Identification of R&D Paradox after the Global Financial Crisis: Korean Case Focusing on the Smart Convergence and Conventional Industries

Abstract

This article empirically explores whether the Korean research and development (R&D) paradox has been intensified during the post-global financial crisis (2009–2018). We employ the augmented production function model to test the intensified R&D paradox, which is defined as a continuous decline in a firm’s output elasticity of R&D investment. Using a data set of 720 R&D-active firms, which have ever received more than one government funding, this study drew the following major conclusions on the whole sample firms and two sub-sample firms (smart convergence and conventional industries). First, the R&D paradox has been intensified in the post-global financial crisis over the past decade. Second, the smart convergence industry shows higher a firm’s output elasticity of R&D investment than the conventional one does. Third, in recent years, R&D investment failed to even have significant effect on the value-added. Last, a firm’s output elasticity of R&D investment was found to be much more vulnerable in large and semi-large firms than in SMEs in Korea. In sum, this study confirms the intensified Korean R&D paradox during the post-global financial crisis in Korea. We discuss the government’s role in resolving the R&D paradox in Korea.

Keywords

R&D paradox a firm’s output elasticity of R&D investment total factor productivity (TFP)smart convergence research and innovation (R&I)open innovation

Introduction

A paradox is defined as ‘a situation or statement that seems impossible or is difficult to understand because it contains two opposite facts or characteristics’, according to the Cambridge dictionary. The paradox in a research and development (R&D) investment expresses conflicting tension between the long-standing belief and the opposite observation (Fragkandreas, 2015). The R&D paradox thus refers to the phenomenon in which R&D activity does not lead to adequate economic profit. There had come out several terms related to the R&D paradox, such as the Swedish paradox, the European paradox, the IT (or Solow) paradox (Edquist & Mckelvey, 1998; Ejermo et al., 2011; European Commission, 1995; Solow, 1987). In the late 1980s, the Swedish paradox, in particular, provided an opportunity to raise issues about the inefficiency of a national innovation system. Fragkandreas (2015) argued underlying factors which might cause the R&D paradox in Sweden; excessively biased allocation of R&D activities in a specific sector, technological lock-in, knowledge transfer problem and globalisation of production all might exacerbate the R&D paradox.

Similar concerns have been on the rise in Korea. The government has been investing in the R&D budget for decades and did not slow the investment down, unlike other countries even in and after the global financial crisis in 2008 (Ma & Dwyer, 2020). However, the government has still observed the unsatisfactory performance of the government R&D despite their continued active investment (Ma, 2019). They attributed such a Korean R&D paradox simply to the inefficiency of government R&D funding, holding the assumption that private R&D investment itself will be efficient enough. Thus, the government has focused mainly on improving their funding scheme to address the Korean R&D paradox; allocating more budget on challenging R&D projects with higher potential benefits, and strengthening the collaboration between industry and academia in the government-sponsored R&D projects (MOTIE, 2019).

However, the Korean R&D paradox needs to be explored in the area of private R&D investment, not confined to government R&D funding, for private firms might have a higher possibility to suffer from the R&D paradox. In reality, firms face unprecedented challenges from turbulent global market competition and rapid technological change. If the paradox arises in private R&D investment, as in government funding, it will be a serious problem, for the amount of private R&D investment is almost three times that of government R&D funding (Ministry of Science & ICT, 2021).

In this aspect, this study aims to quantitatively estimate whether the R&D paradox has been intensified in Korea. Specifically, we operationalise the intensified R&D paradox as a continuous decline in a firm’s output elasticity of R&D investment. In other words, the output elasticity of R&D investment indicates the impact of a firm’s R&D on its added value, that is, how well a firm realises the economic profit from its R&D investment. This study will focus on smart convergence and conventional industries in Korea. In particular, we will focus on the post-global financial crisis, which will allow us to better observe the recent R&D paradox phenomenon.

This study will contribute to the accumulation of new knowledge in that little is known about the paradox of private R&D investment. The main findings in this study are as follows: (a) the R&D paradox has been intensified in the post-global financial crisis over the past decade, (b) the smart convergence industry shows a higher firm’s output elasticity of R&D investment than the conventional one does, (c) in recent years, R&D investment failed to even have a significant effect on the value-added and (d) a firm’s output elasticity of R&D investment was found to be much more vulnerable in large and semi-large firms than in SMEs in Korea.

The remainder of the article is structured as follows: The second section reviews the previous literature on R&D and productivity. The third section describes the research model and methodology. The data and measurement of variables are reported in the fourth section. The fifth section explains estimation results. Finally, the sixth section will present the conclusions.

Literature Review

The study on R&D and productivity has a long history. In 1964, Griliches started to investigate the impact of public R&D expenditure on productivity in the agricultural industry, with his following seminal works (Griliches, 1980, 1995, 1998; Griliches & Mairesse, 1984; Hausman et al., 1984). It was known that R&D investment, in general, affects productivity positively. Meanwhile, the perspective on R&D investment had changed from as an exogenous factor outside of production function into as an endogenous factor within production function. In the 1990s, Romer (1990), Broadberry (1992) and Aghion and Howitt (1992) proposed an endogenous growth model, which emphasised the role of technological change in production. Instead of viewing technological level as given to production from the outside, they assumed that the level of technology was determined by the voluntary and intentional R&D investment of the economic agents and that the technological knowledge from R&D activity has the property of non-rivalry and patrial excludability.

Since the 2000s, empirical research on the impact of R&D investment on productivity had flourished in many counties: Wakelin (2001) for UK firms, Guellec et al. (2001) for sixteen OECD countries, Wang and Tsai (2003) for Taiwan firms, Parham (2009) for Australian firms, Crespi and Zuniga (2012) for six countries across Latin America and Sterlacchini and Venturini (2014) for firms in Italy and Spain. Ugur et al. (2016), through the meta-analysis of prior research in OECD Firms and Industries, found that the elasticity of R&D to productivity ranges from 0.05 to 0.25.

In addition, there were many studies that measured productivity differences by industry and showed consistent results, as summarised in Table 1. It is the level of R&D intensity that seems to play a crucial role in determining productivity. The impact of R&D on productivity is much larger in the high-tech industry and lower in the low-tech industry.

Table 1

Empirical Literature on R&D and Productivity by Industry

No	Author	Major Findings
1	Griliches and Mairesse (1984)	· The more investment in R&D, the higher the productivity. In technology-intensive firms with high R&D intensity, R&D investment has a greater impact on productivity.
2	Wang and Tsai (2003)	· R&D investment has a significant positive impact on total factor productivity, and the impact is even greater in technology-intensive firms.
3	Ortega-Argilés and Brandsma (2010)	· The coefficient of this R&D impact increases as it goes up from low-tech industries to high-tech ones.
4	Kancs and Siliverstovs (2016)	· The impact of R&D on productivity ranges from –0.02 to 0.33, depending on the level of R&D intensity.
5	Ortega-Argiles et al. (2014, 2015)	· In traditional low-tech industries, productivity gains are more related to capital accumulation than R&D expenditure.
6	Montresor and Vezzani (2015)	· The return on knowledge capital through R&D was found to be the largest in the high-tech industry. In addition, physical capital is an important factor in non-high-tech industries.
7	Soltanisehat et al. (2019)	· R&D expenditures in the high-tech and medium high-tech industries impact the most positively and significantly the growth of total factor productivity.
8	Castellani et al. (2019)	· U.S. firms are more capable of converting R&D into productivity gains in the high-tech sector, while EU firms are more likely to achieve productivity gains through capital-embodied technological progress in the medium and low-tech sectors.

Source: The authors.

In this study, we aim to quantitatively measure whether the R&D paradox is intensified in the post-global financial crisis. The results of this study can contribute to the accumulation of academic knowledge in that there are few papers directly dealing with the Korean R&D paradox and will help policymakers to accurately recognise the seriousness of the R&D paradox and make up the basic direction for policy remedy.

Research Model and Methodology

Our model aims to identify the trend in the impact of a firm’s R&D investment on its value-added over the past decade. Following previous literature,¹ we start from typical Cobb–Douglas production functions: Y = AK^β1 L^β2 where Y, K, L are the value-added, capital and labour, respectively. Here, the sum of production elasticity of capital and labour (β1 + β2) indicates the return to scale. In case that the sum is less than one, it reveals decreasing return to scale.

Total factor productivity (A) includes all the other factors affecting a firm’s value-added, except capital and labour. It can be classified into internal and external factors. Internal factors are about a firm’s management system, labour quality, R&D and IT, experiential knowledge, while external factors encompass productivity spillovers, market and trade competition, regulation, labour flexibility, etc. (Syverson, 2011).

A firm’s R&D investment, in particular, is known to play a crucial role in determining its total factor productivity. This study assumes that the impact of a firm’s R&D investment on its value-added would be changing linearly over the years together with a certain mean impact. So, the impact of a firm’s R&D investment on its value-added (γ) is decomposed into two parts: the mean impact over the period (γ¹) and changing impact over a period (γ²). The R&D investment in the model would have a one-year lag effect on the value-added. Our augmented model is as follows:

Y_{i t} = ​ C {(R & D)}_{i t - 1}^{}_{}^{γ 1 + γ 2 T} K_{i t}^{}_{}^{β 1} L_{i t}^{}_{}^{β 2},

(1)

where γ¹ and γ² are the mean and changing impact of R&D on the value-added, and C is constant and T represents time in years. Equation (1) can be rewritten in a natural log-linearised form, and we get our final estimation model for the firm ‘i’ at a specific year ‘t’:

\begin{matrix} y_{i t} = γ_{1} {(R & D)}_{i t - 1} + γ_{2} {(R & D)}_{i t - 1} \times T + β_{1} k_{i t} \\ + β_{2} l_{i t} + ω_{i t} + ε_{i t}, \end{matrix}

(2)

where lowercase letters denote natural log values, ω_it is a firm’s unobserved factors, and ε_it is a random error that is independent and identically distributed.

In Equation (2), the interaction coefficient (γ₂) of R&D and T is of our utmost interest. In case that the coefficient is less than zero, we can interpret that the R&D paradox has been intensified. Otherwise, we can argue that there is no evidence of the R&D paradox.

Simply estimating Equation (2) with Pooled Ordinary Least Square (POLS) will cause upward-biased results. A firm’s unobserved heterogeneity (ω_it) might be simultaneously positively correlated with endogenous variables such as R&D, k and l. This seriously violates the Gauss-Markov assumption in Ordinary Least Square, which will overestimate the coefficient of endogenous variables.

To address the endogeneity, several advanced estimation techniques²—structural estimator and dynamic panel estimator—have been proposed for decades (Ackerberg et al., 2015; Bond & Soderbom, 2005; Levinsohn & Petrin, 2003; Olley & Pakes, 1996; Wooldridge, 2009). Each estimation has, however, underlying restrictive assumptions, which might provide misleading results (Eberhardt & Helmers, 2010). Structural estimators assume strong monotonicity between a firm’s unobserved heterogeneity (ω_it) and a firm’s instrumental variable. A dynamic panel estimator has a crucial assumption that the past value of endogenous variables (e.g., k_{it – 1}, l_{it – 1}) should be uncorrelated with the current firm’s unobserved heterogeneity (ω_it).

Eberhardt and Helmers (2010) argue that sophisticated methodology severely suffers from the data that do not satisfy such strong assumption due to high missing values or persistence. Rammer and Schubert (2018) also cast much doubt on the structural estimation through instrumental variables and opted for a fixed effect (FE) and random effect (RE). Castellani et al. (2019) chose FE estimation for the productivity model, based on the rationale that any methodology produced highly correlated total factor productivity.

This study will hence employ a firm FE and RE estimation with POLS as a baseline. FE estimation can control for a firm’s unobserved time-invariant heterogeneity. It will reduce a significant potential bias in the estimation of the coefficient of endogenous variables, although some bias still arises from a firm’s unobserved time-variant heterogeneity. We will decide either FE or RE based on the observation of the correlation between the error term (ω_it + ε_it) and independent variables in our data for better estimation. In every estimation, we basically control for industry and time effect.

Data and Measurement

The data is a balanced panel including 720 firms, and each firm’s financial information was acquired through Korean Enterprise Data, a credit reporting company. The data consists of each firm’s financial information from 2009 through 2018. The data would be appropriate for this study. Firms in the data are R&D active firms, and the financial data covers the entire period of the post-global financial crisis. We drew all the firms that have ever received more than one government grant from the Korea Evaluation Institute of Industrial Technology (KEIT). Each firm implemented its government-sponsored R&D project as a principal organiser. Considering that a funding agency usually chooses a picking-winner strategy, most firms in our data can be assumed innovative and active in R&D investment. The data would be good because this study is more interested in exploring the R&D paradox phenomenon, especially in R&D active firms, not simply in all the firms, for the last decades after the financial crisis.

This study classified two types of industry, smart convergence industry and conventional industry, for each firm according to its business items and research area. Technological experts from the KEIT participated in this classification. The smart convergence industry consists of four industries: smart manufacturing and service, smart health, smart mobility and smart component. Conventional industry corresponds to the traditional domain technological field without significant ICT convergence.

Table 2 shows the firm’s distribution by the industry and firm size in the data. The firm falls into either the smart convergence industry or the conventional industry quite equally: smart convergence industry 48.5 per cent and conventional industry 51.5 per cent. In terms of firm size, small and medium-sized enterprises (SMEs) account for over 80 per cent. The firm’s composition in our data is quite comparable with whole firm statistics³ in Korea in terms of the dominance of SMEs. Our data, however, show a relatively higher portion of large and semi-large firms than whole firm statistics do. It seems reasonable considering that our data is composed of more innovative firms investing in R&D actively. Table 3 explains what technological fields are covered by each industry.

Table 2

Firm’s Distribution by the Industry and Firm Size

Industry		Large	Semi-Large	SME	Total
Smart convergence	Smart manufacturing and service	0	9	143	152 (21.1%)
	Smart health	2	6	73	81 (11.3%)
	Smart mobility	3	10	34	47 (6.5%)
	Smart component	1	10	58	69 (9.6%)
Conventional	–	21	69	281	371 (51.5%)
Total		27 (3.8%)	104 (14.4%)	589 (81.8%)	720 (100%)

Source: The authors.

Table 3

Description of Each Industry

Industry		Relevant Technological Field
Smart convergence	Smart manufacturing and service	Digital manufacturing equipment, robot, smart industrial machinery, virtual reality, design, information technology, knowledge service
	Smart health	Bio, medicine
	Smart mobility	Electric car, autonomous car, smart aviation
	Smart component	Semiconductor, display
Conventional	–	New material, machinery, manufacturing equipment, shipbuilding, combustion car, clean production, machine component, airplane, metal casting, forging, plating, plant engineering

Source: The authors.

This study employs four major variables: value-added (VA), R&D investment (R&D), capital (K) and labour (L). According to the Bank of Korea’s (BOK) firm analysis methodology, we calculated value-added (VA) as the following: VA = Operating Profit + Salary + retirement allowance + Welfare Benefit + Depreciation + Rent + Taxes and dues.

Capital (K) and labour (L) are measured as a firm’s fixed asset and the number of employees in each firm, respectively. All nominal financial values in VA, R&D and K are converted into real value using BOK’s GDP price deflator (2015 = 100). Then we applied natural log-transformation to all four variables for better estimation as common practice.

Table 4 reports the descriptive statistics of four major variables. The unit of mean, standard deviation and median is dollars ($) in real value. The mean is much greater than the median, and the standard deviation is much greater than the mean. It indicates the right-skewed distribution with quite a long tail in each variable. Descriptive statistics by industries in Table 4 also reveal similar distribution in all the industries. Some difference is also found in average value-added (VA), R&D investment (R&D) and capital (K). Average value-added (VA) and R&D investment (R&D) are about two times higher in the smart convergence industry than in the conventional one. However, the conventional industry has nearly two times higher capital (K).

Table 4

Descriptive Statistics

Industry	Variables	Number of Observations	Mean	Standard Deviation	Median
Whole	VA	7,240	47,311,263	433,441,436	1,622,339
	R&D	6,090	14,544,839	121,182,095	899,021
	K	6,747	203,318,524	1,530,195,249	5,040,676
	L	5,412	665	3,460	110
Smart convergence	VA	3,403	60,631,033	577,651,515	1,031,587
	R&D	2,799	21,119,067	173,717,998	1,013,152
	K	3,210	137,660,504	1,219,615,323	1,805,452
	L	2,355	661	4,634	90
Conventional	VA	3,837	35,498,081	241,475,486	2,300,531
	R&D	3,291	8,953,449	38,020,263	829,066
	K	3,537	262,906,379	1,763,448,725	10,124,748
	L	3,057	668	2,159	124

Source: The authors.

Note: Unit: 1,000 Korean Won (equivalent to about US$ 1).

In Table 5, we simply compare the value-added per R&D investment (VA/R&D), value-added per capital (VA/K) and labour productivity (VA/L) for the sample firms in 2018. The smart convergence industry shows higher value-added per capital (VA/K) and labour productivity (VA/L), whereas the conventional industry does better in the value-added per R&D investment (VA/R&D).

Table 5

Total VA, R&D, K and L in 2018

Industry	VA	R&D	K	L	VA/R&D	VA/K	VA/L
Smart convergence	14,607,920,712	8,274,719,963	61,907,669,073	160,382	1.77	0.24	91,082
Conventional	11,050,071,557	3,161,865,305	87,830,189,580	190,730	3.49	0.13	57,936
Total	25,657,992,270	11,436,585,269	149,737,858,653	351,112	2.24	0.17	73,076

Source: The authors.

We further explored the trend of average value-added (VA) and R&D investment (R&D) over the last decade for all firms in our data, as shown in Figure 1. All firms’ average VA and R&D is on the rise. The slope of VA, however, appears to be slightly lower than the slope of R&D. For the smart convergence industry, average value-added (VA) increases more rapidly than R&D investment (R&D). Remarkably, the average value-added (VA) of the conventional industry shows a declining trend despite more R&D investments.

Figure 1

Source: The authors.

Empirical Results and Robust Check

Table 6 shows the estimation results through FE, RE and POLS. We implemented the Hausman test for checking the endogeneity, i.e., the correlation between the error term (ω_it + ε_it) and independent variables in our data. It reveals that our data has a statistically significant correlation.⁴ Hence, this study will interpret the result mainly based on the FE estimation.

Table 6

Estimation Results (Dependent Variable: Value-Added)

Variables	Fixed Effect			Random Effect			POLS
Variables	Whole Sample	Smart Industry	Conventional Industry	Whole Sample	Smart Industry	Conventional Industry	Whole Sample	Smart Industry	Conventional Industry
R&D	0.058*** (0.017)	0.066*** (0.025)	0.055^** (0.022)	0.114*** (0.013)	0.122*** (0.019)	0.103*** (0.016)	0.249*** (0.011)	0.293*** (0.019)	0.220*** (0.014)
R&D × T	–0.005^** (0.002)	–0.005 (0.003)	–0.005^** (0.003)	–0.001^** (0.0003)	0.0003 (0.0004)	–0.001*** (0.0003)	–0.001*** (0.0004)	–0.0005 (0.001)	–0.002*** (0.0005)
k (Capital)	0.182*** (0.021)	0.163*** (0.027)	0.200*** (0.031)	0.386*** (0.013)	0.353*** (0.020)	0.430*** (0.019)	0.451*** (0.009)	0.414*** (0.014)	0.479*** (0.012)
l (Labour)	0.0002*** (0.00004)	0.0002*** (0.0001)	0.0002*** (0.0001)	0.0002*** (0.00002)	0.0002*** (0.00003)	0.0002*** (0.00003)	0.0001*** (0.00001)	0.0001*** (0.00002)	0.0001*** (0.00001)
Constant	-	-	-	7.350*** (0.224)	7.705*** (0.325)	6.780*** (0.318)	4.563*** (0.156)	4.574*** (0.251)	4.545*** (0.200)
Firm fixed effect	YES	YES	YES	NO	NO	NO	NO	NO	NO
Year fixed effect	YES	YES	YES	NO	NO	NO	YES	YES	YES
Sub-industry fixed effect		-	-	-	-	-	YES	YES	YES
# of obs (firm-year)	4,057	1,737	2,320	4,057	1,737	2,320	4,057	1,737	2,320
# of firms	581	272	309	581	272	309	-	-	-
R-squared	0.044	0.050	0.038	0.598	0.584	0.617	0.701	0.684	0.715
F statistic	39.559*** (df = 4; 3,462)	19.041*** (df = 4; 1,451)	19.552*** (df = 4; 1,997)	2,086.258***	816.685***	1,300.213***	1,187.755*** (df = 8; 4,048)	534.837*** (df = 7; 1,729)	1,452.935*** (df = 4; 2,315)

Source: The authors.

Note: The number in parentheses indicates robust standard errors. ***p < 0.01, **p < 0.05, *p < 0.1.

The R&D paradox coefficient (γ₂) of our greatest interest is revealed significantly as negative in the whole sample model, which is confirmed in POLS estimation as well. The interaction effect is shown in Figure 2. As the year passes by, the slope is getting lower. Even if a firm has increased the same amount of R&D, the firm would realise less expected annual output from the investment than in the previous year. This finding provides us with evidence that the R&D paradox has been intensified for the past decade. In addition, the firms in the conventional industry seem to suffer more from the R&D paradox rather than the ones in the smart convergence industry.

Figure 2

Source: The authors.

A firm’s R&D investment is also confirmed as a strong significant predictor for its production in our data. The elasticity of R&D investment (γ₁) is 0.058 for the whole sample in FE model, implying that a one per cent change in a firm’s R&D investment leads to a 0.058 per cent change in its value-added. The elasticity is observed higher in the smart convergence industry than in the conventional one. Firms in the smart convergence industry seem to better translate their R&D investment into economic performance. It is quite consistent with the stylised fact from prior literature arguing that R&D expenditure in the high-tech industry has a higher impact on total factor productivity, considering that the high-tech firms more likely belong to the smart convergence industry.

Turning to the elasticity of capital and labour on the value-added, we see that both are significantly positive. The elasticity of capital (β₁) is estimated much higher than the elasticity of labour (β₂). It is worth mentioning that the elasticity of capital (β₁) is much higher in the conventional industry than in the smart one. Firms in the conventional industry probably would be more in capital-intensive sectors rather than knowledge-intensive ones. They realise their better economic profit through capital investment in particular. However, observing that the sum of elasticity of capital and labour (β₁ + β₂) is quite smaller than one, we see that all firms face their decreasing return to scale.

For a robust check, we first perform the FE estimation with sales as the dependent variable instead of the value-added. It is confirmed that the results shown in Table 7 are quite similar to the main estimation in Table 6, except that the R&D paradox coefficient (γ₂) is also revealed significant in the smart convergence industry as well as in conventional industry. Second, we implement the FE estimation on each subgroup after dividing the whole sample into two periods (2009–2013 and 2013–2018) as shown in Table 8. Both the elasticity of R&D investment (γ₁) and the R&D paradox coefficient (γ₂) is found strongly significant and more influential in the former period (2009–2013). In contrast, we cannot observe any significance in both coefficients in the latter period (2013–2018). The fact of being no R&D paradox in the later period seems desirable, but the fact that even the elasticity of R&D investment (γ₁) is no more significant tells us of greater severity. A firm’s R&D investment, on average, is not linked to its economic performance. We will discuss this issue later in the conclusion section.

Table 7

Estimation Results (Dependent Variable: Sales).

Variables	Fixed Effect
Variables	Whole Sample	Smart Industry	Conventional Industry
R&D	0.064*** (0.010)	0.082*** (0.017)	0.050*** (0.011)
R&D × T	–0.005*** (0.001)	–0.007*** (0.002)	–0.002^* (0.001)
k (Capital)	0.223*** (0.011)	0.189*** (0.017)	0.263*** (0.015)
l (Labour)	0.0002*** (0.00002)	0.0002*** (0.00004)	0.0003*** (0.00003)
Firm fixed effect	YES	YES	YES
Year fixed effect	YES	YES	YES
# of obs. (firm-year)	4,535	2,003	2,532
# of firms	598	284	314
R-squared	0.148	0.116	0.192
F statistic	169.729*** (df = 4; 3,923)	55.912*** (df = 4; 1,705)	130.777*** (df = 4; 2,204)

Source: The authors.

Notes: The number in parentheses indicates robust standard errors. *** p < 0.01, ** p < 0.05, * p < 0.1.

Table 8

Estimation Results (Dependent Variable: Value-Added)

Variables	Fixed Effect
Variables	Whole Sample		Smart Industry		Conventional Industry
	09–13	13–18	09–13	13–18	09–13	13–18
R&D	0.132*** (0.027)	–0.037 (0.040)	0.143*** (0.041)	–0.005 (0.071)	0.138*** (0.035)	–0.049 (0.051)
R&D × T	–0.029*** (0.006)	0.004 (0.005)	–0.032*** (0.011)	0.0001 (0.008)	–0.033*** (0.008)	0.005 (0.006)
k (Capital)	0.145*** (0.036)	0.120*** (0.037)	0.077 (0.050)	0.138*** (0.045)	0.224*** (0.051)	0.085 (0.065)
l (Labour)	0.0004*** (0.0001)	0.0003*** (0.0001)	0.001*** (0.0002)	0.0003^* (0.0001)	0.0002^** (0.0001)	0.0003^** (0.0001)
Firm fixed effect	YES	YES	YES	NO	NO	NO
Year fixed effect	YES	YES	YES	NO	NO	NO
# of obs. (firm-year)	1,833	2,273	786	987	1,047	1,286
# of firms	491	546	226	255	265	291
R-squared	0.048	0.014	0.050	0.020	0.064	0.009
F statistic	16.818*** (df = 4; 1,334)	6.116*** (df = 4; 1,718)	7.195*** (df = 4; 552)	3.752*** (df = 4; 723)	13.332*** (df = 4; 774)	2.118^* (df = 4; 986)

Source: The authors.

Note: The number in parentheses indicates robust standard errors. *** p < 0.01, ** p < 0.05, * p < 0.1.

Overall, this study found reliable evidence in our data that the R&D paradox has been intensified. Nevertheless, we suspect that there can be considerable heterogeneity among sub-industry sectors or the level of firm size. We, therefore, implement FE estimation on each subgroup in the smart industry. Table 9 shows that the elasticity of R&D investment (γ₁) and the R&D paradox coefficient (γ₂) are all significant in the smart manufacturing and service industry. The smart component industry has positive elasticity of R&D investment and then no R&D paradox effect as is consistent with the estimation in the entire smart industry. The smart health and mobility industry, however, reveal no significance in both coefficients, which might have been caused by the relatively small sample size.⁵ It is also plausible to interpret that there is no return on R&D investment due to the early-stage industry and immature market condition.

Table 9

Estimation Results (Dependent Variable: Value-Added)

Variables	Fixed Effect
Variables	(1) Smart Component	(2) Smart Mfg Svc	(3) Smart Health	(4) Smart Mobility
R&D	0.089^* (0.047)	0.107^** (0.044)	0.084 (0.061)	–0.016 (0.062)
R&D × T	0.001 (0.007)	–0.010^** (0.005)	–0.010 (0.007)	0.004 (0.008)
k (Capital)	0.157^** (0.062)	0.062 (0.043)	0.201*** (0.063)	0.276*** (0.061)
l (Labour)	0.0002^** (0.0001)	0.004*** (0.001)	0.001^* (0.0004)	–0.00005 (0.0001)
Firm fixed effect	YES	YES	YES	NO
Year fixed effect	YES	YES	YES	NO
# of obs. (firm-year)	436	606	420	275
# of firms	62	102	68	40
R-squared	0.067	0.085	0.061	0.110
F statistic	6.467*** (df = 4; 360)	11.429*** (df = 4; 490)	5.459*** (df = 4; 338)	6.847*** (df = 4; 221)

Source: The authors.

Note: The number in parentheses indicates robust standard errors. *** p < 0.01, ** p < 0.05, * p < 0.1.

With regard to the level of firm size, Table 10 shows the estimation results for each group: a large firm group, a semi-large firm group and SMEs. A SMEs group shows a consistent result with our main estimation. The elasticity of R&D investment (γ₁) is significantly positive, and the R&D paradox has been intensified. The results shown in either a large firm group or a semi-large firm group may hint us quite different possibilities, although we acknowledge that the estimation has obvious limitations of the small sample size.⁶ For example, they invest more R&D in challenging noble areas where economic profit can hardly be realised in the short term. We will also discuss this issue further later in the conclusion section.

Table 10

Estimation Results (Dependent Variable: Value-Added)

Variables	Fixed Effect
Variables	Large Firm Group	Semi-Large Firm Group	SMEs Group
R&D	–0.076 (0.060)	–0.032 (0.052)	0.079*** (0.020)
R&D × T	0.0003 (0.006)	0.004 (0.005)	–0.008*** (0.003)
k (Capital)	0.279*** (0.071)	0.188^** (0.089)	0.117*** (0.022)
l (Labour)	0.0002*** (0.00005)	0.001*** (0.0002)	0.004*** (0.0004)
Firm fixed effect	YES	YES	YES
Year fixed effect	YES	YES	YES
# of obs. (firm-year)	201	767	3,089
# of firms	20	90	471
R-squared	0.282	0.052	0.067
F statistic	16.418*** (df = 4; 167)	9.101*** (df = 4; 663)	46.445*** (df = 4; 2604)

Source: The authors.

Note: The number in parentheses indicates robust standard errors. *** p < 0.01, ** p < 0.05, * p < 0.1.

Conclusion

This study explored whether the Korean R&D paradox has been intensified in the post-global financial crisis. We employed the production function model to test the R&D paradox, which was defined as a continuous decline in a firm’s output elasticity of R&D investment. By focusing on smart convergence and conventional industry each in Korea, this study drew the following major conclusions.

First, we confirm that the R&D paradox has been intensified during the post-global financial crisis (2009–2018). This is more noticeable, particularly in the conventional industry, than in the smart convergence one. Our results are also consistent with previous studies, which dealt with the long-term trend in total factor productivity in Korea. Korea Development Institute (KDI, 2020) announced that the contribution of total factor productivity on real GDP in Korea decreased after the global financial crisis, along with the contribution of physical capital to real GDP. Korea Information Society Development Institute (KISDI, 2019) also found that the growth rate of total factor productivity fell 1.9 per cent when comparing before and after the global financial crisis in Korea. It seems very likely that the total factor productivity, including the R&D factor, gradually declined over two decades. It will be meaningful that further study compares the R&D paradox phenomenon over two decades, including pre- and post-global financial crisis, beyond the time scope of this study (2009–2018).

Second, a firm’s output elasticity of R&D investment is higher in the smart convergence industry than in the conventional one. This matches previous research findings that high-tech industries have higher total factor productivity (Castellani et al., 2019; Griliches & Mairesse, 1984; Kancs & Siliverstovs, 2016; Ortega-Argilés & Brandsma, 2010; Soltanisehat et al., 2019; Wang & Tsai, 2003). This is because there is a high possibility that high-tech-related industries were included in the smart convergence industry more than the conventional one. In high-tech industries, a firm’s knowledge assets, such as R&D investment, play a crucial role in creating its value-added (Montresor & Vezzani, 2015). In contrast, in low-tech industries, a firm’s capital accumulation is known to have a greater impact on its value-added than the firm’s knowledge assets do (Ortega-Argiles et al., 2014, 2015). In addition, a firm’s goal of R&D investment might be different in the two industries. High-tech industries prefer to develop new innovative products, but low-tech industries will likely focus more on process innovation to reduce the cost of their existing products.

Third, R&D investment has not affected value-added, particularly in the second half of the past decade. This seems to be highly related to the rising uncertainty of the overall economy. The past ten years were an unprecedented period of great fluctuations due to the low economic growth, intensifying trade conflict between the United States and China, and the emerging digital era. The BOK (2020) reveals that the uncertainty index rose about 1.3 times in the post-financial crisis than the pre-financial crisis. Furthermore, it would be difficult to expect the external environment to change positively in the near future. Therefore, it will become even more essential that a firm strengthen its internal dynamic capability to adapt to the external environment actively.

Last but not least, a firm’s output elasticity of R&D investment was found to be much more vulnerable in large and semi-large firms than in SMEs in Korea. According to the BOK (2020), it was confirmed that the labour productivity of large firms and major industries (i.e., electronics, automobiles, shipbuilding industries) was significantly lowered. Until the mid-2000s, the proliferation of ICT and the expansion of the global value chain (GVC) positively impacted large firms’ productivity improvement, but these effects disappeared in the post-global financial crisis (Tenreyro, 2018).

Now, we would like to discuss some basic directions to resolve the serious R&D paradox in Korea in terms of emerging industry and funding policy.

First, the government’s ultimate goal would be to strengthen the link between research and innovation (R&I) through accelerating knowledge flow in the open system (Rasiah, 2019). The government’s role as pumping water matters more, particularly in the new smart convergence industry, where better productivity is expected than in the conventional industry. In the emerging industry, the government needs to consider shifting its role from a passive market fixer to an aggressive market shaper. At an early stage, the government can play a more dominant and direct role in shaping the industry cluster and then can signal the private sector to invest in new challenging technological development. Hence, the government can take effective policy measures according to the maturity of each industry, which will establish a dynamic innovation system at each industry level (Liu, 2021).

Second, the government’s R&D funding policy needs to be reconsidered and redesigned in terms of budget portfolio, funding instrument and local innovation resources. The budget should be strategically distributed in a more scientific manner to achieve the policy goal effectively instead of mechanically alloca-ting resources for each industry. The funding instrument also needs to be diversified according to technology characteristics, the awardee firm size, etc. The government can implement differentiated funding policies to increase each awardee firm’s total factor productivity (Qi & Yang, 2021). Furthermore, the government should strive to connect local innovation resources and promote an open innovation system, maximising the national innovation capacity (Yoo & Kwak, 2016).

We hopefully find new technological innovation opportunities in the transformational decade to enhance the effect of R&D investment on economic profit (Pyka et al., 2019).

Conceptualization: H.R.M. and D.H.O.; methodology: H.R.M. and C.J.L.; formal analysis: H.R.M.; writing—original draft preparation: H.R.M.; writing—reviewing and editing: H.R.M., C.J.L. and D.H.O.; supervision: D.H.O. All authors have read and agreed to the published version of the manuscript.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Notes

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