Accounting for Productivity Growth: Schumpeterian versus Semi-Endogenous Explanations

Transcription

1 Accounting for Productivity Growth: Schumpeterian versus Semi-Endogenous Explanations Johannes W. Fedderke and Yang Liu ERSA working paper 554 October 2015 Economic Research Southern Africa (ERSA) is a research programme funded by the National Treasury of South Africa. The views expressed are those of the author(s) and do not necessarily represent those of the funder, ERSA or the author s affiliated institution(s). ERSA shall not be liable to any person for inaccurate information or opinions contained herein.

2 Accounting for Productivity Growth: Schumpeterian versus Semi-Endogenous Explanations Johannes W. Fedderke, Yang Liu Abstract This paper examines the nature and sources of productivity growth in South African manufacturing sectors, in international comparative perspective. On panel data estimations, we find that the evidence tends to support Schumpeterian explanations of productivity growth for a panel of countries including both developed and developing countries, and a panel of the South African manufacturing sectors. By contrast, for a panel of OECD manufacturing sectors, semi-endogenous productivity growth is supported. However, we also report evidence that suggests that sectors are not homogeneous. For this reason time series evidence may be more reliable than panel data. Time series evidence for South Africa suggests that prospects for the sustained productivity growth associated with Schumpeterian innovation processes, is restricted to a narrow set of sectors, strongly associated with the chemicals and related sectors, machinery and transport equipment, and basic iron and steel sectors. Semi-endogenous growth finds much weaker support. For the OECD manufacturing sectors, both semi-endogenous and Schumpeterian growth finds support, with semi-endogenous growth more prevalent than for South African manufacturing. The sustained productivity growth associated with Schumpeterian growth frameworks is relatively rare everywhere. (JEL: O47).

3 I. Introduction Sustained productivity growth is not readily achieved under standard growth theory. Under constant returns to scale production technology, steady state precludes increases in per capita welfare, save for exogenous growth in production technology. While under endogenous growth theory sustained productivity growth through investment in knowledge creation and the factors of production that generate knowledge is feasible, the strong rates of return to knowledge required in order to realize the increasing returns to scale requisite for sustained productivity growth have been challenged empirically. The result has been a debate between those who find a falling technological growth rate in the face of an accumulating knowledge base, and those who find the growth rate to be constant and undiminishing in rising stocks of knowledge. Endogenous growth optimism concerning the possibility of sustainable productivity growth is integral to the standard accounts of Schumpeterian growth (see Aghion and Howitt, 1992, and Romer, 1990), and was held to be empirically consistent with the observation of divergent per capita income over the post-colonial and industrialization eras. Empirical challenges to the theory rested on observations of strong increases in research and development personnel in the United States, which should have led to an commensurate increase in economic growth rates according to the Schumpeterian growththeory,but didnot(jones 1995a, 1995b). In response, semi endogenous theory gives up the assumption that knowledge growth is subject to constant returns to scale in knowledge, with the result that the growth of knowledge would decrease as the knowledge stock increases, finally eliminating knowledge creation as a source of sustainable productivity growth (Jones, 1995a, 1995b). By contrast, Type II Schumpeterian growth models maintain a constant return to scale in knowledge, and accountforthenon-responseofproductivitygrowthtoincreasing& personnel by pointing outthatthe& input is spread ever more thinly over a proliferating set of intermediate inputs into production with rising levels of per capita GDP. The increased & input does 1

4 not represent a deepening of & intensity, merely a broader dispersion of the input over more intermediate inputs. Empirical findings are divergent. Ha and Howitt (2007) find support for Type II Schumpeterian productivity growth in an analysis of the U.S. manufacturing sector. Similarly Madsen (2008) reports time series findings that are consistent with Type II Schumpeterian productivity growth, though the theory is unable to account for cross-country total factor productivity growth rates. On the other hand, Barcenilla-Visús et al (2014) report that panel data evidence from a panel of 10 manufacturing sectors across six OECD countries is consistent with semi-endogenous productivity growth. Which of these two competing theoretical frameworks holds matters profoundly for any country seeking sustained growth, in an immediate sense. Under semi-endogenous productivity growth, investment in knowledge is no more a source of sustained welfare improvement than investment in standard factors of production under constant returns to scale production technology. By contrast, under Schumpeterian productivity growth, investment in knowledge does offer the prospect of sustained productivity growth. For policy makers it is important to know what returns might be expected from investment in knowledge resources. In this paper we revisit the ongoing debate. We innovate in three senses. First, we compare the support to emerge for the two theoretical propositions across a range of distinct data sets, including panel data for developed and developing countries, a middle income country (South Africa) manufacturing sector, as well as OECD manufacturing sectors. Second, we employ a range of estimation methodologies, to explore the sensitivity of results to alternative estimators. Third, we take seriously the possibility of sector heterogeneity by estimating sector-specific results by means of time series methodologies. Under panel estimation, our results are mixed. For country-level data, which includes both developed and developing countries, as well as for the South African manufacturing sectors, results consistently favor the Schumpeterian account of productivity growth. By contrast, for the six OECD country manufacturing sectors, panel results favour semi-endogenous 2

5 productivity growth. The panel data results also provide evidence of sector heterogeneity, such that panel data estimation may hide significant sector differences. The South African time series evidence confirms the presence of sector heterogeneity. Specifically, we find that productivity growth in South African manufacturing is likely to be significantly constrained, since Schumpeterian productivity growth is concentrated in the chemicals and related sectors, machinery and transport equipment, and basic iron and steel sectors. OECD manufacturing sectors also prove heterogeneous, with the preponderance of sectors being consistent with semi-endogenous productivity growth, though arguably Schumpeterian productivity growth is also more prevalent than in South African manufacturing. The remainder of the paper is distributed as follows. Section II. reviews the theoretical background, and section III. the associated empirical methodology. In section IV. we report the data, in V. the estimation results, and section VI. wraps up the findings. II. Semi-endogenous and Type II Schumpeterian Growth Theory Under standard neoclassical growth theory, 1 the assumption of constant returns to scale in production technology ensures a declining marginal product of capital. This allows for the standard growth decomposition: (1) = ( ) µ µ ( ) = + = + + µ µ µ + µ µ µ where denotes output, capital, labor, the technology scaling factor, and,the elasticity of output with respect to capital and labor respectively. This clarifies that under standard capital accumulation, such that = = = (with denoting savings, the savings rate, and investment), and exogenous demographic growth, such that 3

6 is effectively a constant over extended time periods, the only source of sustained growth in growth in in excess of the steady state condition of =, willbelocatedin technology,. This is reinforced by the empirical regularity that in developed countries approximately 75% of long growth is attributable to total factor productivity ()growth ( ), substantially overshadowing the contribution of factor accumulation. 2 The South African evidence mirrors the international evidence, in the sense that growth has come to be increasingly reliant on, rather than factor accumulation. 3 The resultant onus to account for the source of technological progress, as met by Schumpeteriangrowththeory, 4 places the long-run source of knowledge accumulation in a knowledge producing sector. Thus, for instance, if final output continues to be produced under constant returns to scale: (2) ( )= X =1 1 where notation is defined as before, denotes the intermediate inputs, human capital engaged in final goods production, production will again be subject to steady state, and sustained growth of output feasible only if 0. Under the increased varieties approach (Romer, 1990) of Schumpeterian theory, the proposed production function of knowledge is simply: (3) = = where denotes the human capital employed in the production of knowledge (as opposed to employed in the production of final goods), denotes the accumulated stock of knowledge, and denotes a productivity (research success) factor. The linearity of the knowledge µ µ production function has the consequence that = 2 2 =0, such that there is no diminishing product of the input into knowledge production. The result is that knowledge growth is unbounded under non-diminishing incentives to invest in tech- 4

7 nology, with symmetrical results for output growth, if these Schumpeterian conditions for knowledge creation are met. In addition, the non-declining returns are also present for the level of knowledge accumulation, = 2 2 =0. The radical prediction, while consistent with the experience of accelerating output and technological growth over the course of the industrial revolution, 5 and suggestions of essentially boundless scope for knowledge accretion, 6 also faced immediate empirical challenge. Specifically, while empirical findings have confirmed a positive impact of & on, the magnitude of the impact fell well short of the strength predicted by Schumpeterian theory. For instance, while the number of & scientists and engineers in the USA increased by 500% over the period, the growth rate of both and has remained unchanged - directly contradicting the predictions of the Schumpeterian theory. 7 Here we consider the implications of two broad responses to this empirical contradiction. A generalization of the Schumpeterian knowledge production function might specify: (4) = 0 1 where denotes the input into knowledge production, such as human capital allocated to & ( ), or the productivity adjusted flow of & expenditure (). It follows that µ µ = 1 0, 2 2 = ( 1) 2 0, aweaker inference than under (3), though the strength of response to remains undiminished. We term this the Schumpeterian Type I formulation. that: Under the "semi-endogenous" growth formulation, in addition Jones (1995b) proposed (5) = such that now µ = ( 1) 2 0. The implication is that as technology becomes more complex ( increases), sustained growth in & labour is required 5

8 to maintain a constant rate of growth. The prediction is that long-run growth, hence per capita GDP growth, is again bounded by the population growth rate, returning the prediction to that of the neoclassical growth model, in which steady state growth is given by the natural rate of growth. 8 An alternative response retains the Schumpeterian framework, while accounting for the Jones (1995a, 1995b) empirical contradiction. Under this approach, the assumption of constant returns to knowledge creation is retained. The empirical contradiction is accounted for by noting that over time, intermediate input product proliferation has a negative effect on productivity growth, since product variety dilutes the impact of & over an ever-increasing array of projects/innovation streams. 9 Now: (6) = µ 0 1 where, denoting product variety, is generally held to be proportional to population size (), output ( ) or the number of patent registrations. Thus growth in the & input,, may be neutralized by the growth in intermediate product variety, accounting for the apparent empirical contradiction of Schumpeterian Type I theory. The normalization of the & input on product variety, provides what we term Schumpeterian Type II theory. A general (nested) formulation, encompassing both semi-endogenous and Schumpeterian Type II theory, is then: (7) = µ 1 with Schumpeterian Type I theory predicting that 0, =1, =0, semi-endogenous theory predicting that 0, 1, =0, and Schumpeterian Type II theory predicting that 0, =1, =1. Neoclassical theory is the restrictive case in which =0, =1. 6

9 Theory: σ φ β Neoclassical =0 =1 n/a Schumpeter 1 0 =1 =0 Semi-endogenous 0 1 =0 Schumpeter 2 0 =1 =1 Table 1: Theory Predictions Table 1 summarizes. III. Empirical Methodology The general nested formulation provided by equation (7), now provides an immediate means of testing for the predictions of semi-endogenous and Schumpeterian theory. Specifically the general model that nests the competing hypotheses provides the empirical specification: (8) ln ( )=ln + ln µ +( 1) ln where denotes the growth rate of, would provide direct estimates of the critical relevant parameters,,. ³ The difficulty is that if ln ( ) (0) and ln ln (1), specification (8) would not be balanced, and would lead to spurious estimation inferences. Hence, confirmation of any of the competing theories would then require that: (9) (10) (11) µ (0) ln + ln +( 1) ln µ 1 = ln = C + ln + ln (0) µ µ 1 ln = C + ln (0) with (1 ) =0confirming Schumpeter Type II theory, and (1 ) 0 confirming semi-endogenous theory in both (10) and (11). In the (10) specification, Schumpeter Type 7

10 II theory requires =1, while semi-endogenous theory requires =0. The discussion in Ha and Howitt (2007) and Madsen (2008) elaborates. As an alternative specification, from (6) we can specify: µ (12) ln =ln + ln ln + ln µ which, provided that ln (1), asitmustbeifln ( ) (0), andln, ln, ln, (1), allows for a direct estimation of both the and parameters. 10 This identification of the precise parameter magnitudes is not feasible under the (10), (11), specifications. In the present study we confirm first that ln ( ) (0), such that testing under (10), (11) or (12) is required. We proceed accordingly. A. Time Series Estimator The time series methodology is the standard VECM approach. The estimation technique is standard, so that our exposition is brief. 11 Consider the general VAR (Vector Autoregressive Estimation) specification given by: (13) = where is a 1 matrix, is the lag length, deterministic terms and a Gaussian error term. Reparametrization provides the VECM specification: X 1 (14) = Γ + Π =1 where Π = 0.Wereferto as the loading matrix, containing the short-run dynamics, while is the matrix containing the long run equilibrium (cointegrating) relationships. The rank,, of the matrix represents the number of cointegrating vectors and is tested for using the 8

11 standard Trace and Maximal Eigenvalue test statistics. Where 1 issues of identification arise. 12 Just identification can proceed by means of restrictions on, orγ. 13 B. Pooled Mean Group Estimator In the panel data estimation, amongst others we employ the Pooled Mean Group (PMG) estimator of Pesaran, Shin and Smith (1999). Consider the unrestricted error correction ARDL( ) representation: 1 1 X X (15) = 1 + β 0 x δ 0 x + + =1 =0 where =12 =12, denote the cross section units and time periods respectively. Here is a scalar dependent variable, x ( 1) a vector of (weakly exogenous) regressors for group, and represents fixed effects. Allow the disturbances s to be independently distributed across and, with zero means and variances 2 0, andassume that 0 for all. Then there exists a long-run relationship between and x : (16) = θ 0 x + =1 2 =1 2 where θ = β 0 is the 1 vector of the long-run coefficients, and s are stationary with possibly non-zero means (including fixed effects). This allows (15) to be written as: 1 1 X X (17) = δ 0 x + + =1 =0 where 1 is the error correction term given by (16), and thus is the error correction coefficient measuring the speed of adjustment towards the long-run equilibrium. This general framework allows the formulation of the PMG estimator, which allows the intercepts, short-run coefficients and error variances to differ freely across groups, but the long-run coefficients to be homogenous; i.e. θ = θ. Group-specific short-runcoeffi- 9

12 cients and the common long-run coefficients are computed by pooled maximum likelihood estimation. Denoting these estimators by, β,, δ and θ, we obtain the PMG estimators by ˆ =1 =1 =, ˆβ =, ˆ =1 =, = 1 1, and =1 ˆδ = =0 1 ˆθ = θ. PMG estimation provides an intermediate case between the dynamic fixed effects (DFE) estimator which imposes the homogeneity assumption for all parameters except for the fixed effects, and the mean group (MG) estimator proposed by Pesaran and Smith (1995), which allows for heterogeneity of all parameters. It exploits the statistical power offered by the panel through long-run homogeneity, while still admitting short-run heterogeneity. The crucial question is whether the assumption of long-run homogeneity is justified, given the threat of inefficiency and inconsistency noted by Pesaran and Smith (1995). We employ a Hausman (1978) test (hereafter test) on the difference between MG and PMG estimates of long-run coefficients to test for long run heterogeneity. 14 Finally, it is worth pointing out that a crucial advantage of the estimation approach of the present paper, is that the dynamics generally argued to be inherent in the growth process are explicitly modelled, while recognizing the presence of a long run equilibrium relationship underlying the dynamics. Thus the justification for the use of the PMG estimator is that it is consistent both with the underlying theory of an homogenous long-run productivity growth relationship and the possibly heterogeneous dynamic time series nature of the data. IV. Data In this study we employ three distinct data sets. The three data sets have the advantage that they present country-level data, for countries at diverse levels of development, countryspecific data for a wide range of sectors within the country, and country and sectoral data for developed economies. This allows us to explore whether the inferences drawn are conditional on the type of data employed, as well as the level of development of the case studies being employed for the study. 10

13 The first data set is comprised of panel data for 13 countries, drawn from the ISIC and World Bank databases from 1996 to We employ country level data, since for many developing countries sectoral data on & expenditure is not readily available, forcing the use of aggregate country-level data. The second data set is given by the South African manufacturing panel data set of Fedderke (2006), for 25 manufacturing sectors from 1973 to Unfortunately the South African data had to be truncated in 1993, since no reliable & data exists after the 1993 time point on a sectoral level. The third data set is given by the Barcenilla-Visús et al (2014) panel data for 6 OECD countries, and 10 manufacturing sectors, from the STAN database from to In terms of estimation, we employ both panel estimators (all three data sets), and time series estimators (the South African and OECD data). Data across the following dimensions was collected: : & input, measured by the Gross Domestic Expenditure on & (GERD) data, normalized on the level of : level, : total employment, measured either as the number of employees (all data sets), or total working hours (OECD) : GDP of country/sector : patents applied for by residents of a country The variables are all the conventionally used in the measurement for product variety. 11

14 Panel 1 Panel 2 Panel 3 Panel 1 Panel 2 Panel 3 Panel Unit Root Tests: Hadri Test Statistic ln ln (0) (1) (0) (1) (0) (1) 083 [020] 078 [022] 194 [097] 418 [100] 1008 [000] 2642 [000] 077 [022] 185 [032] 1127 [000] 2660 [000] 056 [029] 147 [007] [100] [100] [000] [083] [000] [073] ln ln ln ln (0) (1) (0) (1) (0) (1) 1181 [000] 2624 [000] 7161 [000] 146 [007] 080 [021] 170 [096] 788 [000] 027 [039] 1195 [000] 1498 [000] 7587 [000] 055 [071] 8954 [000] 069 [024] 059 [028] 315 [100] Figures in square parentheses are probability values *,**,*** denotes rejection of the null of stationarity at the 1, 5 and 10% levels of significance Table 2: Hadri Unit Root Test V. Estimation Results The regression methods being applied on the 3 panels include Pooled Mean Group (PMG) estimation, Mean Group (MG) estimation, Generalized Method of Moments (GMM), as well as the Ordinary Least Squares (OLS) and Fixed Effects (FE). A. Panel Estimation Results ³ We find that the anticipated possibility that ln ( ) (0) and ln ln (1), is confirmed for our panel data sets. We report the Hadri test for the order of integration of the data, which is defined under the null that the series being tested is stationary, in Table 2. As demonstrated by the test statistics, we confirm that the growth rate of is stationary in levels (hence necessarily in first differences), while both the & input measure (including when normalized on product variety) and the level of prove to be level nonstationary. The panel estimation results are reported in Tables 3 through 5. 12

15 We begin with the estimation of the general specification given by, (10), with no restriction placed on either the or (1 ) parameters, reported in Table 3. Estimation is for Panel 1 (13 country sample), Panel 2 (25 South African manufacturing sectors), and Panel 3 (6 OECD country data for 10 manufacturing sectors). In each case we estimate under generalized methods of moments (GMM), and pooled mean group (PMG) estimators, so as to control for the possibility of endogeneity. For both Panel 1 and Panel 2, results consistently confirm that the (1 ) -coefficient on the level of knowledge,, is statistically significantly 0, such that 1 provided only that the elasticity of & with respect to the growth of knowledge, 0. Thisfinding is invariant to which proxy for product variety is employed (employment, output, or patents), and invariant to whether we employ the GMM or PMG estimators. The implication is thus that the Schumpeterian condition that the response of & to the state of knowledge be at least proportional, is met. In addition, for Panel 1, we find that the -coefficient on our proxy for product variety,, is consistently statistically significantly 0, suchthat& responds positively to product variety. This finding is invariant to which proxy for product variety is employed (employment, output, or patents), and invariant to whether we employ the GMM or PMG estimators. For Panel 2, the findings are mixed. Where the proxy for product variety is given by employment, in Panel 2 we find 0 irrespective of PMG or GMM estimation, though where product variety is given by value added, 0 for the GMM estimator, while 0under the PMG estimator. Note also that where 0is confirmed, the stricter Schumpeterian requirement that =1is generally not supported statistically. The findings for Panels 1 and 2 are thus mixed. For Panel 1 (13 country data set) the findings support Schumpeterian Type II productivity growth. For Panel 2, findings are mixed, with strongly proportional response of & to the level of knowledge, consistent with Schumpeterian Type II productivity growth, but without strictly robust confirmation of the & response to product variety required by Schumpeterian theory. Two possibilities might 13

16 account for this inconsistency. One is that the proxy for product variety (employment, value added) is imperfect at best, especially in the case of employment, which for South Africa is subject to the outcomes dictated by an inefficient labour market. Another is indicated by the rejection of the long-run homogeneity by the Hausman test statistic in at least some of the Panel 2 specifications, which suggests that sector specific timeseriesevidencemaybe more reliable than panel data evidence. Finally, note that the results for Panel 3 (6 OECD countries, with 10 manufacturing sectors) differ starkly from those reported for Panels 1 and 2. Results consistently confirm that the (1 ) -coefficient on the level of knowledge,, is statistically significantly 0, suchthat1 again provided that the elasticity of & with respect to the growth of knowledge, 0. Thisfinding is invariant to which proxy for product variety is employed (employment, output, or working hours), and invariant to whether we employ the GMM or PMG estimators. Reassuringly, this confirms the findings of Barcenilla-Visús et al (2014) on the Panel 3 data, which employed dynamic ordinary least squares estimation. The implication is thus that the semi-endogenous growth condition that the response of R&D to the state of knowledge be less than proportional, is met. For the -coefficient on our proxy for product variety,, results are mixed. Where employment is the proxy for product variety, we find 0 under both PMG and GMM estimation, with value added as proxy, 0 under both PMG and GMM estimators, while with working hours as proxy we have 0 under PMG and 0 under GMM estimation. Note also that the strict semi-endogenous theoretical requirement that =0is nowhere met. To test the robustness of these results, we undertook two additional sets of estimations. First, we reestimated the (10) specification under the restriction that =0,thusforcinga strict semi-endogenous structure on our data. Results are reported in Table 4. In addition, we estimated with pooled OLS (OLS), fixed effects(fe), GMM, PMG, aswellasmean group (MG) estimators. Despite the =0restriction, we continue to find consistently that 1 for both Panels 1 and 2 ((1 ) 0), while for Panel 3 1 under all estimators 14

17 Estimation Results under (10) Measure of Panel 1 Panel 2 Panel 3 Product Variety: PMG GMM PMG GMM PMG GMM Employment (L) 081 h-statistic ( 4766) 085 (1068) 187 [039] Output (Y) 160 h-statistic ( 2262) 157 (1459) 539 [007] Patents (P) 095 h-statistic ( 3327) 043 (2898) 199 [037] 041 ( 2600) 035 (1712) 089 ( 3632) 079 (3137) 073 ( 5572) 045 (5046) 093 ( 790) 006 ( 043) 590 [005] 138 ( 1686) 036 ( 554) 013 [093] 186 ( 4743) 016 ( 436) 224 ( 5211) 089 (2572) 035 (419) 168 (1109) 042 [081] 187 (3042) 142 (4146) 171 [042] Working Hours (WH) 054 h-statistic (1660) 172 (800) 067 [072] Coefficients: (1 ) for ; for The h-statistic is the Hausman test under the null of long-run homogeneity Figures in round parentheses are t-statistics Figures in square parentheses are probability values ***, **, * denotes significance at the 1, 5 and 10% levels Table 3: Panel Estimation Results I 119 (6641) 026 (845) 192 (7375) 082 ( 6873) 115 (6379) 007 ( 233) Panel 1 Panel 2 Panel 3 Estimation Results under (10) with =0restriction OLS FE GMM PMG MG coeff. h-stat 040 ( 798) 136 ( 1249) 109 (2030) 081 ( 1428) 135 ( 1236) 113 (2085) 024 ( 1780) 189 ( 5012) 114 (6396) 091 ( 2202) 395 ( 985) 011 ( 167) 026 [061] 025 [061] 016 [069] 10 6 ( 353) 599 ( 148) 046 ( 052) Coefficients: (1 ) The h-statistic is the Hausman test under the null of long-run homogeneity Figures in round parentheses are t-statistics Figures in square parentheses are probability values ***, **, * denotes significance at the 1, 5 and 10% levels Table 4: Panel Estimation Results II 15

18 Estimation Results under (10) with =1restriction Measure of OLS FE GMM PMG MG Product Variety coeff. h-stat Employment 078 ( 368) Panel 1 Output 016 Patent ( 401) 022 (411) Panel 2 Employment 145 Output Employment ( 1315) 175 ( 1452) 023 (410) Panel 3 Output 089 Working Hours ( 819) 024 (419) 077 ( 1052) 035 ( 639) 034 (610) 143 ( 1302) 174 ( 1437) 028 (504) 079 ( 720) 030 (513) 081 ( 7862) 012 ( 1420) 038 ( 2469) 235 ( 5857) 233 ( 5309) 029 (1617) 082 ( 1844) 132 (1739) 079 ( 4023) 080 ( 2067) 067 (731) 035 ( 160) 098 ( 608) 055 ( 1355) 246 ( 2898) 059 ( 1816) 002 [089] 060 [044] 007 [079] 120 [027] 001 [092] 003 [086] 003 [087] 069 [041] Coefficients: (1 ) The h-statistic is the Hausman test under the null of long-run homogeneity Figures in round parentheses are t-statistics Figures in square parentheses are probability values ***, **, * denotes significance at the 1, 5 and 10% levels Table 5: Panel Estimation Results III 072 ( 129) 015 ( 137) 054 (114) 2015 (108) 038 ( 007) 078 ( 058) 219 ( 130) 082 (048) other than the PMG and MG. Thus the finding that the conditions of Schumpeterian theory are satisfied for Panel 1 and 2, while the conditions for semi-endogenous growth theory are confirmed for Panel 3, emerges for estimation under the =0restriction also. Second, we reestimated the (10) specification under the restriction that =1,thus forcing a strict Schumpeterian structure on our data. Again, we estimated under pooled OLS (OLS), fixed effects (FE), GMM, PMG, as well as mean group (MG) estimators. Again results are broadly consistent to those reported for the -neutral specification of Table 3. For Panels 1 and 2, irrespective of estimator, we consistently find that 1, asrequired by Schumpeterian theory, irrespective of which proxy for product variety is employed. The only exceptions emerge for Panel 1, where Patents proxy for product variety, where 1. Conversely, for Panel 3 (OECD), we find that 1, as required by semi-endogenous theory, except where product variety is proxied for by value added, or under PMG and MG estimation. 16

19 In summary of the panel data evidence, our results from the panel data estimation are thus not conclusive. Evidence for both Schumpeterian and semi-endogenous growth theory emerges, though the evidence is never entirely consistent with the strict theoretical requirements of either framework. Surprisingly, the Schumpeterian case is also strongest for the data set that includes developing countries, and the middle income case of South Africa, and weakest for the set of 6 developed OECD economies of Panel 3. One possible reason for the observed inconsistencies that attaches to all the reported estimations, is that the proxies employed for product variety are imperfect at best. However, given that these measures are standard in studies of this type, and since more reliable measures of product variety are not available, this limitation is not easily remedied. A second explanation of the panel result inconsistencies is that the panel estimators are being employed across potentially heterogeneous sectors (as indicated under PMG estimation), which include semi-endogenous, Schumpeterian, and neoclassical productivity growth consistent processes. For this reason, examination of disaggregated sectoral time series evidence is desirable, to allow for the possibility that the innovation process is not homogeneous across sectors. B. Time Series Estimation Results Given our concerns regarding the possibility of heterogeneity across sectors, we also estimated the association between,the& input, product variety (), and the level of by means of time series methodology for the South African and OECD data. To do so, we employed the (12) specification,soastobeabletoidentifythe and parameters directly. There are two estimation issue that needs to be addressed in the (12) specification that we employ for the time series evidence. In the event that ln (1), it follows that strictly the absolute change in cannot be stationary, (0), sinceln (1) implies that the proportional growth rate of is stationary, (0). However, in the event that tests µ for stationarity are applied to ln (as we do), the log compression of scale may make 17

20 the non-stationarity of the absolute changes difficult to detect. Additional concerns arise from the poor power and size characteristics of unit root tests in the presence of small samples and MA processes in the data. To correct for any tendency of stationarity tests to over-reject the null in favour of stationarity, we err on the side of caution and impose a 1% level of significance throughout our examination of the univariate time series characteristics of the data. The South African Results. We consider sector specific results for 25 South African manufacturing sectors. Despite our concerns regarding the robustness of univariate stationarity tests, as Table 6 shows we consistently find that all of the variables under the (12) specification test (1). For all sectors, and all variables, we report an (1) structureatthe1%levelofsignificance (with thesoleexceptionofln for Wearing Apparel, and ln for Basic Chemicals, which test (1) at the 1.42% and 1.1% levels of significance). We therefore proceed with the estimation of (12) under the VECM methodology, using both employment and GDP as proxies for product variety. Sector specific results are reported in Tables 7 and 8. We report the Trace statistic () fortherankoftheπ-matrix for the null of =0against the alternative that 0, 16 the estimated and coefficients, the estimated error correction term in order to test for stability of the equilibrium adjustment ( 2 0), and additionally whether the cointegrating vector manifests stability under a one standard deviation shock. We also test for the parameter equality across the ln ( ) and ln ( ) variables implied by specification (12) under the null of parameter equality. The estimation results confirm the implication drawn from the panel evidence, of sector heterogeneity. Recall also that the two theories accounting for productivity growth have specific parameter requirements. For semi-endogenous productivity growth, the requirement is that 0and 1. For Schumpeterian productivity growth by contrast the restrictions are 0and 1. Neoclassical productivity growth requires =0and =1. We summarize the detailed findings in terms of implied sector classifications in Table 9. 18

21 µ ln ln ln () ln ( ) ln I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) Food Beverages Tobacco Textiles Wear. Appar Leather Footwear Wood Paper Coke&RP Basic Chem Other Chem Rubber Plastic Glass NMetal. Ind BasIr&St.l BasNFerr Met Metal Products Machinery Electrical Motor Other Trans Furniture Other Indus *,, denote significance at 1%, 1.1% and 1.42% levels respectively Table 6: Augmented Dickey Fuller Test Statistics 19

22 Under these parameter restrictions, six sectors satisfy the strict requirements for Schumpeterian productivity growth ( 0, 1). A further six sectors are weakly consistent with Schumpeterian productivity growth, in the sense of returning =0and 1. Two sectors provided the 1 estimate required by Schumpeterian productivity growth, but the more puzzling finding of 0. Only a single sector fulfilled the requirements of neoclassical productivity growth. Semi-endogenous productivity growth finds only incomplete support. No sector fulfills the strictest requirement for semi-endogenous productivity growth ( 0, 0 1), and only two sectors the weaker requirement of =0, 0 1. However, a number of sectors report a finding of =0, which technically satisfies the requirement that the parameter fall belowunity,thoughitdoesimplythatthereisnoimpactatallonthetimerateofchange of technology in the level of technology. For two sectors =0is paired with a finding of 0, for seven with =0. For one sector we find that =0and 0. Finally, for six sectors the requirement of a unique cointegrating vector under the estimation of (12) is not satisfied, such that these sectors cannot be classified under any of the productivity growth theories. In summary, we note that industry characteristics are certainly heterogeneous, suggesting that time series estimation is a useful supplement to the panel data findings. In addition, the time series evidence favours Schumpeterian productivity growth with greater preponderance (in the strict sense) than it does semi-endogenous productivity growth for South African manufacturing. This finding is thus consistent with the implication drawn from the panel data evidence for South African manufacturing. Note also that Schumpeterian growth appears to be associated with the chemicals and related sectors, Machinery and Transport equipment, and Basic iron and steel. While there is thus good news in terms of the prospect for sustained productivity growth, this is tempered by the fact that the prospects of sustained productivity growth is relatively narrowly focussed amongst South African manufacturing sectors. 20

23 µ Results for: ln =ln + ln ln + ln Sector Prod. Var. Trace lnx lnq lna ecm = Stable Meas. ( 1) c Food L 1 Y 1 Beverages L (037) Y (032) Tobacco L (027) Y (056) Textiles L 1 Y (022) Wearing L (022) Apparel Y 1 Leather L 1 Y 1 Footwear L (018) Y (011) Wood L (015) Y (009) Paper L (011) Y (014) Coke&RP L (036) Y (052) BasChem L (017) Y 1 OthChem L (053) Y 1 Rubber L (090) Y (076) Plastic L (117) Y (141) 031 (094) 029 (036) 198 (108) 299 (123) 329 (081) 299 (107) 012 (041) 018 (033) 258 (156) 053 (057) 038 (086) 096 (062) 039 (031) 004 (025) 108 (013) 031 (054) 179 (328) 374 (139) 018 (117) 183 (103) 140 (066) 108 (060) 141 (049) 091 (074) 265 (061) 055 (065) 127 (082) 036 (051) 107 (065) 062 (058) 056 (030) 052 (022) 210 (054) 220 (072) 210 (027) 266 (106) 192 (111) 595 (100) 012 (185) 028 (190) 045 (025) 043 (025) 093 (021) 076 (018) 080 (019) 108 (023) 110 (011) 104 (011) 071 (021) 069 (021) 060 (023) 066 (023) 058 (031) 060 (028) 079 (028) 082 (022) 077 (023) 060 (018) 108 (024) 097 (024) 004 [085] 018 [067] 253 [011] 124 [027] 452 [003] 293 [009] 008 [078] 001 [094] 238 [012] 128 [026] 009 [076] 116 [028] 201 [016] 102 [031] 1923 [000] 057 [045] 006 [080] 061 [043] 002 [088] 130 [025] Table 7: South African Manufacturing Sector VECM Estimation Results I 21

24 µ Results for: ln =ln + ln ln + ln Sector Prod. Var. Trace lnx lnq lna ecm = Stable Meas. ( 1) c Glass L (020) 105 (107) 083 (085) 061 [044] Y (020) NMetMin L 1 Y (010) BIroSteel L (021) Y (024) Basic NFer L (028) Metals Y 1 MetProd L 1 Y 1 Machinery L (013) Y (008) Elec L 1 Mach Y 1 Motor L 1 Y 1 Other L 1 Transport Y (001) Furn L 1 Y 1 Other L (006) Industry Y (004) 053 (075) 243 (061) 100 (073) 051 (092) 121 (121) 065 (091) 088 (037) 018 ( 008) 005 (117) 131 (007) 024 (086) 023 (040) 306 (068) 316 (091) 080 (029) 191 (050) 311 (047) 156 (012) 105 (029) 028 (101) 079 (023) 083 (022) 105 (020) 077 (029) 078 (028) 115 (030) 075 (023) 070 (020) 055 (052) 088 (027) 090 (027) 018 [067] 793 [000] 083 [036] 003 [086] 023 [063] 071 [040] 131 [025] 190 [017] 0001 [098] 121 [027] Table 8: South African Manufacturing Sector VECM Estimation Results II 22

25 0 =0 0 1 =1 1 0 Wear.App Textiles ( ) Bas. Chem. ( ) =0 Beverages (Y) Paper Oth. Ind. (L) Beverages (L) Footwear BasNonFerrMin Coke & RP Wood (L) Oth. Chem. Plastic Rubber (L) Glass BasIronSteel NonMetMin Machinery (L) Oth. Ind. (Y) 0 Tobacco (Y) Tobacco (L) Wood (Y) Textiles ( ) Bas. Chem. ( ) Rubber (Y) Machinery (Y) Oth. Transport r1 Food Leather Met Prod Elec.Mach. Motor Furniture Y,L indicate estimation under GDP and Employment product variety. Results are consistent where neither product variety proxy (Y or L) is indicated. indicates elasticity parameter under R&D input and product variety respectively. Results are consistent where neither elasticity parameter ( ) is indicated. Table 9: Time Series Data South African Industry Classification 23

26 The OECD Evidence. We consider sector specific results for 10 manufacturing sectors, for 6 OECD countries, providing results for a total of 60 sectors. The univariate time series characteristics of the data are reported in Tables 10 and 11. In general, all sectors and all variables report an (1) structure. There are only two qualifications. First, the presence of a structural break in the early 1990s for a number of countries necessitated the use of the Perron (1989) version of the ADF test statistic, under the critical values reported in Perron (1989, 1990). This applied most extensively to the employment and working hour time series, and especially for Finland. Second, the poor power characteristics of unit root tests is in evidence for the employment and working hour series particularly for France, and to a lesser degree in Spain, with the tests struggling to establish even (1). Under this caveat, given the theoretical implausibility of an (2) structure, our estimation proceeds under the assumption that all series are stationary in first differences. We therefore proceed with the estimation of (12) under the VECM methodology, using employment (), GDP ( )andworkinghours() as proxies for product variety. Sector specific results are reported in Tables 12 and 17. We report the Trace statistic () forthe rank of the Π-matrix for the null of =0against the alternative that 0, 17 the estimated and coefficients, the estimated error correction term in order to test for stability of the equilibrium adjustment ( 2 0), and additionally whether the cointegrating vector manifests stability under a one standard deviation shock. We also test for the parameter equality across the ln ( )andln ( ) variables implied by specification (12) under the null of parameter equality. The estimation results again confirm the implication drawn from the panel evidence of sector heterogeneity, under the classification requirements implied by the theoretical requirements of semi-endogenous growth ( 0, 1), Schumpeterian productivity growth ( 0, 1), or neoclassical productivity growth ( =0, =1). Again we summarize the detailed estimation evidence in terms of the implied sectoral classification in Tables 18 24

27 µ ln ln ln () ln ( ) ln () ln Canada I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) Food Textiles Paper Chemicals Rubber NMM B&F Met Machinery Elec Transport Finland Food # # # # Textiles # # # # Paper # # # # Chemicals # # # # Rubber # # # # NMM # # # # B&F Met # # # # Machinery # # # # Elec # # # # Transport # # # France Food Textiles # # # # Paper Chemicals Rubber NMM B&F Met Machinery Elec Transport *,, denote significance at 1%, 2.5% and 5% respectively. # denotes Perron test under structural break. Table 10: Augmented Dickey Fuller Test Statistics 25

28 µ ln ln ln () ln ( ) ln () ln Italy I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) Food Textiles Paper Chemicals Rubber NMM # # # # B&F Met Machinery Elec Transport Spain Food Textiles Paper Chemicals Rubber NMM B&F Met Machinery Elec Transport USA Food Textiles # # Paper Chemicals Rubber NMM B&F Met Machinery Elec Transport *,, denote significance at 1%, 2.5% and 5% respectively. # denotes Perron test under structural break. Table 11: Augmented Dickey Fuller Test Statistics 26

29 and 19. Under these parameter restrictions, nine sectors satisfy the strict requirements for Schumpeterian productivity growth ( 0, 1). A further seven sectors are weakly consistent with Schumpeterian productivity growth, in the sense of returning =0and 1. Five sectors provided the 1 estimate required by Schumpeterian productivity growth, but also 0. Neoclassical productivity growth again finds little support, with only one sectors potentially satisfying the parameter restrictions. While semi-endogenous productivity growth again finds only incomplete support, it does so for a greater proportion of sectors (compared to South African manufacturing). No sector fulfills the strictest requirement for semi-endogenous productivity growth ( 0, 0 1), and two sectors satisfy the weaker requirement of =0, 0 1. However, a number of sectors report a finding of =0, which technically satisfies the requirement that the parameter fall below unity, though it does imply that there is no impact at all on the time rate of change of technology in the level of technology. For fourteen sectors =0is paired with a finding of 0. For nineteen sectors =0is paired with a finding of =0, while for eight sectors, we find that =0and 0. While in South African manufacturing no estimation result returned a finding of 0, for the OECD this is the case for a number of sectors. Again, while technically satisfying the 1 requirement of semi-endogenous theory, it carries the even more dramatic implication that the time rate of change technology declines in the level of technology. For ten sectors, 0 and 0, for two sectors 0 and =0, and for four sectors, 0 and 0. Finally, for 12 sectors the requirement of a unique cointegrating vector under the estimation of (12) is not satisfied, such that these sectors cannot be classified under any of the productivity growth theories. In summary, as for South African manufacturing, OECD industry characteristics are certainly heterogeneous, again suggesting that time series estimation is a useful supplement 27

30 µ Results for: ln =ln + ln ln + ln Sector Prod. Cointegration lnx lnq lna ecm = Stable ( 1) c Food L (079) Y (115) WH (077) Textiles L 1 Y (021) WH 1 Paper L (023) 1 Y WH 1 Chem. L (067) Y 1 WH 1 Rubber L 1 Y 1 WH 1 NMM L (046) Y (041) WH (048) B&F.Met. L 1 Y 1 1 WH Machinery L (039) Y (044) WH (036) Elec. L (828) Y (571) WH (2256) Trapsp. L (011) Y (015) WH (011) 291 (247) 256 (290) 295 (283) 122 (096) 269 (101) 547 (163) 358 (104) 440 (123) 302 (108) 050 (073) 106 (085) 094 (063) 3837 (2043) 1282 (1558) 7749 (5798) 001 (024) 033 (022) 003 (022) 220 (177) 511 (320) 209 (190) 638 (093) 088 (087) 359 (072) 194 (129) 710 (152) 243 (133) 154 (057) 288 (111) 152 (055) 6536 (394) 1884 (1829) (1043) 121 (014) 077 (034) 120 (014) Table 12: Canada VECM Time Series Evidecne (032) 092 (029) 095 (031) 101 (031) 073 (026) 017 (023) 083 (025) 083 (027) 082 (025) 076 (024) 077 (025) 078 (025) 002 (79 3) 003 (002) 001 (0003) 096 (011) 095 (011) 096 (011) 139 [024] 125 [026] 114 [029] 329 [007] 4 43 [004] 262 [011] 346 [006] 433 [004] 205 [015] 025 [061] 070 [040] 102 [031] 077 [038] 177 [018] 113 [029] 000 [096] 090 [034] 004 [084] No No No

31 µ Results for: ln =ln + ln ln + ln Sector Prod. Cointegration lnx lnq lna ecm = Stable Variety ( 1) c 124 Food L (049) Y (049) WH (049) Textiles L (032) Y (041) WH (042) Paper L (038) Y (045) WH (043) Chem. L (087) Y (103) WH (077) Rubber L (036) Y (037) WH (033) NMM L (036) Y (035) WH (037) B&F Met. L 1 Y 1 1 WH Machinery L (067) Y (067) WH (068) Elec.. L (054) Y (055) WH (050) Trapsp. L (027) Y (000) WH (026) (237) 379 (382) 070 (198) 034 (032) 050 (049) 044 (040) 347 (145) 574 (274) 345 (142) 4382 (743) 2005 (542) 2734 (539) 217 (119) 272 (154) 164 (105) 035 (081) 049 (107) 039 (073) 088 (144) 094 (169) 081 (114) 101 (099) 184 (115) 064 (085) 167 (070) 003 (010) 137 (057) 219 (156) 189 (248) 147 (157) 049 (083) 080 (076) 160 (107) 175 (063) 405 (229) 238 (071) 2096 (211) 1900 (612) 1537 (182) 023 (060) 344 (146) 050 (059) 141 (083) 098 (081) 149 (084) 070 (072) 024 (171) 076 (073) 007 (029) 209 (147) 008 (027) 191 (065) 008 (001) 187 (062) (016) 120 (016) 115 (016) 156 (025) 141 (018) 137 (017) 146 (014) 130 (013) 126 (012) 035 (006) 093 (013) 047 (008) 151 (021) 159 (022) 156 (022) 139 (017) 138 (017) 138 (017) 133 (018) 132 (018) 132 (018) 140 (021) 132 (020) 139 (020) 135 (017) 190 (020) 136 (017) 005 [083] 014 [070] 014 [070] 297 [008] 054 [046] 037 (054) 223 [014] 124 [026] 072 [040] 924 [000] 599 [001] 699 [001] 407 [004] 366 [006] 389 [005] 001 [091] 002 [087] 002 [090] 001 [092] 001 [094] 000 [094] 000 [099] 023 [063] 019 [067] 055 [046] 018 [067] 030 [058]

32 µ Results for: ln =ln + ln ln + ln Sector Prod. Cointegration lnx lnq lna ecm = Stable Variety ( 1) c Food L (023) 1 Y WH 1 Textiles L (016) Y (020) WH (019) Paper L (057) Y (113) WH (086) Chem. L (055) Y (035) WH (048) Rubber L 1 Y 1 WH 1 NMM L (060) Y 1 1 WH B&F Met. L 1 Y 1 WH 1 Machinery L (032) Y (026) WH (033) Elec. L 1 Y (126) WH (088) Transp. L 1 Y WH (524) 076 (026) 087 (032) 260 (050) 1043 (485) 881 (482) 931 (499) 180 (379) 019 (252) 295 (201) 032 (204) 400 (174) 520 (223) 358 (175) 497 (450) 513 (471) 1054 (167) 302 (137) 181 (112) 767 (169) 773 (422) 098 (669) 1016 (510) 058 (141) 157 (260) 274 (089) 061 (141) 090 (105) 604 (188) 023 (113) 589 (521) 073 (096) Table 14: France VECM Time Series Results 095 (011) 137 (017) 138 (018) 131 (013) 120 (018) 112 (017) 115 (018) 132 (021) 125 (024) 130 (025) 111 (024) 159 (024) 155 (020) 153 (020) 081 (025) 080 (025) 116 [028] 075 [039] 064 [042] 683 [000] 382 [005] 310 [008] 327 [007] 003 [087] 000 [097] 126 [026] 001 [092] 484 [003] 279 [009] 237 [012] 027 [060] 039 [053] 30

33 µ Results for: ln =ln + ln ln + ln Section Prod. Cointegration lnx lnq lna ecm = Stable ( 1) c Food L (022) Y (042) WH (020) Textiles L 1 Y 1 1 WH Paper L (021) Y (021) WH (019) Chem. L 1 Y 1 1 WH Rubber L (041) Y (040) WH (040) NMM L (039) Y (037) WH (040) B&F.Met. L (019) Y (018) WH (017) Machinery L (012) Y 1 WH 1 Elec. L 1 Y 1 WH (017) Trapsp. L 1 Y WH (218) 341 (200) 497 (185) 916 (551) 842 (216) 788 (539) 001 (069) 008 (064) 009 (070) 453 (330) 280 (255) 419 (281) 017 (234) 254 (211) 100 (194) 200 (132) 179 (089) 432 (145) 404 (252) 505 (147) 808 (238) 2629 (415) 548 (265) 060 (109) 102 (151) 041 (102) 387 (206) 937 (382) 327 (226) 050 (139) 181 (131) 115 (135) 005 (072) 137 (016) Table15:ItalyVECMTimeSeriesResults (018) 076 (017) 076 (018) 083 (019) 088 (018) 076 (019) 105 (023) 103 (023) 106 (023) 124 (027) 126 (027) 124 (026) 058 (020) 061 (021) 057 (020) 113 (019) 060 (021) 399 [005] 068 [041] 280 [009] 183 [018] 800 [000] 171 [019] 024 [063] 032 [057] 026 [061] 118 [028] 062 [043] 139 [024] 000 [099] 068 [041] 024 [062] 104 [031] 207 [015]

34 µ Results for: ln =ln + ln ln + ln Sector Prod. Cointegration lnx lnq lna ecm = Stable ( 1) c Food L (013) 1 Y WH (010) Textiles L (010) Y (011) WH (010) Paper L (034) Y (942) WH (031) Chem. L (029) 1 Y WH 1 Rubber L (060) 1 Y WH (053) NMM L (068) 1 Y WH (064) B&F.Met. L 1 Y 1 1 WH Machinery L (031) 1 Y WH 1 Elec. L 1 Y 1 WH 1 Trapsp. L (092) Y (099) WH (095) 027 (169) 065 (156) 132 (152) 169 (195) 141 (140) 099 (204) 126 (219) 272 (242) 341 (286) 092 (201) 064 (165) 071 (135) 040 (113) 058 (103) 731 (241) 536 (182) 649 (210) 159 (063) 153 (070) 263 (190) 178 (103) 323 (208) 298 (212) 320 (212) 412 (237) 155 (103) 092 (201) 192 (188) 147 (189) 114 (189) 021 (118) 196 (178) 839 (265) 210 (187) Table 16: Spain VECM Time Series Evidence (022) 064 (022) 076 (024) 075 (025) 076 (024) 097 (024) 098 (024) 097 (024) 075 (023) 107 (020) 107 (020) 109 (020) 108 (021) 112 (022) 104 (022) 097 (021) 100 (022) 000 [096] 002 [089] 069 [041] 061 [044] 083 [036] 039 [054] 011 [073] 135 [024] 113 [029] 011 [074] 020 [065] 006 [080] 005 [083] 002 [089] 655 [001] 573 [002] 648 [001]

35 µ Results for: ln =ln + ln ln + ln Sector Prod. Cointegration lnx lnq lna ecm = Stable ( 1) c Food L 1 Y 1 WH (037) Textiles L 1 Y (036) WH 1 Paper L 1 Y 1 WH 1 Chem. L 1 Y 1 WH (743) Rubber L (041) 1 Y WH (044) NMM L (1112) Y (124) WH (5294) B&F Met. L (052) Y (052) WH (050) Machinery L (095) Y (092) WH (082) Elec. L (066) Y (076) WH (068) Transp. L (069) Y (058) WH (066) 476 (375) 425 (136) 1391 (587) 395 (153) 247 (145) (5983) 1934 (574) (27533) 023 (082) 038 (100) 032 (086) 011 (145) 103 (219) 016 (148) 131 (140) 037 (200) 029 (148) 216 (205) 200 (168) 058 (209) 190 (133) 143 (075) 069 (081) 326 (091) 251 (094) (3452) 435 (745) (13717) 214 (061) 254 (124) 217 (058) 099 (034) 239 (281) 109 (036) 085 (037) 014 (266) 059 (040) 322 (083) 005 (228) 293 (090) Table 17: USA VECM Time Series Results (024) 077 (020) 108 (019) 151 (018) 151 (018) 004 (001) 033 (009) 001 (28 3) 099 (025) 099 (025) 099 (025) 095 (024) 099 (024) 098 (024) 082 (028) 079 (029) 079 (029) 085 (027) 082 (024) 086 (026) 102 [031] 264 [010] 014 [071] 053 [047] 001 [094] 546 [002] 571 [002] 328 [007] 013 [072] 004 [084] 005 [082] 001 [092] 004 [085] 002 [088] 077 [038] 000 [100] 000 [096] 112 [029] 033 [056] 016 [069] No

36 Canada 0 =0 0 1 =1 1 0 Food Textiles Elec. (Y) Chem. Elec. (L,WH) =0 Machinery Transport (Y) Transport (L,WH) 0 Paper NMM (Y,WH) NMM (L) r1 Rubber B&FMet Finland 0 =0 0 1 =1 1 0 Textiles (L) Transport (Y) =0 NMM (L,WH) Textiles (Y,WH) NMM (Y) Rubber (WH) Machinery 0 Paper (L,WH) Food Paper (Y) Rubber (Y) Rubber (L) Chem (L,Y) Chem (WH) Elec. Transport (L,WH) r1 France B&FMet. 0 =0 0 1 =1 1 0 Textiles ( ) (WH) Machinery ( )(L) Paper ( ) (L,WH) Elec. (Y) =0 Food Chem (Y) NMM Elec. (WH) 0 Textiles (L) Textiles (Y) Chem (WH) Textiles ( ) (WH) Paper (Y) Machinery (Y) Paper ( ) (L,WH) Chem (L) Machinery ( )(L) Machinery (WH) r1 Rubber B&FMet Transport Y,L,WH indicate estimation under GDP, Employment and Working Hours product variety. Results are consistent where no product variety proxy (Y,L,WH) is indicated. indicates elasticity parameter under R&D input and product variety respectively. Results are consistent where neither elasticity parameter ( ) is indicated. Table 18: OECD Sector Classification I 34

37 Italy 0 =0 0 1 =1 1 0 Paper (L,Y) Elec. =0 Rubber NMM (L,Y) NMM (WH) B&F Met 0 Food (L,WH) Food (Y) Paper (WH) Machinery r1 Textiles Chem. Transport Spain 0 =0 0 1 =1 1 0 Transport (Y) Transport (L,WH) =0 Textiles (L,WH) Textiles (Y) Paper (L,Y) Paper (WH) Chem. NMM Machinery 0 Rubber Food r1 B&F Met. Elec. USA 0 =0 0 1 =1 1 0 Chem. NMM ( )(L) NMM ( ) (Y) =0 Food Elec. (L) Machinery (L,WH) B&F Met. Machinery (Y) Transport (L,WH) Elec. (Y,WH) Transport (Y) 0 NMM (WH) NMM ( ) (Y) Textiles Rubber NMM ( )(L) r1 Paper Y,L,WH indicate estimation under GDP, Employment and Working Hours product variety. Results are consistent where no product variety proxy (Y,L,WH) is indicated. indicates elasticity parameter under R&D input and product variety respectively. Results are consistent where neither elasticity parameter ( ) is indicated. Table 19: OECD Sector Classification II 35

38 to the panel data findings. While for South African manufacturing the preponderance of findings favoured Schumpeterian productivity growth, for the OECD the preponderance of sectors aligns with semi-endogenous productivity growth though Schumpeterian productivity growth is also supported for a number of OECD manufacturing sectors. Again, therefore, the time series evidence is consistent with the panel data evidence. However, note also that the sector specific findings show considerable variation across both the precise magnitude of the and the parameters, which may serve to explain why panel data evidence have been inconsistent in previous studies. For the OECD as for South Africa, then, prospects for sustained Schumpeterian productivity growth is narrowly concentrated in a few sectors, though relative to South Africa there is more extensive evidence for the weaker semi-endogenous form of productivity growth. VI. Conclusion and Evaluation This paper examines the nature of productivity growth across a range of data sets, covering developed and developing countries, 25 South African manufacturing sectors, as well as the manufacturing sectors of six OECD countries. Our test is for the presence of semi-endogenous or Schumpeterian patterns of productivity growth. Under panel estimation, our results are mixed. For our country-level data, which includes both developed and developing countries, as well as for the South African manufacturing sectors, results consistently favor the Schumpeterian account of productivity growth, indicating strong rates of return to knowledge creation. By contrast, for the six OECD country manufacturing sectors, panel results favour semi-endogenous productivity growth, with the associated inference of weaker returns to knowledge creation. These findings are robust to a range of alternative specifications of the test, as well as a range of alternative estimators(ols,fe,gmm,pmg,mg).ourresultsfromthepaneldataestimationare thus not conclusive, with evidence for both Schumpeterian and semi-endogenous growth theory emerging. It is surprising that the Schumpeterian case is strongest for the data set that 36

39 includes developing countries, and the middle income case of South Africa, and weakest for the set of 6 developed OECD economies of Panel 3. One of the more nuanced findings from the panel data is that there is evidence of sector heterogeneity, such that panel data estimation may hide significant sectors differences (with the partial exception of PMG and MG estimators). For this reason we also considered time series evidence for the South African and OECD data, for which a sufficient number of observations are available to render time series estimation feasible. Results are consistent with the existence of considerable sectoral heterogeneity. The implication of the South African time series findings is first, to confirm the inference that we drew from the panel data evidence: there is no guarantee that sectors are homogenous in terms of the characteristics of their productivity growth. Only six sectors of the South African manufacturing sector appear to follow a Schumpeterian productivity growth regime in the strict sense of satisfying all requirements of the theory, though a further six sectors follow Schumpeterian productivity growth weakly, in the sense that they meet some of the restrictions on parameter space (high rate of return on knowledge, but insignificant elasticity on R&D and product variety proxy). Nonetheless, the second implication of the time series evidence is that Schumpeterian productivity growth is favoured with greater preponderance (in the strict sense) than it does semi-endogenous productivity growth for South African manufacturing - consistent with the panel data findings. Third, we note that Schumpeterian growth in South African manufacturing appears to be concentrated in the Chemicals and related sectors, Machinery and Transport equipment, and Basic iron and steel. While there is thus some prospect for sustained productivity growth in South African manufacturing, such prospects are also narrowly focussed amongst South African manufacturing sectors. For the majority of South African manufacturing sectors, the inference is instead that productivity growth will not be sustained, and will instead be constrained by the natural rate of growth of the sector. For an economy in need of strong and sustained growth performance, this is not good news. 37

40 For the OECD time series results, three distinct implications follow. First, as for the South African data, the findings confirm sectors heterogeneity in terms of the characteristics of their productivity growth. An additional form of heterogeneity in the OECD is that results prove to be very sensitive to which proxy for product variety is employed. For the OECD the preponderance of sectors aligns with semi-endogenous productivity growth, though Schumpeterian productivity growth is also supported for a number of OECD manufacturingsectors. Whilethetimeseriesevidenceisthusbroadlyconsistentwiththepanel data evidence, the sector specific findings also show considerable variation across both the precise magnitude of the and the parameters, which may serve to explain why panel data evidence have been inconsistent in previous studies. Here too, then, prospects for sustained Schumpeterian productivity growth is narrowly concentrated in a few sectors, though relative to South Africa there is more extensive evidence for the weaker semi-endogenous form of productivity growth. Results for the OECD sectors indicates that the two North American economies (Canada and USA) have more sectors identified as Schumpeterian than the European economies included in the study (Finland, France, Italy and Spain). By contrast, Finland has the most sectors identified with a positive & elasticity towards productivity growth. More specifically, each of the two North American economies has six sectors that satisfy the 1 requirement of Schumpeterian growth under all or some of the proxies for product variety, whereas each of the four Europeans economies has only two (Finland, France and Italy) or three (Spain). Such findings predict that the North American economies have stronger potential for unbounded productivity growth across more sectors in the future. On the other hand, for all of the six OECD economies considered in this study, at least 50% of the ten sectors included in the study are more readily classifiable as subject to semi-endogenous than Schumpeterian productivity growth (5 for Canada, 6 for Italy and USA, 7 for France and Spain, 9 for Finland). This finding is consistent with those reported by Barcenilla-Visús et al (2014). 38

41 Figure 1: Association between and for both Schumpeterian and Semi-endogenous sectors. sigma_x denotes obtained from ln, sigma_q denotes obtained from ln. Given the sectoral heterogeneity that emerges from the time series evidence, we note that sector-specific time series modelling may be preferable to panel data analysis. Finally, we also illustrate the association between the -parameter estimates and the estimates of the -parameter from our estimations. We do so in Figure 1 for both Schumpeterian and semi-endogenous sectors, including both sectors that strictly and weakly satisfy the theoretical requirements. Figure 2 repeats for the Schumpeterian sectors, and Figure 3 for the semi-endogenous sectors, in both instances under the strict interpretation of the theory only. TheevidenceofFigure1suggeststhatforSouthAfricanmanufacturingthereisapositive association between and, while this association is absent for OECD manufacturing. However, recall that the OECD results incorporate both Schumpeterian and semi-endogenous productivity growth model consistent results. On separating the two types of sectors, note that in Figure 2 for the Schumpeterian sectors the positive association is again present, while for the semi-endogenous sectors of Figure 3 it is not. This finding is reassuring, since it sug- 39

42 Figure 2: Association between and for Schumpeterian sectors. obtained from ln, sigma_q denotes obtained from ln. sigma_x denotes Figure 3: Association between and for Semi-endogenous sectors. sigma_x denotes obtained from ln, sigma_q denotes obtained from ln. 40