Power Law Distributions of Patents as Indicators of Innovation
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{"title"=>"Power Law Distributions of Patents as Indicators of Innovation", "type"=>"journal", "authors"=>[{"first_name"=>"Dion R.J.", "last_name"=>"O'Neale", "scopus_author_id"=>"14025613000"}, {"first_name"=>"Shaun C.", "last_name"=>"Hendy", "scopus_author_id"=>"6603876052"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84870773622", "pmid"=>"23227144", "sgr"=>"84870773622", "doi"=>"10.1371/journal.pone.0049501", "issn"=>"19326203", "pui"=>"366234520", "arxiv"=>"1204.6549"}, "id"=>"f04fa456-b8cd-3eff-bc97-414e582e2d69", "abstract"=>"The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Here we present evidence that the distribution of patents amongst applicants within many countries is well-described by power laws with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.", "link"=>"http://www.mendeley.com/research/power-law-distributions-patents-indicators-innovation", "reader_count"=>44, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Student > Doctoral Student"=>4, "Researcher"=>8, "Student > Ph. D. Student"=>13, "Student > Postgraduate"=>2, "Student > Master"=>2, "Other"=>5, "Student > Bachelor"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Student > Doctoral Student"=>4, "Researcher"=>8, "Student > Ph. D. Student"=>13, "Student > Postgraduate"=>2, "Student > Master"=>2, "Other"=>5, "Student > Bachelor"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Unspecified"=>3, "Engineering"=>3, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>3, "Agricultural and Biological Sciences"=>4, "Business, Management and Accounting"=>8, "Physics and Astronomy"=>7, "Psychology"=>1, "Social Sciences"=>3, "Computer Science"=>8, "Economics, Econometrics and Finance"=>2, "Materials Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Materials Science"=>{"Materials Science"=>1}, "Social Sciences"=>{"Social Sciences"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>7}, "Psychology"=>{"Psychology"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>4}, "Computer Science"=>{"Computer Science"=>8}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>8}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>3}}, "reader_count_by_country"=>{"New Zealand"=>1, "United States"=>3, "Luxembourg"=>1, "Taiwan"=>1, "Brazil"=>1, "Mexico"=>1, "Slovenia"=>1, "Paraguay"=>1, "Portugal"=>1, "Germany"=>1, "Spain"=>1}, "group_count"=>2}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/531083"], "description"=>"<p>Best fit power law exponents calculated for the empirical (filled triangles) and simulated (empty squares) patent distributions of each country as a function of . The linear least square fits are, respectively, (, ) and (, ).</p>", "links"=>[], "tags"=>["exponents", "inversely", "correlated", "patents"], "article_id"=>201581, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g007", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Power_law_exponents_are_inversely_correlated_with_the_average_number_of_patents_per_applicant_/201581", "title"=>"Power law exponents are inversely correlated with the average number of patents per applicant.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:13:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/530408"], "description"=>"<p>The CDFs of EPO patent distributions for all 22 countries, ordered by country code, are indicated by blue circles. The slope of the best-fit power law model is shown as a black dotted line. The match to a power law fit is generally good.</p>", "links"=>[], "tags"=>["functions", "fits", "22", "countries"], "article_id"=>200906, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cumulative_density_functions_and_power_law_fits_for_the_22_countries_in_the_data_set_/200906", "title"=>"Cumulative density functions and power law fits for the 22 countries in the data set.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:09:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/530281"], "description"=>"<p>Upper plot: Number of EPO (European Patent Office) patent applications (filled triangles) and unique applicants (open squares) versus national population, for the 22 countries in the OECD HAN data set. The dashed line indicates the slope which the data would follow if they scaled linearly – in the absence of agglomeration effects. Lower plot: Ratio of number of applicants to number of patents () for the same data. The least squares best fit has a slope of and indicating a poor correlation and little dependence on population.</p>", "links"=>[], "tags"=>["patents"], "article_id"=>200775, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scaling_of_number_of_patents_and_patent_applicants_with_country_size_/200775", "title"=>"Scaling of number of patents and patent applicants, with country size.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:08:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/530832"], "description"=>"<p>Just as the total biomass of an ecosystem can be used to rescale the distribution for the frequency of organisms with a particular body mass in some area, total expenditure on R&D in a country can be used to rescale the distribution for the frequency of applicants in a country who have filed a particular number of patents. The left-hand plot shows the unscaled data, with each country indicated by a different color/shape of symbol. The right-hand plot shows the same data after the frequencies are scaled by business expenditure on R&D (millions of US dollars). The role played by GERD (gross expenditure on R&D) is similar. The one country for which the distribution does not match the others after rescaling (pink triangles) is China; a country which has only a recent record of filing patents at the EPO.</p>", "links"=>[], "tags"=>["rescales"], "article_id"=>201333, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g005", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Expenditure_on_R_amp_D_rescales_national_patent_distributions_/201333", "title"=>"Expenditure on R&D rescales national patent distributions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:11:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/530534"], "description"=>"<p>Values of , with their associated estimated uncertainties, for the 22 countries in the EPO HAN data set (black), sorted by , along with average values (red), and their associated standard deviations, for simulated data. For each country’s simulation, the growth rate was determined by the ratio from Tab. 1.</p>", "links"=>[], "tags"=>["sorted"], "article_id"=>201034, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g003", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Power_law_exponents_sorted_by_rank_/201034", "title"=>"Power law exponents, sorted by rank.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:10:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/530675"], "description"=>"<p>Correlation between the country rank of the empirical power law exponent and the country rank based on average export ubiquity ( as reported in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049501#pone.0049501-Hidalgo1\" target=\"_blank\">[26]</a>). The dashed line indicates the linear least-squares fit and has slope 0.71 (, ).</p>", "links"=>[], "tags"=>["exponents", "correlated", "exported"], "article_id"=>201175, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g004", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Power_law_exponents_are_correlated_with_the_8220_ubiquity_8221_of_exported_products_/201175", "title"=>"Power law exponents are correlated with the “ubiquity” of exported products.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:11:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/531201"], "description"=>"<p>The best fit of the empirical data to a power law model is achieved with a power law exponent and cut-off . The estimated standard deviation in these parameters is also given. In the case of the standard deviation of , two estimates are given. The first, , is calculated using a bootstrap method via the Matlab code which accompanies <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049501#pone.0049501-Clauset1\" target=\"_blank\">[21]</a>. The estimate is obtained via the analytic expression eqn. (3.6) of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049501#pone.0049501-Clauset1\" target=\"_blank\">[21]</a> which gives an estimate for the standard error , assuming that the underlying distribution is well fitted by a power law (i.e. the -value is large). The estimate is calculated via the bootstrap method. The values for indicate the “goodness of fit” of the empirical data to a power law model. Also given, is the number of applicants and the total number of patents held.</p>", "links"=>[], "tags"=>["distributions", "22"], "article_id"=>201701, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.t001", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_statistics_for_the_patent_distributions_of_the_22_countries_/201701", "title"=>"Summary statistics for the patent distributions of the 22 countries.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 19:13:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/530988"], "description"=>"<p>Power law exponents for EPO patent distributions of 22 OECD countries versus GERD (left) and BERD (right) intensity – gross, resp., business expenditure on R&D as a percentage of GDP. Vertical bars indicate the estimated standard error in the values, horizontal bars indicate the standard deviation in the time averaged (1995–2006) OECD data. The trend appears to be bimodal. For GERD, resp. BERD, intensity below approximatley 3% resp. 2% there is an inverse correlation between the power law exponent and the intensity of R&D spending. Beyond this level, the trend appears to reverse, though data in this region are limited. The blue lines indicate the least-squares linear regression fit to the data, excluding the three right-most points corresponding to Finland, Sweden and Israel (left to right). The linear fits are (, ) and (, ).</p>", "links"=>[], "tags"=>["exponent", "inversely", "correlated"], "article_id"=>201491, "categories"=>["Information And Computing Sciences", "Mathematics", "Science Policy"], "users"=>["Dion R. J. O’Neale", "Shaun C. Hendy"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049501.g006", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Lower_values_of_the_exponent_are_inversely_correlated_with_R_D_spending_/201491", "title"=>"Lower values of the exponent are inversely correlated with R&D spending.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 19:12:46"}

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Relative Metric

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