The Impact Of Regulation On Innovation - Harvard University
The Impact of Regulation on Innovation Philippe AghionAntonin BergeaudCollege de France and LSEBanque de FranceJohn Van ReenenMIT and Centre for Economic Performance, LSEMarch 2019AbstractWe study the impact of labor regulation on innovation. We exploit the threshold in labor market regulations in France which means that when a firm reaches 50employees, costs increase substantially. We show theoretically and empirically thatthe prospect of these regulatory costs discourages firms just below the thresholdfrom innovating (as measured by patent counts). This relationship emerges whenlooking nonparametrically at patent density around the regulatory threshold andalso in a parametric exercise where we examine the heterogeneous response of firmsto exogenous market size shocks (from export market growth). On average, firmsinnovate more when they experience a positive market size shock, but this relationship significantly weakens when a firm is just below the regulatory threshold. Usinginformation on citations we show suggestive evidence (consistent with our model)that regulation deters radical innovation much less than incremental innovation.This suggests that with size-dependent regulation, companies innovate less, but ifthey do try to innovate, they “swing for the fence”.JEL classification: O31, L11, L51, J8, L25Keywords: Innovation, regulation, patent, firm size. We would like to thank Costas Meghir for tremendous help with an earlier version of this paper andMatthieu Lequien for his invaluable help with the data.1
1IntroductionThere is a considerable literature on the economic impacts of regulations, but relativelyfew studies on the impact of regulation on technological innovation. Most analyses focuson the static costs (and benefits) of regulation rather than on its dynamic effects. Yetthese potential effects on innovation and growth are likely to be much more important inthe long-run. Harberger triangles may be small, but rectangles can be very large. Manyscholars have been concerned that slower growth in countries with heavy labor regulation,could be due to firms being reluctant to innovate due to the burden of red tape. Theslower growth of Southern European countries and parts of Latin America have often beblamed on onerous labor laws (see for example, Gust and Marquez, 2004; Bentolila andBertola, 1990, Bassanini et al., 2009).Identifying the innovation effects of labor regulation is very challenging. The OECD,World Bank, IMF and other agencies have developed various indices of the importanceof these regulations, based on examination of laws and (sometimes) surveys of managers.These indices are then often included in econometric models and sometimes found to besignificant. Unfortunately, these macro indices of labor law are correlated with many otherunobservable factors that are hard to convincingly control for.1 To address this issue weexploit the well-known fact that many of these regulations are size contingent, only kickingin when a firm gets sufficiently large. In particular, the burden of French labor legislationsubstantially increases when firms employ 50 or more workers. Firms of 50 workers or moremust create a works council (“committee d’entreprise”) with a minimum budget of 0.3% oftotal payroll, establish a health and safety committee, appoint a union representative andso on (see Appendix A for a more thorough presentation of size contingent regulationsin France). Several authors have found that these regulations have an important effecton the size of firms (Garicano et al., 2016; Gourio and Roys, 2014; Ceci-Renaud andChevalier, 2011). Unlike the US firm size distribution, for example, in France there is aclear spike in the number of firms that are just below this regulatory threshold.2Existing models that seek to rationalize these patterns have not considered how thisregulation could affect innovation, as technology has been assumed exogenous. But when1Furthermore, it may be that the more innovative countries are less likely to adopt such regulations (e.g.Saint-Paul, 2002).2Often, it is hard to see such discontinuities in the size distribution at regulation thresholds (e.g. Hsiehand Olken, 2014).1
firms are choosing whether or not to invest in innovation, regulations are also likely tomatter. Intuitively, firms may invest less in R&D as there is a very high cost to growing ifthe firm crosses the regulatory threshold. In the first part of the paper we formalize thisintuition in a step-by-step model of endogenous innovation. Our model delivers two mainpredictions. First, a regulatory threshold should discourage innovation mostly for firmsbelow the threshold that are close to the threshold. Second, the discouraging effect of theregulatory threshold on innovation by firms close to the threshold, should be weaker formore important innovations.We take these predictions to the data. More specifically, we use the discontinuousincrease in regulation cost at the regulatory threshold size to test the theory in twoways. First, we investigate non-parametrically how innovation changes with firm size.As expected there is a sharp fall in the fraction of innovative firms just to the left ofthe regulatory threshold which is suggestive of a chilling effect of the regulation on thedesire to grow. Furthermore, this relationship is only visible for lower value patents (asmeasured by future citations) - there is no visible effect for highly cited patents. The ideais that regulation may deter low quality innovations which have little social value, but ifa firm is going to innovate it will try to “strike for the fence” to avoid being only slightlyto the right of the threshold. Intuitively, the growth benefits of innovation are less if itbrings the firm into the regulatory regime.Although the descriptive evidence is suggestive, there could be many other reasons whyfirms are heterogeneous near the regulatory threshold, so we turn to a stronger test usingthe panel dimension of our data. Specifically, based on the view that an increase in marketsize should have a robust positive effect on innovation (e.g. Acemoglu and Linn, 2004),we examine the heterogeneous response of firms with different sizes to exogenous demandshocks. We use an shock based measure based on changes in growth in export productmarkets (HS6 by country) interacted with a firm’s initial distribution of exports acrossexport markets (see Hummels et al., 2014; Mayer et al., 2016 and Aghion et al., 2018). Wefirst show that these positive market size shocks significantly raise innovative activity. Wethen examine the heterogeneity in firm responsiveness to these export shocks dependingon lagged firm size. We show that there is a sharp reduction in firm responsivenessto innovation exactly before the regulatory threshold. Consistent with intuition andour simple model, firms appear reluctant to take advantage of exogenous market growththrough innovating when they will be hit by a tsunami of labor regulation. As notedabove, the impact of regulation may be less problematic if it discusses only incremental2
innovations. In our empirical analysis, we uncover evidence that the fall in innovation justbefore the threshold is strongest for low value patents (as measured by future citations)and not observable for the patents which subsequently receive many citations.In the rest of the Introduction we turn first to some related literature, then in Section2 we sketch our theory, our empirical analysis in Section 3 and some concluding remarksin Section 4.Related LiteratureOur paper is related to a vast literature examining the effects of regulation (particularlabor laws) on economic outcomes. Several recent papers in this literature take structural approaches such as Braguinsky et al. (2011) on Portugal and Garicano et al., 2016on France. Guner et al. (2006, 2008) also consider a Lucas model with size-contingentregulation. None of these papers allows firms to influence their productivity throughinnovation choices as we do, however.One branch of the literature looks at whether labor laws can encourage some kinds ofinnovation. Acharya et al. (2013a) argue that higher firing costs reduce the risk of firmsholding up employees’ innovative investments by dismissing them ex post. They find evidence in favor of this using macro time series variation for four OECD countries. Acharyaet al. (2013b) also finds positive effects using staggered roll out of employment protectionacross US states.3 Griffith and Macartney (2014) use multinational firms patenting activity across subsidiaries located in different countries with various levels of employmentprotection laws (EPL).4 Using this cross sectional identification, they find that radicalinnovation was negatively effected by EPL, but incremental innovation was, if anything,boosted.5 Relatedly, there are many papers examining the impact of union power (whichis affected by labor regulation) on innovation.6 This literature tends to find that theimpact of unions and regulation are ambiguous and contingent on the type of innovation(e.g. radical/incremental) and other features of the economic environment (e.g. negative3This is the same empirical variation used by Autor et al. (2007) who actually found falls in TFP andemployment.4See also Cette et al. (2016) who document a negative effect of EPL on capital intensity, R&D expendituresand hiring of high skill workers.5Note that this is the opposite of what we find using our within country identification. Labor regulationdiscourages low value innovation, but has no impact on high value innovation.6See Menezes-Filho et al. (1998) for a survey and evidence. The common view is that the risk of ex posthold-up by unions reduces innovation incentives (Grout, 1984). But if employees need to make sunkinvestments there could be hold up by firms (this is the intuition of the Acharya et al., 2013a,b papers).3
effects are stronger in high labor turnover industries).Another recent literature has documented empirically how distortions can affect aggregate productivity through misallocations of resources away from more productive firmsand towards less productive firms. As Restuccia and Rogerson (2008) have argued,7 thesedistortions mean that more efficient firms produce too little and employ too few workers.Hsieh and Klenow (2009) show that these misallocations account for a significant proportion of the difference in aggregate productivity between the US, China and India andBartelsman et al. (2013) confirm this using micro data on OECD countries.8 One issuewith these approaches is that the causes of the random distortions are a bit of a “blackbox”. We contribute by this literature by introducing an explicit source of distortion,namely the regulatory firm size threshold, and by looking at how this regulation interactswith exogenous export shocks for firms with different size.9The heterogeneous effects of demand shocks on types of innovation is also a themein the literature of the effects of the business cycle on innovation (Schumpeter, 1939;Shleifer, 1986; Barlevy, 2007; Aghion et al., 2012). Recent work by Manso et al. (2019)suggests that large positive demand shocks (booms) generate more R&D, but this tendsto “exploitative” (incremental) rather than “exploratory” (radical) innovation. We findthat the impact of regulation following a demand shocks discourages incremental (butnot radical) innovation.Finally, our paper is also related to the more general literature using tax “kinks” toidentify behavioral parameters (e.g. Saez, 2010; Chetty et al., 2011; Kleven and Waseem,2013). Kaplow (2013) discuses issues in the optimal structure of size-related regulations.We contribute to this literature by bringing innovation and patenting into the picture.The structure of the paper is as follows. Section 2 develops a simple model of how theamount and importance of innovation can be affected by firm size regulation. Section 3develops the empirical analysis. Section 4 concludes.7See also Parente and Prescott (2000) or Bloom and Van Reenen (2007).In development economics many scholars have pointed to the “missing middle”, i.e. a preponderanceof very small firms in poorer countries compared to richer countries (see Banerjee and Duflo, 2005, orJones, 2011). Besley and Burgess (2000) suggest that heavy labor regulation in India is a reason whythe formal manufacturing sector is much smaller in some Indian states compared to others.9See e.g. Bergeaud and Ray (2017) for a discussion. Another issue, is that regulatory distortions in thesemodels typically only have second order effects on welfare if they preserve the size ranking of firms (seeHopenhayn, 2014). If regulations can also affect growth through innovation (as we argue), then theymight have first order effects on welfare.84
2Theory2.1Benchmark model without regulationWe consider a economy with a continuum of individuals with intertemporal utility ofconsumptionZe ρt ln ct dtU (c) and where the consumption good (or final good) is produced using a continuum of intermediate inputs. In each input sector i there are two potential producers, Ei and Fi . Thefinal good is produced according to:1Zln xi di,ln y 0wherexi xEi xFiandxj Aj ljwhere: (i) lj is the amount of labor used by firm j {Ei , Fi } to produce the amount xjof intermediate input; (ii) Aj γ kj is firm j’s current productivity, where γ 1 and kjis firm j’s current technological level .Then we know that the equilibrium profit of a technological leader in sector i is equalto:πj 1 1(Aj /Afi ),where Afi is the next best technology (or fringe technology) in sector i.We first consider the case where the maximum technological gap kEi kFi betweenthe leader and the follower in any intermediate sector, is equal to 1. Then sectors canbe either unleveled, with a technological gap equal to one between the leader and thefollower, or neck-and-neck with a technological gap of zero between the leader and thefollower.In an unleveled sector the leader’s profit flow is equal to (see Aghion et al., 2005):1π1 1 ,γwhereas the follower’s profit is equal to zero:π 1 05
More over, the leader will employ1γωl1 units of labor, where ω w/y is the output-adjusted wage rate which is constant insteady-state and which we take here as given for simplicity. The follower will employl 1 0units of labor as it does not operate.In a neck-and-neck sector, we follow Aghion et al. (2005) and assume a positive degreeof collusion between the two firms in that sector, which leads to asymmetric equilibriumwhere each of the two competing firms in the sector makes profits:π0 (1 )π1 ,where (1/2, 1], and where each of the two firms employsl0 12γωunits of labor.Innovation takes place step-by-step: to move up one technological step with Poisson2probability nm (resp. nm h)10 a firm currently in stage m must invest α n2m units of laborin R&D. Then, if Vm denotes the productivity-adjusted market value of a firm currentlyin stage m, where m { 1, 0, 1},we have the Bellman equations:11(B1)ρV1 π1 (n 1 h)(V0 V1 );(1)ρV1 π1 (n 1 h)(V0 V1 );ρV0 π0 n0 (V 1 V0 ) max{n0 (V1 V0 ) αn0ρV 1 π 1 max{(n 1 h)(V0 V 1 ) αn 110n2 1};2n202};(2)(3)The parameter h is a *help* factor which captures the fact that, due to knowledge spillovers fromfrontier firms, it is easier to catch with the technological frontier than to push up the frontier (seeAghion et al, 2005).11Here we make use of the Euler equation:r g ρ.6
wheren0 n0in a symmetric equilibrium, and where, by first order conditions:V1 V0 αn0(4)V0 V 1 αn 1 .(5)Eliminating the V ’s between the equations (1), (2), (3), (4) and (5), yields two equations in the two unknowns n 1 and n0 , namely:n20 (ρ h)n0 (π1 π0 ) 0;2n2 1n2 (ρ n0 h)n 1 (π0 π 1 ) 0 0.222.2Effect of the labor regulatory thresholdIntroducing a regulation cost τ for firms that employ l 1/γω units of labor, will onlyaffect leaders in unleveled sectors (as in levelled sectors l 12γω 1/γω, thereby leadingto the net equilibrium profit flows:πb1 π1 τ ;πb0 π0 ;πb 1 π 1 .Then n 1 and n0 will satisfy:n20 (ρ h)n0 (π1 τ π0 ) 0;2n2 1n2 (ρ n0 h)n 1 (π0 π 1 ) 0 0,22(6)(7)It is easy to show that n0 is more sharply decreasing in τ than n 1 12 . In other words, firmsthat are below - but closer to - the regulation threshold will reduce innovation intensityby more than firms far below the threshold, but n 1 will also go down as τ increases.12Differentiate equation (7) with respect to τ :n 1 n 1 n 1 n0 (ρ n0 h) n0 0, τ τ τ(ρ h n 1 n0 )7 n 1 n0 n0 τ τ
We can also show that 2 n0 0. τ γIn other words, a regulation cost is less discouraging the bigger the size of the innovation.To prove this claim, note first that solving the quadratic equation in n0 yields:n0 (ρ h) p(ρ h)2 2 (π1 τ ).This in turn implies that: n0 p τ(ρ h)2 2 (π1 d)which, in absolute value, is clearly decreasing in π1 . But π1 is itself increasing in the sizeof innovation γ. This establishes the claim.2.3PredictionsThe main predictions from the above model are:Prediction 1: A regulatory threshold reduces innovation mostly for firms below thethreshold but close to the threshold.Prediction 2: The discouraging effect of the regulatory threshold on innovation byfirms close to the threshold, is weaker for more drastic innovations.In the remaining part of the paper we confront these predictions to the data.3Empirical analysis3.1DataOur data comes from the French fiscal authority which consistently collects balance sheetsof all French firms on a yearly basis from 1994 to 2007 (“FICUS”). We restrict attention n0 n 1 τ τSincen0n 1 n0 ρ h( n τ 1 ) n0n 1 n0 ρ h 1,it follows that the impact of the regulation on employment for the laggard firm0is less than the impact on the firms in the levelled sectors ( n τ ).8
to non-government businesses and take patenting information from Lequien et al. (2017).This uses the PATSTAT Spring 2016 database and matches it to FICUS using an algorithm which matches the name of the affiliate (holder of the IP rights) on the patent frontpage to a firm whose name and address is the closest. The accuracy of the algorithmis weaker for firms that are below 10 employees so we focus on firms larger than this.Since we are interested in a regulation that affects firms at 50 employees, we also focuson firms below an upper size threshold. Consequently, in our main results we stick toan employment bandwidth of between 10 and 100 employees - i.e. we restrict the mainsample to firms with between 10 and 100 workers in 1994 (or the first year they appearin the data).13 More details about the data source are given in Appendix B.Our main sample consists of 154,582 distinct firms over 1,439,396 observations. Ofcourse, the majority of these firms do not innovate, as defined as having at least onepatent over the sample period. We report basic descriptive statistics in Table 1, wecan see that on average, firms file on average 0.023 patents per year and, conditionalon innovating, 0.44 per year. As is well known, the distribution of innovation is highlyskewed with a small number of firms owning a large share of the patents in our sample.However, since we do not include the largest French firms in our data, the skewness is lesspronounced than what is documented by Aghion et al. (2018).3.2Nonparametric evidenceFigure 1 shows the share of firms with at least one patent in each employment size bin(measured in the current year t) over all our main sample (see Panel A of Table 1). Overthe size distribution as a whole, there is an almost linear relation with size: larger firmsare increasingly likely to patent (see Akcigit and Kerr, 2018, for example). However, justbefore the regulatory threshold at 50 employees there appears to be a discontinuity as theshare of innovative firms suddenly decreases. The innovation outcome measure is takenover the whole sample period from 1994 to 2007, but the same is true if we considerdifferent definition of innovative firm as reported in Online Appendix Figure C1.Figure 2 repeats this analysis by the quality of the patent. We measure quality by theusing the number of future citations. For each cohort-year of patents we calculate whether13We show robustness of the results to changing this bandwidth (see in particular Table C2 in AppendixC). Note that the sample selection allows employment that can be more than 100 employees or lowerthan 10 employees in some years.9
Table 1: Descriptive statisticsPanel A: All 99539,000018917,8111126989,64691Panel B: Subset of innovative 4610,1670.440.57181,90400324,25201Notes: These are descriptive statistics on our data. Panel A is all firms and Panel B conditions on firms who filed for a patent at least once over the 1994 to 2007 period (“Innovative”firms). We restrict to firms who have between 10 to 100 employees in 1994 (or the the firstyear they enter the sample). There are 154,582 firms and 1,294,139 observations in PanelA and 4,180 firms and 66,844 observations in Panel B.the patent was in the top 10% of the citation distribution (squares) or the other 90%.The Figure shows the fraction of firms at each employment level who had these typesof patents. It is clear that the drop-off in patents just below the regulatory threshold isbarely visible for patents in the top of the quality distribution and invisible for others.This is consistent with the idea that the regulation discourages low value innovations butnot higher value innovation.143.33.3.1Parametric analysisEstimation equationWe now turn to our parametric investigation of how firms respond to market size shocks.More specifically, we estimate the regression equation (8): i,t βL?i,t 2 γ[ Si,t 2 P(log(Li,t 2 ))] δ[ Si,t 2 L?i,t 2 ] ψs(i,t) τt εi,t (8) Y14As with Figure 1, Figure 2 considers the innovation outcome over the whole period of observations.Variations around this can be found in Figure C2 in the Online Appendix C.10
Figure 1: Share of innovative firms at each employment levelShare of innovative firms.08.06.04.020020406080100EmploymentNotes: share of firms with at least one priority patent against employment at t. All observations are pooled together. Employment bins have been aggregated so as to include at least 10,000 firms. The sample is based on allfirms with initial employment between 10 and 100 (154,582 firms and 1,439,396 observations, see Panel A of Table 1).Figure 2: Share of innovative firms at each employment level and quality of innovationShare of innovative firms.08.06.04.020020406080100EmploymentBottom 90%Top 10%Notes: share of firms with at least one priority patent in the top 10% most cited (grey line) and the share of firmswith at least one priority patent among the bottom 90% most cited in the year (black line). All observations are pooledtogether. Employment bins have been aggregated so as to include at least 10,000 firms. The sample is based on allfirms with initial employment between 10 and 100 (154,582 firms and 1,439,396 observations, see Panel A of Table 1).11
where: Yi,t is a measure of innovation; L?i,t is a binary variable that takes value 1 if firmi is close to, but below the regulatory threshold at time t; Si,t 2 is an exogenous shockthat triggers shifts in innovation; ψs(i,t) is a set of industry dummies and τt is a set oftime dummies (s(i, t) denotes the main sector of activity of firm i at t), P(log(Li,t 2 )) is apolynomial in log(Li,t 2 ) and εi,t is an error term. We use a two year lag of the shock sincethere is likely to be some delay between the market opportunity shock, the an increasein research effort and the filing of a patent application.We use growth rates of Y definedas:15 i,t Y3.3.2 Yt Yt 1Yt Yt 1if Yt Yt 1 0otherwise0ShocksTo construct the innovation shifters Si,t 2 , we rely on international trade data to buildexport demand shocks following Mayer et al. (2016) and Aghion et al. (2018). The construction of such shocks are explained at length in Aghion et al. (2018). In a nutshell, welook at how foreign demand for a given product changes over time by measuring the changein imports to all countries worldwide but France. We then build a product/destinationportfolio for each French firm i, and weight the foreign demands for each product by therelative importance of that product for firm i. More specifically, firm i’s export demandshock at date t is defined as:Si,t X s,j,t ,ωi,s,j,t0 I(9)s,j Ω(i,t0 )where: Ω(i, t0 ) is the set of products and destinations associated with positive exportquantities by firm i in the first year t0 in which we observe that firm in the custom data;16ωi,s,j,t0 is the relative importance of product s and destination j for firm i at t0 , defined asfirm i’s exports of product s to country j divided by total exports of firm i in that year;Is,j,t is country j’s demand for product s, defined as the sum of its imports of product sfrom all countries except France.15This is essentially the same as in Davis and Haltiwanger (1992) for employment dynamics except thatwe set the variable equal to zero when a firm does not patent for two periods. Results are robust toconsidering other types of growth rates (see the last 3 columns of Table C2 in Appendix C).16French customs data are available from 199412
3.3.3Testing the main predictionTo estimate equation (8), we need to make some further restrictions in our use of thedataset. First, shock S is only defined for exporting firms, that is, firms that appearat least once in the customs data from 1994 to 2007. Second, in order to increase theaccuracy of our shock measure, we restrict attention to the manufacturing sector. Notonly are most innovative firms within the manufacturing sector, but these firms are alsomore likely to take part in the production of the goods they export (see Mayer et al.,2016). Our main regression sample is therefore composed of 21,740 firms and 186,337observations.Table 2 presents the results of estimating equation (1), i.e. regressing the change inpatents today on the lagged shock. Column (1) shows, consistently with earlier work, thatfirms facing a positive exogenous export shock are significantly more likely to increase theirpatenting activity. A 10% increase in market size increases patents by about 3%. Column(2) includes a control for the lagged level of log(employment) and also its interaction withthe shock. The interaction coefficient is positive and significant, indicating that there isa general tendency for larger firms to respond more to the shock than smaller firms. Thisis what we should expect since both, the market size effect and the competition effect ofa positive export shock, are more positive for more productive firms (see Aghion, et. al,2018). Column (3) generalizes this specification by adding in a quadratic term in laggedemployment and its interaction with the shock.Column (4) of Table 2 returns to the simpler specification of column (1) and includes adummy a the firm was just below the regulatory threshold (45-49 employees) at t 2 andthe interaction of this dummy with the shock. Our key coefficient is on this interaction,and it is clearly negative and significant. This is our main result: innovation in firms justbelow the threshold is significantly less likely to respond to positive demand opportunitiesthan in firms further away from the threshold. Our interpretation is that when a firmis near the threshold, there is a large “tax” on growth because of the regulatory cost ofbecoming larger than 50 employees. Consequently, such a firm will be more reluctantto invest in innovation in response to this new demand opportunity. Indeed, they mayeven cut their innovative activities to avoid the risk of crossing the threshold. It mightbe the case that the negative interaction of the threshold and the shock could be dueto some omitted nonlinearities. Hence in column (5) we also include lagged employmentand its interaction with the shock (as in column (2)). These do have explanatory power,13
but our key interaction coefficient remains significant and negative and we treat this asour preferred specification. Column (6) adds quadratic employment term and its interaction following column (3). Our key interaction remains significant and these additionalnonlinearities are insignificant.We depict the relationship between innovation and the shock in Figure 2. This figureplots the implied marginal effect of the market size shock on innovation for different firmsizes using the coefficients in column (5) of Table 2. We see that innovation in larger firmstends to respond more positively to the export shock than in smaller firms. But at theregulatory threshold there is a sharp fall in the derivative of innovation with respect tothe shock, consistent with our modelColumn (7) of Table 2 shows the results from a tough robustness test where we include a full set of firm dummies. Given that the regression equation is already specifiedin first differences, this amounts to allowing firm-specific time trends. The key interaction between the market size shock and the threshold dummy remains significant. Thesample underlying Table 2 is limited to manufacturing firms. Column (8) also adds innon-manufacturing firms. The relationship remains negative, although with a smallercoefficient and is less precisely determined. This is likely to be because patents are amuch more noisy measure of innovation in non-manufacturing firms. Does the numberof patents simply fall because firms are less likely to grow and relatively smaller firms doless innovation? Column (9) provides a crude test by including the growth of employmenton the right hand side o
the leader and the follower in any intermediate sector, is equal to 1. Then sectors can be either unleveled, with a technological gap equal to one between the leader and the follower, or neck-and-neck with a technological gap of zero between the leader and the follower. o(seeAghionetal.,2005 .
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