (1970). The first measure 𝑣𝑣𝑠𝑠 comes from Swamy (1967)’s formula of absolute deviation as shown in equation (1). The second measure 𝑣𝑣𝑦𝑦𝑦𝑦 is the non-weighted version in Yotopoulos and Lau (1970) as in equation (2). The third measure 𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦 is 𝑣𝑣𝑦𝑦𝑦𝑦 weighted only by relative sector sizes, and fourth measure 𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦 – the most comprehensive one – has 𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦 weighted by both relative sizes and sectoral income elasticities as in equation (3). Thus, for robustness, we will run a set of four growth regressions, each with a version of the imbalance index.

Data for the remaining variables are obtained from the Penn World Tables (hereinafter referred to as PWT) and the World Bank – World Development Indicators database (hereinafter referred to as WDI). The variables extracted are:

• 𝑌𝑌: Real GDP (output) from PWT;

• 𝑁𝑁: Working age population (population aged 15-64) from WDI; This variable was used in Mankiw et.al. (1992) as an approximation of the labor force size. We use also this to compute 𝑦𝑦 (Real GDP per worker) as 𝑌𝑌 over 𝑁𝑁, and 𝑛𝑛 (growth rate of labor) as the average growth rate of 𝑁𝑁 over the period from

3 The emphasis here is “might” because, for example, heteroskedasticity results exchangeability problem, but it does not result any problems with interpreting the structural coefficients. (See Durlauf et al., 2005, and Brock and Durlauf, 2001)

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1971-2014.

• 𝑔𝑔𝑖𝑖 + 𝛿𝛿𝑖𝑖: The sum of technical growth and depreciation rates is assumed to be 0.05 following Mankiw et al. (1992);

• 𝑠𝑠: Share of gross capital formation in GDP at the current PPPs from PWT; • 𝑠𝑠𝑠𝑠ℎ: Secondary School Enrollment Rate (gross) from WDI.

All data except for the real GDP, are averaged over the period from 1971 to 2014. Appendix A contains more detailed data notes. 4.4 Results We ran a set of five regressions, with the first one being the baseline Solow growth regression, and the following four contain different versions of the index of imbalance (included as the non-Solow growth determinant as discussed in 4.3). The results are shown in table 6 below. Table 6: Cross-country Growth Regression Results

𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩

𝒗𝒗𝑩𝑩

𝒗𝒗𝒚𝒚𝒚𝒚

𝒗𝒗𝒚𝒚𝒚𝒚𝒚𝒚

𝒗𝒗𝒚𝒚𝒚𝒚𝒚𝒚

𝑙𝑙𝑛𝑛(𝑦𝑦0)

-0.623 (0.059)***

-0.596 (0.055)***

-0.579 (0.051)***

-0.583 (0.052)***

-0.566 (0.052)***

𝑙𝑙𝑛𝑛(𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)

-0.154 (0.351)

-0.233 (0.341)

-0.236 (0.307)

-0.153 (0.313)

-0.194 (0.308)

𝑙𝑙𝑛𝑛(𝑠𝑠)

0.629 (0.137)***

0.555 (0.129)***

0.505 (0.121)***

0.512 (0.123)***

0.504 (0.12)***

𝑙𝑙𝑛𝑛(𝑠𝑠𝑠𝑠ℎ)

0.753 (0.110)***

0.749 (0.103)***

0.718 (0.102)***

0.713 (0.104)***

0.694 (0.103)***

𝑙𝑙𝑛𝑛(𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝑛𝑛𝑠𝑠𝑖𝑖)

-0.035 (0.043)

-0.094 (0.037)**

-0.168 (0.042)***

-0.197 (0.044)***

𝐶𝐶𝐶𝐶𝑛𝑛𝑠𝑠𝑡𝑡𝑖𝑖𝑛𝑛𝑡𝑡

4.018

(1.055)*** 3.446

(1.048)*** 3.324

(0.923)*** 3.405

(0.929)*** 3.096

(0.917)***

N 145 133 129 132 131

Adj-𝑅𝑅2 0.5227 0.5802 0.6245 0.6280 0.6365

MSE 0.52877 0.47416 0.43637 0.4473 0.44035

Mean VIF 2.12 2.00 2.01 1.99 2.00 Sources: Authors’ own estimations Results from the baseline Solow growth regression are consistent with the theoretical prediction of the Solow model itself, as well as the estimations in Mankiw et al. (1992) in terms of the signs of the estimated coefficients. Other than coefficient for the sum of population growth, technical growth, and depreciation rates (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿), all estimated

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coefficients are statistically significant. The statistically significant negative coefficient for 𝑙𝑙𝑛𝑛(𝑦𝑦0) also indicates the evidence for conditional 𝛽𝛽-convergence.

All four Barro regressions show robust estimates for traditional Solow variables; and the increase of adjusted 𝑅𝑅2 when index of imbalance is included indicates that sectorial imbalance does help explain additional variations in growth rates across countries. Regarding the sign of the estimated coefficient for the index of imbalance, all four regressions report negative coefficient, which supports the balanced growth hypothesis. However, when the index of imbalance is calculated with Swamy’s formula, the estimated coefficient is not statistically significant, and the increase of adjusted 𝑅𝑅2 from the 𝑅𝑅2in the baseline regression is limited. On the other hand, when Yotopoulos & Lau’s formula is used, the estimated coefficient becomes statistically significant at 5% and 1% level for the non-weighted version (𝑣𝑣𝑦𝑦𝑦𝑦) and weighted versions (𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦, 𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦), respectively. Moreover, the adjusted 𝑅𝑅2 also increases more drastically (by more than 10%) when compared with the baseline regression. And finally, the mean Variance Inflation Factor (VIF) (reported in the bottom of table 6) is low, implying that the problem of multicollinearity is quite negligible in these regressions.

Recall that the fundamental difference between the Swamy’s and Yotopoulos & Lau’s formulae for the index of imbalance is that the earlier uses absolute deviation, whereas the latter uses the coefficient of variation (standard deviation of sectoral growth rates weighted by GDP growth rate). While we are more convinced by Yotopoulos & Lau (1970) in that coefficient of variation is a better measure of relative sectoral imbalance across countries due to the varying growth rates of different countries, it is still useful to compare all of the regression results with the correlation analysis conducted in section 3. The correlation coefficients between aggregate growth rates and indices of imbalance across countries are mostly positive and statistically significant when Swamy’s formula is used; however the correlation coefficients are positive but statistically insignificant when Yotopoulos & Lau’s formula is used. It seems that when correlation analysis is conducted, empirical evidence tends to steer towards the unbalanced growth hypothesis. However, when cross-country Solow growth regression is used, the estimated coefficients for the indices of imbalance are all negative, and when Yotopoulos & Lau’s formulae is used, they are statistically significant. Hence, the regression analysis tends to support the balanced growth hypothesis. Thus, we can conclude from here that, as long as one believes the Solow specification as a reasonable model for a country’s growth, then the most recent cross-country evidence tends to support the balanced growth hypothesis.

Does the negative effect of sectoral imbalance on aggregate growth hold for countries across different income groups and levels of development? To answer this question, we conduct the above regression analysis with our sample segmented into developed and developing, and high-income and low-income countries.4 In these

4 We classified the countries according to the World Bank’s “New country classification by income level: 2018-2019.” In our paper, developed = high-income countries, developing = all other countries (upper middle income, middle income and lower middle income) in WB’s article; high-income = high income and upper middle-income countries, low-income = lower middle income and low income countries in WB’s article.

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regressions the index of imbalance used is 𝑣𝑣𝑦𝑦𝑦𝑦𝑦𝑦, which is the most comprehensive index that incorporates both sectorial weights and elasticities. The results of the five (all, developed, developing, high-income and low-income) regressions are presented in table 7 below. Table 7: Cross-country Growth Regression Results with Segmented Sample

𝑨𝑨𝒚𝒚𝒚𝒚

𝑫𝑫𝑩𝑩𝒗𝒗𝑩𝑩𝒚𝒚𝑫𝑫𝑫𝑫𝑩𝑩𝑫𝑫

𝑫𝑫𝑩𝑩𝒗𝒗𝑩𝑩𝒚𝒚𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫

𝑯𝑯𝑫𝑫𝑫𝑫𝑯𝑯

𝑳𝑳𝑫𝑫𝒚𝒚

𝑙𝑙𝑛𝑛(𝑦𝑦0)

-0.566 (0.052)***

-0.723 (0.107)***

-0.707 (0.077)***

-0.594 (0.080)***

-0.756 (0.108)***

𝑙𝑙𝑛𝑛(𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)

-0.194 (0.308)

0.375 (0.559)

-0.558 (0.516)

-0.125 (0.439)

-0.877 (0.843)

𝑙𝑙𝑛𝑛(𝑠𝑠)

0.504 (0.120)***

0.415 (0.288)

0.434 (0.131)***

0.600 (0.205)***

0.336 (0.144)**

𝑙𝑙𝑛𝑛(𝑠𝑠𝑠𝑠ℎ)

0.694 (0.103)***

0.175 (0.452)

0.642 (0.108)***

0.363 (0.291)

0.543 (0.115)***

𝑙𝑙𝑛𝑛(𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝑛𝑛𝑠𝑠𝑖𝑖)

-0.197 (0.044)***

-0.196 (0.091)**

-0.224 (0.048)***

-0.152 (0.069)**

-0.248 (0.053)***

𝐶𝐶𝐶𝐶𝑛𝑛𝑠𝑠𝑡𝑡𝑖𝑖𝑛𝑛𝑡𝑡

3.096

(0.917)*** 8.604

(1.901)*** 3.285

(1.477)** 5.282

(1.137)*** 2.878

(2.585)

N 131 42 89 73 58

Adj-𝑅𝑅2 0.6365 0.7287 0.6498 0.6400 0.6950

MSE 0.44035 0.40359 0.41923 0.42177 0.40090

Mean VIF 2.00 2.13 1.58 2.07 1.41 Sources: Authors’ own estimations

The estimated coefficients for the index of imbalance are consistently negative for all regressions, indicating support for the balanced growth hypothesis regardless of income and level of development segmentation. However, the level of statistical significance is higher for developing and low-income countries compared with developed and high-income countries. The robust and strong supports for the balance growth hypothesis found for developing and low-income countries might pose an important developmental challenge for these countries according to Hirschman (1958), because those are the countries that are likely to have limited resources to support a balanced growth of all sectors; in other words, the ”Big Push” as in Rosenstein-Rodan (1961) might not be affordable for them. However, this position is debatable for reasons to be discussed in the following section.

Furthermore, these regressions also show that the effects accumulation of human capital (as measured by secondary school enrollment rate) on growth is not statistically significant for developed and high-income countries. In fact, the empirical literature on the effect of human capital on growth is inconclusive, since authors such as Benhabib and

16

Spiegel (1994) and Pritchett (2001) have also found weak to none relationship between human capital and growth. While the discussion on possible reasons for such results is beyond the scope of our paper, the strong results found for developing and low-income countries suggests the importance of education for economic growth. 5 This poses yet another developmental challenge, given the amount of resources (both immediate and sustained over the years) that is often required to build a strong national education system. 5. Conclusion In this paper, we empirically revisited the balanced and unbalanced growth hypotheses debate by conducting two related analyses. First, we updated the empirical tests appeared in the literature by calculating cross-country correlation coefficient between aggregate growth and various measures of sectorial imbalance using a newer and more comprehensive international dataset. Second, following Barro (1991), we included the index of imbalance as the additional growth determinant in a set of cross-country Solow growth regressions to test its effects on growth. What conclusion can we draw from our revisit of the forgotten debate? Recall that when the empirical tests were first conducted in 1970s, Swamy (1967) found strong support for the unbalanced growth hypothesis whereas Yotopoulos and Lau (1970) found strong support for the balanced growth hypothesis. We updated their studies in section 3, and found that when the index of imbalance is constructed based on Swamy (1967), the unbalanced growth hypothesis is still supported for most periods, consistent with Swamy’s original finding. However, when the index of imbalance is constructed based on Yotopoulos and Lau (1970), the results are inconclusive due to statistical insignificance. Thus our efforts of updating these studies could not deliver any clear and robust contribution to the debate. However, when cross-country Solow growth regressions are conducted with index of imbalance included as a non-Solow growth determinant, the overall results are robust with negative estimated coefficient for index of imbalance regardless of how it is calculated. Additionally, the coefficients are statistically significant and negative even when we segmented countries by incomes and development levels. Thus, we can conclude that, overall our Solow growth regression analysis supports the balanced growth hypothesis. While the balanced growth hypothesis is supported in the cross-country growth regression framework, a few words of caution need to be discussed. First of all, the validity of the results still depends on one’s belief that whether Swamy (1967) or Yotopoulos and Lau (1970) has a more reasonable measure for sectorial imbalance. If one believes in Swamy (1967), then the estimated coefficient would not be statistically significant. That is said, as mentioned before, we are more convinced by Yotopoulos and Lau (1970)’s coefficient of variation measure because it takes into account variations in average growth rates across countries. Second, even if one agrees with Yotopoulos and Lau (1970)’s measure of imbalance, one can still question the validity of Solow’s growth 5 Detailed discussions can be found in Sunde and Vischer (2015), Hanushek and Kimko (2000), and Temple (1999).

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specification. Despite the fact that it is the most well-known model of growth in economics, the Solow model has its limitations. In addition, there also exists alternative growth models with very different specifications. Thus, our support for the balanced growth hypothesis should also be conditioned on the validity of Solow growth model, which is often not an empirical question, but rather a philosophical one. One interesting extension of this line of research would be to test the robustness of our results by running cross-country growth regressions based on different (perhaps demand-side) growth models. At this moment, the only conclusion we can reach is: as long as one believes that Solow growth model is a reasonable way of characterizing the steady state growth of a nation and Yotopoulos and Lau (1970)’s measure of sectorial imbalance is a better approximation of sectorial imbalance than Swamy’s (1967) or any other alternatives, then we have found strong support for the balanced growth hypothesis using cross-country growth regression analysis.

The revival of the balanced and unbalanced growth debate also has some

important implications on industrial policies. It might appear to some readers that the unbalanced growth doctrine supports ‘selective’ industrial policies that deliberately target particular sectors or even firms, whereas the balanced growth doctrine supports ‘general’ industrial policies where the emphasis is providing things like education, research and development, and infrastructure that benefit all industries equally. (Chang, 1994; UNECA, 2016; Salazar-Xirinachs et al., 2014) The mainstream view these days tend to favor ‘general’ industrial policies rather than industrial polices that selectively ‘pick the winners’. However, a careful examination of the balanced and unbalance growth doctrines will reveal that the balanced growth hypothesis also has allowance for ‘selective’ industrial policies. Since there are no proven economic laws that guarantee balanced growth in a laissez-faire free-market setting, if balanced sectorial growth is found to be supportive of the overall growth of the nation, then government policies should target on the sectors that are lagging behind so that the country’s growth will be more balanced. 6 Therefore, if unbalanced growth doctrine supports ‘picking the winners’, then balanced growth doctrine would support ‘helping the losers’, which is also a type of ‘selective’ industrial policy. But which industries should be selected and targeted? This becomes an important empirical question, and we hope the type of analysis conducted in the present paper can at least contribute to finding the answers.

From this perspective, Hirschman (1953)’s concern over developing countries’

lack of resources to engage in balanced growth might not necessarily be valid. If it is feasible for a country to go on the unbalanced growth path by ‘selecting the winners’ like what Hirschman (1953) suggests, it would also be feasible for then to go on the balanced growth path by ‘helping the losers’. As shown in section 4.4, the support for balanced growth hypothesis is found to be particularly strong for developing and low-income countries. The policy implication therefore is that governments of these countries should consider targeting the sectors that are falling behind in the process of economic development if overall economic growth is their key objective. Last but not least, this finding also sheds light on the counterintuitive finding by Kucera and Jiang (2018) that 6 Although Streeten (1959) argues that there might be a natural tendency for industries and firms that are lagging behind to move ahead to overcome sectorial imbalance in a free and “enterprising” society.

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high-growth countries such as China, India and South Korea often experience all-around increase in productivity over time. While some of the policies those countries adopted at particular points in time might seem to be sector-specific, over a longer time horizon, it is more likely that those countries still followed a balanced growth path.

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Bibliography Barro, R. "Determinants of economics growth: a cross-country empirical study." Vol. 5698. National Bureau of Economic Research, 1996. Barro, R. "Economic growth in a cross section of countries." The Quarterly Journal of Economics 106, no. 2 (1991): 407-443. Benhabib, J., and M. Spiegel. "The role of human capital in economic development evidence from aggregate crosscountry data ." Journal of Monetary Economics 34 (1994): 143-73. Brock, W., and S. Durlauf. "Growth empirics and reality." The World Bank Economic Review 15, no. 2 (2001): 229-272. Chang, H. The Political Economy of Industrial Policy. London: Macmillan, 1994. Durlauf, S., and S. Blume. The New Palgrave Dictionary of Economics. London: Palgrave Macmillan, 2008. Durlauf, S., P. Johnson, and J. Temple. Growth Econometrics. Vol. 1, in Handbook of Economic Growth, by S. Durlauf and P. Aghion, 555-677. Oxford: Elsevier, 2014. Hanusheck, E., D. Kimko, and J. Hall. "Schooling, labor-force quality, and the growth of nations." American Economic Review 90 (2000): 1184-208. Lewis, A. The Theory of Economic Growth. Homewood, IL: Richard D. Irwin, 1955. Krugman, P. Development, Geography and Economic Theory. Cambridge, MA: MIT Press, 1995. Kucera, D., and X. Jiang. "Structural transformation in emerging economies: leading sectors and the balanced growth hypothesis." Oxford Development Studies, 2018: Forthcoming. Mankiw, G. "The growth of nations." Brookings Paper on Economic Activity 1 (1995): 275-326. Mankiw, G., D. Romer, and D. Weil. "A contribution to the empirics of economic growth." The Quarterly Journal of Economics 107, no. 2 (1992): 407-437. Murphy, K., A. Shleifer, and R. Vishny. "Industrialization and the Big Push." Journal of Political Economy 5 (1989): 1003-1026. Nath, S. "The theory of balanced growth." Oxford Economic Papers 14, no. 2 (1962): 138-153.

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Pritchett, L. "Where has all education gone? ." World Bank Economic Review 15 (2001): 367-391. Salazar-Xirinachs, J., I. Nubler, and R. Kozul-Wright. Transforming Economies: Making Industrial Policy Work for Growth, Jobs and Development. Geneva: International Labor Organization, 2014. Streeten, P. "Unbalanced growth." Oxford Economic Papers 11, no. 2 (1959): 167-190. Sunde, U., and T. Vischer. "Human capital and crowth: specification matters." Economica 82 (2015): 368-90. Sutcliffe, R. "Balanced and unbalanced growth." The Quarterly Journal of Economics 78, no. 4 (1964): 621-640. Swamy, S. "Statistical evidence of balanced and unbalanced growth." The Review of Economics and Statistics 49, no. 3 (1967): 288-303. Temple, J. "A positive effect of human capital on growth." Economics Letters 65 (1999): 131-134. Ulasan, B. "Openness to international trade and economic growth: a cross-country empirical investigation." Economics Discussion Papers. no. 2012-25. Kiel Institute for the World Economy, 2012. United Nations Economic Commission for Africa. Transformative Industrial Policy for Africa. Ethiopia: UNECA, 2016. Yotopoulos, P., and J. Nugent. "A balanced-growth version of the linkage hypothesis: a test." The Quarterly Journal of Economics 87, no. 2 (1973): 157-171. Yotopoulos, P., and L. Lau. "A test for balanced and unbalanced growth." The Review of Economics and Statistics 52, no. 4 (1970): 376-384.

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Appendix A. Data notes Real GDP per capita (RPC)

Calculated by dividing output-side real GDP at chained PPPs (rgdpo in PWT) by population (pop in PWT, with unit converted from million people to person).

Population, total (TPt) Total population in year t recorded in the WDI database.

Labour force (LF) Defined as the total population between ages 15-64 (Ulasan, 2012). Data collected from WDI database.

Real GDP per worker (RPW) – y variable

RPW = RPC*TP/LF for the year 2014 Initial GDP per worker (RPW_0) – y0 variable

RPW in 1971

Population growth – n variable Average population growth rate between 1971-2014 n = (1/44)*log(TP2014/TP1971)

Investment rate – s variable Average of Share of Gross Capital Formation at Chained PPPs (csh_i in PWT database) over the 1971-2014 period.

School enrollment rate – edu variable Average gross rate of secondary school enrollment from 1971-2014. Enrollment rate data was taken from the WDI database.

Depreciation and technological growth rate 𝑔𝑔𝑖𝑖 + 𝛿𝛿𝑖𝑖: The sum of technical growth and depreciation rates is assumed to be 0.05 following Mankiw et al. (1992);