R&D, industrial policy and growth

Dang, Alicia H.; Samaniego, Roberto M. Article R&D, industrial policy and growth Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Dang, Alicia H.; Samaniego, Roberto M. (2022) : R&D, industrial policy and growth, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 8, pp. 1-42, https://doi.org/10.3390/jrfm15080344 This Version is available at: https://hdl.handle.net/10419/274866 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Journal of Risk and Financial Management 15: 344. https://doi.org/10.3390/ jrfm15080344 Academic Editor: Shigeyuki Hamori Received: 18 May 2022 Accepted: 2 August 2022 Published: 4 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article R&D, Industrial Policy and Growth Alicia H. Dang 1and Roberto Samaniego 2,* 1Department of Economics, Union College, Schenectady, NY 12308, USA 2Department of Economics, George Washington University, Washington, DC 20052, USA *Correspondence: r[email protected] Abstract: An issue with estimating the impact of industrial support is that the firms that receive support may be politically connected, introducing omitted variable bias. Applying fixed-effects regressions on Vietnamese panel data containing several proxies for political connectedness to correct this bias, we find that firms that receive industrial support in the form of tax holidays experience more rapid productivity growth, particularly in R&D-intensive industries, and less so among politically connected firms. These findings do not appear to be due to the presence of financing constraints. We then develop a second-generation Schumpeterian growth model with many industries, and show that tax holidays disproportionately raise productivity growth in R&D-intensive industries. These results are significant and important for governments, especially those in transition and developing countries, in better targeting their industrial policy to facilitate higher productivity growth. Keywords: industrial subsidies; R&D intensity; productivity growth; Schumpeterian models; tax holidays; political connections 1. Introduction Industrial policy is common around the world, yet the mechanisms through which industrial support might affect firms are not fully understood. In developing economies, industrial support has recently been found to improve industry performance (Aghion et al. 2015;Lin 2003). Questions remain, for example, as to whether industrial support encourages growth by stimulating innovation, or whether industrial support enables firms to overcome financing constraints. A confounding factor is that industrial support may not be exogenous: politically connected firms may be more likely to receive support, leading to omitted variable bias—particularly in a developing country context (Khwaja and Mian 2005;Li et al. 2008). We identify the channels through which industrial support affects economic outcomes by focusing on industry variation. It is known since at least Cobb and Douglas (1928) that industries vary in the technology of production: for example, the production of Machinery is more capital-intensive and more R&D-intensive than the production of Textiles. By examining which technological characteristics interact with industrial support, we narrow down the key channels whereby industrial support affects firm performance. We address the problem of omitted variable bias by using a firm-level panel database from Vietnam. Vietnamese data are particularly useful because they contain multiple proxies we can use to measure the political connectedness of firms. In addition, the use of panel data allows us to condition on firm-level fixed effects, which powerfully conditions on any idiosyncratic firm-level characteristics that might affect productivity, observed or otherwise. We find that industrial support, measured using tax holidays as in Aghion et al. (2015), raises firm productivity growth. 1 Tellingly, we find that it particularly raises productivity growth for firms in R&D-intensive industries. This suggests that the appropriate class of models for understanding the impact of industrial support on economic growth is the class of R&D-based growth models. Our finding is consistent with Ang and Madsen (2011), J. Risk Financial Manag. 2022,15, 344. https://doi.org/10.3390/jrfm15080344 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 344 2 of 42 who find that R&D-based growth models are the class of models most consistent with the growth experience of the East Asian “miracle” economies. Interestingly, we do not find that industrial support particularly raises the productivity of firms in industries that might be expected to suffer from financing constraints. This indicates that our results concerning R&D are likely due to channels that do not involve financing constraints. 2 We also find that industrial support is less beneficial to politically connected firms, underlining the importance of conditioning on connections. Finally, we develop a general equilibrium R&D-driven growth model with many industries, extending the one-sector framework of Howitt (1999), in order to show that R&D-based growth models can broadly account for our empirical findings. In the model, we show that industrial support encourages productivity growth particularly among firms that are in R&D-intensive industries, as in the data. This is so even though there are no financing constraints in the model. Instead, it occurs simply because lower taxes increase the returns to successful R&D. This is so even though the model does not display scale effects. We conclude that industrial support mainly encourages growth by increasing the return to R&D, rather than by alleviating financing constraints that might hinder R&D, and that politically connected firms are less likely to benefit from this support. Our paper relates to several bodies of literature as detailed in Section 1.1 below, including those on industrial policy and political connections. Aghion et al. (2015) explore industrial policy in China, and Acemoglu et al. (2018) develop and calibrate a model in which operational subsidies that target innovation by highly productive firms may improve welfare. Harrison et al. (2019) find that both state owned enterprises (SOEs) and former SOEs in China, while still having access to government assistance, fall behind private firms in terms of productivity. Fang et al. (2018) find that removing opportunities for corruption makes subsidies more effective at stimulating innovation. Section 2describes the sources of data, and provides details on our empirical strategy. Section 3reports empirical results and the main robustness checks. Section 4describes the model economy and its equilibrium. Section 5concludes. 1.1. Related Literature 1.1.1. Literature on Industrial Policy In the extensive literature on industrial policy, most studies pursue one of two approaches. A first approach is qualitative, offering a historical perspective into the stages of development of different economies to generate policy frameworks that might explain their growth experiences (Amsden 1992;Chang 2002;Lin 2003;Wade 1990). More recent work on industrial policy examines links between industrial policy and economic development using quantitative tools. For example, Aghion et al. (2015) explore industrial policy in the context of the Chinese economy among large and medium enterprises between 1998 and 2007. They show that industrial policies targeted at competitive sectors or aimed at promoting competition improve productivity growth. 3 They argue that such industries benefit from support because competitive pressure motivates firms to innovate in order to differentiate horizontally, which in turn fosters productivity growth. This contrasts with the consensus regarding industrial policy in more developed economies, which is generally viewed as having reduced productivity by propping up failing firms—see Leonard and Van Audenrode (1993), Samaniego (2006) and Ranasinghe (2014). Meanwhile, Acemoglu et al. (2018) use U.S. Census micro data to estimate the parameters of a model of firm-level innovation, productivity growth and reallocation with endogenous entry and exit. They show that industrial policy subsidizing the operations of existing firms that are of “low type” in terms of innovative capacity would negatively affect growth and aggregate welfare. Their policy experiment of a subsidy of 5 percent of GDP for incumbent firms’ operations leads to a reduction in welfare of about 1.5 percent because it deters entry by new “high-type” firms. Meanwhile, a reduction of subsidies to low-type firms coupled with an increase in financial support to R&D activities of high-type firms J. Risk Financial Manag. 2022,15, 344 3 of 42 encourages the entry of more productive firms and the exit of low-type firms. Their paper places a strong emphasis on innovation, and recommends the type of industrial policy that focuses on subsidizing R&D by highly productive firms. This argument is echoed by Boeing et al. (2016) who find that R&D spending had a positive effect on the productivity of publicly listed Chinese firms in the 2001–2011 period. 1.1.2. Literature on Political Connections Also using Chinese data, Harrison et al. (2019) find that, while private firms that used to be state owned enterprises (SOEs) still have better access to government assistance compared to private firms, both privatized SOEs and SOEs fall behind private firms in their profitability. These results suggest that industrial support may be endogenous: firms that have ties with the government tend to get more state support, yet these firms may be less productive or have other characteristics related to outcome variables. This indicates the importance of conditioning on political connectedness when estimating the impact of industrial support. Akcigit et al. (2018) present further evidence that businesses with political connections tend to perform worse than average. They develop a model of firm dynamics in which firms face a tradeoff between investing in innovation and strengthening their political connections. Using Italian data from 1993 to 2014, they find that firm-level political connections are ubiquitous, especially among large enterprises. However, industries with more politically connected firms are found to have weaker productivity growth. They also find that the firms that lead the market are much more likely to invest in political connections and less likely to innovate. Together, these findings suggest that the productivity impact of industrial support depends on the stage of development, and on the presence of political connections. Additionally, some studies have uncovered evidence that firms with political connections enjoy better access to financing. For example, Rand (2017) find in Vietnamese small and medium enterprise data that political connectedness, proxied by Communist party membership of the owner or manager of each firm, decreases the likelihood of firms being credit-constrained. Li et al. (2008) find that political connections improve Chinese firms’ access to loans from banks and other state institutions, and that private firms with political connections perform better after controlling for human capital and other variables. Their paper concludes that political connections have a positive impact on firm performance in countries with weaker market institutions and legal frameworks. Meanwhile, Khwaja and Mian (2005) define political connectedness as the participation of a firm’s director in an election. Using loan data from over 90, 000 Pakistani firms from 1996 to 2002, the authors investigate rent-seeking activities among politically connected firms through firm fixedeffects and variations for the same firm across lenders over time, finding that politically connected firms borrow 45 percent more and have 50 percent higher default rates. However, as pointed out in Rajan and Zingales (1998), observing that a firm draws on external finance does not tell the observer whether this occurred because credit constraints were relieved, or whether they obtained more financing because they were more productive for some other reason that increased their demand for financing. 1.1.3. Literature on Industry Variation Our strategy to measuring the impact of industrial support is to draw on the extensive literature that studies the impact of industry variation in the technology of production. For example, Rajan and Zingales (1998) define external finance dependence (EFD) as the tendency of an industry to rely on external funds, and use it to study the impact of financial development on industry growth, finding that financial development encourages growth in high-EFD industries. Ilyina and Samaniego (2011) find a link between EFD and R&D intensity. Braun and Larrain (2005) study whether industries where firms have a greater tendency to use intangible assets are more sensitive to the business cycle, as a way of detecting whether changes in financing conditions are an important channel of the business cycle. We will instead exploit industry variation in the technology of production to identify J. Risk Financial Manag. 2022,15, 344 4 of 42 the channels through which industrial support affects firm performance. For example, if we find that industrial support disproportionately increases productivity growth in high-EFD industries or in low-tangibility industries, we might conclude that industrial support works by relieving credit constraints. Given that the literature indicates that politically connected firms are not the same as a typical firm, we also require data that contain proxies for political connections. 1.1.4. Literature on Measuring Political Connections Political support measures tend to be single binary proxy variables. Harrison et al. (2019) measure connections based on whether or not a firm was once a SOE. Others such as Li et al. (2008) use Communist party membership, and Wu et al. (2012) define political connectedness according to whether or not a firm’s manager or chairman is currently serving or has previously served in the government or the military. In this paper, however, we will measure political connectedness using multiple binary proxy variables that are jointly significant. This way, unlike the related literature, we do not rely on one particular proxy being or not being suitable. The related literature tends to have only one proxy for political connections, if any, such as Khwaja and Mian (2005) or Li et al. (2008). Instead, we identify multiple binary indicators to proxy for unobserved heterogeneity, as suggested in Williams (2019). We show that our binary proxies represent different dimensions of political connections that need to be accounted for in examining the impact of industrial policy on firm productivity—otherwise, the model could still suffer from omitted variable bias. The analysis of multiple industry interactions also allows us to sort between different channels whereby industrial support might impact economic outcomes. Finally, our model shows that an R&D-based growth model that does not display scale effects can be extended to a heterogeneous multi-industry context to account for our empirical findings without resort to financing constraints. 2. Data and Methods 2.1. Data Description We rely mainly on two sources of data: (i) data from six rounds of the bi-annual survey on Vietnamese small and medium enterprises (henceforth the SME Survey) in the manufacturing sector between 2005 and 2015, 4 and (ii) data from the Compustat database of financial, statistical and market information on active and inactive companies in the United States. While the SME Survey provides firm-level data on industrial support, productivity growth and political connections, Compustat allows us to calculate the technological variables that proxy for R&D intensity and financing constraints at the industry level. The SME Survey follows the World Bank’s definitions of micro, small and medium enterprises. Micro enterprises employ up to 10 workers, small enterprises up to 50 workers and medium enterprises up to 300 employees. The sampling strategy is consistent across all rounds of the survey including 2500 to 2800 enterprises and re-interviewing surviving firms every survey year. The survey focuses on non-state enterprises, including private and cooperative companies, limited liability companies, joint stock companies without capital from the state, and household enterprises which are defined as privately owned economic organizations not registered and operational under the Enterprise Law (Central Institute for Economic Management 2015). The population of non-state manufacturing enterprises is drawn from a representative sample of the Establishment Census from 2002 and the Industrial Survey 2004–2006 conducted by the General Statistics Office (GSO) of Vietnam. The survey is conducted in selected districts in 10 provinces or central cities including Ha Noi, Ho Chi Minh City, Hai Phong, Long An, Ha Tay, Quang Nam, Phu Tho, Nghe An, Khanh Hoa and Lam Dong, and uses a stratified sample by type of ownership to make sure all types of ownership are represented. Informal firms are defined as those that do not have a Business Registration License or tax code and are not registered with district authorities according to the Central Institute for Economic Management (2015). J. Risk Financial Manag. 2022,15, 344 5 of 42 Descriptively, Table 1shows the number of firms in the survey by province and year, while Table 2shows the distribution of firms by number of workers and type of ownership. Since each round of the survey obtains data on the previous year, the reported years are those to which survey data correspond. Table 1. Distribution of Firms by Province and Year. Province 2004 2006 2008 2010 2012 2014 Ha Noi 310 296 299 291 284 297 Phu Tho 283 255 271 254 261 255 Ha Tay 400 394 383 349 347 372 Hai Phong 217 206 227 220 203 223 Nghe An 394 359 370 353 358 343 Quang Nam 176 173 167 166 167 171 Khanh Hoa 102 92 97 99 91 99 Lam Dong 94 89 74 82 85 90 HCMC 701 630 635 591 632 658 Long An 143 138 133 126 136 133 Total 2820 2632 2656 2531 2564 2641 Table 2. Distribution of Firm Observations by Number of Employees and Type of Ownership (unbalanced panel). Number of Employees Type of Ownership 1–50 51–100 101–200 201–300 >300 Household enterprise 10,305 35 3 3 0 Private enterprise 1153 74 34 13 11 Partnership 36 6 0 0 1 Cooperative 369 43 17 4 3 Private limited company 2456 390 235 55 20 Joint stock company with state capital 13 7 8 6 5 Joint stock company without state capital 368 79 65 9 9 Joint venture with foreign capital 02000 Local state enterprise 3 0 1 0 2 Total 14,703 636 363 90 51 As shown in Table 2, about 70% of the firms in our data are small household enterprises, which reflects the situation of the Vietnamese economy where the majority of small and medium businesses are micro enterprises. At the same time, small and medium businesses are considered the central momentum of economic development for the Vietnamese economy: in 2013, non-state enterprises employed almost 60% of the country’s total workforce (Central Institute for Economic Management 2015). As such, it is important to understand the structure and characteristics of this SME sector in order to identify the best policy options to encourage productivity growth for a developing economy such as Vietnam. It is also worth noting that the industries represented in the data are not limited to the manufacturing sector: they also include agriculture/primary production and services because there was some sector switching among firms over time in the sample, which is not uncommon for SMEs in a transition economy such as Vietnam. J. Risk Financial Manag. 2022,15, 344 6 of 42 All financial variables and those used to calculate total factor productivity are converted to real terms using national GDP deflators and winsorized at the 1% and 99% levels to minimize the possibility that outliers might distort the results of our analyses. Table 3provides descriptive statistics on some key variables in this paper. Table 3. Descriptive Statistics. Variable Mean Std. Dev. Max. Min. Labor (number of employees) 22 56 2561 1 Gross output (million VND) 1359.6 3204.9 21,851.3 13.15 Value added (million VND) 339.2 689.1 4294.2 2.1 Fixed assets (million VND) 1008.5 1924.5 12,041.6 2.6 Material cost (million VND) 959.6 2423.9 16,528 0.05 Log of TFP (Olley–Pakes) 3.15 0.78 8.98 −6.8 Tax holiday (million VND) 38.21 89.78 613.9 0 Log of tax holiday 2.46 1.53 6.41 −9.7 Indicator of state ownership status (binary) 0.003 0.05 1 0 Indicator of export status (binary) 0.08 0.27 1 0 Note: Labor measures the total number of employees working for an enterprise. The measurement of total factor productivity (TFP) growth follows Olley–Pakes method and is described in Appendix A. 2.2. Empirical Strategy We employ fixed-effects panel regressions to explore (i) the relationship between political connectedness and industrial policy, and (ii) the impact of industrial support in the form of tax holidays on firm performance, controlling for political connections. This underlines the importance of conditioning on political connections when studying the impact of industrial support. Then, we examine possible mechanisms underlying that impact including (i) the channel of R&D intensity, and (ii) the easing of financing constraints. 2.3. Impact of Political Connections on the Allocation of Industrial Support We first explore the relationship between political connectedness and government support. Affirmative results would highlight the importance of controlling for political connectedness for understanding the impact of industrial policy on productivity growth. Since the distribution of tax holidays is quite skewed in the data, we use the natural log of tax holiday (denoted as Lntax) instead of its absolute value in order to avoid having outliers drive our results. The graphs showing the distribution of the tax holiday variable and its log are presented in Appendix C. We estimate the following equation: Lntaxijt =θ1Zijt +θ2Sjt +βPcijt +fi+Dt+εijt (1) where Lntaxijt is the natural log of the amount of tax holiday firm i in industry j enjoys each year. Pcijt measures the level of political connectedness of each firm in a given year, fi is firm fixed effects and Dt is time fixed effects. This way we account for any time-varying conditions that might affect productivity such as the state of the business cycle, as well as any firm characteristics that might affect productivity, so that the remaining variation in productivity must be accounted for only by firm-time-specific variables. Zijt is a vector of firm-level control variables including state ownership indicator, export status and firm size (total number of workers) and Sjt is a vector of industry-level control variables including number of firms and the level of intra-industry competition measured by the Lerner Index. We expect a positive and statistically significant coefficient on Pcijt i.e., β , which means that the more politically connected a firm is, the more tax holiday it receives, controlling for firm heterogeneity and time-varying factors. The level of political connectedness is represented by seven dummy variables already available in the dataset thanks to the innovative content of the questionnaire, part of which aims to understand firms’ social networks. For each of these variables, the value of 1 J. Risk Financial Manag. 2022,15, 344 7 of 42 represents political connectedness and 0 represents the lack thereof. The seven binary proxies are listed and defined in Table 4. Table 4. Binary Variables Representing Political Connectedness. Variable Name Definition Pc 1 Assistance at startup received from local authorities Pc 2 Previous work status: whether manager was an employee of an SOE Pc 3 Political Party Membership: whether manager was a Party member Pc 4 Sales structure: % of goods sold to SOEs or local authorities of 30% or higher Pc 5 % of procurement: % of goods procured from SOEs of 30% or higher Pc 6 Selection of SOEs as suppliers or under direction by local authorities Pc 7 Obtainment of services from SOEs Here, the political party membership of the firm’s director or manager is represented by the third binary variable of political connection (Pc 3). In addition, the other six binary variables show other aspects of political connectedness, for example whether the firm received and assistance from local authorities at its early stage (Pc 1), whether the firm is directed by local authorities to select state-owned enterprises (SOEs) as its suppliers (Pc 6), or whether the firm’s sales or procurement are disproportionately with SOEs (Pc 4 and Pc 5). This paper follows Williams (2019) in the recognition of the multi-dimensionality of otherwise omitted variables (in our case, political connectedness) as represented by these seven variables. This assertion on the multidimensional nature of political connectedness is supported by the values of correlations between these seven binary proxies as shown in Table 5. While most of these political connection variables are positively and significantly correlated with each other, the magnitudes of these correlations remain low, and some correlations are negative or insignificant, which suggests that these variables capture different aspects of political connectedness. Table 5. Pairwise Correlations of Political Connection Variables. Pc 1 Pc 2 Pc 3 Pc 4 Pc 5 Pc 6 Pc 7 Pc 1 1 Pc 2 0.0136 1 Pc 3 0.0284 * 0.2468 * 1 Pc 4 0.0359 * 0.0743 * 0.0436 * 1 Pc 5 0.0262 * 0.0488 * 0.0240 * 0.1079 * 1 Pc 6 −0.0093 −0.0121 0.0081 0.0087 0.0304 * 1 Pc 7 0.0756 * − 0.0556 * 0.0173 * 0.0294 * −0.0066 0.0226 * 1 Note: * p< 0.5. In the regression model, political connectedness is constructed in two ways: (i) as a vector of all seven of its dimensions, and (ii) collapsed into a sum of the seven dimensions for each firm in each year. The sum variable represents each firm’s degree of political connected in an aggregate sense, and would thus be meaningful for the assessment of how overall political connections interact with the allocation of tax subsidies. Among the industry-level control variables, the Lerner Index represents the magnitude of importance of markups, defined as the difference between price and marginal cost with respect to the firm’s total value added. We follow Aghion et al. (2015) in first aggregating operating profits, capital costs and sales at the industry level then calculating the Lerner index as the ratio of operating profits less capital costs to sales. The value of Lerner index should vary between 0 and 1 with 0 reflecting perfect competition in which there should be no excess profits above capital costs. Therefore, the variable representing the degree of competition is defined as ( 1 −Lerner−Index) so that a greater value of this variable represents a greater level of competitiveness. We include this variable as Aghion et al. J. Risk Financial Manag. 2022,15, 344 8 of 42 (2015) argue that it is important to control for the level of intra-industry competition when exploring the impact of industrial policy on firm performance. Regarding tax holidays, we follow Aghion et al. (2015) in defining a firm as a recipient of a tax holiday in a year if that firm paid less than the statutory income tax rate. The amount of tax holiday for each firm is calculated as the difference between the amount of tax firm would have to pay given the statutory tax rates and the amount of tax they actually paid. For example, if the statutory income tax rate is 25% while a firm actually paid 20%, the tax holiday that firm enjoyed would be calculated by multiplying that firm’s operating profits by 5%. According to PricewaterhouseCoopers (2017), the corporate income tax rate in Vietnam was 25% until 2014. Table 6shows the amount of tax holiday that Vietnamese SMEs enjoyed from 2005 to 2015. The first row of the table shows the number of firms which did not enjoy any tax incentive each year i.e., value of 0 for tax holiday. Table 6. Vietnamese SMEs’ tax holidays between 2005 and 2015 (Unit: Million VND). Amount of Tax Holiday Year (Million VND) 2004 2006 2008 2010 2012 2014 Total 0 256 75 93 109 2536 206 3275 >0 to 10 1736 1474 1477 1334 28 1512 7561 10 to 50 534 748 684 706 0 631 3303 50 to 100 126 147 173 171 0 131 748 100 to 300 122 121 154 143 0 93 633 >300 46 67 75 68 0 68 324 Total 2820 2632 2656 2531 2564 2641 15,844 As shown in Table 6, the number of firms that did not receive any tax holiday declined from 2004 to 2008 and then slightly increased in 2010 before reaching an unusually high number in 2012 and going back to similar level with pre-2012 period in 2014. A possible reason why there are as many as 2536 firms that did not enjoy any tax benefit in 2012 is that out of 2564 firms in the winsorized sample, 2435 firms reported making zero gross profit for that year. This shows that the SME sector of Vietnam was struggling after the global financial crisis and in particular in the years of 2011 and 2012—consistent with the information that 49,000 SMEs closed down in 2011. 5 Even if we consider year 2012 as an outlier, in the robustness checks section we show that our results are robust to the exclusion of year 2012 from the dataset. 2.4. Impact of Industrial Support on Firm Productivity Next, we explore the effects of industrial policy in the form of tax holidays on firmlevel productivity. We expect that firms with political connections are less productive than other firms, and that the former would use tax benefits less productively than firms that are not politically connected. For this purpose, our regression includes the log of total factor productivity (TFP) as the dependent variable instead of tax holiday, and the log of tax holiday now as one of the explanatory variables: lnTFPijt =θ1Zijt +θ2Sjt +β1Lntaxijt +β2Techijt +fi+Dt+εijt (2) lnTFPijt =θ1Zijt +θ2Sjt +β1Lntaxijt +β2Techijt +δ1Pijt +δ2Pijt ×Lntaxijt +fi+Dt+εijt (3) where Lntaxijt is the log of tax holiday, lnTFPijt is the log of TFP of firm i in industry j at time t , Techijt is a dummy variable representing whether the firm received technical assistance from government at each time, Pijt is the vector of political connection indicator J. Risk Financial Manag. 2022,15, 344 15 of 42 Table 11. Cont. (1) (2) (3) (4) (5) TFP_OP TFP_OP TFP_OP TFP_OP TFP_OP Firm Size (Number of Employees) −0.00210 *** −0.00210 *** −0.00211 *** −0.00210 *** −0.00211 *** (0.000563) (0.000565) (0.000570) (0.000566) (0.000566) SOE Indicator 0.270 0.259 0.254 0.256 0.254 (0.254) (0.251) (0.251) (0.251) (0.251) Industry Size (Number of Firms) 0.00164 * 0.00166 ** 0.00159 * 0.00158 * 0.00156 * (0.000847) (0.000831) (0.000845) (0.000840) (0.000854) Industry Competition Level 0.121 0.115 0.128 0.139 0.128 (0.237) (0.236) (0.238) (0.238) (0.238) Pc 1 −0.0572 −0.0580 −0.0531 −0.0549 −0.0556 (0.0821) (0.0821) (0.0823) (0.0821) (0.0822) Pc 2 0.0554 0.0559 0.0548 0.0553 0.0544 (0.0520) (0.0518) (0.0519) (0.0520) (0.0520) Pc 3 −0.108 −0.111 −0.112 −0.111 −0.112 (0.0749) (0.0752) (0.0754) (0.0753) (0.0753) Pc 4 0.0837 0.0872 0.0769 0.0751 0.0764 (0.0767) (0.0769) (0.0782) (0.0766) (0.0778) Pc 5 0.0505 0.0522 0.0519 0.0518 0.0524 (0.0791) (0.0787) (0.0786) (0.0792) (0.0791) Pc 6 −0.842 −0.809 −0.822 −0.849 −0.831 (0.627) (0.625) (0.627) (0.634) (0.626) Pc 7 0.0628 0.0617 0.0607 0.0635 0.0625 (0.0471) (0.0469) (0.0471) (0.0472) (0.0471) Interaction Term Pc 1 & Log of Tax Holiday 0.0534 * 0.0541 * 0.0521 * 0.0530 * 0.0528 * (0.0275) (0.0276) (0.0276) (0.0275) (0.0276) Interaction Term Pc 2 & Log of Tax Holiday −0.0247 −0.0250 −0.0242 −0.0243 −0.0241 (0.0171) (0.0171) (0.0171) (0.0171) (0.0172) Interaction Term Pc 3 & Log of Tax Holiday 0.000595 0.000980 0.00253 0.00223 0.00273 (0.0225) (0.0226) (0.0226) (0.0225) (0.0226) Interaction Term Pc 4 & Log of Tax Holiday −0.0222 −0.0234 −0.0206 −0.0198 −0.0202 (0.0236) (0.0237) (0.0241) (0.0237) (0.0240) Interaction Term Pc 5 & Log of Tax Holiday −0.0389 −0.0395 −0.0402 −0.0399 −0.0401 (0.0253) (0.0251) (0.0251) (0.0253) (0.0253) Interaction Term Pc 6 & Log of Tax Holiday 0.221 0.202 0.215 0.226 0.217 (0.229) (0.230) (0.227) (0.232) (0.228) Interaction Term Pc 7 & Log of Tax Holiday −0.0155 −0.0155 −0.0146 −0.0155 −0.0153 (0.0128) (0.0127) (0.0127) (0.0129) (0.0127) EFD −0.0569 (0.0579) Interaction Term EFD & Log of Tax Holiday 0.0285 J. Risk Financial Manag. 2022,15, 344 16 of 42 Table 11. Cont. (1) (2) (3) (4) (5) TFP_OP TFP_OP TFP_OP TFP_OP TFP_OP FIX −0.213 (0.317) Interaction Term FIX & Log of Tax Holiday 0.0876 (0.116) LMP 0.970 (1.289) Interaction Term LMP & Log of Tax Holiday 0.0242 (0.411) DEP 0.179 (0.545) Interaction Term DEP & Log of Tax Holiday −0.0623 (0.215) Year Fixed Effects Yes Yes Yes Yes Yes R20.188 0.188 0.188 0.188 0.187 Robust standard errors in parentheses, clustered at the firm level All regressions include firm fixed effects and year dummies. * p< 0.1, ** p< 0.05, *** p< 0.01. It can be seen from the results that tax benefits lead to an increase in firm-level productivity as the coefficients on the log of tax holiday are positive and significant in both specifications. The coefficient of 0.253 in model specification (2) implies that an increase in tax holiday by 1% is associated with an increase of 0.253% in firm-level TFP. This coefficient increases to 0.275 in model specification (3), showing that when political connectedness is controlled for, tax holidays have a greater effect on firm productivity, and that firms without political connections would be more productive with tax holidays than firms that are politically connected. In addition, the political connection variables are also found to be jointly significant. Observe that not all the political connections interactions have the same sign. While the preponderance of the literature finds that political connections weaken any positive impact of industrial support on firm outcomes, the fact that we find this is not necessarily always the case is consistent with Ouyang and Zhang (2019). This underlines the importance of using several proxies for political connections—both for adequately conditioning on political connections, and for adequately identifying their impact. The positive and significant value of the coefficient of the interaction term between R&D intensity and tax holiday in Table 11 indicates that industries that are more R&D intensive would be more productive with tax subsidies from the government. Lack of significant results on the other technological variables representing financing constraints indicate that relieving financing constraints is not the main way industrial policy affects firm-level productivity. Later we study government technical assistance to firms and tariff rates as alternative instruments of industrial policy, finding they do not seem to have a significant impact on firm performance. We conclude that industrial support in the form of tax holidays increases productivity growth, particularly in R&D intensive industries, and particularly among firms that are not politically connected. We also find no evidence that financing constraints play a role in these results. J. Risk Financial Manag. 2022,15, 344 17 of 42 3.3. Robustness Checks We check the robustness of the results with respect to (i) the setting of tariff rates at the industry level as an alternative proxy of industrial policy, and (ii) a combination of “stickier” political connection variables to address endogeneity concerns. Additional robustness checks are performed in Appendix Dwith regard to (i) alternative measures of TFP i.e., TFP calculated using OLS Fixed Effects (FE) and the Levinsohn–Petrin methods, (ii) alternative underlying mechanisms i.e., the mechanism proposed by Aghion et al. (2015) where industrial policy works through fostering competition measured by the Herfindahl index representing the dispersion of subsidies within each industry, (iii) the consideration of the skewed distribution of R&D intensity by repeating the regression either by dropping values of zero or with bootstrapped errors, (iv) excluding 2012 to make sure the results hold without major outliers, (v) subsamples of firms of different sizes, and (vi) post-estimation tests. 3.3.1. Use of Tariff Rates as Industrial Policy In the industrial policy literature, tariffs are also considered a measure of industrial policy, one that can be affected by political connections: see Grossman and Helpman (1994) and Goldberg and Maggi (1999). A higher tariff rate signifies protectionism against foreign competition. A low tariff rate, however, means cheaper imports of inputs for production. Therefore, it is not clear what impact tariff rates have on firm performance. We test this industrial policy measure by including tariff rates at the industry level instead of tax holidays as the proxy for industrial policy in the regression model. We obtained tariff data from the World Bank Integrated Trade Solution (WITS) platform for corresponding years and calculated tariff rates imposed by Vietnam at the industry level. The tariff rate in use is the average maximum input tariff rate that the Vietnamese government set for countries with Most Favored Nations status. The tariff rates by industry from 2004 to 2014 are shown in Table 12. Table 12. Vietnam’s Average Tariff Rates by Manufacturing Industry from 2004 to 2014 (%). Sector 2004 2006 2008 2010 2012 2014 Primary production/Agriculture 15.2 15.3 12.6 10.1 9.8 10.1 Food and beverages 32.8 32.6 24.5 21.5 20.3 20.7 Tobacco 65.0 65.0 82.5 80.0 78.6 80.0 Textiles 32.8 32.8 10.1 10.0 10.0 10.0 Apparel 48.4 48.4 20.4 20.1 19.8 19.8 Leather 29.0 29.0 23.0 20.2 18.4 18.4 Wood 12.9 12.9 11.1 9.1 8.6 8.4 Paper 20.1 20.1 16.9 14.4 12.8 12.7 Publishing and printing 21.9 21.9 16.5 13.6 12.7 12.3 Refined petroleum etc. 5.6 5.6 3.4 4.7 3.7 4.6 Chemical products etc. 4.4 4.4 3.6 3.0 2.6 2.6 Rubber 18.5 18.5 16.4 14.5 13.2 12.8 Non-metallic mineral products 24.4 24.4 21.3 20.0 19.0 19.1 Basic metals 4.2 4.2 2.4 2.7 2.5 2.9 Fabricated metal products 18.8 18.8 16.4 15.2 14.5 14.7 Electronic machinery, computers, radio, tv, etc. 10.7 10.7 8.1 7.1 6.2 6.3 Motor vehicles etc. 53.8 53.9 36.7 40.1 35.7 34.3 J. Risk Financial Manag. 2022,15, 344 18 of 42 Table 12. Cont. Sector 2004 2006 2008 2010 2012 2014 Other transport equipment 15.4 15.4 14.3 13.4 12.3 12.3 Furniture, jewellery, toys, music equipment etc. 17.2 17.2 13.9 12.1 11.5 11.6 Services 8.5 8.3 7.4 6.6 6.2 6.4 When we include the measure of tariffs at the industry level instead of tax holiday in the right hand side of the regressions, we do not obtain significant results for the coefficients on the tariff variable, which suggests that preferential treatment in terms of tariff rates at the industry level does not seem to have an impact on firm productivity. These results are shown in Table 13 below. Table 13. Robustness Checks with Tariff Rates at the Industry Level as Additional Policy Measure. (1) TFP_OP Tariff 0.000264 (0.000640) Technical Assistance (Dummy) 0.00677 (0.0571) Firm Size (Number of Employees) −0.00142 *** (0.000220) SOE Indicator 0.152 (0.176) Industry Size (Number of Firms) 0.000987 (0.000707) Industry Competition Level −0.163 (0.260) Firm Fixed Effects Yes Year Dummies Yes Number of observations 10955 R20.0194 Robust standard errors in parentheses, clustered at the firm level. * p< 0.1, ** p< 0.05, *** p< 0.01. 3.3.2. Combination of “Stickier” Political Connection Variables As the level of firm productivity is controlled for with the inclusion of firms’ fixed effects, an additional robustness check is conducted to verify that any reverse causality between political connection and firm productivity e.g., firms seek to change their level of political connectedness in response to their productivity shocks, is not a significant concern. We thus select the political connection variables that are less easy to adjust over time i.e., “stickier” or less sensitive to productivity shocks in other words, and rerun the regressions with those connection variables only. The variables we select are those related to the firms’ links to an SOE (variables 4, 5 and 7). The coefficient on tax holiday remains stable with these alternative regressions, which confirms the validity of the identification strategy as shown in Table 14 below. J. Risk Financial Manag. 2022,15, 344 19 of 42 Table 14. Robustness Checks with “Stickier” Political Connection Variables. (1) TFP_OP Log of Tax Holiday 0.271 *** (0.0157) Technical Assistance (Dummy) −0.0700 (0.0618) Firm Size (Number of Employees) −0.00216 *** (0.000570) SOE indicator 0.230 (0.250) Industry size (Number of Firms) 0.00155 * (0.000835) Industry Competition Level 0.136 (0.237) Pc 4 (Sales structure) 0.0759 (0.0778) Pc 5 (Procurement structure) 0.0645 (0.0780) Pc 7 (Obtainment of services from SOEs) 0.0427 (0.0472) Interaction term Pc 4 & Tax Holiday −0.0192 (0.0240) Interaction term Pc 5 & Tax Holiday −0.0450 * (0.0249) Interaction term Pc 7 & Tax Holiday −0.00885 (0.0129) Firm Fixed Effects Yes Year Dummies Yes Number of observations 8572 R20.186 Robust standard errors in parentheses, clustered at the firm level. * p< 0.1, ** p< 0.05, *** p< 0.01. 4. Discussion In this section, we present an extension of the Howitt (1999) framework, generalized to allow for many heterogeneous industries. 8 In the model, industries vary in terms of their market size and, as in Schmookler (1966), this leads R&D intensity to vary endogenously across industries, because larger product markets encourage innovation by offering greater returns to successful innovators. Some empirical studies of specific products or industries find some evidence of a demand-innovation link—for example, Newell et al. (1999), Popp (2002) and Acemoglu and Linn (2004). These findings underline the importance of demand in providing incentives for R&D. There is also broad aggregate empirical support for creative-destruction style models, see for example Ha and Howitt (2007), Madsen (2008) or Ang and Madsen (2011). In particular, Ang and Madsen (2011) find that this class of model best explains the experience of the East Asian “miracle” economies. An interpretation of our paper is that it provides new cross-sectional support for this kind of model. In the model, there is a quality ladder that firms may approach by performing R&D. Thus, technology adoption requires investment, consistent with the findings in Cohen and Levinthal (1990) and Griffith et al. (2004). As a spillover, this absorptive R&D also reveals the path to adopting further technologies in the future. J. Risk Financial Manag. 2022,15, 344 20 of 42 4.1. Household Preferences Time is continuous, and there is a [0, 1] continuum of dynasties, each of mass Lt= L0egt L. We assume that the rate of population growth gt L>0 is exogenous. There are I∈N types of final good in the economy, each produced by a separate industry. There exists in turn [0, Qit] continuum of varieties of each good i≤I . Let chit be consumption of variety h of good i at date t . Dynastic preferences over consumption ct are: Z∞ 0e−rtLtu(ct)dt (5) where u is the instantaneous utility function and r is the discount rate. Consumption ct is an aggregate of the agent’s consumption cit of each good i≤I , which is in turn an aggregate over the varieties h∈[0, Qit]: ct= I ∏ i=1cit ωiωi ,cit =ZQit 0chitdh,i∈{1, . . . , I}(6) where the preference parameter ωi is the equilibrium share of expenditure devoted to good i , which will be a key determinant of equilibrium R&D intensity. Each agent is also endowed with one unit of labor that may be spent working in production, or in research, as described below. In either case, it earns the competitive wage wt. Their budget constraint is I ∑ i=1 qit ZQit 0cihtdh ≤Πt+wt(Lt−Rt)+Tt≡LtSt(7) where we have used the fact that all varieties h of any good i are perfect substitutes, so they all command the same price qit in equilibrium. 9 Here Πt equals after-tax profits from various sources, and Tt is a lump sum transfer, both in terms of the numeraire. Rt , to be expanded upon later, is the use of labor in research rather than goods’ production. Also wt is the competitive wage. We set wt= 1 so labor is the numeraire, and define St as income per capita, in terms of the numeraire. 4.2. Final Goods Each variety h of good i is supplied by a monopolist (below the variety index h is suppressed for simplicity). Each monopolist holds a patent on the technology for producing that variety, indexed by the date v at which the innovation took place (its vintage). At any date t , the production function for any given variety of good i for this monopolist is yit(v)=Aivxα it , where yit(v) is output, xit is input of a variety-specific intermediate and Aiv is the productivity of the monopolist’s technology. The monopolist solves: max{qit Aivxα it −pitxit}(1−τ)(8) where qit is the price of good i and pit is the marginal cost of the intermediate. Here τ is the tax rate on earnings. The solution to (8) implies: pit(xit)=αqiv Aitxα−1 it (9) 4.3. Intermediate Goods A patent-holding monopolist produces the intermediate xit using labor. The monopolist solves the static profit maximization problem: max xit {pit(xit)xit −wtxit}(1−τ), (10) J. Risk Financial Manag. 2022,15, 344 21 of 42 where the inverse demand curve pit(·)is given by (9), so this becomes (1−τ)max xit {αqit Aivxα it −wtxit}. The solution to this problem is xi(v,t)=α2qit Aiv wt1 1−α , (11) so that output of the variety equals yit(v)≡Aivα2qit Aiv wtα 1−α . Thus, pre-tax profits for a patent holder are: πir(v,t)≡qit Aiv wα t1 1−α π(12) where π≡hα×α2α 1−α−α2 1−αi . This also implies that, if πip(v,t) are the pre-tax profits of the final good producers, then: πip(v,t)=(1−α)(qit Aiv)1 1−αα2 wtα 1−α (13) 4.4. Vertical Innovation Agents may invest in R&D in order to uncover the technology to produce the intermediate good corresponding to a variety of good i at the current frontier productivity Amax it , which grows at rate gi . If an agent dedicates Nit units of labor to R&D in industry i , she harvests innovations at rate λNit . It will be convenient to define ¯ Nit as the total resources devoted to vertical innovation in industry i , and ¯ nit =¯ Nit Qit as the amount of vertical R&D per variety of good i . Since one firm produces each variety it is also interpretable as the vertical R&D per firm in industry i. Growth in the frontier technology Amax it is determined by spillovers from research. If the total amount of R&D in industry i is Nit , then the flow of new technologies for producing good iis ˙ Amax it =λ¯ Nit Amax it Qit σ. (14) This function assumes that new technologies depend on the rate of innovations λ¯ Nit . The parameter σ indicates the intensity of technological knowledge spillovers. The numerator Qit reflects the idea that research effort is dissipated across varieties Qit , the key mechanism of the Howitt (1999) model for avoiding scale effects. Finally, the spillover function (14) depends positively on the current frontier level Amax it , reflecting a “standing on shoulders” effect for which Ngai and Samaniego (2011) among others find evidence. As a result, the growth rate of the technology frontier in industry iis: gi≡˙ Amax it Amax it =λ¯ Nit Qit σ=λ¯ nitσ. (15) A successful innovator replaces the incumbent monopolist, and earns expected discounted profits ˜ Vit where ˜ Vit =Z∞ te−(r+λ¯ nis)s(1−τ)πis(t,s)ds. (16) The exponent λ¯ nis reflects the fact that, in expectation, future researchers may in turn displace the innovator. This displacement rate is λ¯ Nis Qis , because it is increased by the J. Risk Financial Manag. 2022,15, 344 22 of 42 research effort of others, and dissipated by there being more varieties across which future innovation might occur. Notice that τ enters ˜ Vit . This is because taxes reduce the potential earnings of successful researchers. It will be convenient to define Vit ≡˜ Vit/(1−τ) , which does not depend on any taxes. Thus, we have that the marginal return to spending a unit of labor on research in industry i is λVit(1−τ) . The marginal cost is wt , the price of labor. These must be equal when R&D input is optimal: λ(1−τ)Vit =wt. (17) Combining (12), (16) and (17), optimal vertical R&D choices satisfy: wt=(1−τ)λZ∞ 0e−(r+λ¯ nis)s"qis Amax it wα s1 1−α π#ds. (18) 4.5. Horizontal Innovation Agents may also invest in producing new varieties of any good i . If agents invest Mit units of labor in the production of new varieties in industry i , the flow of new varieties is given by: ˙ Qit =Ψ(Mit,Qit)(19) where Ψ is increasing and homogeneous of degree one. This structure assumes that having more varieties aids the production of new varieties, another “standing-on-shoulders” effect. Let hit =Mit/Qit , the horizontal R&D per firm, and define ψ(·)≡Ψ(·, 1) . We can rewrite (19) as: ˙ Qit =Ψ(hit, 1)Qit =ψ(hit)Qit. A horizontal innovation in industry i draws its productivity level Aiv from the existing distribution in industry i . It is straightforward to show that the expected discounted profits of a monopolist with technology of vintage v is Aiv Amax it 1 1−α˜ Vt . As a result, the expected profits from a horizontal innovation are: E"Aiv Amax it 1 1−α#˜ Vt where the expectation is taken over the distribution of Aiv at date t . If fi(v,t) is the distribution of firms over v at date t , then this expectation becomes Rt −∞Aiv Amax it 1 1−αfi(v,t)dv . For horizontal R&D allocations to be optimal, the marginal cost of R&D must equal this expression, times the marginal effect of an additional unit of labor devoted to production of new varieties in industry i . The marginal flow of new varieties is Ψ1(Mit,Qit)= dhΨMit Qit ,1Qiti dMit =Ψ1Mit Qit , 1=ψ0(hit) . Thus, optimal horizontal R&D allocations satisfy: 10 wt=ψ0(hit).E"Aiv Amax it 1 1−α#Vt(1−τ). (20) 4.6. Government The government collects taxes and redistributes them as a lump sum transfer Tt , balancing its budget every period. If fi(v,t) is the distribution of firms over v at date t industry i, the corresponding measure is Qit fi(v,t), and the balanced budget condition becomes: J. Risk Financial Manag. 2022,15, 344 23 of 42 Tt=τ∑ i Qit Zt −∞πip(v,t)fi(v,t)dv +τ∑ i Qit Zt −∞πir(v,t)fi(v,t)dv This notation also allows us to define after-tax profits Πt: Πt=(1−τ)∑ i Qit Zt −∞πip(v,t)fi(v,t)dv +(1−τ)∑ i Qit Zt −∞πir(v,t)fi(v,t)dv. This means that in equilibrium the household’s balanced budget condition must satisfy: LtSt=wt Lt−∑ i Nit −∑ i Mit!+∑ i Qit Zt −∞πip(v,t)fi(v,t)dv +∑ i Qit Zt −∞πir(v,t)fi(v,t)dv. 4.7. Stationary Equilibrium Definition 1. A stationary equilibrium (or “equilibrium” henceforth) is a set of initial conditions {Qi0,fi(·, 0)}i≤I and allocations such that households are optimizing based on their budget constraints, the government balances its budget every period, nit =ni at all dates t and hit =hi at all dates. Proposition 1. Equilibrium exists and is unique. Proof. See Appendix B. Definition 2. Research intensity in industry i at date t is defined as research expenditure per firm in industry i,11 ρit =(Nit +Mit)wt Qit =(nit +hit)wt. Set labor as the numeraire so wt= 1 at all dates. In Appendix Bwe show that, in equilibrium, nit =¯ ni=max   0, (1−τ)πωiSL0 α2α 1−αQi0 −r λ1+1 1−ασ   . (21) which does not depend on time. In addition, we are able to show that hit does not vary across time nor across industries. It follows that variation in research intensity depends only on ¯ ni, so that: Proposition 2. In equilibrium, (i) research intensity is constant over time in all industries—ρit =¯ ρi; (ii) equilibrium research intensity is positive in at least one industry, provided r is sufficiently small; (iii) equilibrium research intensity ¯ ρi is increasing in ωi/Qi0 –strictly among industries i:¯ ρi> 0. Proposition 2 tells us that, in our multi-industry environment, the key determinant of research intensity is market size, normalized by the initial number of varieties. This is a twist on the original idea of Schmookler (1966): the market size that is available to an innovator depends both on the preference parameter ωi and on the intensity of competition in that market—given initially by Qi0—which dissipates the returns to R&D. J. Risk Financial Manag. 2022,15, 344 24 of 42 Proposition 2 might also appear to suggest that a larger economy (i.e., with a larger initial value of L0 ) might have higher R&D intensity and thus productivity growth—even if the model structure avoids the “scale effects” problem that economies with a growing population grow at an accelerating rate. However it is worth underlining that the model as it stands takes L0 and {Qi0}i as given and independent variables—it does not provide a theory of {Qi0}i . A further extension of the model might imply that a larger economy would also have a larger number of varieties—i.e., that, just as growth over time in Lt leads to proportional growth in Qit , one might expect the same to be true in cross section across countries with different levels of L0 , so that a higher value of L0 is related to a proportional increase in Qi0 . In this case the scale effect in levels of L0 would be absent. We leave this for future work as it is not the focus of the paper. Our most important empirical result is that tax holidays particularly increase productivity in research-intensive industries. This result also holds in the model economy. Definition 3. Industrial support (or a tax holiday) is a decrease in τ. Proposition 3. Industrial support has a non-decreasing impact on productivity growth in all industries. Moreover, industrial support disproportionately increases productivity growth in high- R&D industries. In partial equilibrium, Equation (21) and Proposition 2 would suggest that d2¯ ni dτd(ωi/Qi0)< 0, so that lowering taxes would disproportionately increase R&D activity in the industries that were more R&D intensive to begin with. The fact that gi depends positively on ¯ ni , and that ¯ ni depends non-negatively on ωi/Qi0 , would then seem to deliver the result in Proposition 3. However, in general equilibrium, income S is endogenous and depends on taxes τ . As a result, the proof of Proposition 3 requires also showing that this result continues to hold in general equilibrium and is not overturned when S is endogenous to taxes. Overall, the model economy indicates that the positive interaction of research intensity with industrial support is to be expected in a multi-sector Schumpeterian growth model. A more nuanced conclusion would take into account that in the model economy the only source of variation in research intensity is ωi/Qi0 . The model has additional determinants of research intensity, such as λ and σ , which could in principle differ across industries. We do not do so as Equation (21) indicates that the interaction between R&D and taxes—whether direct or indirect through S —must involve the market size parameter ωi , not λ nor σ . Thus, the broader conclusion is that a multi-sector Schumpeterian growth model delivers the interaction in the data provided that the main determinants of crossindustry variation in research intensity are market-size or competition effects along the lines of Schmookler (1966). 5. Conclusions We study the mechanisms through which industrial policy might have an impact on economic outcomes by examining which industry characteristics interact with tax holidays. Specifically, we explore the impact of industrial policy on firm-level productivity using a dataset of Vietnamese SMEs. We use Vietnamese data because they contain a variety of information regarding various dimensions of firms’ political connections. Conditioning on political connections is important as the literature indicates that the level of political connections is related to the likelihood of receiving industrial support, as well as the extent thereof. The use of firm-level panel data also allows us to condition on any firmspecific characteristics that could affect the results but which might otherwise be difficult to measure. First of all, we find that, while tax benefits help increase overall firm-level productivity, their effect on firm productivity is stronger among firms that are not politically connected. J. Risk Financial Manag. 2022,15, 344 31 of 42 This is negative if and only if: (1−τ) S×dS dτ<1 (A17) Additionally, comparing across industries, d¯ ni dωi Qi0 =(1−τ)πSL0 α2α 1−α (A18) Then d2n∗ i dωi Qi0dτ=−πSL0 α2α 1−α +(1−τ)πL0 α2α 1−α S0(A19) It is easy to show this is negative (so higher taxes particularly hurt productivity growth in the R&D intensive industries) provided condition (A17) holds. We now work to demonstrate (A17) holds. Start from the fact that Walras’ Law implies all labor must be used up in equilibrium, so that ∑ i Nit Lt +∑ i Mit Lt +∑ i Qit Zt −∞x(v,t)fi(v,t)dv =Lt since xi(v,t)=α2qit Aiv wt1 1−α , (A20) this becomes ∑ i Ni0 L0 +∑ i Mi0 L0 +∑ i Qi0 L0Z1 0α2qit Aiv wt1 1−α1 aσa1 σda =L0 ∑ i Ni0 L0 +∑ i Mi0 L0 +α2α 1−α∑ i Qi0 L0 α−2α 1−αL0S0 Qi0 ωiσ 1−α+1 1 σ 1−α+1!=L or ∑ i Ni0 L0 +∑ i Mi0 L0 +∑ i Sωi=L0 or simply ∑ i Ni0 L0 +∑ i Mi0 L0 +S=L0 or ∑ i Qi0 L0 ¯ ni+∑ i ¯ hQi0 L0 +S=L0(A21) The total derivative of (A21) with respect to τbecomes: ∑ i Qi0 L0 dni dτ+dψ0−1 dx (x)−λ1+σ1 1−α∑ i Qi0 L0 +S0=0 (A22) The middle term is positive.15 If the first one is positive then dS dτ<0. Recall that dnit dτ=−πωiSL0 α2α 1−αQi0 +(1−τ)πωiL0 α2α 1−αQi0 ×dS dτ(A23) which is positive iff −S+(1−τ)×dS dτ>0 (A24) J. Risk Financial Manag. 2022,15, 344 32 of 42 which requires dS dτ> 0. So if dnit dτ> 0 then dS dτ> 0 and Equation (A22) implies that dS dτ< 0. This is a contradiction. Hence, it must be that dni dτ< 0. This implies that condition (A17) must hold, which in turn implies that d2n∗ i dωi Qi0dτ< 0. This completes the proof of Proposition 3, as industrial support is defined as a decrease in τ. Appendix C. Graphs on Distribution of Tax Holiday Variables Figure A1. Tax Holiday Distribution. Figure A2. Distribution of the Log of Tax Holiday. Appendix D. Additional Robustness Checks Appendix D.1. Alternative Measures of Firm Performance The pattern of results hold with TFP calculated using OLS FE method as well as Levinsohn–Petrin method i.e., the coefficient on the log of tax holiday in model specification (2) is greater than that in model specification (1), and the coefficient on the interaction term of the log of tax holiday and level of R&D intensity is significant and positive. In the following tables, we present the mechanism checking with R&D intensity and indicate the presence of political dummies and interaction terms. J. Risk Financial Manag. 2022,15, 344 33 of 42 Table A3. Robustness Checks with TFP Measured Using OLS FE method (TFP_OLSFE). (1) (2) (3) TFP_OLSFE TFP_OLSFE TFP_OLSFE Log of Tax Holiday 0.287 *** 0.314 *** 0.312 *** (0.0159) (0.0164) (0.0166) Technical Assistance (Dummy) −0.0528 −0.0522 −0.0539 (0.0563) (0.0551) (0.0550) Firm Size (Number of Employees) −0.00170 *** −0.00165 *** −0.00165 *** (0.000364) (0.000353) (0.000351) SOE Indicator 0.271 0.292 0.303 (0.219) (0.229) (0.230) Industry Size (Number of Firms) 0.00136 * 0.00134 0.00142 * (0.000808) (0.000817) (0.000821) Industry Competition Level 0.239 0.258 0.253 (0.215) (0.217) (0.217) RND −0.341 (0.377) Interaction Term RND & Log of Tax Holiday 0.238 * (0.141) Political Dummies No Yes Yes Interaction Terms Political Dummies & Log of Tax Holiday No Yes Yes Number of observations 8583 8513 8513 R20.235 0.239 0.240 Robust standard errors in parentheses, clustered at the firm level. All regressions include firm fixed effects and year dummies. * p< 0.1, ** p< 0.05, *** p< 0.01. Table A4. Robustness Checks with TFP Measured Using Levinsohn–Petrin method (TFP_LP). (1) (2) (3) TFP_LP TFP_LP TFP_LP Log of Tax Holiday 0.262 *** 0.286 *** 0.284 *** (0.0152) (0.0162) (0.0163) Technical Assistance (Dummy) −0.0701 −0.0705 −0.0724 (0.0599) (0.0587) (0.0586) Firm Size (Number of Employees) −0.00237 *** −0.00231 *** −0.00231 *** (0.000634) (0.000622) (0.000621) SOE Indicator 0.259 0.280 0.292 (0.234) (0.243) (0.245) Industry Size (Number of Firms) 0.00141 * 0.00141 * 0.00149 * (0.000818) (0.000826) (0.000830) Industry Competition Level 0.196 0.214 0.208 (0.219) (0.221) (0.220) RND −0.406 (0.363) J. Risk Financial Manag. 2022,15, 344 34 of 42 Table A4. Cont. (1) (2) (3) TFP_LP TFP_LP TFP_LP Interaction Term RND & Log of Tax Holiday 0.266 * (0.139) Political Dummies No Yes Yes Interaction Terms Political Dummies & Log of Tax Holiday No Yes Yes Number of observations 8586 8516 8516 R20.203 0.207 0.208 Robust standard errors in parentheses, clustered at the firm level. All regressions include firm fixed effects and year dummies. * p< 0.1, ** p< 0.05, *** p< 0.01. Appendix D.2. Alternative Mechanism Using the Herfindahl Index formula to measure the degree of competition at the industry level, we test the predictions made in Aghion et al. (2015) that a tax policy targeted at a more competitive industry would have a greater impact on output and innovation, and consequently productivity, and that there exists complementarity between tax holidays and the degree of competition in the presence of political constraints. For this purpose, we include a new variable called Compherftax which measures the degree of dispersion of tax incentives within each industry, consistently with Aghion et al. (2015). Comperftax is measured using the following formula: Compher f taxi,j,t=1−Her f−tax =∑ h∈j,h/∈i TaxHolidayijt Sum−TaxHolidayjt !2 (A25) Her f−tax is the Herfindahl index of tax holiday measured using the share of tax incentive each firm receives relative to the total amount of tax benefits given to the industry. The square of this Herfindahl index is an indicator of the level of competitiveness within that industry: the smaller this value is, the greater the degree of tax holiday dispersion and thus competitiveness within the sector. Compher f taxi,j,t is measured by taking 1 subtracted by the square of Herfindahl index for tax holiday to make this measure correlate positively with level of competitiveness: a greater value of Compher f taxi,j,t indicates a more competitive industry. Note that the firm’s own tax holiday is subtracted from the Herfindahl measure for each firm, making Compher f taxi,j,t exogenous to the firm’s performance in order to mitigate the potential endogeneity of this policy instrument. As such, in the regression specification, the variable Compher f taxi,j,t (denoted as Ci,j,t in the equations below) would replace the Lerner index variable as the variable representing competition, and instead we add the interaction term between the Herfindahl index and the log of tax holiday. Our regression specification is as follows: lnTFPijt =θ1Zijt +θ2Sjt +β1Lntaxijt +β2Techijt +β3Ci,j,t+γ1Lntaxijt ×Ci,j,t+fi+Dt+εijt (A26) and lnTFPijt =θ1Zijt +θ2Sjt +β1Lntaxijt +β2Techijt +β3Ci,j,t+γ2Lntaxijt ×Ci,j,t+δ1Pijt +δ2Pijt ×Lntaxijt +fi+Dt+εijt (A27) An affirmative appraisal of the mechanism would suggest significant and positive values of γ1and γ2. J. Risk Financial Manag. 2022,15, 344 35 of 42 However, the coefficients on the interaction term between Lntaxijt and Ci,j,t are statistically insignificant in both regression specifications as shown in Table A5. This suggests that targeting more competitive industries is not the way that industrial policy works in Vietnam, possibly due to the presence of political constraints. Table A5. Robustness Checks with Targeting Mechanism Focusing on Competition. (1) (2) TFP_OP TFP_OP Log of Tax Holiday 0.275 *** 0.297 *** (0.0382) (0.0418) Comp_HerfTax 0.0974 0.0959 (0.141) (0.143) Interaction Term Comp_HerfTax & Log of Tax Holiday −0.0254 −0.0236 (0.0431) (0.0438) Technical Assistance (Dummy) −0.0611 −0.0592 (0.0615) (0.0604) Firm Size (Number of Employees) −0.00216 *** −0.00210 *** (0.000575) (0.000564) SOE Indicator 0.242 0.256 (0.241) (0.251) Industry Size (Number of Firms) 0.00139 0.00138 (0.000874) (0.000884) Industry Competition Level 0.104 0.120 (0.238) (0.240) Political Dummies No Yes Interaction Terms Political Dummies & Log of Tax Holiday No Yes Number of observations 8547 8477 R20.182 0.187 Robust standard errors in parentheses, clustered at the firm level. All regressions include firm fixed effects and year dummies. * p< 0.1, ** p< 0.05, *** p< 0.01. Appendix D.3. Accounting for the Skewed Distribution of R&D Intensity As shown in Table 7, the distribution of the measure of R&D intensity is skewed with many values of zeros, prompting the need for robustness checks on the results of regression (4) with respect to R&D. These robustness checks are particularly important as R&D intensity is identified as the only technological characteristic that significantly interacts with the impact of industrial policy on firm productivity. We perform these robustness checks with the following two alternative regressions: (i) one with bootstrapped errors, and (ii) the other without the values of zeros for R&D intensity. Appendix D.3.1. Bootstrapped Errors Using bootstrapped errors instead of robust standard errors clustered by firm identity indicator, regression (4) still gives us a significant and positive coefficient on the interaction term between R&D intensity and the log of tax holiday, as shown in Table A6 below. Since the main focus of this robustness check is the said interaction term that indicates the underlying mechanism of industrial policy, the result table indicates the presence of political dummies and their interaction terms with the tax holiday variable instead of listing their coefficients out specifically. J. Risk Financial Manag. 2022,15, 344 36 of 42 Table A6. Robustness Checks on R&D Intensity with Bootstrapped Errors. (1) TFP_OP Log of Tax Holiday 0.273 *** (0.0138) RND −0.358 (0.368) Interaction Term RND & Log of Tax Holiday 0.267 ** (0.118) Technical Assistance (Dummy) −0.0663 (0.0476) Firm Size (Number of Employees) −0.00210 ** (0.00100) SOE Indicator 0.270 (0.328) Industry Size (Number of Firms) 0.00164 * (0.000888) Industry Competition Level 0.121 (0.233) Year Fixed Effects Yes Pol Dummies Yes Interaction Terms Political Dummies & Log of Tax Holiday Yes Number of observations 8513 R20.188 Bootstrapped errors in parentheses. * p< 0.1, ** p< 0.05, *** p< 0.01. Appendix D.3.2. Dropping Values of Zeros in R&D Intensity Repeating regression (4) by dropping the values of zeros in R&D intensity, I still obtain a positive and significant coefficient on the interaction term between R&D intensity and the log of tax holiday, as shown in Table A7 below. Table A7. Robustness Checks on R&D Intensity by Dropping Values of Zeros. (1) TFP_OP Log of Tax Holiday 0.268 *** (0.0249) RND −0.805 * (0.450) Interaction Term RND & Log of Tax Holiday 0.324 ** (0.156) Technical Assistance (Dummy) −0.154 (0.104) Firm Size (Number of Employees) −0.00317 *** (0.000780) SOE Indicator 0.402 (0.410) Industry Size (Number of Firms) 0.00158 (0.00145) J. Risk Financial Manag. 2022,15, 344 37 of 42 Table A7. Cont. (1) TFP_OP Industry Competition Level 0.248 (0.358) Year Fixed Effects Yes Political Dummies Yes Interaction Terms Political Dummies & Log of Tax Holiday Yes Number of observations 3294 R20.173 Robust standard errors in parentheses, clustered at the firm level. * p< 0.1, ** p< 0.05, *** p< 0.01. Appendix D.4. Analysis on the Data Set Excluding Year 2012 Table A8 below shows the results of the fixed-effects panel regressions for each of the three model specifications on the data set excluding data for year 2012, which is an outlier in several ways discussed earlier. The major pattern of results also holds for this subsample. Table A8. Robustness Checks with the Dataset Excluding Year 2012. (1) (2) (3) TFP_OP TFP_OP TFP_OP Log of Tax Holiday 0.255 *** 0.274 *** 0.272 *** (0.0151) (0.0163) (0.0164) Technical Assistance (Dummy) −0.0674 −0.0656 −0.0675 (0.0615) (0.0603) (0.0602) Firm Size (Number of Employees) −0.00217 *** −0.00212 *** −0.00211 *** (0.000584) (0.000570) (0.000569) SOE Indicator 0.142 0.172 0.185 (0.224) (0.243) (0.247) Industry Size (Number of Firms) 0.00155 * 0.00154 * 0.00164 * (0.000836) (0.000845) (0.000848) Industry Competition Level 0.121 0.132 0.127 (0.235) (0.237) (0.237) RND −0.315 (0.368) Interaction Term RND & Log of Tax Holiday 0.251 * (0.137) Political Dummies No Yes Yes Interaction Terms Political Dummies & Log of Tax Holiday No Yes Yes Number of observations 8564 8494 8494 R20.184 0.188 0.188 Robust standard errors in parentheses, clustered at the firm level. All regressions include firm fixed effects and year dummies. * p< 0.1, ** p< 0.05, *** p< 0.01. J. Risk Financial Manag. 2022,15, 344 38 of 42 Appendix D.5. Firm Subsamples of Different Sizes In this section, we perform robustness checks on firms of different sizes: we divide the data set into two subsamples: a subsample of all firm observations with 50 or fewer employees (consistent with the definition of small firms), and the other subsample containing the rest of the firms. We run the baseline regression on these two subsamples of firms to check the validity of our main results across different firm size groups while still controlling for firm size (number of employees). These results are presented in Table A9 below. Table A9. Robustness Checks with Different Firm Size Groupings. (≤50 Employees) (>50 Employees) TFP_OP TFP_OP Log of Tax Holiday 0.294 *** 0.183 *** (0.0165) (0.0510) Technical Assistance (Dummy) −0.0274 −0.0666 (0.0713) (0.116) Firm Size (Number of Employees) −0.0197 *** −0.00137 *** (0.00180) (0.000234) SOE Indicator 0.265 0.161 (0.369) (0.160) Industry Size (Number of Firms) 0.00235 *** −0.00565 (0.000796) (0.00395) Competition Level 0.179 0.994 (0.239) (1.651) Year Fixed Effects Yes Yes Number of observations 7749 834 R20.215 0.194 Robust standard errors in parentheses, clustered at the firm level. * p< 0.1, ** p< 0.05, *** p< 0.01. As can be seen in the table above, tax holiday still has significant and positive results across different groups of firm sizes. While most of the dataset is comprised of small enterprises with 50 employees or fewer (about 90%), the impact of tax holiday seems a lot stronger on the productivity of small enterprises compared with larger enterprises. Appendix D.6. Post-Estimation Tests and Correction Given the panel nature of our data and analysis, we perform two post-estimation tests including (i) a modified Wald test for groupwise heteroskedasticity in the residuals of the fixed-effects regression model according to our main specification (2), and (ii) the Woolridge test for autocorrelation in panel data. The modified Wald test returns a large test statistic with p=0.000, rejecting the null hypothesis of homoskedasticity and suggesting heteroskedasticity. We correct for this by rerunning the regression with robustly estimated residuals and get the same results with our original regression as shown in Column (1) of Table A10 below, confirming the robustness of our findings. The Woolridge test returns an F statistic = 9.298, p = 0.002, rejecting the null hypothesis of no first-order autocorrelation. We correct for this by rerunning the regression allowing for AR(1) disturbance, and also get the same results with our original regression as shown in Column (2) of Table A10 below, confirming the robustness of our findings. J. Risk Financial Manag. 2022,15, 344 39 of 42 Table A10. Corrected Regressions. (1) (2) TFP_OP TFP_OP Log of Tax Holiday 0.253 *** 0.254 *** (0.0149) (0.0112) Technical Assistance (Dummy) −0.0647 −0.0323 (0.0616) (0.0857) Firm Size (Number of Employees) −0.00216 *** −0.00163 *** (0.000578) (0.000214) SOE Indicator 0.241 −0.113 (0.241) (0.392) Industry Size (Number of Firms) 0.00153 * 0.000838 (0.000835) (0.00104) Competition Level 0.115 −0.831 (0.235) (1.073) Year Fixed Effects Yes Yes Robustly Estimated Residuals Yes No AR(1) Disturbance No Yes Number of observations 8583 4791 R20.183 0.299 Robust standard errors in parentheses, clustered at the firm level. * p< 0.1, ** p< 0.05, *** p< 0.01. Appendix E. Alternative Definition of R&D Intensity Define R&D intensity Rit in industry i as R&D divided by expenditures (expenditures other than R&D: results would clearly be the same if R&D were included). Then Rit =nitwit Rpit(xit(a))xit(a)da =n Rxitαqit Aitxα−1 it f(a)da =n R(qit Ait)1 1−ααα+1 1−αf(a)da =n qi0Amax i01 1−αRa1 1−ααα+1 1−αf(a)da where xit(a) is the use of xit by a producer with technology gap a . Using the monopolist’s first order condition (9) and the optimal choice of the producer (11) to substitute for pit(·) and xit(a) , and then using the optimal R&D condition (A11) to substitute for qi0Amax i0 , we have that Rit =nit r+λnit +λ¯ nitσ1 1−αX where X is a positive constant that does not vary across industries. Since in equilibrium nit =nidoes not vary over time, the same is true of Rit. dRit dni =r+λni+λniσ1 1−α−nλ+λσ 1 1−α r+λni+λniσ1 1−α2=r r+λni+λniσ1 1−α2>0 so since dRit dωi =dRit dni ×dni dωi J. Risk Financial Manag. 2022,15, 344 40 of 42 we have that sgndRit dωi=sgndni dωi. An alternative definition would be to include R&D expenditures among “expenditures”. In this case, we would have ˆ Rit =nitwit Rpit(xit(a))xit(a)da +nitwit Note that 1 ˆ Rit =1 Rit +1. As a result sgndRit dωi=sgndˆ Rit dωi. Notes 1For robustness, we also examine the impact of tariffs as a form of industrial support. 2 This finding does not imply that financing constraints do not exist, nor that they are not important for growth, just that the main impact of industrial support on firm productivity is not by relieving financing constraints. 3 This contrasts with an earlier literature on industrial support targeted at import substitution. The survey of Harrison and Rodríguez-Clare (2010) finds no systematic impact on productivity of such policies. 4 The Vietnamese SME Survey, collected biennially since 2005, is a collaborative effort of the Central Institute for Economic Management (CIEM), the Institute of Labor Science and Social Affairs (ILSSA), the Development Economics Research Group (DERG) at the University of Copenhagen, and UNU-Wider. 5 http://vietnamnet.vn/vn/ban-doc/49000-doanh-nghiep-pha-san-moi-truong-kinh-doanh-gap-kho-43982.html (accessed on 1 June 2017). 6 Hausman test statistic = 39.70, p= 0.000, rejecting the null hypothesis that the firm-level effects are adequately modeled by a random-effects model. 7χ2= 9414, p= 0.000, rejecting the null hypothesis of the existence of unit root. 8 Howitt (1999) presents a version of the Aghion and Howitt (1992) model of growth through creative destruction, but modified so as to avoid scale effects. 9 In Appendix Bwe show that the right hand side of (7) grows at the same rate as the population in equilibrium, as does the left hand side, because growth in consumption and prices offset each other and the number of varieties grows at the same rate as the population. 10 Later we show that fi(v,t)=f(a), where a=Avt/Amax it . The form of fis such that: E"Ait Amax it 1 1−α#=1 1+σ 1−α . 11 An alternative definition of R&D intensity would be as research expenditures per firm divided by expenditures, which is closer to the notion in the data. We show in Appendix Ethat Proposition 2 applies if we adopt such a definition instead. 12 https://www.econ.ku.dk/derg/dergarchive/miscellaneous/vietnam/ (accessed on 1 June 2018). 13 https://www.wider.unu.edu/database/viet-nam-sme-database (accessed on 1 June 2018). 14 https://www.marketplace.spglobal.com/en/ (accessed on 1 June 2018). 15 Note that ψis increasing and concave, so ψ0is decreasing, so ψ0−1is decreasing and so dψ0−1 dx (x)<0). References Acemoglu, Daron, and Joshua Linn. 2004. Market Size in Innovation: Theory and Evidence from the Pharmaceutical Industry. The Quarterly Journal of Economics 119: 1049–90. [CrossRef] Acemoglu, Daron, Ufuk Akcigit, Harun Alp, Nicholas Bloom, and William Kerr. 2018. Innovation, Reallocation, and Growth. American Economic Review 108: 3450–91. [CrossRef] Ackerberg, Daniel A, Kevin Caves, and Garth Frazer. 2015. Identification Properties of Recent Production Function Estimators. Econometrica 83: 2411–51. [CrossRef] Aghion, Philippe, and Peter Howitt. 1992. A Model of Growth through Creative Destruction. Econometrica 60: 323–51. [CrossRef]