Understanding the geographical distribution of innovation in England: density, accessibility and spillover effects

Figures & data

Figure 1. Patent intensity by lower super output area (LSOA), 2017.

Notes: Patents per 10,000 working-age population in each LSOA. Readers of the print article can view the figures in colour online at https://doi.org/10.1080/00343404.2023.2252900

Sources: Patents data are from the Intellectual Property Office (IPO) (see the text for derivation); working population data are from the National On-line Manpower Information System (NOMIS).

A choropleth map of England showing the spatial distribution of patent intensity. Highlights the specific concentrations of patenting activity across England.

Figure 2. Trademark intensity by lower super output area (LSOA), 2017.

Note: Trademarks are per 10,000 working population in each LSOA.

Sources: Trademark data are from the Intellectual Property Office (IPO) (see the text for derivation); working population data are from the National On-line Manpower Information System (NOMIS).

A choropleth map of England showing the spatial distribution of trademark intensity. Highlights the very widespread location of clusters of trademarks across almost all areas of England.

Figure 3. Registered design intensity by lower super output area (LSOA), 2017.

Note: Registered designs are per 10,000 working population in each LSOA.

Sources: Designs data are from the Intellectual Property Office (IPO) (see the text for derivation); working population data are from the National On-line Manpower Information System (NOMIS).

A choropleth map of England showing the spatial distribution of design intensity. Highlights the widespread location of clusters of designs across both urban and rural areas.

Figure 4. Population density (persons/km²) by lower super output area (LSOA), 2015.

Source: Office of National Statistics (ONS).

A choropleth map of England showing the spatial distribution of population density. Highlights the gradients of density and strong concentration in main urban centres.

Figure 5. Multi-mode journey time to the nearest town centre, 2015.

Note: Values are the shortest journey time (min) by car or public transport to nearest town centre in 2015. No data are available for Wales or for areas where the journey time is greater than 120 min.

Source: Department of Transport.

A choropleth map of England showing the spatial distribution of minimum journey time to the nearest town centre. Highlights lack of accessibility in costal and border areas.

Table 1. Spatial autoregressive (SAR) models for patent intensity and related diagnostics.

	North East	North West	East	East Midlands	London	South East	South West	West Midlands	Yorkshire and Humber
Population density (log)	−0.017	0.212*	0.428***	0.128	−0.266	0.283**	0.067	0.205	0.105
	(0.187)	(0.123)	(0.161)	(0.171)	(0.245)	(0.127)	(0.134)	(0.179)	(0.164)
Population density × Population density (log)	−0.016*	−0.024***	−0.034***	−0.033***	−0.004	−0.039***	−0.024***	−0.047***	−0.022***
	(0.008)	(0.006)	(0.008)	(0.008)	(0.009)	(0.007)	(0.007)	(0.009)	(0.008)
Journey time (log)	−1.007**	−0.432	0.186	−0.700	−1.215	−0.823**	−0.999***	−1.905***	−1.039**
	(0.485)	(0.273)	(0.489)	(0.625)	(0.977)	(0.343)	(0.352)	(0.520)	(0.431)
J time × J time (log)	0.086	0.044	−0.024	0.020	0.097	0.059	0.081**	0.204***	0.110**
	(0.054)	(0.029)	(0.060)	(0.077)	(0.105)	(0.039)	(0.039)	(0.064)	(0.051)
Population density × Journey Time (log)	0.063*	0.015	−0.005	0.079**	0.055	0.053**	0.054***	0.096***	0.037
	(0.032)	(0.019)	(0.025)	(0.031)	(0.050)	(0.021)	(0.020)	(0.031)	(0.028)
Number of observations	1636	4230	3420	2659	4717	4784	3001	3298	3194
F(..)	196.2	372.52	272.43	241.71	338	344	235.82	446.09	318.34
Rho	0	0	0	0	0	0	0	0	0
SAR coefficients
Population density – adjacent (log)	0.001	−0.001	−0.001	0.014	−0.012**	−0.017**	0.018	0.008	−0.005
	(0.011)	(0.007)	(0.011)	(0.010)	(0.005)	(0.008)	(0.012)	(0.009)	(0.010)
Patent intensity – adjacent (log)	0.794***	0.706***	0.666***	0.415**	0.793***	0.677***	0.532***	0.621***	0.675***
	(0.236)	(0.138)	(0.187)	(0.207)	(0.123)	(0.163)	(0.188)	(0.133)	(0.185)
Wald test of spatial terms – Chi2 (2)	14.28	31.14	18.25	12.88	42.82	17.5	25.73	29.85	15.64
Wald test of spatial terms – Rho	0	(0.000)	(0.000)	0.002	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)

Table 2. SAR models for trademark intensity and diagnostic material.

	North East	North West	East	East Midlands	London	South East	South West	West Midlands	Yorkshire and Humber
Population density (log)	−0.083	1.662***	0.802**	0.250	0.186	0.131	0.764***	1.397***	0.000
	(0.465)	(0.296)	(0.322)	(0.371)	(0.619)	(0.265)	(0.284)	(0.362)	(0.341)
Population density × Population density (log)	−0.082***	−0.136***	−0.107***	−0.096***	−0.037	−0.082***	−0.107***	−0.170***	−0.077***
	(0.021)	(0.015)	(0.017)	(0.018)	(0.023)	(0.014)	(0.016)	(0.018)	(0.016)
Journey time (log)	−7.053***	0.043	−1.887*	−4.018***	−1.241	−1.621**	−1.643**	−3.541***	−5.035***
	(1.189)	(0.654)	(0.964)	(1.384)	(2.473)	(0.713)	(0.728)	(1.065)	(0.907)
J time × J time (log)	0.794***	0.000	0.144	0.341**	0.155	−0.015	0.095	0.401***	0.489***
	(0.130)	(0.070)	(0.117)	(0.172)	(0.264)	(0.081)	(0.081)	(0.130)	(0.108)
Population density × Journey Time (log)	0.297***	−0.048	0.119**	0.255***	−0.016	0.207***	0.110***	0.142**	0.240***
	(0.079)	(0.046)	(0.051)	(0.067)	(0.127)	(0.043)	(0.041)	(0.062)	(0.059)
Number of observations	1638	4214	3434	2660	4661	4818	3015	3295	3187
F(..)	403.42	1100.18	948.95	727.61	1234.5	1371.27	715.42	1163.95	1098.88
Rho	0	0	0	0	0	0	0	0	0
SAR coefficients
Population density – adjacent (log)	−0.013	−0.075***	−0.055**	−0.032	−0.138***	−0.122***	−0.083***	−0.054***	−0.061***
	(0.030)	(0.019)	(0.026)	(0.027)	(0.018)	(0.020)	(0.027)	(0.020)	(0.023)
Trademark intensity – adjacent (log)	0.621***	0.635***	0.500***	0.551***	0.724***	0.478***	0.556***	0.544***	0.524***
	(0.144)	(0.079)	(0.089)	(0.099)	(0.066)	(0.073)	(0.094)	(0.084)	(0.089)
Wald test of spatial terms – Chi2 (2)	24.97	66.67	38.12	47.73	119.58	50	37.06	43.63	35.71
Wald test of spatial terms – Rho	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)

Table 3. SAR models for registered design intensity and diagnostic material.

	North East	North West	East	East Midlands	London	South East	South West	West Midlands	Yorkshire and Humber
Population density (log)	−0.032	0.490***	−0.089	0.233	0.109	0.140	0.366***	0.251	0.192
	(0.196)	(0.126)	(0.143)	(0.161)	(0.288)	(0.125)	(0.130)	(0.170)	(0.155)
Population density × Population density (log)	−0.016*	−0.030***	−0.009	−0.028***	−0.013	−0.024***	−0.029***	−0.030***	−0.028***
	(0.009)	(0.006)	(0.007)	(0.008)	(0.011)	(0.007)	(0.007)	(0.008)	(0.007)
Journey time (log)	−1.290**	0.214	−1.074**	−0.595	0.279	−0.545	−0.004	−0.788	−0.874**
	(0.505)	(0.276)	(0.427)	(0.596)	(1.120)	(0.333)	(0.338)	(0.495)	(0.414)
J time × J time (log)	0.127**	0.004	0.101*	0.056	−0.049	0.037	0.001	0.105*	0.087*
	(0.055)	(0.030)	(0.052)	(0.073)	(0.121)	(0.038)	(0.038)	(0.061)	(0.049)
Population density × Journey Time (log)	0.062*	−0.039*	0.063***	0.030	−0.004	0.038*	−0.004	0.021	0.038
	(0.033)	(0.020)	(0.023)	(0.029)	(0.058)	(0.020)	(0.019)	(0.029)	(0.027)
Number of observations	1640	4217	3430	2658	4684	4817	2999	3293	3186
F(..)	81.73	252.26	167.7	154.08	217.8	249.9	96.31	206.9	300.86
Rho	0	0	0	0	0	0	0	0	0
SAR coefficients
Population density – adjacent (log)	−0.025**	−0.018**	0.005	0.002	−0.015**	−0.007	−0.014	0.007	−0.006
	(0.011)	(0.007)	(0.010)	(0.009)	(0.006)	(0.008)	(0.010)	(0.008)	(0.009)
Trademark intensity – adjacent (log)	0.875***	0.948***	0.673**	0.729***	1.041***	0.872***	0.941***	0.643***	0.883***
	(0.299)	(0.179)	(0.271)	(0.169)	(0.165)	(0.151)	(0.231)	(0.204)	(0.158)
Wald test of spatial terms – Chi2 (2)	11.15	28.02	13.03	23.84	39.55	40.09	17.45	13.92	33.36
Wald test of spatial terms – Rho	0.004	(0.000)	0.002	(0.000)	(0.000)	(0.000)	(0.000)	0.001	(0.000)

DATA AVAILABILITY

The statistical data used here are from the Office of National Statistics (ONS) and are Crown copyright and reproduced with the permission of the controller of HMSO and the Queen’s Printer for Scotland. The use of the ONS statistical data in this work does not imply the endorsement of the ONS in relation to the interpretation or analysis of the statistical data. The analysis upon which this paper is based uses research datasets that may not exactly reproduce National Statistics aggregates.