Aggregate returns to social capital: Estimates based on the augmented augmented-Solow model

Journal of Macroeconomics 31 (2009) 376–393

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Aggregate returns to social capital: Estimates based on the augmented augmented-Solow model Hirokazu Ishise a, Yasuyuki Sawada b,* a b

Department of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, USA Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

a r t i c l e

i n f o

Article history: Received 2 February 2007 Accepted 18 August 2008 Available online 16 September 2008

JEL classification: E26 O10 O40 Keywords: Social capital Economic growth The augmented-Solow model

a b s t r a c t We extend the augmented-Solow model to estimate the aggregate output elasticity and depreciation rate of social capital that characterize aggregate returns. The estimated output elasticity is approximately 0.1. While social capital positively affects economic growth, the magnitude is much smaller than that of other production inputs. The estimated depreciation rate is at least 10% per annum, which is higher than that of physical capital. The median value of the implied aggregate return of social capital is approximately 19.11% at the global level. In OECD countries, it is likely to be considerably smaller than the individual returns, suggesting the fallacy of composition. While there is no systematic relationship between GDP per capita and returns to physical or human capital, the aggregate returns to social capital seem to be negatively related to the level of development. Ó 2008 Elsevier Inc. All rights reserved.

1. Introduction Social capital has been used as a key concept to explain the unobserved heterogeneity in the economic performance of people, communities, and countries (Dasgupta and Serageldin, 2000). In general, social capital is recognized as the informal forms of institutions and organizations that are based on the social relationships, networks, and associations that create shared knowledge, mutual trust, social norms, and unwritten rules (Durlauf and Fafchamps, 2005). The concept of social capital is a combination of these intangible objects; therefore, it has remained elusive by nature since Loury (1977) introduced it into modern social science research and Coleman (1988) popularized it in sociology. What, then, are the aggregate returns to social capital? Is it even possible to quantify these seemingly intangible returns? We aim to answer these questions. Many reduced-form micro studies have found positive returns to social capital (Durlauf and Fafchamps, 2005; Fafchamps and Minten, 2002). However, as Durlauf and Fafchamps (2005) and Fafchamps (2006) argue, individual returns are often poor predictors of aggregate returns. If social capital enables certain individuals or groups to capture rents at the expense of others, social capital becomes individually remunerative yet socially unproductive.1 Olson (1982) specified that such examples include the formation of trade unions, political parties, and lobbyist groups. Fafchamps (2006) referred to this situation as the ‘‘fallacy of composition”. In contrast, social capital can generate positive externalities that are not entirely appropriated by the owners of social capital, because informal institutions, which are subsets of social capital, can supplement underdeveloped market mechanism (Aoki and Hayami, 2001). In this case, individual returns to social capital will underestimate social returns.

* Corresponding author. Tel.: +81 3 5841 5572; fax: +81 3 5841 5521. E-mail addresses: [email protected] (H. Ishise), [email protected] (Y. Sawada). 1 Social capital may facilitate collusion among group members, which is not socially productive (Fafchamps and Minten, 2002). 0164-0704/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2008.08.002

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Accordingly, private returns to social capital from microlevel social capital studies should not be considered as evidence that social capital is also socially beneficial. An important empirical question pertains to determining whether it is fallacy of composition problems or positive externalities that exist. In order to estimate the aggregate returns to social capital, an independent empirical framework should be designed and carefully implemented. While the existing macrolevel literature led by Knack and Keefer (1997) and Temple and Johnson (1998) found a positive correlation between social capital and economic growth, there has been no comprehensive study of the macroeconomic effects of social capital – the aggregate returns to social capital or the degree of social capital’s contribution to economic growth – within the Solow framework that considers all the econometric issues. We aim to bridge this gap in the existing literature by closely following the empirical strategy of Mankiw et al. (1992) and Nonneman and Vanhoudt (1996). Mankiw et al. (1992) (hereafter, MRW) extended the canonical Solow model by incorporating human capital and estimating the degree of the contributions of both physical and human capital to economic growth. Nonneman and Vanhoudt (1996) augmented the augmented-Solow model of MRW by adding R&D investment so as to quantify the social rate of return for technological knowledge. Our basic strategy is to augment the MRW model by including social capital as an additional production input in order to estimate the output elasticity of social capital. This allows us to quantify the aggregate returns to social capital as compared with other types of capital.2 With regard to the selection of appropriate data for social capital, we confine our consideration of social capital to a source of economic development that improves social connectivity through information sharing and mutual communication. In particular, we follow Ostrom (2000), which emphasizes the importance of shared knowledge when defining the concept of social capital. In addition, through a comprehensive survey on social capital, covering both micro-and macro literature, Durlauf and Fafchamps (2005) concluded that mutual communication is one of the most important common components of its different definitions. While it is not straightforward to quantify the total stock of social capital that is defined in this manner, flow investments in social capital should be observed by newspaper readership, phone call frequency, letter and electronic mail exchanges, the number of radio listeners and televiewers, and so on. We adopt a portion of such flow data and apply it to extend and estimate the augmented-Solow model of MRW by including social capital as an additional production input. Contrary to the standard reduced-form growth regression approach to the role of social capital in economic growth,3 our strategy enables us to estimate the structural parameters associated with aggregate returns to social capital. To preview our results, three important findings emerge from our empirical analysis. First, the upper bound of the output elasticity of social capital is estimated to be approximately 0.10. While social capital positively affects economic growth, the magnitude of the effect is smaller than that of physical and human capital and labor inputs. Second, the aggregate returns to social capital appear to be almost negligible for OECD countries. Yet, the returns are much higher for developing countries, which suggests that the aggregate effect of social capital is systematically related to the level of development. Third, the depreciation rate of social capital is estimated to be approximately 10% per annum and is considerably higher than that of physical capital. This may result from the fact that social capital is intangible and is, thus, easily eroded by nature unless continuous investment efforts are made. The remainder of this paper is organized as follows. In the next section, we briefly describe the procedure to augment the augmented-Solow model of MRW. Section 3 explains the data and our choice of variables in order to quantify the concept of social capital. In Section 4, we present the main empirical results of the augmented augmented-Solow model with the new social capital variables. We then consider the relationship between our estimates and those of the existing studies on the role of social capital in economic growth and calculate the aggregate return to social capital. Section 5 proffers a set of robustness tests of our empirical results. In the final section, we discuss the direction of future research. 2. The augmented augmented-Solow model We extend the MRW model by considering three types of capital input, i.e., physical capital, human capital, and social capital, which are denoted by K i ðtÞ; i ¼ k; h; s, respectively, in addition to labor input, LðtÞ and labor-augmenting technology level, AðtÞ.4 While we examine more flexible CES production functions and test the constant-returns-to-scale assumption in Section 5, the baseline specification is assumed to have the following constant-returns-to-scale Cobb–Douglas production function with share parameters for physical, human, and social capital, represented by a; b; and c, respectively:

YðtÞ ¼ K k ðtÞa K h ðtÞb K s ðtÞc ðAðtÞLðtÞÞ1abc ;

ð1Þ

2 Despite its simplicity, this structural approach is subject to the common problem of the Barro (1991) type regression, which has been criticized, for example, by Quah (1993, 1996), Brock and Durlauf (2001), and Durlauf et al. (2005). It is known that the convergence equation suffers from the problem of the mean reversion, i.e., Galton’s fallacy (Quah, 1993). Another problem is that the cross-country analysis contains a maximum of a couple of hundred observations, and all of the countries are inherently heterogenous. Later, we will explore several possible solutions to the heterogeneity problem, including the panel technique of Islam (1995), the sample splitting approach proposed by Hansen (2000), and the use of a more flexible function form, i.e., the constant elasticity of substitution (hereafter, CES) production function (Masanjala and Papageorgiou, 2004). Yet, as pointed out by Durlauf et al. (2005), these solutions require some assumptions on the data generating process. This issue is not specific to growth literature, but general to any type of structural estimations. In other words, we take all the required assumptions as granted in order to estimate the structural parameters. 3 For example, Knack and Keefer (1997), Temple and Johnson (1998), Helliwell and Putnam (1995), Zak and Knack (2001), Beugelsdijk et al. (2004). 4 Nonneman and Vanhoudt (1996) develop an augmented version of the augmented-Solow model that incorporates R&D investment. Our model replaces the R&D in their model with social capital. The model can also be regarded as a special case of Bajo-Rubio (2000).

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where we impose the assumptions that a; b; c 2 ½0; 1Þ and a þ b þ c 2 ½0; 1Þ. Following MRW, we postulate that the law of motion for each capital is common across the country, with the depreciation rate for the ith capital being di . The rate of the labor-augmenting technological progress is denoted by g, with the initial technology level, Að0Þ, which follows an internationally common distribution. The population growth rate is n and the time-invariant country-specific saving rates for ~i ¼ K i =AL. Then, ~ ¼ Y=AL and k each type of capital are represented by si ; i ¼ k; h; s. We define efficiency labor unit values as y under this environment, we can derive Solow’s basic equation in efficiency labor unit as follows:

~_ ¼ s y ~ k i i ~  ðn þ g þ di Þki ;

ð2Þ

~_ ¼ 0; thus, it is straightforward to show that the steady state per efficient labor income where i ¼ k; h; s. In the steady state, k i is expressed as follows:

~ ¼ y



sk n þ g þ dk

a 

sh n þ g þ dh

b 

ss n þ g þ ds

1 c !1ab c

:

ð3Þ

Suppose that the depreciation rate is the same for all types of capital, 8idi ¼ d,5 and that ln AðtÞ ¼ ln Að0Þ þ gt with ln Að0Þ ¼ a þ e, where e  Nð0; r2e Þ. Then, the log per capita income can be represented by the following equation:

ln

  YðtÞ a b c aþbþc ¼ a þ gt þ lnðsk Þ þ lnðsh Þ þ lnðss Þ  lnðn þ g LðtÞ 1abc 1abc 1abc 1abc þ dÞ þ e:

ð4Þ

This equation is a straightforward extension of the MRW level regression equation. This equation implies that if each country is in the steady state in year t, the log per capita income can be expressed as a log linear function of the saving rates for the three types of capital inputs, population growth rate plus g þ d,6 and a constant term, a þ gt, as well as a random error term, e. Following MRW, we estimate the level Eq. (4) in the following two ways. First, we estimate the unrestricted model by regressing log per capita income on the three saving rates and other variables on the right-hand side. Second, we estimate the following restricted model with parameter restrictions on a; b, and c:

ln

  YðtÞ a b c ¼ a þ gt þ ½lnðsk Þ  lnðn þ g þ dÞ þ ½lnðsh Þ  lnðn þ g þ dÞ þ LðtÞ 1abc 1abc 1abc  ½lnðss Þ  lnðn þ g þ dÞ þ e:

ð5Þ

Then, we employ the delta method to estimate the factor share parameters and their standard errors. Following MRW, we can also derive a growth equation on the transition path toward the steady state:

~ðtÞ  ln y ~ð0Þ ¼ h½ln y ~  ln y ~ð0Þ; ln y

ð6Þ

ðnþgþdÞð1abcÞt 7

~ and using the notation y  Y=L ¼ y ~A, we obtain the where h  1  ekt ¼ 1  e . By substituting Eq. (3) for y following convergence equation for the augmented augmented-Solow model:

ln

yðtÞ a b c aþbþc lnðsk Þ þ h lnðsh Þ þ h lnðss Þ  h lnðn ¼ ah þ gt þ h yð0Þ 1abc 1abc 1abc 1abc þ g þ dÞ  h ln yð0Þ þ he:

ð7Þ

The equation implies that under all the maintained assumptions, per capita income growth is explained by the determinants of the steady state income as well as the initial income level. In Eq. (7), k in h is the parameter representing the speed of convergence. Using Eq. (5) or a similarly restricted version of Eq. (7), we can explicitly estimate the factor share of the three capital stocks. 3. Data In order to construct the data set excluding social capital, we follow the data compilation procedure of MRW and Bernanke and Gürkaynak (2002), whereby the MRW model is reestimated using updated data until the year 1995. The other data sets that we employ include the following: the Penn World Tables (PWT) Mark 6.1, World Development Indicators (WDI) of World Bank (2003), and World Population Prospects (United Nations Population Division, 2005). The Data appendix explains the details of the data sources and provides a description of the variables employed in this paper.8 Durlauf and Fafchamps (2005) provides a comprehensive survey on empirical strategies to quantify social capital, both in the micro- and macro-contexts. In particular, our theory requires data on the saving rate of social capital accumulation in our

5 6 7 8

We examine the assumption later. We follow MRW and assume that g þ d ¼ 0:05. The procedure to derive Eq. (6) is available upon request from the corresponding author. The data set employed in this paper, which includes social capital, is available upon request.

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augmented MRW model. However, in addition to the fact that the concept of social capital remains elusive, almost none of the existing studies distinguish social capital stock from social capital investments. MRW argues that in general, when we estimate a variant of the augmented Solow model, the primary question is whether the available data on capital correspond more closely to the stock level of capital or to its saving rate. Since the theory requires the latter, we carefully elaborate a proxy variable for the saving rate of social capital.9 In the literature, there are two widely used macro variables of social capital. The first variable, called Trust, was compiled by Knack and Keefer (1997) using data from the World Values Surveys (World Values Study Group, 1999). This variable is constructed from the survey result of the following question: ‘‘Generally speaking, would you say that most people can be trusted, or that you can’t be too careful in dealing with people?” Trust is the percentage of respondents in each nation who replied that ‘‘most people can be trusted” after deleting the ‘‘don’t know” response. Therefore, this variable appears to capture the stock of social capital. The other variable is the social development indicator, SOCDEV, a composite variable of 41 social, political, and economic indicators, which was originally constructed by Adelman and Morris (1967), Temple and Johnson (1998). In the SOCDEV variable, Temple and Johnson (1998) concluded that the COMMS variable, which is a weighted average of the number of radios per head and the rate of newspaper circulation, is a good proxy for the strength of civic communities, reflected in trust and membership; thus, it is probably the best way to capture social capital. Since a radio is a durable good, the number of radios is considered a stock variable. On the other hand, newspaper circulation can be regarded as a flow variable that captures people’s savings and investments in shared knowledge, which is an important aspect of social capital, as highlighted in Ostrom (2000). Accordingly, we adopt the NEWS variable, which is defined as the number of daily newspapers circulated per 1000 people, as a proxy variable for the saving rate of social capital. The data is extracted from WDI. Other important investments in shared knowledge as social capital should be in the form of letter exchanges. Therefore, we also consider the POSTAL variable, which is defined as the average number of letter-post items posted per inhabitant, divided by 1000. The data is taken from the Universal Postal Union (Universal Postal Union, 2005).10 Data availability is another justification for the use of the NEWS and POSTAL variables. These two variables are easily obtainable for a larger set of countries and for a longer time period than the Trust and SOCDEV variables. As Zak and Knack (2001) indicated, the result of Knack and Keefer (1997) may suffer from a sample selection bias because their data is mainly derived from OECD countries. We may effectively mitigate this problem by using the NEWS and POSTAL variables, which are widely available in the cross-section of countries.11 We also perform a variety of robustness tests in order to check the validity of these two variables. 4. Estimation results This section is composed of four subsections. First, we present our main estimation results.12 Second, we compare our results with those in the existing reduced-form estimations. Third, we estimate the depreciation rate of social capital and thereby test the full depreciation hypothesis. Finally, we quantify the aggregate returns to social capital. 4.1. The augmented augmented-Solow model The first column of Table 1 displays our main results for the level Eqs. (4) and (5) with the NEWS variable. The adjusted R2 is improved from 0.78 of MRW to 0.81.13 The estimated output elasticity with respect to social capital, c, is 0.10 for the sample countries and is statistically significant. This result indicates that social capital positively and significantly affects economic growth, although the magnitude is smaller than that of the effects of physical and human capital.14 The second column of Table 1 summarizes the estimation results of the growth Eq. (7) with the NEWS variable. First, the adjusted R2 is 0.57 and the model fitness improves again if we compare the results with those of MRW. The c parameter is

9 For example, in the case of physical capital, the stock of the capital is measured by the capital stock in national accounts. The flow of physical capital is capital formation and the saving rate is captured by, for example, the net national saving rate. In the case of human capital, the Barro-Lee index of the average schooling level of the working-age population is widely used in growth regression and is regarded as a stock measure of human capital (Barro and Lee, 2000). The flow of human capital is rarely considered, whereas MRW quantifies the saving rate of human capital in terms of the percentage of the working-age population in secondary schools, i.e., Secondary enrollment ratio  (Population aged 15–19/Population aged 15–64). 10 In our data period (1960–2000), the importance of the Internet should be minimal; thus, we exclude it. 11 Both NEWS and POSTAL may be regarded as the degree of investments in social infrastructure capital, rather than those in social capital, which can be defined as an intensity of face-to-face communication or investments in local public goods. However, aggregate-level social capital should involve both these types of communication and investments. Accordingly, we believe that NEWS and POSTAL are not necessarily too crude to measure aggregate social capital. 12 We also replicate the MRW model using the original PWT 4.0 data, the PTW 6.0 data used by Bernanke and Gürkaynak (2002), and new data based on PTW 6.1 for the period 1960–1985. The results are reported in the full paper. 13 The lower block of the table reports the results of the restricted regression. The F-statistics and the corresponding p-value examine the validity of the restriction. The p-value for the model restriction suggests the invalidity of the restriction in this particular specification, but it is not a common result, as demonstrated later. The comparable MRW specification estimation is included in the full paper. 14 The estimated share parameters a and b are 0.19 and 0.23, respectively, and are smaller than the estimated parameters that are based on the augmentedSolow model. However, it is not easy to derive a plausible value for each share parameter a priori. If we follow the logic of MRW, in our augmented augmentedSolow model, the shares of physical and human capital would also be lower than those estimated by MRW. Moreover, while the production of social capital may require tangible inputs such as physical capital and labor, there will be no real compensation for social capital per se.

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Table 1 Augmented augmented-Solow model, 1960–2000 Model

Level

Growth

Level

Growth

Growth

Growth

Growth

Social capital

NEWS

NEWS

POSTAL

POSTAL

Latest Trust

Earliest Trust

SOCDEV

Number of observations

98

98

96

96

51

51

56

Constant

5.97 (1.19)

3.30 (1.03) 0.45 (0.08) 0.40 (0.09) 0.29 (0.10) 0.10 (0.04)

7.82 (1.27)

4.58 (1.13) 0.47 (0.08) 0.31 (0.10) 0.33 (0.09) 0.13 (0.04)

3.18 (1.28) 0.53 (0.09) 0.44 (0.12) 0.57 (0.14)

3.69 (1.30) 0.53 (0.09) 0.45 (0.11) 0.53 (0.14)

3.90 (1.58) 0.63 (0.11) 0.26 (0.10) 0.32 (0.13)

0.02 (0.09) 1.69 (0.43) 0.58 0.54 0.34 0.0189 (0.0049)

1.50 (0.43) 0.11 (0.10) 0.59 0.55 0.34 0.0187 (0.0048)

0.26 (0.11) 1.24 (0.51) 0.61 0.57 0.36 0.0251 (0.0076)

4.74 (0.78) 0.50 (0.09) 0.51 (0.11) 0.58 (0.14)

4.91 (0.77) 0.50 (0.09) 0.50 (0.11) 0.53 (0.14)

5.59 (0.92) 0.63 (0.11) 0.28 (0.10) 0.34 (0.13)

0.06 (0.09) 0.56 0.54 0.34 2.33 0.13 0.0173 (0.0046) 0.32 (0.06) 0.36 (0.06) 0.04 (0.06)

0.15 (0.09) 0.58 0.55 0.34 1.36 0.25 0.0110 (0.0049) 0.33 (0.06) 0.35 (0.06) 0.10 (0.06)

0.26 (0.11) 0.59 0.57 0.36 1.72 0.20 0.0116 (0.0042) 0.22 (0.08) 0.27 (0.08) 0.21 (0.11)

ln y60 ln sk ln sh ln ss

0.34 (0.12) 0.50 (0.11) 0.19 (0.05)

0.22 (0.12) 0.58 (0.10) 0.22 (0.04)

ln ks lnðn þ g þ dÞ R2 R2 s.e.e. Implied k Restricted model constant

2.20 (0.43) 0.82 0.81 0.51

1.15 (0.38) 0.59 0.57 0.41 0.0147 (0.0035)

1.61 (0.46) 0.83 0.82 0.49

0.82 (0.39) 0.60 0.58 0.40 0.0161 (0.0036)

9.01 (0.11)

4.05 (0.65) 0.42 (0.07) 0.42 (0.09) 0.29 (0.10) 0.10 (0.04)

9.40 (0.14)

4.71 (0.67) 0.47 (0.07) 0.31 (0.10) 0.32 (0.09) 0.13 (0.03)

ln y60 sk ln nþgþd sh ln nþgþd ss ln nþgþd

0.42 (0.12) 0.50 (0.12) 0.22 (0.05)

0.24 (0.12) 0.58 (0.10) 0.23 (0.04)

ln ks 2

R R2 s.e.e. F-stat.a p-valuea Implied k

0.81 0.81 0.52 6.61 0.01

Implied a

0.19 (0.05) 0.23 (0.05) 0.10 (0.03)

Implied b Implied c

0.58 0.57 0.41 0.86 0.36 0.0138 (0.0032) 0.34 (0.06) 0.23 (0.07) 0.08 (0.05)

0.83 0.82 0.49 1.58 0.21

0.12 (0.06) 0.28 (0.04) 0.11 (0.03)

0.60 0.58 0.40 0.02 0.89 0.0160 (0.0035) 0.25 (0.07) 0.26 (0.06) 0.11 (0.04)

Standard errors appear in parentheses. SOCDEV is not a logged variable. a Testing the restriction.

0.08 and is marginally significant. The rate of convergence, k, is comparable to the rate obtained by MRW and the model restrictions cannot be rejected, which supports the validity of our model. The third and fourth columns of Table 1 present the estimation results of the level and growth equations, respectively, using POSTAL as a variable for the saving rate of social capital. The quantitative results of estimated c are surprisingly similar to those obtained using the NEWS variable. The estimated c is 0.11 for both level and growth specifications. In sum, the overall estimation results of the augmented augmented-Solow model suggest that the inclusion of social capital as an additional production input generates improvements in the fitness of the Solow model. Moreover, the implied values of the structural parameters fall into the range of 0.08–0.11. 4.2. The reduced-form growth regression model vs. the augmented augmented-Solow model In this subsection, we explicitly compare the reduced-form growth regression approach by Knack and Keefer (1997) and Temple and Johnson (1998) with our augmented augmented-Solow model. While Knack and Keefer (1997) and Temple and

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Johnson (1998) adopt a standard approach by incorporating social capital into the Barro regression as an independent variable, this approach inhibits inferences on the relative contribution of social capital and other capital. Moreover, as is evident from Eqs. (4) and (7), it is difficult to justify the use of the stock value instead of the saving rate of social capital. Yet, there are at least two ways to justify the inclusion of the stock of social capital rather than the saving rate of social capital in Eqs. (4) and (7). First, we can work on a specification with the steady state condition. Second, we can assume the full depreciation of social capital. First, in the steady state, we can rewrite the level regression Eq. (4) in order to replace the saving rate of social capital with ~s =y ~_ s ¼ 0 in the steady state, from Solow’s basic Eq. (2) for social capital, we obtain ss ¼ ðn þ g þ ds Þk ~. its stock variable. Since k 15 By combining this with Eq. (4), we derive another representation of the level regression equation:

ln



YðtÞ LðtÞ

 ¼

1abc a b aþb c  ða þ gtÞ þ ln sk þ ln sh  lnðn þ g þ dÞ þ ln ks 1ab 1ab 1ab 1ab 1ab 1abc þ e: 1ab

ð8Þ

The corresponding growth equation is written as

ln

yðtÞ 1abc a b c aþb  ¼h a þ gt þ h lnðsk Þ þ h lnðsh Þ þ h ln ks  h lnðn þ g yð0Þ 1ab 1ab 1ab 1ab 1ab 1abc e: þ dÞ  h ln yð0Þ þ h 1ab

ð9Þ

Eq. (9) given above justifies the inclusion of the stock of social capital as an independent variable, suggesting the validity of Knack and Keefer (1997) and Zak and Knack (2001). Since it is advisable to employ the steady state level of social capital stock ðks Þ, we extract the Trust variable at the latest possible period and add it as an additional independent variable in the level and growth regression equations. The fifth column of Table 1 displays the estimation results of the growth Eq. (9) by including the latest Trust variable as an independent variable. The implied level of the elasticity, c, is 0.04, which is much smaller than the results obtained by the saving rate models. Moreover, this parameter is statistically insignificant. However, this result may suffer from an endogeneity bias; thus, it would be more plausible to employ social capital data for the earliest period possible. This is replicated in the following case. The second way to justify the use of social capital stock in the regression equation is to assume the full depreciation of social capital, i.e., ds ¼ 1. Under this assumption, we can show that the growth regression model becomes almost identical to that shown in Knack and Keefer (1997) and Temple and Johnson (1998). Note that with the assumption that ds ¼ 1, for all t it is straightforward to demonstrate that ss ¼ ð1 þ n þ gÞks ðtÞ=yðtÞ for all t. Combining this expression with the growth Eq. (7) under the assumption that dk ¼ dh ¼ d and ds ¼ 1, we obtain

ln

yðtÞ a b c aþb lnðsk Þ þ h lnðsh Þ þ h ln ks ð0Þ  h lnðn ¼ ah þ gt þ h yð0Þ 1abc 1abc 1abc 1abc   1ab þ g þ dÞ  h ln yð0Þ þ he: 1abc

ð10Þ

In this case, the equation includes the initial value of the stock of social capital. We estimate the regression Eq. (10) using the initial level of the social capital variables adopted by Knack and Keefer (1997) and Temple and Johnson (1998), i.e., Trust and SOCDEV, respectively. The last two columns of Table 1 proffer the estimation results with the full sample including the initial level of social capital16. With the initial Trust variable, the implied level of the elasticity, c, becomes 0.10, which is consistent with the previous estimates. On the other hand, with the SOCDEV variable, the estimated elasticity becomes approximately 0.2, which may necessitate further investigation. In sum, it can be said that we obtain structural parameter estimates that are largely consistent with the empirical results of Knack and Keefer (1997). However, the results of Temple and Johnson (1998) are not necessarily comparable to our estimated structural parameters in columns 1–4 of Table 1.17 4.3. Test of full depreciation In order to verify the validity of the full depreciation assumption in the last subsection, we estimate the depreciation rate for social capital. If we suppose that dk ¼ dh ¼ d and ds –d, the growth regression Eq. (7) can be rewritten as follows:

15 MRW derives this type of equation in their Eq. (12) for the case of human capital. It is also straightforward to derive a corresponding growth equation, which is Eq. (18) of Islam (1995). 16 Since SOCDEV takes negative values in some countries, we treat it as the log of the stock of social capital. One of the regression equations run by Temple and Johnson (1998) has exactly the same form as this growth regression, although they regard SOCDEV as a total factor productivity (TFP) shifter. 17 A possible reason for the similarities of the results for the stock variable, Trust, and the saving rate variable is a high correlation among these variables. The correlation coefficient of the saving rate variable, NEWS, with the stock variable, Trust, is 0.624. Accordingly, it is not surprising to obtain reasonable estimates, even when we utilize social capital stock variables.

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Table 2 Growth regressions for 1960–2000, nonlinear least squares estimation /0

/1

Coefficient 3.24 0.45 (S.E.) (0.99) (0.07) Number of observations = 98, SSR = 15.63, s.e.e. = 0.41 3.30

/2

/3

/4

/5

/6 ð¼ ds þ gÞ

0.40 (0.11)

0.29 (0.10)

1.10 (0.35)

0.10 (0.03)

0.12 (0.00)

0.10

0.05a

Corresponding OLS baseline parameters with restriction in Table 1 0.45 0.40 0.29 1.15

Heteroskedasticity robust standard errors appear in parentheses. Estimated by NLS using the Gauss–Newton method. Initial values are set as baseline OLS coefficients. a Imposed restriction.

ln

yðtÞ a b aþb lnðsk Þ þ h lnðsh Þ  h lnðn þ g þ dÞ  h ln yð0Þ ¼h yð0Þ 1abc 1abc 1abc   c ss ln þh þ ½gt þ h ln Að0Þ: 1abc n þ g þ ds

ð11Þ

Next, we postulate the estimation equation for Eq. (11):

ln

  yðtÞ ss ¼ /0 þ /1 lnðsk Þ þ /2 lnðsh Þ þ /3 lnðn þ g þ dÞ þ /4 ln yð0Þ þ /5 ln þ u; yð0Þ n þ /6

ð12Þ

where /i are the coefficients to be estimated. The coefficient of our interest is /6 because the model implies that /6 ¼ g þ ds . According to the reliable estimates of Young (1995) and Hsieh (2002) for high-performing East Asian countries as well as developed countries, g should be less than 2%. Hence, we can still obtain the lower bound of the depreciation rate. Eq. (12) is estimated by a nonlinear least squares (NLS) method. In Table 2, the estimated parameters are similar to those under the simplified estimation of Eq. (7) in Table 1 and the estimated value of ds þ g is approximately 12%, where the coefficient is statistically significant. Accordingly, it would be reasonable to consider that the lower-bound estimate of the depreciation rate of social capital is approximately 10% per annum. 18 The depreciation rate of social capital is much higher than that of physical capital, which is supposed to be approximately 3%–5% (Romer, 1989; Nadiri and Prucha, 1996). The result may suggest that unlike physical capital, continuous investments will be necessary in order to maintain a certain level of social capital. This may result from the fact that social capital is intangible and, thus, is easily eroded by nature, unless continuous investment efforts are made. 4.4. Aggregate returns to social capital By applying Eq. (8) of Nonneman and Vanhoudt (1996), the steady-state social returns to or net marginal productivities of each capital – the net depreciation of capital – can be expressed as

oY n þ g þ di  di ¼ wi  di ; oK i si

ð13Þ

where wi ¼ a; b; c corresponds to i ¼ k; h; s, respectively. On the basis of the estimation in the previous subsection, the depreciation rate of social capital is set at 10% per annum for the baseline calculation. Following Nonneman and Vanhoudt (1996), we assume that the depreciation rates for physical and human capital are both 3%. Figs. 1–3 represent kernel density functions of computed returns to physical, human, and social capital, respectively, based on Eq. (13) with the baseline parameter values of Table 3.19 Table 3 presents the median values of these returns for the full sample, intermediate income countries, sub-Saharan Africa, Latin America, (East, Southeast, and South) Asia, and OECD countries. We report the median values across countries in order to remove the effects of outliers. The third row represents the aggregate returns to social capital that are based on the NEWS variable with baseline parameters.20 The table indicates that the social rates of return are 19.11%, 8.17%, and 6.50% for full sample, intermediate income countries, and OECD countries, respectively. These returns are smaller than those to physical and human capital in the intermediate income and OECD countries. The aggregate return to social capital for developing economies, especially in sub-Saharan Africa, is considerably high, which reflects an extremely low accumulation of social capital. The aggregate return to social capital for OECD countries is negative, which 18 ^ 6 ¼ 1, we strongly reject the hypothesis that ds þ g ¼ 1. Hence, our data rejects the model of the full depreciation of By testing the null hypothesis that / social capital. However, it also rejects the assumption of MRW, i.e., di þ g ¼ 0:05, which was also employed in our previous estimates. Hence, the common depreciation assumption of MRW may generate biased results despite its greater tractability. 19 The more ‘‘formal” approach to our estimation may be to employ non-parametric estimations. An application of nonparametric estimation on growth empirics includes Quah (1993), Quah (1996), and Johnson (2005). 20 The results based on the POSTAL variable reveal considerably higher returns in developing countries. One possible reason for this is that saving rates based on POSTAL are unreasonably low in low-income countries.

383

2 0

1

Density

3

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H. Ishise, Y. Sawada / Journal of Macroeconomics 31 (2009) 376–393

0

.2

.4

.6

.8

1

rk

1.5 0

.5

1

Density

2

2.5

Fig. 1. Kernel density of return to physical capital (rk).

0

.5

1

1.5

2

2.5

rh Fig. 2. Kernel density of return to human capital (rh).

indicates the seriousness of the fallacy of composition, hypothesized by Durlauf and Fafchamps (2005) and Fafchamps (2006), in developed countries. While there is no systematic relationship between GDP per capita and returns to physical or human capital (Figs. 4 and 5), there appears to be a negative relation between the aggregate effect of social capital and the level of development (Fig. 6).

H. Ishise, Y. Sawada / Journal of Macroeconomics 31 (2009) 376–393

.6 0

.2

.4

Density

.8

1

384

0

1

2

3

4

rs Fig. 3. Kernel density of return to social capital (NEWS; rs).

Table 3 Median aggregate returns to physical, human, and social capital (%) Type of capital

Physical Human Social (NEWS) Physical Physical Human Human Social (NEWS) Social (NEWS) Social (NEWS) Social (NEWS) Social (NEWS)

Parameter values

Sample

Elasticity ðwi Þ

Depreciation ðdi Þ

Full

Inter-mediate

Sub-Saharan Africa

Latin America

Asia

OECD

0.34 0.23 0.08 0.20 0.25 0.20 0.25 0.10 0.10 0.20 variousa variousb

0.03 0.03 0.10 0.03 0.03 0.03 0.03 0.03 0.10 0.10 0.10 0.10

13.52 22.39 19.11 6.72 9.15 19.08 24.56 16.77 26.39 62.77 22.75 19.11

13.62 24.54 8.17 6.77 9.22 20.95 26.93 9.03 12.71 35.42 8.17 10.44

15.54 25.20 203.55 7.91 10.63 21.52 27.66 124.67 256.93 523.86 123.47 176.85

19.37 25.17 9.92 10.16 13.45 21.50 27.62 3.15 14.90 39.81  0.04 12.41

10.59 17.07 23.99 4.99 6.99 14.45 18.82 11.52 32.48 74.97 45.23 53.73

13.87 13.61 6.50 6.92 9.41 11.45 15.06 0.56 5.63 0.01 6.94 5.19

Estimation is based on Eq. (13). g is set at 0.02. a Using the ‘‘Average” in Table 6. b Using the ‘‘Median” in Table 6.

A possible interpretation of the negative correlation between the rate of return of social capital and the level of development could be that when an economy is underdeveloped, missing markets and market imperfections are major constraints on a wide variety of transactions (e.g., Aoki and Hayami, 2001; Besley, 1995). Under such a situation, social capital complements markets, which implies positive externality and, thus, creates aggregate benefits to the economy. In other words, social capital bridges the gap in formal market mechanisms through informal enforcement mechanisms. Yet, in a developed economy, the economic growth depends on technological progress, not capital accumulation. Moreover, development may create a variety of rents in the economy. Accordingly, social capital may generate individual profitability within a social capital network, but it has socially wasteful effects, i.e., the ‘‘fallacy of composition”. In terms of social returns to social capital, in developed economies, the negative effects of social capital may outweigh the market facilitation benefits. The results of level and growth regressions (Table 1) and aggregate returns to capital (Table 3, Fig. 6) can be summarized as follows. First, social capital tends to have level effects, but not growth effects. In MRW and our model, growth on the transition path is driven by two factors: the distance between initial income and the steady state level of income and the tech-

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1.2

1

rk

0.8

0.6

0.4

0.2

0 2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

4.3

4.5

log GDP/capita 2000 Fig. 4. Log of GDP per capita (2000) and return to physical capital.

2.5

2

rh

1.5

1

0.5

0 2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

4.3

4.5

log GDP/capita 2000 Fig. 5. Log of GDP per capita (2000) and return to human capital.

nological progress rate. The existence of level effects can be verified by the positive share parameter and saving rate of social capital. A consistent explanation for the lack of growth effects of social capital may be that the technological progress rate is only weakly related with the level or saving rate of social capital. This can occur if social capital involves a free rider problem or the fallacy of composition in the research and development process of new technologies. 5. Robustness analyses We conduct the following robustness analyses.21 First, we examine the validity of the Cobb–Douglas production function. Then, we address the issue related to the parameter heterogeneity. Finally, we conduct a set of further robustness analyses.

21

The results not included here appear in the full paper.

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4 3.5 3 2.5

rs

2 1.5 1 0.5 0 2.5 -0.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

4.3

4.5

log GDP/capita 2000 Fig. 6. Log of GDP per capita (2000) and return to social capital (NEWS).

5.1. The validity of the Cobb–Douglas specification While the Cobb–Douglas specification enables us to make a straightforward interpretation and draw clear comparisons to the literature, the constant returns to scale Cobb–Douglas production function might be a strong assumption. Following Masanjala and Papageorgiou (2004), we replace the Cobb–Douglas production function with the CES production function with social capital as an additional production input.22 Let the production function be

 1 YðtÞ ¼ aK k ðtÞq þ bK h ðtÞq þ cK s ðtÞq þ ð1  a  b  cÞðAðtÞLðtÞÞq q :

ð14Þ

As a straightforward extension of Eq. (6) in Masanjala and Papageorgiou (2004), the second-order approximation of the level and growth equations yield linear estimation equations, which can be estimated by OLS. However, we also estimate the structural parameters imposing the restriction implied by the model and using the NLS.23 Table 4 reports the estimation results. The OLS estimations of the specified models are in the upper block, and the lower block reports the implied coefficients obtained from the restricted model. The last row displays the estimated elasticity of the substitution parameter, q ¼ 1  1=r. If q ¼ 0 (i.e., r ¼ 1), the model is reduced to the Cobb–Douglas model. Only the first coefficient in Table 4 rejects the Cobb–Douglas specification, and the deviation from the Cobb–Douglas parameter is small, even in the first case.24 Moreover, we cannot reject the null hypothesis that c equals 0.1 in any of the specifications. 5.2. Potential heterogeneity25 We use two different methodologies to examine the issue of parameter heterogeneity. First, we relax the assumption of an internationally common initial productivity level by panel estimation to mitigate the endogeneity and omitted variable biases. In our estimations, we work with the fixed effect estimation for each five-year observation from 1975 to 1995. This fixed effect (or within) model also resolves potential heterogeneity in a linear manner. Since the POSTAL variable is not available as long panel data, we only employ NEWS as the social capital variable. We also perform panel estimations for each region. Table 5 presents the results of the pooled OLS and fixed effect (within) estimations. The estimation results are largely comparable to those of the baseline model. However, the implied physical capital share is small and the estimated c in the growth regression is insignificantly different from zero. This may reflect the fundamental difference of the level and growth 22 We also conduct a variant of the variable addition test to examine the validity of the constant returns to scale nature of the Cobb–Douglas production function. This particular test supports our baseline specification. Duffy and Papageorgiou (2000) also estimate the CES model using the stock of capital (not saving rate). However, we choose the method proposed by Masanjala and Papageorgiou (2004) because we have limited observations of the stock of social capital variable. 23 While the explanatory variables of the OLS estimations are presented in Table 4, the structural interpretations of the coefficients and implied restrictions are explained in the full paper. 24 This small deviation from the Cobb–Douglas model is comparable to the findings of Duffy and Papageorgiou (2000) and Masanjala and Papageorgiou (2004) for the augmented-Solow model. 25 See Brock and Durlauf (2001) and Durlauf et al. (2005) for a summary of these issues.

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H. Ishise, Y. Sawada / Journal of Macroeconomics 31 (2009) 376–393 Table 4 Augmented augmented-Solow model with the CES production function Model

Level

Growth

Level

Growth

Social capital

NEWS

NEWS

POSTAL

POSTAL

Number of observations

98

98

96

96

Constant

10.13 (1.33)

10.41 (1.54)

0.33 (0.29) 0.02 (0.23) 0.62 (0.13) 0.49 (0.52) 0.13 (0.13) 0.03 (0.13) 0.03 (0.03) 0.23 (0.09) 0.05 (0.05) 0.08 (0.06) 0.89 0.87 0.42

6.92 (1.47) 0.62 (0.10) 0.32 (0.27) 0.02 (0.21) 0.37 (0.14) 0.23 (0.49) 0.18 (0.12) 0.06 (0.12) 0.03 (0.03) 0.13 (0.09) 0.05 (0.05) 0.05 (0.06) 0.66 0.61 0.39

0.90 (0.34) 0.30 (0.32) 0.25 (0.13) 0.88 (0.58) 0.05 (0.13) 0.10 (0.14) 0.05 (0.05) 0.13 (0.11) 0.04 (0.05) 0.05 (0.04) 0.86 0.84 0.47

5.77 (1.55) 0.51 (0.09) 0.60 (0.29) 0.14 (0.27) 0.11 (0.11) 0.46 (0.50) 0.08 (0.11) 0.05 (0.12) 0.03 (0.05) 0.05 (0.09) 0.01 (0.05) 0.03 (0.04) 0.63 0.59 0.40

0.09 (0.12) 0.23 (0.14) 0.21 (0.09) 0.14 (0.04) 1.16 (0.05)

0.23 (0.18) 0.23 (0.19) 0.15 (0.11) 0.12 (0.07) 1.13 (0.08)

0.09 (0.12) 0.33 (0.12) 0.13 (0.06) 0.09 (0.06) 1.10 (0.07)

0.24 (0.19) 0.28 (0.17) 0.11 (0.09) 0.05 (0.10) 1.06 (0.11)

ln y60 ln sk ln sh ln ss lnðn þ g þ dÞ sk Þ2 ðln nþgþd



2 sh ln nþgþd



2 ss ln nþgþd

  

ln sshk ln sshs ln ssks

2 2 2

R2 R2 s.e.e. Restricted modela Implied a Implied b Implied c Implied q Implied

r

Heteroskedasticity robust standard errors appear in parentheses. a NLS estimated by the Gauss–Newton Method Initial values: the Cobb–Douglas case (Table 1).

regressions, as suggested in the baseline estimation.26 Table 6 summarizes panel estimation results for various subsamples along with the full-sample OLS estimations. In fact, the estimated c parameters for each group are not uniform, possibly due to fewer variations within the group and a limited number of observations. While the share parameter for sub-Saharan African countries is relatively small and that for Asia is large, the regional variation is not necessarily systematic and the difference does not alter the estimated returns to social capital in Table 3. Second, we follow Hansen (2000) to identify potential heterogeneity across samples. The method separates the sample into two groups on the basis of the chosen threshold variable. Following Hansen (2000) and Masanjala and Papageorgiou (2004), we select the initial income level and literacy rate as two potential threshold variables and implement the sample splitting test developed by Hansen (2000).27 Contrary to the detection of multiple regimes for the MRW specification by Hansen (2000), our augmented model has a unified regime when we use NEWS as a social capital variable (Table 7). This may suggest that the addition of social capital effectively captures the heterogeneity. The estimation result using the POSTAL variable as a proxy of social capital suggests the existence of multiple regimes, but the second stage splitting test does not support any meaningful evidence of further regimes. Table 8 provides the estimation results of each regime with the POSTAL variable. Interestingly, the estimated c for the high initial income group is similar to the baseline; however, c is much smaller for the low income group and is not statistically different from zero.

26 Alternatively, it can simply be attributed to the lack of reliable panel data to estimate the augmented augmented-Solow model because it is difficult to obtain data on saving rates for human and social capital for each year throughout the period. 27 The Matlab package is downloadable from Professor Bruce Hansen’s Web page, .

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Table 5 Panel estimation using NEWS, 1975–1995 Model method

Level pooled OLS

Level within

Growth pooled OLS

Growth within

Number of observations

468

468

468

468

Constant

7.64 (0.36)

ln yt1 0.22 (0.04) 0.18 (0.04) 0.31 (0.02) 1.21 (0.13) 0.42

ln sk ln sh ln ss lnðn þ g þ dÞ s.e.e. Implied k Restricted model constant

0.07 (0.03) 0.15 (0.03) 0.10 (0.03) 0.39 (0.13) 0.19

8.95 (0.04)

ln yt1 sk ln nþgþd sh ln nþgþd ss ln nþgþd

s.e.e. F-stat. p-value Implied k

0.25 (0.04) 0.17 (0.04) 0.33 (0.02) 0.43 13.38 0.00

0.08 (0.03) 0.15 (0.03) 0.10 (0.02) 0.19 0.29 0.59

0.14 (0.02) 0.10 (0.02) 0.19 (0.01)

0.06 (0.02) 0.11 (0.02) 0.07 (0.02)

Implied a Implied b Implied c

0.75 (0.16) 0.09 (0.01) 0.11 (0.01) 0.02 (0.01) 0.02 (0.01) 0.18 (0.04) 0.13 0.0025 (0.0004)

0.23 (0.03) 0.11 (0.02) 0.01 (0.02) 0.01 (0.01) 0.19 (0.07) 0.11 0.0065 (0.0008)

0.83 (0.12) 0.09 (0.01) 0.11 (0.01) 0.01 (0.01) 0.02 (0.01) 0.13 0.67 0.41 0.0024 (0.0004) 0.47 (0.04) 0.06 (0.04) 0.09 (0.04)

0.23 (0.03) 0.11 (0.02) 0.01 (0.02) 0.01 (0.01) 0.11 1.85 0.17 0.0066 (0.0008) 0.24 (0.04) 0.02 (0.05) 0.03 (0.05)

Standard errors appear in parentheses.

Table 6 Summary of the estimated c coefficients for each subsample estimation Model

Social capital

Method

Full

Inter-mediate

Sub-Saharan Africa

Latin America

Asia

OECD

Level

NEWS

OLS

0.10 (0.03) 0.11 (0.03) 0.19 (0.01) 0.07 (0.02) 0.08 (0.05) 0.11 (0.04) 0.09 (0.04) 0.03 (0.05)

0.10 (0.03) 0.09 (0.03) 0.19 (0.01) 0.07 (0.02) 0.09 (0.05) 0.09 (0.05) 0.05 (0.05) 0.08 (0.06)

0.01 (0.09) [33] 0.09 (0.07) [32] 0.10 (0.02) [132] 0.07 (0.03) [132] 0.02 (0.13) [33] 0.09 (0.10) [32] 0.07 (0.12) [132] 0.02 (0.07) [132]

0.06 (0.05) [22] 0.17 (0.07) [22] 0.23 (0.02) [102] 0.08 (0.06) [102] 0.07 (0.10) [22] 0.25 (0.11) [22] 0.10 (0.11) [102] 0.47 (0.30) [102]

0.23 (0.08) [12] 0.11 (0.09)[12] 0.18 (0.04) [60] 0.10 (0.04) [60] 0.25 (0.11) [12] 0.12 (0.15) [12] 0.17 (0.13) [60] 0.12 (0.22) [60]

0.19 (0.07) [23] 0.24 (0.04) [22] 0.14 (0.03) [126] 0.16 (0.10) [126] 0.07 (0.14) [23] 0.20 (0.07) [22] 0.03 (0.05) [126] 0.13 (0.11) [126]

0.05 0.07

0.04 0.09

0.13 0.15

0.07 0.11

Level

POSTAL

OLS

Level

NEWS

Pooled OLS

Level

NEWS

Within

Growth

NEWS

OLS

Growth

POSTAL

OLS

Growth

NEWS

Pooled OLS

Growth

NEWS

Within Average c Median c

0.09 0.10

[98] [96] [468] [468] [98] [96] [468] [468]

0.08 0.09

[76] [74] [384] [384] [76] [74] [384] [384]

Standard errors appear in parentheses. The number of observations appear in square brackets.

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H. Ishise, Y. Sawada / Journal of Macroeconomics 31 (2009) 376–393 Table 7 Sample splitting test à la Hansen (2000) Social capital

Level

Sample

Number of Observations

Threshold variable

Threshold estimate

Bootstrap p-value

NEWS

First

Full Full Full Full

91 91 88 88

y60 LR60a y60 LR60a

2467.3 49.0 2467.3 49.0

0.55 0.28 0.02 0.16

y60 > 2467:3 y60 > 2467:3 y60 6 2467:3 y60 6 2467:3

59 59 29 29

y60 LR60a y60 LR60a

8990.9 61.0 1491.6 27.0

0.59 0.18 0.38 0.18

First POSTAL

Second

Number of high

Number of low

59

29

The estimation is based on Hansen’s matlab package for sample splitting tests. The number of bootstrap replications is 1000. The trimming percentage is 0.15. The errors allow for heteroskedasticity. a Literacy rate in 1960.

Table 8 Multiple regime growth regression with the POSTAL variable Regime

Y 1960 L1960

Number of observations Constant

59 7.34 (0.76) 0.77 (0.08) 0.37 (0.11) 0.27 (0.10) 0.18 (0.03) 0.29 0.23 (0.06) 0.17 (0.06) 0.11 (0.03)

ln y60 ln sk  lnðn þ g þ dÞ ln sh  lnðn þ g þ dÞ ln ss  lnðn þ g þ dÞ s.e.e. Implied a Implied b Implied c

> 2467:3

Y 1960 L1960

6 2467:3

29 5.93 (1.55) 0.71 (0.20) 0.29 (0.14) 0.45 (0.13) 0.03 (0.08) 0.46 0.20 (0.11) 0.31 (0.07) 0.19 (0.17)

The estimation is based on Hansen’s matlab package for the sample splitting estimation. The coefficients are estimated by restricted regressions. Heteroskedasticity robust standard errors appear in parentheses.

5.3. Further robustness issues This subsection represents results from further robustness analyses. The main results are summarized in Table 9.28 First, we simultaneously employ the NEWS and POSTAL variables because they do not necessarily capture the same aspect of social capital. While the former is likely to track the degree of impersonal public knowledge sharing, the latter captures private, mostly bilateral, information sharing. The estimation results, which are not reported in this paper (available from the corresponding author) suggest that POSTAL has a higher share than NEWS, which implies that peer-to-peer information sharing is more important in facilitating aggregate production than public knowledge sharing, which may be sufficiently achieved, particularly in developed countries. Second, in order to eliminate the potential endogeneity bias of the saving rates of social capital, instrumental variable (IV) estimation is conducted.29 The instruments include all of the values in 1960, the area size of each country (in log form), and the damages of capital stock caused by World War II (Cook, 2002). To estimate the IV model, we use the efficient two-step generalized method of moments (GMM) estimation, which provides heteroskedasticity-consistent estimators. If we include n þ g þ d; sk , and sh as our instruments, the estimated c falls in the range of 0.06–0.11, which is close to that of the OLS estimates (Table 9). Accordingly, we may conclude that the test results support the reliability of the results that are based on OLS. Third, we employ an alternative set of variables for social capital. Following Knack and Keefer (1997), we utilize the GROUPS variable as a proxy for the saving rate of social capital, which is defined as the average number of groups cited

28 29

The detailed results are reported in the full paper. For example, social capital is more likely to be created when income is higher, which implies a reversed causality (Fafchamps, 2006).

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H. Ishise, Y. Sawada / Journal of Macroeconomics 31 (2009) 376–393

Table 9 Summary of robustness checks Estimated c Coefficient

(S.E.)

Social capital

Number of Observations

Model

R2 or p-value of Hansen’s J

Estimation method

0.08 0.01 0.21 0.18 0.11 0.03 0.03 0.03 0.09 0.06 0.10 0.11

(0.24) (0.32) (0.11) (0.07) (0.04) (0.04) (0.03) (0.03) (0.04) (0.03) (0.03) (0.03)

NEWS POSTAL NEWS POSTAL NEWS GROUPS O-GROUPS P-GROUPS NEWS NEWS NEWS POSTAL

78 75 38 37 38 33 33 33 98 93 98 98

Level Level Level Level Level Level Level Level Level Level Level Level

p-value = 0.53 p-value = 0.67 p-value = 0.96 p-value = 0.49 p-value = 0.58 R2 ¼ 0:87 R2 ¼ 0:87 R2 ¼ 0:87 R2 ¼ 0:85 R2 ¼ 0:88 R2 ¼ 0:82 R2 ¼ 0:84

Efficient Efficient Efficient Efficient Efficient OLS OLS OLS OLS RWLS OLS OLS

GMMa GMMa GMMa GMMa GMMb

0.27 0.05 0.15 0.18 0.06 0.01 0.02 0.03 0.08 0.05 0.09 0.10

(0.37) (0.53) (0.19) (0.07) (0.04) (0.06) (0.05) (0.05) (0.05) (0.04) (0.05) (0.04)

NEWS POSTAL NEWS POSTAL NEWS GROUPS O-GROUPS P-GROUPS NEWS NEWS NEWS POSTAL

38 37 38 37 38 33 33 33 98 93 98 96

Growth Growth Growth Growth Growth Growth Growth Growth Growth Growth Growth Growth

p-value = 0.85 p-value = 0.34 p-value = 0.94 p-value = 0.34 p-value = 0.37 R2 ¼ 0:62 R2 ¼ 0:63 R2 ¼ 0:63 R2 ¼ 0:64 R2 ¼ 0:71 R2 ¼ 0:61 R2 ¼ 0:61

Efficient Efficient Efficient Efficient Efficient OLS OLS OLS OLS RWLS OLS OLS

GMMa GMMa GMMa GMMa GMMb

Average c Median c

Level 0.09 0.09

Growth 0.09 0.07

Overall 0.09 0.08

a b c

Note IV: IV: IV: IV: IV:

Baselinec Baselinec Baselinec and Cook’s WWII Baselinec and Cook’s WWII Baselinec and Cook’s WWII

Including regional dummies Dependent variable is GDP per capita Dependent variable is GDP per capita IV: IV: IV: IV: IV:

Baselinec Baselinec Baselinec and Cook’s WWII Baselinec and Cook’s WWII Baselinec and Cook’s WWII

Including regional dummies Dependent variable is GDP per capita Dependent variable is GDP per capita

Saving rates ðsk ; sh ; ss Þ and n þ g þ d are treated as endogenous variables. Saving rate of social capital ðss Þ is treated as an endogenous variable. Constant, log of area (km2), GDP/worker in 1960, Barro-Lee index in 1960, sk in 1960, sh in 1960, price of consumption and investment goods in 1960.

per respondent in each country. The definitions of GROUPS, Putnam-esque groups (P-GROUPS), and Olsonian groups (OGROUPS) closely follow Knack and Keefer (1997).30 Table 9 proffers the estimated c coefficients using the GROUPS variables. With the P-GROUPS and O-GROUPS variables, the estimated level of c is much smaller than the results using NEWS or POSTAL and is statistically insignificant. We may attribute these results to an attenuation bias due to measurement errors or to the lack of sufficient number of observations. Fourth, we employ a procedure developed by Temple (1998) to eliminate outliers. Before checking for outliers, we follow Temple (1998) and include regional dummy variables. Then we employ the least trimmed squares method, which was proposed by Rousseeuw (1984) and Rousseeuw and Leroy (1987). Then, after eliminating the identified outliers,31 we estimate the models using only in-sample observations.32 This procedure is regarded as a simplified version of the reweighted least squares (RWLS). The level regression result reported in Table 9 is comparable to the baseline results. Finally, following the recommendation of Hoeffler (2002), the GDP per worker is replaced with the GDP per capita because the use of GDP per worker may suffer from an endogenous change in the labor supply structure (Hoeffler, 2002). Our quantitative results are essentially similar to our baseline regression results. According to the bottom row of Table 9, the point estimates of c are distributed around its mean value, 0.09. The point estimate of c is more stable in the level regression than in the growth regression. Moreover, the model fitness is better in the level regression (see Table 1).

30 The GROUPS include (a) social welfare services for elderly, handicapped, or deprived people; (b) religious or church organizations; (c) education, arts, music, or cultural activities; (d) trade unions; (e) political parties or groups; (f) local community action on issues like poverty, employment, housing, racial equality; (g) third world development or human rights; (h) conservation, the environment, ecology; (i) professional associations; and (j) youth work, e.g., scouts, guides, youth clubs. Groups b, c, and j are identified as Putnam-esque groups, while groups d, e, and i are groups with redistributive goals and are called Olsonian groups (Putnam et al., 1993; Olson, 1982; Knack and Keefer, 1997). 31 See the full paper, which lists all the trimmed samples. 32 In order to mitigate the computational burden, we slightly modified the method. Once the outliers are identified, they are all excluded from the secondstage sample.

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6. Concluding remarks In this paper, by augmenting the augmented-Solow model of MRW, we constructed and implemented an empirical model to uncover the aggregate output elasticity of social capital, which characterizes the aggregate returns to social capital. Considering the recent developments in empirical studies on social capital, we believe that we take one step forward in quantifying the role of social capital in comparison with other production inputs. Our empirical results reveal that while social capital significantly contributes to economic growth, the upper bound of the elasticity of social capital to output is approximately 0.1 and is significantly smaller than that of physical and human capital. This small but significantly positive effect of social capital is moderately robust after treating various econometric issues. As a by-product, our estimation results indicate that the depreciation rate of social capital is at least 10% per annum, which is significantly higher than that of physical capital. The cross-country medians of the aggregate returns to social capital that are based on the NEWS variable are 19.11%, 8.17%, and 6.50% for the full sample, intermediate income countries, and OECD countries, respectively. These returns are generally smaller than those to physical and human capital. In particular, the value for OECD countries is negative. If we compare our results with those of microstudies on social capital, it is much smaller for these countries. Our results support the view that the measurement of social capital in developed countries involves a serious fallacy of composition – arising from collusive behavior among group members – rather than positive externalities (Durlauf and Fafchamps, 2005; Fafchamps, 2006). Moreover, the aggregate effect of social capital appears to be negatively related to the level of development. However, some issues remain in our analysis. First, while quantifying social capital is difficult, it will be rewarding to seek more appropriate measures of social capital in future studies. This paper should be regarded as the starting point of the structural approaches to estimating the effect of social capital on economic growth. Second, admittedly, structural approaches have their inherent cost; it is not easy to test the validity of theoretical structure per se. In our context, we employed a variant of the canonical Solow model that imposes a specific set of assumptions on the data generating process in order to estimate the structural parameters, following the standard tradition of the structural estimation. Finally, besides social capital, which was our focus, other variables can be regarded as important production inputs that generate economic growth. Our framework is easily extended to estimate the structural parameters of other variables in the context of growth models. Such extensions may be carefully investigated in future studies. Acknowledgements This project has been supported by the JSPS Center of Excellence (COE) Program Grant provided to the Research Center for the Relationship between Market Economy and Non-Market Institutions (CEMANO), Faculty of Economics, University of Tokyo. We would like to thank the editor, Chris Papageorgiou, and an anonymous referee of the journal for their constructive review comments and suggestions. We would also like to thank Marcel Fafchamps, Yujiro Hayami, Nazrul Islam, Ryuzo Sato, the seminar participants at Korea and Kyoto Universities, and the 2006 Far Eastern Meeting of the Econometric Society held in Beijing for their useful comments. The full version of the paper and the data set are available upon request from the corresponding author. Appendix A. Data appendix A.1. Data sources Data is extracted from five cross-country data sets: Penn World Table Mark 6.1 (PWT) (Heston et al., 2002) World Development Indicators (WDI) (World Bank, 2003) World Population Prospects (WPP) (United Nations Population Division, 2005) World Values Survey (WVS) (World Values Study Group, 1999; Inglehart et al., 2003; European Values Study Group and World Values Survey Association, 2005)  Postal Statistics (Universal Postal Union, 2005)

   

We also use the data set of Mankiw et al. (1992), which is available on Gregory Mankiw’s Web page,33 and that of Bernanke and Gürkaynak (2002), which is available on Ben Bernanke’s Web page.34 The variables denoted as ‘‘Cook’s WW II” are obtained from Cook (Cook, 2002).35 33 34 35

. . The complete data set employed in this paper is available upon request.

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A.2. Variable construction Each variable is set as follows. Note that except for the saving rate of social capital, we reproduce the estimation strategy of Mankiw et al. (1992) and/or Bernanke and Gürkaynak (2002).  yð¼ Y=LÞ: Constant price GDP per capita times working-age population ratio. The GDP per capita is taken from PWT, and the working-age population rate is taken from WDI.  n: Working-age population growth rate, calculated from WDI’s working-age population data.  g þ d: Set at 0.05 following MRW.  sk ð¼ I=YÞ: The average share of real investment (including government investment) in real GDP. This is taken from PWT. sk in 1960 is used as one of the instruments.  sh (School): Secondary enrollment ratio  (Population aged 15–19/Population aged 15–64). These population rates are taken from WPP. The secondary enrollment ratio is taken from WDI.  ss : The main results use daily newspaper circulation (NEWS) from WDI. We take the average of each five-year period from 1975 to 1995 because the data set includes each five-year periods beginning from 1975. For 2000, the countries whose data are collected are limited and the growing presence of information technology probably leads to a fall in the importance of newspapers; thus, we delete data for the year 2000. POSTAL is the average number of letter-post items posted per inhabitant, divided by 1000. The data is obtained from the Postal Statistics. Since the data is accumulated annually after 1980, we take the annual average from 1980 to 2000. GROUPS and its subcategories are calculated from WVS. The definitions of GROUPS, O-GROUPS, and P-GROUPS are those of Knack and Keefer (1997). GROUPS divided by 10 and the others by 3 provides the total number for the category in each index. Note that the division (by 1000; 10; 3) is perfectly arbitrary because of the log-linear form of the estimation models.  Trust (earliest possible data): The Trust measure is taken from WVS. If more than two data are available for a country, we select the measure for the earliest period possible. This is the method followed in Knack and Keefer (1997), Zak and Knack (2001), and Beugelsdijk et al. (2004).  Trust (latest possible data): The Trust measure is taken from WVS. The only difference is to choose the index from the latest available data.  SOCDEV: Drawn from, Adelman and Morris (1967, p. 170). It is exactly the same index used by Temple and Johnson (1998).  Barro-Lee: Average years of schooling of the working-age population, which corresponds to the years in Barro and Lee (2000).  Area: Each country’s area in 1995, taken from WDI.  Price of consumption (or investment) goods in 1960: obtained from PWT.  Cook’s WW II: These are indices related to the damages on capital stock caused by World War II, which were constructed by Cook (2002).

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