Foreign R&D spillovers to the USA and strategic reactions
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Ziesemer, Thomas Working Paper Foreign R&D spillovers to the USA and strategic reactions UNU-MERIT Working Papers, No. 2021-015 Provided in Cooperation with: Maastricht Economic and Social Research Institute on Innovation and Technology (UNU-MERIT), United Nations University (UNU) Suggested Citation: Ziesemer, Thomas (2021) : Foreign R&D spillovers to the USA and strategic reactions, UNU-MERIT Working Papers, No. 2021-015, United Nations University (UNU), Maastricht Economic and Social Research Institute on Innovation and Technology (UNU-MERIT), Maastricht This Version is available at: https://hdl.handle.net/10419/326774 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. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-sa/4.0/
#2021-015 ForeignR&DspilloverstotheUSAandstrategicreactions ThomasH.W.Ziesemer Published26March2021 MaastrichtEconomicandsocialResearchinstituteonInnovationandTechnology(UNU‐MERIT) email:[email protected]u|website:http://www.merit.unu.edu Boschstraat24,6211AXMaastricht,TheNetherlands Tel:(31)(43)3884400
UNU-MERIT Working Papers ISSN 1871-9872 Maastricht Economic and social Research Institute on Innovation and Technology UNU-MERIT UNU-MERIT Working Papers intend to disseminate preliminary results of research carried out at UNU-MERIT to stimulate discussion on the issues raised.
Foreign R&D Spillovers to the USA and Strategic Reactions Ziesemer, Thomas H.W., Department of Economics and UNU-MERIT, Maastricht University1.Email: [email protected].ORCID:0000‐0002‐5571‐2238. Abstract. We re-consider the traditional result of zero or negative foreign R&D spillovers or strategic reactions to the USA using accumulated shocks in a vector-error-correction model (VECM) for the period 1963-2017. Foreign private and public R&D stocks have a positive and statistically significant effect on US public R&D and labour-augmenting technical change (LATC). US private R&D reacts positively to foreign private R&D and negatively to foreign public R&D shocks. Foreign public and private R&D react positively to US public R&D. All variables react positively to US private R&D. From the time profile of the simulated VECM, we calculate the sum of discounted (at 4%) net gains for (i) additional private and public US R&D, and (ii) for policies reacting to foreign private and public R&D shocks with additional domestic private and public R&D. Additional private and public US R&D expenditures have very high internal rates of return. R&D investments in reaction to shocks from foreign R&D are profitable. All LATC reactions are transitional suggesting semi-endogenous growth for the USA. Keywords: Growth, productivity, R&D, reaction functions, spillovers, CVAR. JEL-codes: C51, O30, O38, O47, O51. 1. Introduction Ever since foreign R&D capital stocks were introduced into firm or macro-level regressions explaining factor productivity, the literature on international R&D spillovers finds that the spillovers (including competition effects) to the United States are zero or negative (see Luintel and Khan 2004).2 That result is based on the long-term relations of country-by- country vector-error-correction models (VECM), which are adequate in dealing with country heterogeneity. R&D capital stocks of foreign countries used in these studies include either total aggregated R&D or only business R&D expenditures. Similarly, Atukeren (2007) finds no effect of spillovers or competitive reactions from the European Union on the USA. Bernstein and Mohnen (1998) find no effect of spillovers from Japan on the USA, but rather only one from the USA to Japan. We do not deal with Japan or the European Union separately, but our analysis can be seen as one of a joint effect as the foreign R&D capital stock for the US in our data consists of those of the EU15, Japan, and Canada. An exception to the result that the USA does not receive spillovers is a paper by Luintel and Khan (2009). They provide panel System GMM estimates with interaction terms. Foreign knowledge stocks, constructed from triadic patent data, interact with the domestic ones and domestic human capital, and have a positive impact on the change of domestic patent stocks, which in turn have a positive impact on TFP. The country-specific interaction terms and their indirect link to a country-specific TFP equation are a construct capturing heterogeneity and show a partial effect of foreign positive spillovers to the USA. This paper differs from ours in *IamgratefultoLucSoeteandBartVerspagenforstimulatingdiscussionsandtoBartforprovidingtheR&D stockdata. 2EarlierliteraturefindingthesameresultissummarizedbyCinceraandvanPottelsberghedelaPotterie (2001).
several respects: (i) They look at foreign triadic and domestic patents and TFP whereas we look at R&D expenditures and LATC; (ii) they investigate partial relations between these variables whereas we investigate multiple dynamic interactions between R&D expenditure stocks. (iii) Our R&D expenditure stocks are differentiated between publicly and privately performed R&D whereas their patent data are not distinguishing between business owned and publicly owned (as by universities and other non-university research institutions). An important contribution of their paper is that it indicates the possibility that considering heterogeneity may lead to a different result than the one of no spillovers to the USA. We use foreign public (non-business) R&D capital stocks besides those of foreign business R&D stocks for the period 1963-2017 in a VECM. This allows extending the analysis of Luintel and Khan (2004) by way of including foreign public R&D stocks. This possibility makes two questions interesting: First, are there international R&D spillovers to the USA when we distinguish between private and public foreign R&D and include both? Second, is it advantageous for the US to react to R&D spillovers with a policy of additional private and public investment? In order to answer these questions, we do not only consider the partial effects of long-term relations, but also analyse the effects of permanent policy changes to the growth rates of R&D variables in the transition to the long-term relations of a VECM. This way we get results that include all the feedback reactions on each other of domestic and foreign private and public R&D as well as LATC from all equations of the VECM.3 In section 2 we briefly describe the data showing that they are in line with closely related literature. In section 3 we explain the econometric procedure for estimation of the VECM and the results from it leading to a baseline simulation in log-levels and growth rates of all variables. In section 4 we study the growth and R&D policy effects of shocks to domestic and foreign public and private R&D. In section 5 we show the results from calculating the benefits, costs and gains from additional public and private R&D, either on a country’s own initiative or as reaction to foreign R&D enhancements. Section 6 argues that permanent changes leading to transitional effects on LATC suggests having a semi-endogenous growth model for the USA. Section 7 summarises and concludes. 2. Literature 2.1 Theory In the absence of strategic behaviour, spillovers from foreign R&D are defined to be positive if foreign R&D reduces the unit costs of domestic firms. This leads to higher quantities and R&D investment, but less so if subsidies are lower than optimal in combination with spillovers close to public goods and more so if firms ignore the spillovers which strengthen their competitors (Spence 1984; Bernstein and Mohnen 1998). Under Bertrand competition with product differentiation, if goods are substitutes, both, domestic and foreign R&D, have positive effects on the domestic quantity, and there are upward (downward) sloping reaction 3ThisapproachissimilartothatofBottazziandPeri(2007)whoconsiderdifferentvariablesthough,R&D workersandpatents.
functions in the R&D stage if there are positive (negative) spillovers (Carlson 2008). Positive R&D investment reactions therefore can be linked to spillovers under cost minimisation without strategic reactions and under Bertrand competition in substitutes. Under Cournot competition without spillovers, reaction functions of the R&D stage are negatively sloped when goods are substitutes (d’Aspremont and Jacquemin 1988), also when R&D goes into product quality (Taba and Ishii 2016). Taba (2016) shows that in the case of Cournot competition in substitutes, foreign R&D in product quality may reduce the domestic quantity directly and also indirectly via the downward sloping R&D reaction function if spillovers are small. Conversely, for sufficiently large spillovers, we get positive direct effects of foreign R&D and positive indirect effects via the upward sloping R&D reaction function. In sum, static Cournot and Bertrand duopoly models have positively sloped R&D reaction functions, where in case of Cournot models strong spillovers are needed; in their derivation, competition on the product market stage is already taken into account. Positively sloped reaction functions are the reason why positive Granger causality from one country’s R&D to another country’s R&D is one way of analysing spillovers, besides effects on cost and productivity (Atukeren 2007). In racing models with ‘winner-takes-all’ property, reaction functions are upward sloping (de Bondt 1996) if the competition threat is stronger than the profit incentive (Beath et al. (1989). This is the case in the absence of spillovers. By implication, when using Granger causality as in Atukeren (2007) and impulse responses in this paper we do not necessarily capture spillovers on LATC, but perhaps only competitive reactions of R&D, which affect LATC. However, reaction functions for timing may have negative slopes allowing for submissive reactions, meaning a firm takes more time for invention in reaction to a quick invention by the competitor (Scherer 1991). If racing models with upward sloping reaction curves are of minor importance compared to all the other models mentioned above, concluding that there are spillovers on the basis of shocks of foreign R&D and all feedbacks enhancing the R&D and LATC of the USA may still be legitimate although some of the effects may come from strategic behaviour.4 In case of n private firms in Cournot competition getting R&D subsidies and one public research institute, reaction functions for public and private R&D depending on each other have positive (negative) reaction curves only if the public R&D has a positive (negative) spillover (Cabon-Dhersin and Gibert 2020). In international applications it is assumed that one of the firms are foreign and the other is domestic. We therefore report above only the results for the non-cooperative equilibria of the games. Simulation results below will be interpreted in the spirit of reaction functions of the R&D literature. Positive reactions suggest spillovers in all models except those of patent races where we may get positively sloped reaction functions also without spillovers. David and Hall (2000) model the basics of the interaction of public and private R&D with focus on the labour market for researchers. Public R&D competes researcher away from private R&D. Spillovers from public to private R&D and hiring of public R&D workers by 4Mohnen(1997)discussesdistinguishingR&Dspilloversinadditionfromrentspillovers,productivityspillover andknowledgespillovers.
for private R&D reduce this labour-reallocation effect. Enhancement of public and private R&D therefore requires an elastic labour supply of researchers. The complementary interaction of private and public R&D with productivity growth is also modelled in a microfounded macroeconomic model by Gersbach et al. (2021), where the exogenous acquisition type of FDI encourages public R&D expenditures but diminishes the effects of public R&D. A theoretical growth model for the interaction of domestic public and private R&D and productivity with endogenous reaction of foreign R&D variables is Ziesemer (2020a), who discusses additional closely related theoretical literature. 2.2 Evidence Scherer (1991) finds quick positive reactions of US R&D flows to Japan’s R&D and vice versa relating them to R&D racing but not to spillovers; the US reaction is first submissive and then aggressive in terms of change of R&D expenditures. R&D spillovers are pertinent in endogenous growth theory. Bayoumi et al. (1996) have introduced them into the MULTIMOD model in a log-log specification making total factor productivity dependent on domestic and foreign R&D capital stocks. A shock on US R&D stocks spill over to all other countries enhancing their GDP. For most countries, the increase in the GDP levels is less than for the USA (see also Helpman 2004, ch.5 for a summary). Spillovers are positive but increase international inequality. This raises the question, whether foreign R&D spills over from other countries to the USA as well. Hammadou et al. (2014) show an effect from private on publicly funded R&D for a panel of 14 European countries. Link et al. (2020) provide evidence for ten European countries that firms doing R&D are using knowledge from public research institutes more than firms that do not do R&D. This is also suggestive of the complementary nature of public and private R&D, which is the second crucial link in our VECM and the shocks. Soete et al. (2020a,b) show the public-private complementarity for R&D stocks for a number of OECD countries using VECMs. Ziesemer (2020b) shows it for Japan. Ziesemer (2020a, 2021a) surveys the older literature on this complementarity. Bacchini et al. (2020) show complementarity between public and private R&D flows in a macroeconomic estimation for Italy. All these papers cite many others also finding this complementarity, which therefore is also part of this paper. Several of these papers show the two-way causality of public and private R&D. 3. Data It follows from the introduction that we have to consider private and public domestic and foreign R&D stocks as well as the labour-augmenting technical change for the USA. We do not follow the suggestion of Luintel et al. (2014) to include human capital because R&D expenditures used here in the form of stocks include those for human capital. The LATC data from Ziesemer (2021b) are derived from CES functions including human capital for alternative elasticities of substitution; we explore using data derived for CES = 0.7, 0.8, 0.9,
0.99. The data for the R&D stocks in 2005 US dollars for the period 1963-2017 are an updated version of those used in Soete et al. (2020b) applying the perpetual inventory method to OECD flow data with depreciation rate of 0.15 (Hall et al 2010; Luintel et al. 2014) and distance weights for the construction of foreign R&D capitals stocks. In the literature, imports, foreign direct investment, and migration have been used as weights without any of them being clearly better than the others. They all depend on distance in gravity equations and therefore Soete et al. (2020a, b) use distance as a weighting scheme. Stocks of privately performed R&D grow more quickly than public R&D stocks in the periods 1978-2000 with outliers 1993/94, and 2013-2017, and public R&D grows more quickly before 1978 and in the period 2001-2012. Figure 1 below shows that the net result is a higher private R&D stock. 4. Econometrics, estimation results and baseline simulation The culture of VECMs is to keep the models small as in Luintel and Khan (2004) and Bottazzi and Peri (2007) because the number of coefficients increases strongly with the number of regressors.5 For univariate unit root tests, we use Dickey-Fuller GLS test, the augmented Dickey-Fuller test without and with breakpoints and the Zivot-Andrews test with breakpoint. We find that LATC and the R&D stock variables have near unit roots (see appendix) in the form of high p-values and coefficients below 0.95 when structural breaks are allowed, but often closer to unity when breaks are ignored. Breaks are strongly dispersed across variables and tests, indicating that there is no break for a joint model. The log of GDP is leaning more to being I(0) as its coefficients are between 0.44 and 0.92 rather than unity. When including it, the GDP variable reacts too strongly on R&D shocks, deviates too strongly from the LATC paths,6 and has a low adjusted R-square, also in an earlier version of this paper with data only until 2014. We therefore exclude LGDP from the VECM. A VAR in the five variables has three lags according to all lag length selection criteria. The stability test for the VAR with three lags shows that the model is unstable, and we use four lags, because the damage from using too short rather than too long lags is larger. The trace test for three lags and a linear trend suggests having four cointegrating equations (r=4) at the five percent level of statistical significance. The maximum-eigenvalue test suggests three cointegrating equations (r = 3). Jusélius et al. (2014) suggest deciding in favour of more cointegrating equations and less unit roots because of the low power of both, the individual and the system test for unit roots. By implication, we would have a system with K-r = 5-4 = 1 unit roots or I(1) components or variables. In contrast, Hjalmarsson and Österholm (2010), considering the problem of near-unit roots, which we found in the unit root analysis above, suggest rejecting a hypothesis in cointegration tests only if both, the trace test and the maximum-eigenvalue test suggest rejection. We therefore do not reject the hypothesis of ‘at most 3 ce’ and thereby assume having three cointegrating equations. Our result is in line with this suggestion for the five-percent significance level. At the 10 percent level we would have 5Lütkepohl(2007)providesasupportivenon‐technicaldiscussionforthis. 6ThisalsohappenswhenwetreatLGDPasI(0)andmodelanextendedVECMassuggestedbyFisheretal. (2016).
r=K and thereby no unit root in the system (see Davidson and MacKinnon 2004). These and the following properties hold for alternative VECMs using LATC variables based on CES = 0.7-0.99. The Doornik-Hansen test for multivariate normality shows that the error probability of rejecting the null hypothesis of normality is between 0.32 and 0.7 for the four CES versions, so we do not reject the null. The Lagrange multiplier test rejects the hypothesis of serial correlation at the five percent level except for lag 2 when LATC is used as derived under a CES = 0.7. The null hypothesis of no heteroscedasticity can be rejected at an error probability of 0.27 to 16.6%, so we do not reject it. As LATC from CES = 0.7 has serial correlation we do not use it. On all other criteria LATC from CES = 0.8, denoted LTH08, perform better than those from higher CES (see appendix). This value is in the ranges found for the USA by Antras (2004), 0.3 to 0.9, and Knoblach et al. (2020), 0.45-0.87. The VECM with the linear trend7 has the following long-term or cointegrated equations (CE) written in the form of having all variables on the same side of the equation (t-values in parentheses) as used in equations (4)-(8) below. CE1 = E(u1(-1)) = LTH08(-1) - 0.34LBERDST(-1) + 0.32LPUBST(-1) -0.015t - 0.895 (1) [-3.44][3.14] [-3.22] Here and below, we have chosen normalisations which lead to the low coefficients allowing to test whether the variables have vanishing significance. LTH08 is positively related to the business R&D stock, BERDST, and negatively to public R&D, LPUBST, the latter two often competing for the same resources. A trend of 1.5 percent is detrending the variables and could describe the growth in the absence of R&D. As the coefficients of the R&D variables are almost identical up to the sign, LTH08 grows with one third of R&D growth plus 1.5% exogenous growth. LTH08 is therefore growing less quickly than the private R&D stocks as suggested in the recent literature on semiversus fully endogenous growth (Minniti and Venturini 2017) and on modern stagnation (Hall 2017; Bloom et al 2020). However, it would be premature to conclude against fully- and in favour of semi-endogenous growth because we see here decreasing returns to one argument only and others may also play a role and are considered next. CE2 =E(u2(-1)) = LBERDST(-1) - 2.33LPUBST(-1) + 1.64LFPUBST(-1) - 3.29 (2) [-12.97][7.87] Public R&D is driving private R&D but is reduced by foreign public R&D. Both are only partial effects, which we can interpret as R&D reaction functions, possibly with implicit spillover effects as in duopoly models. Private R&D is partly basic R&D (see Soete et al. 2020b) and that part may be reduced if there is more foreign public R&D doing basic R&D. CE3 =E(u3(-1)) = LPUBST(-1) - 0.14LBERDST(-1) - 0.36LFBERDST(-1) -0.017t -5.95 (3) 7Severalpapersmentionedabovedonotincludeatimetrendinthecointegratingequationordonotreportit althoughtheyarereportedinthedatadescriptionandaremostlikelynotstochasticbutratherdeterministic.
spillovers from foreign public to US private R&D because there is no positive reaction as the model would show under positive spillovers. The increase in LTH08 is limited to a maximum of four percent above baseline, and it becomes statistically insignificant after ten years. It indicates effects of positive spillovers of foreign public R&D or strategic reactions of US public R&D. With clearly increasing, positive and about equal long-term effects on LPUBST and LFPUBST, CE1 and CE3 get positive and CE2 gets negative. The only clear effect than is that dLFPUBST goes below its old steady-state value because LPUBST and LFPUBST are high, implying that LFPUBST has a destabilising and US LPUBST a stabilising partial effect in (8). For accumulated permanent changes, the long-term relations do not return to zero. ‐.3 ‐.2 ‐.1 .0 .1 .2 5 1015202530 AccumulatedResponseofLTH08toLFPUBST ‐.8 ‐.6 ‐.4 ‐.2 .0 .2 .4 5 101520253 0 AccumulatedResponseofLBERDSTtoLFPUBST ‐.4 ‐.2 .0 .2 .4 .6 5 1015202530 AccumulatedResponseofLPUBSTtoLFPUBST ‐0.4 ‐0.2 0.0 0.2 0.4 0.6 0.8 1.0 5 101520253 0 AccumulatedResponseofLFBERDSTtoLFPUBST .0 .1 .2 .3 .4 .5 5 1015202530 AccumulatedResponseofLFPUBSTtoLFPUBST AccumulatedResponsetoGeneralizedOneS.D.Innovations 90%CIusingHall'spercentilebootstrapwith999bootstrapreps Figure 5 The effects of the shock to the foreign public R&D stock.
Figure 6 shows that a shock of 0.3% to foreign private R&D has a slightly positive impact on US private R&D going four percent beyond baseline. The effect is statistically significant for seven years. A zero effect as in Luintel and Khan (2004), or a submissive effect Atukeren (2007) or the first-year effect in Scherer (1991) appears only after 14 years and is insignificant. The impact on LTH08 is positive as in Eaton and Kortum (1997) the panel analysis of Coe and Helpman (1995) but less than the effect on domestic private R&D. Foreign private and domestic and foreign public R&D show a larger reaction of similar size. This makes CE1 and CE3 again positive and CE2 negative. The latter implies again that dLFPUBST goes below its old steady-state growth rate. .00 .02 .04 .06 .08 .10 .12 .14 12345678910 AccumulatedResponseofLTH08toLFBERDST ‐.04 .00 .04 .08 .12 12345678910 AccumulatedResponseofLBERDSTtoLFBERDST .00 .05 .10 .15 .20 .25 12345678910 AccumulatedResponseofLPUBSTtoLFBERDST .00 .04 .08 .12 .16 .20 12345678910 AccumulatedResponseofLFBERDSTtoLFBERDST ‐.04 .00 .04 .08 .12 .16 12345678910 AccumulatedResponseofLFPUBSTtoLFBERDST AccumulatedResponsetoGe neralizedOneS.D.Innovations 90%CIusingHall'spercentilebootstrapwith999bootstrapreps Figure 6 The effects of the shock to the foreign private R&D stock 1967-2200.
5 Internal rates of return and sum of discounted net gains from permanent shocks For all four types of shocks, we have seen that all variables react positively, with only the case of a shock to foreign public R&D having statistically insignificant reactions of domestic and foreign private R&D. This does not yet ensure though that the costs incurred in terms of additional private and public investment are larger than the returns. We define the returns here as the change of GDP as obtained from the change of LATC compared to baseline,11 which is the hypothetical increase of the GDP from getting more LATC, calculating the elasticity from a CES function and keeping other factors like labour and capital constant. The costs are the additional private and public R&D expenditures. We take the log-difference between baseline and shock simulation for each point in time and then calculate the cost change per period. Having flow changes, we can take the difference between gross gains and additional costs, discount them and add them up. In the first instance, we discount with the standard interest rate of four percent and calculate the sum of discounted net gains from 1963 until 2017 where the GDP data end. Then we try to find the internal rate of return, defined as the discount rate that brings the sum of discounted net gains to zero. We also consider the gain per period as a share of GDP without any discounting. The results are summarised in Table 1. Table 1 Effects of permanent shocks of one standard deviation of the growth rate Shock on growth rate of equation Sum of net gains discounted at 4% in US$ bill. Internal rate of return Average gain /GDP 1963-2017 (6) public domestic R&D stock 5496 ∞ (a) 0.035 (5) private domestic R&D stock 8317.4 ∞ (a) 0.055 (8) public foreign R&D stock 761 (b) 0.0225 0.0026 (7) private foreign R&D stock 2676.7 (c) -0.034 0.016 (a) There are no periods of losses. (b) gains followed by losses after 1997. (c) Gains followed by losses after 2004. For the shock to public domestic R&D stocks of one standard deviation in the USA in Figure 3 , the sum of net gains discounted at 4% is positive for all years and goes to 5496 billion US dollars in 2017. The internal rate of return is infinity because there are no periods of losses. The undiscounted gains as a share of GDP are 3.5% on average over 1963-2017. A shock to private domestic R&D stocks of one standard deviation in a VECM, considering all sub-sequent costs of domestic private and public R&D and all effects on LATC shown in 11Ziesemer(2021)obtainstheLATCdatafromtheCESfunction𝑌𝛼𝐾 1𝛼𝐴𝐻𝐿 ,solvingitfor AandusingmainlyPWT9.1data.Forthisfunction,theelasticityofproductionofYwithrespecttoAis𝜀 1𝛼 .ThiselasticitycanbecalculatedforeachyearalsobyinsertingdatafromPWT9.1.Itgoesfrom 0.64in1950to0.656in1991whereitremainswithupsanddownsuntil2009;thenitgoesdownto0.653in 2017.Thenwecalculatedlog(GDP)𝜀 𝑑𝑙𝑜𝑔𝐿𝐴𝑇𝐶foreveryyear,wheredlog(LATC)isthepercentage deviationfrombaseline.Multiplicationofdlog(GDP)withGDPgivesdGDP,theincreaseofGDPthroughthe policyshockrepresentingthebenefitorreturn.
Figure 4, has an effect of 8317 billion US dollars until 2017 when the discount rate is 4%. The internal rate of return is again infinity because there are no periods of losses. For reactions to shocks from foreign public investment in Figure 5, the sum of net gains when discounting at 4% is 762 billion US dollars, meaning that expected losses from foreign R&D effects can be turned positive through own public and private investment reactions. Competition or spillovers trigger profitable reactions. As late losses dominate early gains in the absence of discounting, the internal rate of return of only 2.6% is needed to give low weight to late losses. For reactions to shocks from private foreign investment in Figure 6, we find positive discounted gains when using a 4% rate of 2676 billion US dollars with an internal rate of return of -0.034 percent. The investments following a foreign spillover or competition shock are profitable from 1963 to 2004 and then gains get negative; the internal rate of return is negative because gains come first and losses later. Early gains are not outweighed by later losses. To find the rate of return which makes gains zero we need to give higher weights to late losses. If the project could be stopped in 2004 and losses are thereby avoided, the discounted gains would be US$ bill. 3050 (15219) for a discount rate of 4% (-0.034%). The old standard result, showing no or negative spillovers or competition effects does not hold for our VECM for the USA distinguishing public and private domestic and foreign R&D. The USA react to foreign private R&D what may be seen as spillover under perfectly competitive reactions or competition under oligopolistic strategic reaction. The reactions appear in the long-term relation and in the impulse responses. The yearly net gains averaged over all periods for the four scenarios range between 1.6 and 5.5 percent of the GDP. Those from foreign spillovers are at the lower end of the range but far from negligible. 6 Permanent policy effects? If the long-term relations are in equilibrium, the model of equations (4)-(8) could in principle be solved for five growth rates. Figures 3-6 plot LATC growth rate differences comparing the policy scenarios 1-4 to those of the baseline. Expected effects are positive for domestic public R&D shocks for 57 years, for domestic private R&D shocks for 80 years, for reactions to foreign public R&D shocks 32 years, and for reactions to foreign private R&D shocks 43 years. The evidence from our model for the USA would support semi-endogenous growth theory because growth rate effects from permanent policy shocks are not permanent. In line with of the decreasing returns shown in Figure 2 we get a temporary policy effect from permanent changes in the spirit of semi-endogenous growth. This is in line with Ziesemer (2020c) and Fernald and Jones (2014), but in contrast to Ha and Howitt (2007). As four of the five residuals have received permanent shocks, it is instructive to look at the effects on the growth rates of public and investment in Figure 3-6 . Public investment compared to baseline keep growing in all four cases of self-initiated policies or policies
reacting to foreign shocks. Private investment keeps growing only when the shock also comes from private investment. In conclusion, public investment a backbone for all types of growth policies, especially when the economy reacts to foreign shock. 7 Summary and conclusion Summing up, empirical econometrics can identify spillovers only when abstracting from strategic behaviour (Bernstein and Mohnen 1998). Economic theory can distinguish between spillovers and reaction functions only when pre-fixing ideas as to which oligopoly model is relevant. Combining economic theory and empirical econometrics also only works when prefixing on a model as Scherer (1991) did abstracting from spillovers. Similarly, Granger causality (Atukeren 2007) and VECM without (Luintel and Khan 2004) and with impulses (this paper) can analyse countries’ reactions without knowing whether they are from reaction functions with or without spillover. Instead of following the empirical literature using one stock variable for total foreign R&D expenditures we have used two, one for business R&D and one for non-business R&D. A VECM for the USA then shows that foreign and domestic public and private R&D stocks are all endogenous variables. Applying the methodology of looking at the consequences of permanent changes shows that shocks to foreign public and private R&D stocks affect the US economy positively (not zero, negative, submissive) by way of driving US public R&D and LATC upward whereas private R&D goes up temporarily in response to foreign private R&D shocks and even goes down in response to a foreign public R&D shock. Permanent changes of US public and private R&D have transitional effects on LATC for some decennia. Calculation of the net gains, discounted at 4% interest rate, from the time paths of model solutions of the VECM (first done by Soete et al (2020b) shows that the investments in reaction to shocks of the two foreign R&D variables are profitable. This result complements that of Luintel and Khan (2009) who show significantly positive effects for patent data. By implication, it is unlikely that both old results of no spillovers to the US from the EU and Japan hold simultaneously, but we cannot exclude the possibility that there are no spillovers, and the reactions are completely strategical in the spirit of oligopolistic reaction curves. In a perspective of publicly or privately financed R&D the period of shift to private financing goes from 1985-2013 interrupted in 2009 where privately financed R&D falls (Archibugi and Filippetti 2018), which is seven years later than that for performance perspective. In a basic versus applied perspective for 16 countries listed by Gersbach et al. (2020) the average shifts to basic R&D and so do 9 of 16 countries (including the USA) comparing the year 2000 to 2009. All together this means that after 2000 there is a shift to basic, publicly performed R&D, which is increasingly financed privately. Van Reenen (2020) suggests a.o. to increase federal funding for the USA. Our results show that additional US public and private R&D would have a net gain per unit of GDP, a high net present value after discounting at a rate of four percent, and a positive gain/GDP ratio. Permanent shocks have transitory effects for
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Appendix unit root tests Unit root tests without and with break point (a) Variable LGDP LTFP LBERDST LPUBST LFBERDST LFPUBST PROIL ADF without breakpoints. Dependent Variable: D(logx); coefficient of lagged level variable. Coeff. -0.12 -0.1 -0.06 -0.055 -0.0039 -0.0024 -0.103 t-value p-val. -2.01 0.58 -1.66 0.756 1.97 0.60 -2.13 0.51 -2.72 0.0765 -2.25 0.19 -1.79 0.38 Dickey-Fuller-GLS without breakpoints. Dependent Variable: D(GLSRESIDUAL); coefficient of lagged residual. Coeff. -0.08 -.096 -0.05 -0.03 0 -0.0147 -0.0677 t-val. (e) p-val.(g) -1.56 0.125 -1.63 0.11 -3.11 0.0031 -1.93 0.06 0.69 0.49 -0.973 0.335 -1.32 0.19 Zivot-Andrews unit-root test with breakpoint determination for intercept and trend. t-value unit r (f) -5.577 no -4.19 Yes -4.415 yes -4.21 yes -3.62 Yes -4.22 yes -3.31 yes Break year 2008 1974 1995 2001 1984 2008 1986 ADF unit-root test with break Coeff.(b) 0.443 0.46 0.39 0.64 0.798 0.91 0.775 0.926 0.94 0.87 0.81 0.898 0.75 0.008 p-val. (c) 0.018 <0.01 0.31 0.29 <0.01 0.80 <0.01 0.76 0.777 <0.01 0.0245 <0.01 0.84 0.0112 Break date (d) 2007 2008 1978 1984 1994 1985 1974 1974 1990 1996 2006 2004 1983 1986 Unit root No or near Near near near Near near near (a) In DF-GLS and ADF, intercept and trend (if significant); AIC for lag length; (b) Coefficient for a lagged level in the ADF equation; F-test for intercept + trend break point, or Dickey- Fuller min-t in the absence of trend or intercept break; first value in cell for innovational outlier, second for additive outlier, also for p-values and break dates. (c) p-value for unit root. (d) break date for innovational outlier and additive outlier. (e) critical 10% value about (-2.6, - 2.9); value not more negative have a unit root. (f) t-Statistic critical value: for 1%, -5.57, for 5% -5.08, for 10%, -4.82. (g) p-value for the coefficient given above. The ADF test would suggest that all variables have a unit root, with the exception of LFBERDST at the ten percent level. As the test has low power it may give us too many unit root results. However, the DF-GLS test, which is known to have better power properties indicates unit roots at the five percent level except for LBERDST. In the presence of breaks there might be less unit roots. However, the Zivot-Andrews unit root test assuming one break suggests unit roots for all variables except for LGDP. The Vogelsang-Perron ADF test with breakpoints allows (rejection of) breakpoints for intercept, trend or both. It indicates unit roots except for LGDP and LFPUBST although the coefficients are fairly high for LFPUBST. Overall, the tests allowing for breakpoints suggest no unit root for LGDP; ignoring breaks we have near unit roots. For LFPUBST the evidence is mixed, and we assume that there is a near unit root. The coefficients are all below unity and even below 0.95. Except for LGDP and LPUBST, the variables have different break years across tests. They may be caused by shocks in related variables, which are not included in the uni-variate tests. Break years also differ across variables rather than showing a common break period for a joint model.