Online only Appendix: Electronic Supplementary Material
A1. Penalized fixed effect quantile regression
Koenker (2004) penalized fixed effect quantile regression is implemented by estimating the coefficients, of each independent variable (i.e. the partial derivative of the conditional quantile of growth ( with respect to a particular independent variable), at quantiles , where indexes the quantiles at10%, 25%, 50%, 75%, 80%, 90%. Estimation is implemented using Koenker (2004) penalised fixed effect quantile regression, minimising Expression 1:
Expression 1: Penalised fixed effect quantile regression estimator
Where is an index for the firms, and j the observations for each firm and, is the piecewise linear quantile loss function used for each quantile regression as described by Koenker and Bassett (1978).
The penalized fixed effect estimator produces slope coefficient estimates for each selected quantile, but the fixed effect for each firm are independent of quantiles, thereby avoiding estimating fixed effects for each different quantile regression.Estimation is performed by minimising the expression selecting weights for each of the quantiles which control for the influence of quantiles on the estimation of and applying a penalty term to penalise the vectors of fixed effect coefficients, shrinking these coefficients toward zero.The importance of the penalty term is controlled by selecting a value of (Koenker, 2004).We set and select an even weighting of across quantiles. Varying the choice of weights made only minor changes to the reported results.For a detailed discussion of this method see Koenker (2004).Standard errors are constructed via a generalized bootstrap with unit exponential weights sampled for each firm.
For comparison we also report regression results for OLS and least squares (within) fixed effect estimators with robust errors using Huber-White sandwich estimators.We also run standard quantile regression estimation using Koenker and Basset (1978) method, but preferring bootstrapped standard errors with 1000 repetitions due to the presence of heteroskadasticity.
A2. Robustness testing
In this section we report the results of our robustness testing. First we consider the effect of changing the data year used as a breakpoint. We consider the effects of changing the breakpoint by +/-5 years. Next we consider whether our results are robust to the effect of M&A activity and additional lags.
Given our decision to split our sample into pre/post-1980 periods, we check whether our results for the R&D–growth relationship are sensitive to this exact date by adjusting the split year by +/- 5 years. In Tables 9 and 10 we report the results of the coefficient of R&D intensity and R&D scale from our model discussed in Section 4 modifying how the data are broken into two periods. We report results for the 90% quantile, including coefficients for R&D intensity and R&D scale. For reference we also include our measures of innovation, VC and patent persistence. Both tables give support for our results reported in Section 5.1.
Table 9 reports the coefficient of R&D intensity and R&D scale for firms at the 90% quantile initially using data from 1963 to 1975. We then increase the length of the period in one year increments toshow results for the period 1963 to 1985. We find our result that R&D intensity has a negative influence on growth is confirmed with a statistically significant negative coefficient when the data period ends in the years 1979, 1980 and 1981. The absence of a statistically significant relationship between R&D intensity and growth for periods ending before 1979 may reflect the absence of an R&D-growth relationship for earlier years, but may also be related to the decreasing sample size. The fact that the coefficient value of R&D intensity is reported as negative until the break point year of 1983, gives further support of our results in Section 5, that R&D intensity has a negative relationship with growth for HGF in the pre-1980 period. The results for R&D scale in Table 10 show statistically significant and positive coefficients for periods ending 1980, 1981, and 1982. In periods ending earlier than 1980 we find no statistically significant relationship between R&D scale and growth for HGF, although the value of the estimated coefficient of R&D scale remains stable over time. The absence of a statistically significant relationship maybe related to the lower frequency of observations when reducing the number of years included.
Table 10 reports the coefficient of R&D intensity and R&D scale for firms at the 90% quantile initially using data from 1976 to 2002. We then reduce the length of the data period in one year increments until reporting results for the period 1985 to 2002. Table 10 provides strong support of our discussion of the post-1980 period in Section 5.1, particularly that the coefficients of R&D intensity and R&D scale are both significant and positive post-1980.
In Tables 11 and 12 we report our robustness checks for the results reported in Section 5 by extending our regression model withadditional control variables for M&A and growth lags, as described in Section 4. In Table 11, we show that adding a three year lag of growth, the coefficient of R&D intensity and R&D scale in the pre-1980 period become insignificant and reduce in value dramatically. The effects of including additional lags indicate that pre-1980 growth is more predictable, and agrees with our discussion of the evolution of growth in Section 3 that this period reflects a weak competitive environment. However, given our results in Table 11 for including a one and two year lagged growth variable are very similar, the changes from adding a 3 year lagged growth variable may also be due to the loss of observations for each firm in the sample as a result of increasing the number of lags. In Table 12 we find our results are robust to including measures of M&A[1] whether controlled for using acquisition value (Acq value) or acquisition dummies (AcqDV). Finally, our results for R&D intensity and R&D scale post-1980 shown in Table 12 are robust to including additional control variables and consistentwith those reported in Table 7.
Table 9 Sensitivity of 90% quantile results to time period selection (pre-1980 +/- 5 years)
Start / Finish / R&D intensity / R&D scale / Persist / VC1963 / 1975 / -0.10446 / 0.03301 / 0.01756 / 0.26796**
(0.37398) / (0.0297) / (0.02766) / (0.11867)
1963 / 1976 / -0.29177 / 0.03334 / 0.00823 / 0.22661*
(0.30862) / (0.02531) / (0.03043) / (0.11821)
1963 / 1977 / -0.2998 / 0.03396 / 0.00235 / 0.23652**
(0.28926) / (0.0259) / (0.03058) / (0.11348)
1963 / 1978 / -0.28312 / 0.03107 / 0.00281 / 0.24759***
(0.22918) / (0.02408) / (0.02492) / (0.09166)
1963 / 1979 / -0.50101** / 0.03311 / -0.00114 / 0.18553**
(0.22821) / (0.02205) / (0.02521) / (0.08694)
1963 / 1980 / -0.56129*** / 0.03737* / -0.01143 / 0.18454***
(0.18392) / (0.01993) / (0.02099) / (0.07059)
1963 / 1981 / -0.54451*** / 0.03766** / -0.00647 / 0.1775***
(0.15824) / (0.0177) / (0.01803) / (0.06176)
1963 / 1982 / -0.23354 / 0.04162** / 0.01134 / 0.24058***
(0.17299) / (0.01901) / (0.01994) / (0.08511)
1963 / 1983 / 0.16782 / 0.03795 / 0.01659 / 0.25925
(0.29696) / (0.02326) / (0.02365) / (0.18082)
1963 / 1984 / 0.12179 / 0.03583 / 0.01733 / 0.25986
(0.24939) / (0.02183) / (0.02069) / (0.16194)
1963 / 1985 / 0.40909 / 0.03124 / 0.01864 / 0.28802
(0.26341) / (0.02616) / (0.02297) / (0.22743)
Note: *** 1% ** 5% * 10% significance level, standard error in brackets.
Table 10 Sensitivity of 90% quantile results to time period selection (post-1980 +/- 5 years)
Start / Finish / R&D intensity / R&D scale / Persist / VC1976 / 2002 / 0.1482** / 0.22134*** / 0.02525 / 0.13738**
(0.07005) / (0.04753) / (0.02678) / (0.05903)
1977 / 2002 / 0.14537** / 0.2254*** / 0.02625 / 0.13424**
(0.06923) / (0.04843) / (0.02768) / (0.05832)
1978 / 2002 / 0.14403** / 0.23723*** / 0.02395 / 0.13437**
(0.06786) / (0.04881) / (0.02794) / (0.05726)
1979 / 2002 / 0.1444** / 0.24078*** / 0.03531 / 0.11935**
(0.06644) / (0.05133) / (0.02957) / (0.05765)
1980 / 2002 / 0.14377** / 0.25013*** / 0.03289 / 0.12181**
(0.06626) / (0.05409) / (0.03009) / (0.05741)
1981 / 2002 / 0.14354** / 0.25391*** / 0.03337 / 0.1203**
(0.06763) / (0.05725) / (0.03207) / (0.05757)
1982 / 2002 / 0.14369** / 0.26015*** / 0.03251 / 0.12032**
(0.06707) / (0.06115) / (0.03411) / (0.05744)
1983 / 2002 / 0.14404** / 0.26646*** / 0.04298 / 0.1083*
(0.0672) / (0.06329) / (0.03599) / (0.0589)
1984 / 2002 / 0.14417** / 0.26664*** / 0.03936 / 0.10907*
(0.07095) / (0.06206) / (0.0371) / (0.061)
1985 / 2002 / 0.14492** / 0.29891*** / 0.0303 / 0.11625*
(0.06902) / (0.07309) / (0.03974) / (0.05929)
1986 / 2002 / 0.1432** / 0.27689*** / 0.03213 / 0.10321*
(0.06845) / (0.07398) / (0.04239) / (0.0602)
Note: *** 1% ** 5% * 10% significance level, standard error in brackets.
Table 11 Extended basic model 1963-80 penalized quantile regression with fixed effect estimates for 90% quantile only
1 / 2 / 3 / 4 / 5Coefficient / Std error / Coefficient / Std error / Coefficient / Std error / Coefficient / Std error / Coefficient / Std error
Sales / -0.05763*** / (0.01297) / -0.0642*** / (0.01277) / -0.05786*** / (0.01634) / -0.04489*** / (0.01533) / -0.04407*** / (0.01595)
gri,t-1 / 0.3918*** / (0.08233) / 0.36843*** / (0.07710) / 0.29387*** / (0.09331) / 0.18454*** / (0.06733) / 0.19954*** / (0.06942)
R&D intensity / -0.58892*** / (0.20572) / -0.56129*** / (0.18392) / -0.54451** / (0.24155) / -0.01381 / (0.24519) / -0.03362 / (0.23971)
VC / 0.1814** / (0.07797) / 0.18454*** / (0.07059) / 0.11231* / (0.06483) / 0.01667 / (0.06754) / 0.0028 / (0.07960)
Persist / -0.00487 / (0.02197) / -0.01143 / (0.02099) / -0.01897 / (0.02710) / -0.01349 / (0.02459) / -0.01909 / (0.02815)
Age / 0.03195 / (0.03558) / 0.02826 / (0.03314) / 0.0353 / (0.04038) / 0.05771 / (0.03901) / 0.04964 / (0.03962)
R&D scale / 0.03737* / (0.01993) / 0.04549* / (0.02673) / 0.00613 / (0.02546) / -0.00596 / (0.02703)
gri,t-2 / 0.2216** / (0.08600) / 0.12365** / (0.05597) / 0.14327*** / (0.05424)
gri,t-3 / 0.20374** / (0.09191) / 0.18535* / (0.09730)
Acq value / 0.00423 / (0.00348)
Acq valuet-1 / -0.00138 / (0.00259)
Acq valuet-2 / -0.00348 / (0.00263)
α / 0.14715 / (0.11332 / 0.19195* / (0.18392) / 0.12946 / (0.11474) / 0.20683 / (0.12764) / 0.2342* / (0.12402)
Obs / 452 / 452 / 452 / 452 / 452
Note: *** 1% ** 5% * 10% significance level, standard error in brackets. Column 2 is repeated from Table 6. Acq DV has no recorded values prior to 1980.
Table 12 Extended basic model 1981-2002 - penalized quantile regression with fixed effect estimates for 90% quantile only
1 / 2 / 3 / 4 / 5Coefficient / Std error / Coefficient / Std error / Coefficient / Std error / Coefficient / Std error / Coefficient / Std error
Sales / -0.09524*** / (0.01150) / -0.13208*** / (0.01393) / -0.11731*** / (0.01522) / -0.11024*** / (0.01696) / -0.11089*** / (0.01678)
gri,t-1 / -0.14257*** / (0.04030) / -0.10747*** / (0.04073) / -0.12599*** / (0.04114) / -0.09366* / (0.05130) / -0.10961** / (0.05285)
R&D intensity / 0.18385** / (0.08230) / 0.14544** / (0.06859) / 0.15986*** / (0.06385) / 0.2531** / (0.10311) / 0.24995** / (0.10198)
VC / 0.13284* / (0.07119) / 0.11513* / (0.06483) / 0.10975** / (0.07594) / 0.10536 / (0.07446) / 0.11082 / (0.06861)
Persist / 0.04307 / (0.03484) / 0.02248 / (0.03395) / 0.0168 / (0.03782) / 0.01738 / (0.03752) / 0.00965 / (0.04003)
Age / 0.00911 / (0.02492) / -0.00734 / (0.02529) / -0.04897* / (0.02847) / -0.01112 / (0.03196) / -0.00032 / (0.03456)
R&D scale / 0.24069*** / (0.05595) / 0.2112*** / (0.05666) / 0.14867** / (0.06191) / 0.13421** / (0.06343)
gri,t-2 / -0.07237 / (0.06001) / -0.13225** / (0.06287) / -0.10418 / (0.06355)
gri,t-3 / 0.02069 / (0.04660) / 0.03529 / (0.04932)
Acq DV / 0.39783*** / (0.08190) / 0.36128*** / (0.08948) / 0.37732*** / (0.09198)
Acq DV t-1 / 0.09596 / (0.07026) / 0.11469 / (0.07163) / 0.11067 / (0.07498)
Acq DV t-2 / 0.00721 / (0.06749) / 0.03689 / (0.06641) / 0.0424 / (0.07404)
Acq value / 0.00803** / (0.00414)
Acq value t-1 / 0.00668 / (0.00466)
Acq value t-2 / -0.00287 / (0.00324)
α / 0.7939*** / (0.09955) / 0.94201*** / (0.11334) / 1.01018*** / (0.13050) / 0.90869*** / (0.14685) / 0.93151*** / (0.14286)
Obs / 1723 / 1723 / 1723 / 1723 / 1723
Note: *** 1% ** 5% * 10% significance level, standard error in brackets.
1
[1]These results also show that dropping R&D scale has no consequential effect on our reported results for R&D intensity.