A Reappraisal Using a Composite Indicator of Patent Quality∗

Patterns of Innovation during the Industrial Revolution: a Reappraisal using a Composite Indicator of Patent Quality∗

Alessandro Nuvolari†a, Valentina Tartarib, and Matteo Trancheroc

aScuola Superiore Sant’Anna, Pisa, Italy bCopenhagen Business School, Copenhagen, Denmark cHaas School of Business, UC Berkeley, USA

August 5, 2019

Abstract

We introduce a new bibliographic quality indicator for English patents granted in the period 1700-1850. The indicator is based on the visibility of each patent both in the contemporary legal and engineering literature and in modern authoritative works on the history of science and technology. The indicator permits to operationalize empirically the distinction between micro- and macroinventions. Our findings indicate that macroinventions did not exhibit any specific time clustering, while at the same time they were characterized by a labor-saving bias. These results suggest that Mokyr’s and Allen’s views of macroinventions, rather than conflicting, should be regarded as complementary.

Keywords: Industrial Revolution; Patents; Macroinventions; Microinventions.

JEL Code: N74, O31

∗Acknowledgements: The authors want to thank Bart Verspagen, Tania Treibich, Abhishek Nagaraj, Sameer Srivas- tava, as well as participants to seminars at University Cˆoted’Azur, UNU-MERIT, Berkeley-Haas and to EMAEE 2019 at SPRU - University of Sussex for their helpful comments. We are indebted to Joel Mokyr, Ralf Meisenzahl, Morgane Louenan, Olivier Gergaud and Etienne Wasmer for sharing their data. The usual disclaimers apply. †Corresponding author: Alessandro Nuvolari, Scuola Superiore Sant’Anna, Pisa, Italy. Postal address: c/o Institute of Economics, Scuola Superiore Sant’Anna, Piazza Martiri 33, 56127, Pisa, Italy. E-mail: [email protected].

1 1 Introduction

Technical change has traditionally occupied a central place in the historiography of the Indus- trial Revolution. Not surprisingly, both contemporaries and historians have regarded technological progress as one of key-factors shaping the dramatic economic and social transformations taking place in England during XVIII and XIX centuries. This interest in technical change has resulted in a very rich qualitative literature which has provided detailed descriptions of technological advances both in a broad, comprehensive perspective (Landes 1969; Mokyr 1990; Trinder 2013) and at the level of spe- ciﬁc technologies, such as steam power (Hills, 1989), textiles (Hills, 1970) and iron production (Hyde,

1977).

In this context, the distinction between microinventions and macroinventions originally proposed by Mokyr (1990) has established itself as a particularly useful notion for providing an insightful characterization of the patterns of technical change. In Mokyr’s original formulation, microinventions are “[. . . ] small, incremental steps that improve, adapt and streamline existing techniques already in use, reducing costs, improving form and function, increasing durability, and reducing energy and raw material requirements”, whereas macroinventions are “[. . . ] those inventions in which a radical new idea, without clear precedent, emerges more or less ab nihilo” (Mokyr 1990, p. 13). The distinction between micro- and macroinventions is intuitively appealing and is consistent with many qualitative accounts of the contours of technical change during the Industrial Revolution (Landes 1969; Mathias

1969). However, at closer inspection, the notions of microinventions and macroinventions appears of diﬃcult empirical operationalization, especially if one is interested in reconstructions of broad patterns of technical change spanning more than one speciﬁc technology or industry.

In this respect, an established tradition in economic history has resorted to patents to provide quantitative assessments of the rate and scope of technical change (Sullivan 1989, 1990; Khan and

Sokoloff 1993). However, one of the well-known limitations of simple patent counts is that they do not take into account the different quality of the inventions in question (O’Brien et al., 1995), thus preventing a straightforward empirical identification of macroinventions. For modern patents, economists of innovation have addressed this issue by designing a number of indicators of patent quality based on the use of patent citations, geographical coverage (i.e., size of the patent family) and renewals (Van Zeebroeck, 2011). These indicators are not immediately applicable to the case of the English patent system during the Industrial Revolution. Remarkably, when writing The Lever of Riches in 1990, Mokyr pessimistically concluded that “[. . . ] patent statistics [in the Industrial

2 Revolution period] do not permit us to distinguish between radical and minor inventions” (Mokyr

1990, p. 82).

In this paper, we introduce a new composite indicator of the quality of English patents for the period 1700-1850. Our indicator of patent quality is a substantial reﬁnement of the bibliographic indicator proposed by Nuvolari and Tartari (2011) based on Bennet Woodcroft’s Reference Index of Patents of Invention, 1617-1852. We construct our new composite indicator by complementing

Woodcroft’s Reference Index with information collected from a wide array of modern sources on the history of technology. These diﬀerent sources of information concerning the quality of each individual patent are aggregated using the approach introduced by Lanjouw and Schankerman (2004). The resulting Bigliographic Composite Index (BCI) that we propose provides a reliable selection of the most revolutionary technological breakthroughs of the period, and we validate its reliability through extensive robustness checks. The integration of multiple sources allows the construction of an index of patent quality that provides the opportunity for a large-scale empirical operationalization of the notions of micro- and macroinventions, at least for the subset of patented inventions. In turn, this will lead us to reappraise a number of interpretative conjectures on the sources and eﬀects of macro- and microinventions and on their interconnections (Allen 2009; Mokyr 2010; Crafts 2011; Allen 2018).

We ﬁnd evidence that the distinction between macro- and microinventions is supported by the patent evidence, with the series of macroinventions showing characteristics remarkably close to the original theorizing of Mokyr (1990). In particular, the series of macroinventions shows statistical properties that are consistent with a signiﬁcant role of serendipity in determining their occurrence.

Vice versa, microinventions tend to come after the appearance of major breakthroughs, and to be correlated with the economic cycle. We also document that macroinventions were characterized by a labor-saving bias which is consistent with the High Wage Economy interpretation of the Industrial

Revolution proposed by Allen (2009). However, unlike what has been suggested by Allen (2009), macroinventions were not the result of the activities of “outsiders”, that is inventors working in diﬀerent industrial sectors. A detailed study of patents in mechanical engineering further allows to test speculations of the historical literature on the role of machine users in innovation (MacLeod and

Nuvolari, 2009), which we ﬁnd were mostly responsible of minor improvements.

Our work is connected also to the ongoing efforts on the construction of indices of historical technological progress. In this field, one traditional approach has been the estimation of indices of labour productivity or TFP (Crafts and Harley 1992; Crafts 2014), which however are indirect measures of technical change, often based on fragile data, and fraught with difficulties (Nelson, 1973).

3 Our efforts are closer in spirit to the recent attempts to construct direct proxies of technical change pioneered by Alexopoulos (2011), who proposed an indicator based on the number of new book titles in different fields of technology, and Kelly et al. (2018), who employed textual analysis of US patent documents to develop a new index of patent quality that can be used as a measure of technological change.1

2 Literature review

The English patent system did not undergo major changes from the adoption of the Statute of

Monopolies in 1624 to the reform of 1852. This relative uniformity, coupled with the precise recording of the date and details of the patents granted, makes patents an invaluable source to investigate the dynamics of innovation during the Industrial Revolution (Sullivan 1989, 1990).

Still, historical patent data suﬀer from several pitfalls that can make their use problematic (MacLeod,

1988). The ﬁrst major limitation is that obviously not all inventions were patented (Nuvolari 2004;

Moser 2005). But as aptly noted by Schmookler (1966), this should stimulate research eﬀorts on indicators of unpatented inventions that can usefully integrate the patent evidence, rather than leading to a dismissal of patents as an insightful source.

A second important issue is the heterogeneity of patents in terms of their technological and economic significance, i.e. what we can refer to as their relative “quality”. This, of course, applies to modern patents as well (Scherer and Harhoff, 2000). However, the patent system of the time had some features that exacerbated this problem. The English system was one of registration and not of examination and this means that patents were not subjected to any systematic check concerning their novelty or relevance. Sometimes patents lacked technological feasibility altogether, as the relatively high number of “perpetual motion” machines patented testifies (MacLeod et al., 2003).

Accordingly, constructing a plausible index capable to weight each patent according to its technological and economic signiﬁcance is a crucial step to use patents for assessing the contours of technical change in this period. Unfortunately, standard modern indicators of patent quality, such as patent citations and data on renewals (Van Zeebroeck, 2011) are not available: the early English patent system neither prescribed to document prior art by citing other patents, nor it required renewal fees.

It is necessary, therefore, to devise new approaches.

In a seminal paper, Khan and Sokoloﬀ (1993) have pioneered the assessment of the quality of

1For the period of the Industrial Revolution, there have been also attempts to develop indicators of technical change at industry level, see Kelly and O´ Gr´ada(2016) and Kelly and O´ Gr´ada(2019).

4 historical patents by collecting systematic data on the patenting activity of American “great inventors”, where by this term they understood the inventors included in the Dictionary of American Biography.

The underlying assumption is that their inventions were presumably more valuable from a technological or economic point of view than those of all other inventors. In particular, they systematically compare the patents of great inventors with the remainder of the patent corpus as a way to test the differences between macro- and microinventions. Using this method, they find that there were no significant differences between the two kinds of invention. Khan (2018) has recently carried out a similar exercise for the English case using the evidence from the Oxford Dictionary of National Biography.

In a diﬀerent vein, Nuvolari and Tartari (2011) have argued that the Reference Index of Patents of

Invention, 1617-1852 edited by Bennet Woodcroft can be employed to construct a plausible indicator of the quality of English patents before 1852. The Reference Index was a component of a larger set of indexes that were published on requests of the Patent Oﬃce Commissioners after the patent reform of 1852.2 The Reference Index is structured in chronological order and for each single patent it gives a list of all the sources in the contemporary technical and legal literature that discussed the details of the patent in question. In this way, the number of references listed in the Reference Index captures the

“visibility” of each patent in the contemporary specialized literature, providing a reasonable proxy for its relative technical and economic signiﬁcance. The basic intuition is akin to modern bibliographical indexes of research impact based on citations. The approach of Nuvolari and Tartari (2011) is to use the time-adjusted count of references as a score for each patent (dubbed as WRI*).3

The index proposed by Nuvolari and Tartari (2011) has been used in a number of recent studies as a suitable indicator of patent quality (e.g. Squicciarini and Voigtl¨ander2015, Zeev et al. 2017,

Dowey 2017), while Hanlon (2015) has adopted the same approach to construct a quality indicator for cotton patents in the period 1855-1876. Furthermore, in his research Sean Bottomley has found that patents litigated were characterized by higher values of the WRI* index compared with regular patents, whereas patents granted also in Scotland and Ireland were characterized by higher values of the

2Before the reform of 1852, a patent application could be lodged in anyone of these three Public Offices in London: Rolls Chapel Office, Petty Bag Office and Enrolment Office. The system lacked an effective search catalogue providing easy access to the specifications of existing patents. With the reform of the patent system, the new Patent Office Commissioners decided to address this problem by funding a major publication of indexes and abridgments of the patents granted from 1617 to 1852. The Commissioners entrusted this task to Bennet Woodcroft, professor of machinery, patent agent and himself an inventor. Together with the Reference Index, Woodcroft and his team of clerks published an Alphabetical Index of Patentees, a Chronological Index of Patents and a Subject Index of Patents. The publication of these indexes was followed by a further attempt to summarize and classify by subject all the existing patent specifications by publishing a series of Abridgments of Patent Specifications. Each of these volumes contained a succinct description of all the patent specifications pertaining to a specific technological subject (Nuvolari and Tartari, 2011). 3The fixed-effect time adjustment is necessary in order to take into account the different age of patents and, accordingly, their different exposure to citations/referencing. Note that a similar approach is also routinely used for patent citations in modern patents (Hall et al., 2002).

5 WRI* index compared with patents granted only in England (Bottomley 2014a, 2014b). All together this evidence represents a signiﬁcant corroboration of the intuition underlying the construction of the index.

At the same time, it is worth acknowledging that the WRI* is not immune from limitations and that there is room for significant improvements. The compilers of the Index had to examine a wide and highly heterogeneous corpus of literature without the benefit of hindsight, therefore it is not surprising that a few patents covering important breakthroughs such as the John Kay’s flying shuttle or Henry Cort’s puddling process resulted in a low number of references. Indeed, it is hard to tell, in each specific case, if the low number of references is due either to a minor impact of the patent in the literature or to some biases in the sifting process from the side of the compilers. The bulk of the literature considered by the examiners appeared in early years of the 19th century, which might explain why some older important inventions ended up being short-changed. On the other hand, the compilers’ view reflected the spirit of the time, being attracted by curious or seemingly promising inventions that in actual terms did not fulfill their promise. A case in question is patent number 556 granted to Jonathan Hulls for a steamboat, which raised a good deal of attention by contemporaries, but it was of extremely limited practical significance.4

In this paper, we construct a new composite indicator of patent quality that overcomes these shortcomings. After extensive search, we assembled a suitable corpus of authoritative modern reference texts on the history of science and technology and biographical dictionaries of scientists and inventors that can be used to integrate Woodcroft’s Reference Index. These new data sources can plausibly capture complementary dimensions of patent quality, and we combine them to create a single composite index that improves the signal-to-noise ratio of the WRI*.

3 The construction of the Bibliographic Composite Index

3.1 Data Sources

We have constructed a dataset consisting of three patent quality indicators for the 13,070 English patents granted in the 1700-1850 period. First, we consider the visibility of each patent in the contemporary engineering and legal literature, as summarized in Woodcroft’s Reference Index (henceforth,

WRI). This indicator has been originally proposed by Nuvolari and Tartari (2011) and it counts the

4Considered the pioneer of steam navigation, Jonathan Hulls (1699-1758) was a British inventor that obtained the ﬁrst patent for a steam-propelled ship. Hulls’ patent achieved a certain popularity and was certainly of inspiration for the subsequent work of Symington and other inventors, but there is no evidence that his steam tugboat ever led to practical trials or applications (Robinson, 2004).

6 number of times each patent was mentioned in specialized publications. A typical entry of the WRI is reported here as Figure 1. The patent in question (patent 913) is the one granted in 1769 to James

Watt for the separate condenser. Not surprisingly, Watt’s breakthrough invention is mentioned in a signiﬁcantly higher number of references than the comparatively incremental improvement to the making of small shot (making it more “solid, round, and smooth”) patented by William Watts in 1782

(patent 1347 in Figure 2). An interesting feature of the Reference Index as quality indicator is that the centralized process of collection of references carried out by Woodcroft and his clerks should limit possible biases arising from heterogeneity in citations behavior and strategic considerations that aﬄict modern patent citations.

[Figure 1 about here]

[Figure 2 about here]

Our second patent quality indicator is based on the relative visibility of each patent in modern reference books on the history of science and technology. This approach is similar to the one adopted originally by Schmookler (1966) who compiled lists of “important inventions” for a number of industries on the basis of a scrutiny of specialized historical and engineering references. In our case we considered ten reference books (the full list is reported in Appendix A). For each patent we count the total number of times it is mentioned in this set of sources, obtaining in this way a quality score that we call Patent Eminence (PAT EM). This procedure was adopted by Kleinknecht (1990) for constructing a quality indicator based on the integration of different lists of radical innovations. We find that our set of sources has a high degree of internal consistency (Cronbach’s alpha coefficient=0.829)5 and it effectively singles out the most eminent patents without noteworthy omissions (see Appendix B).

The third quality indicator considers the relative visibility of the patentee in biographical dictionaries and other similar sources. Khan and Sokoloff (1993) have first used this approach for identifying the inventors responsible for the most historically significant inventions in the US case. More recently,

Nicholas (2011) used this empirical strategy to ﬁnd the subset of US patents with higher technological relevance, while Khan (2018) has carried out a study of British “great inventors” using the same method. We collected data from nine biographical dictionaries and ad hoc lists comprising the most prominent inventors of the Industrial Revolution (details again in Appendix A). This third quality indicator, which we term Inventor Eminence (INV EM), is constructed in an analogous way to the previous ones by counting the number of sources that mentions each patentee, and it shows again a high degree of internal consistency (Cronbach’s alpha coeﬃcient=0.884). Table 1 summarizes the

5On the interpretation of the Cronbach’s alpha coeﬃcient, see for instance Bland and Altman (1997).

7 number of patents and inventors cited by each of the sources used.

[Table 1 about here]

The three quality indicators that we have constructed can plausibly capture complementary dimensions of patent quality. We suggest that the references retrieved from Woodcroft’s Reference Index should be better equipped to assess relatively unknown microinventions, while measures of patent and inventor eminence are better suited to gauge macroinventions thanks to the beneﬁt of hindsight. Table

2 shows that the three indicators display significant positive correlations but their Spearman’s rank correlation coefficients are rather low, confirming that they are indeed capturing different features of patent quality. In other words, Table 2 suggests that these lists reflect a number of relatively independent assessments of the historical significance of inventions.

[Table 2 about here]

As expected, the use of quality indicators derived from modern bibliographic sources substantially mitigates some idiosyncrasies of the original WRI* proposed by Nuvolari and Tartari (2011). For instance, the new quality indexes we assembled are able to downplay the role of curious or absurd patents that received attention for reasons beyond their genuine technological or economic signiﬁcance.

Table 3 compares two patents granted in 1736. These are Jonathan Hulls’ patent for a steam-boat mentioned before and John Kay’s patent for the ﬂying shuttle (which has a surprisingly low value of WRI). The table shows that, in this case, Patent and Inventor Eminence provide a more reliable assessment of the relative quality of these two inventions.

[Table 3 about here]

Similarly, Table 4 compares Richard Arkwright’s famous patents for the water-frame and the carding machine. The ﬁrst was the breakthrough invention that revolutionized the cotton spinning industry, while the second is a patent that was at the centre of spirited legal controversy and that was eventually revoked after a legal trial. The heated discussion around this contentious patent explains the higher number of references of this patent in the Reference Index, relatively to the water-frame.

In this case, the Patent Eminence indicator is the quality indicator which seems more in line with the established wisdom.

[Table 4 about here]

3.2 Index construction

The combinations of individual indicators into a single composite variable is an intuitively appealing approach to retain the common information signalling patent quality while removing the noise and

8 idiosyncrasies of speciﬁc individual sources (Van Zeebroeck, 2011). Accordingly, we adapt the approach pioneered by Lanjouw and Schankerman (2004) to our sample of historical patents.

Figure 3(a) contains the average number of references per year or per decade in Woodcroft’s

Reference Index, whereas figure 3(b) shows the average scores of Patent and Inventor Eminence per decade. Due to the expansion of the specialized literature discussing patent specifications, the average number of references per patent recorded in the Reference Index displays an increasing trend. On the contrary, the average number of citations by modern sources is slightly decreasing during the last decades considered. Taken together, Figure 3 suggests that using the raw number of references as indicators to compare patents granted in different years would lead to potentially biased results.

Further, it is also likely that the number of references would be aﬀected by the type of technology covered in the patent. Note, however, that these types of problems are present in modern patent data as well: for example, the computerization of patent databases during the 1980s enhanced the search of prior art for inventors and patent examiners leading to an increase in the average number of citations per patent. Hence, as it is done with citations for contemporary patents, it is important to adjust the indicator for time and industry eﬀects (Hall et al., 2002).

[Figure 3 about here]

In order to account for systematic temporal and sectoral eﬀects, we estimate the following three separate Poisson regressions with robust standard errors:6

PM PN (α+ βmDyearm+ δnDsectorn) WRIi = e m=1 n=1

PM PN (α+ βmDyearm+ δnDsectorn) P AT EMi = e m=1 n=1

PM PN (α+ βmDyearm+ δnDsectorn) INV EMi = e m=1 n=1

where Dyearm are the dummies for the decades from 1700 to 1850 (M = 15), Dsectorn are the sectoral dummies (N = 21), and WRIi, P AT EMi, INV EMi are the the raw reference scores to patent i and its inventor, respectively. In practice, each quality indicator is regressed against industry and time dummies in order to eliminate the systematic eﬀects discussed above. The residuals of each regression capture the share of variance attributable to the “intrinsic” quality of the patent.

As a ﬁnal step, we extract from these residuals a latent common factor using a structural equation model (SEM) represented in Figure 4 (Lanjouw and Schankerman, 2004).7 This is tantamount to estimating a multiple-indicator model with one latent common factor:

6As a robustness check, we also run negative binomial regressions ﬁnding nearly identical results. 7As a matter of fact, this approach reaches the same results of a conﬁrmatory factor analysis where the number of retained factors has been constrained to one (Schreiber et al., 2006).

9 yki = αk + λkqi + ki

th th where yki indicates the value of the k indicator for the i patent (k = 1, 2, 3 and i = 1,..., 13070) and q is the common factor with factor loadings λk. From the estimation of this structural equation model, we derive the value of the latent factor for each patent (qi). As discussed by Lanjouw and Schankerman (2004), the common factor gathers the unobserved characteristic of patents that inﬂu- ences all the indicators used. Accordingly, we consider the latent common factor q as a composite measure of patent quality that we label Bibliographic Composite Index (BCI). The factor loadings λ of the common factor are reported in Table 5.

[Figure 4 about here]

[Table 5 about here]

The distribution of the BCI is shown in Figure 5. The index is extremely skewed with a very long tail, which is consistent with the notion of the bulk of the distribution concentrated on microinventions alongside with a restricted set of macroinventions.

This result is in line with the distribution of patent value found in modern patents (Silverberg and

Verspagen, 2007), and the replication of this stylized fact has often been considered as a preliminary validation of composite indexes of patent quality (De Rassenfosse and Jaffe, 2015). In any case, in this paper, we prefer to adopt a very cautious approach and use our composite quality index in an ordinal rather than cardinal way, considering only the relative ranking of the patents according to the index. Note that the rankings we obtained are robust to many other aggregation procedures not reported here (factor analysis; Borda ranking; nonlinear SEM specifications). Similarly, constructing the BCI using Poisson residuals of regressions that employ different sets of time and industry controls produces highly overlapping sets of the top quality patents, confirming the general robustness of the procedures used to construct the index (Table 20 in the Appendix).

[Figure 5 about here]

3.3 Index validation

We validate our composite indicator by performing several robustness checks. First, the list of top-quality patents seems, prima facie, to oﬀer a very plausible selection of the most revolutionary inventions of the Industrial Revolution (Table 22 in the Appendix B). Among the most important inventions, our indicator correctly lists Watt’s separate condenser, Wheatstone’s telegraph, the spinning jenny of Hargreaves. Notably, the Bibliographic Composite Index is also eﬀective in gauging the

10 relative importance of lesser known inventions. Consider for instance the case of the power loom, described in detail by Allen (2018). While the macroinvention developed by Cartwright was a functioning prototype but with still limited economic application, the major reﬁnements that led to productivity improvements were the result of R&D by skilled mechanics such as Thomas Johnson and later

Richard Roberts. The importance of these technical improvements is ﬁnely captured by the BCI, that collocates these patents in the 95th percentile of the quality distribution.

As a further validation exercise, we compared the BCI with some independent measures of patent quality. We consider the patents whose inventors paid an extra fee to extend their coverage to Scotland and Ireland (Bottomley, 2014b). Also, we assembled lists of patents that were litigated in court

(Bottomley, 2014a) and patents for which patentees petitioned the Parliament asking a time extension.

The rationale of using these variables is based on empirical studies showing that modern valuable patents tend to have larger families (Lanjouw et al., 1998), are likely to be involved in court cases

(Lanjouw and Schankerman, 2001) and are renewed for longer lifespans (Lanjouw et al., 1998). By means of Fligner-Policello test of stochastic equality we show that patents with large geographical scope, that requested time extensions or that were the object of lawsuits are characterized by higher scores of the BCI (Table 6). We also present the test for the subsets of patents ﬁled after 1734 (when the speciﬁcation became a universal requirement) and after the famous ruling on Liardet v. Johnson

(1778), which further elaborated on the speciﬁcation requirements (Nuvolari and Tartari, 2011). All the results hold if we employ Mann-Whitney-Wilcoxon test.

[Table 6 about here]

Furthermore, the BCI is a signiﬁcant improvement when compared with the WRI* index of Nu- volari and Tartari (2011). The BCI is better equipped for discriminating true breakthroughs from patents which garnered many references for reasons not connected to their intrinsic quality. Using again the Fligner-Policello of stochastic equality, we show in Table 7 that the BCI is able to individuate

“bad” patents. In this case, we look at patents in steam engineering and we use as samples of ﬂawed patents the list of patents covering perpetual motion machines scorned by Dircks (1861) and the set of technically unfeasible steam engines discussed by MacLeod et al. (2003). The table also shows that the WRI* indicator is less eﬀective in these cases.

[Table 7 about here]

Finally, some important innovations of the industrial revolution such as the boring machine, the spinning jenny and the rolling process for metalworking were characterized by very low WRI* scores

(Table 8). With the beneﬁt of hindsight of the components measuring patent and inventor eminence,

11 the BCI gives a very plausible collocation of these patents in the highest quality percentile. The same goes for the patents contained in Table 3 discussed before. In this case, the BCI recognizes the breakthrough character of Kay’s ﬂying shuttle (placing it among the very top inventions, while Hulls’ patent is only in the 75th percentile of the index distribution).

[Table 8 about here]

To conclude, the BCI as a composite indicator combining both contemporaries’ assessments and modern perspectives seems to provide a fairly reliable assessment of the quality of inventions of the

English patents in the 1700-1850, eﬀectively improving the signal-to-noise ratio with respect to the

WRI*.

4 Patterns of Innovation during the Industrial Revolution

The conceptualization of inventive activities in terms of macro- and microinventions originally proposed by Mokyr (1990) has featured prominently in the recent debates on the origins of the Industrial

Revolution. For example, the distinction between microinventions and macroinventions has been used in several studies in order to account for the dynamics of productivity during the Industrial Revolution

(Crafts 1995; Allen 2009; Broadberry and Gupta 2009).

Following the original formulation, a number of interpretative conjectures on the sources and eﬀects of macro- and microinventions and on their interconnections has emerged in the literature

(Allen 2009; Meisenzahl and Mokyr 2011; Crafts 2011; Allen 2018). Mokyr (1990) originally claimed that macroinventions, being result of serendipitous ﬁndings, did not respond to economic incentives

(Yaqub, 2018). This is in contrast with Allen (2009), who has argued that macroinventions actually responded to economic signals by substituting capital and energy for high-wage labour (the high wage economy conjecture); put differently, macroinventions can be interpreted as innovations induced by a peculiar wage and price configuration (Allen 2009, p. 141).8 Allen’s point is that macroinventions did require major investments in terms of time and economic resources in order to transform inchoate ideas into viable prototypes. These investments were likely to be undertaken only in response to major profit opportunities which explains the sensitivity of macroinventions to economic signals.

Allen also suggested that microinventions resulted from local learning eﬀorts of “insiders” to the industry, while true breakthroughs were largely due to “outsiders” (Allen 2009, p. 149). This theme seems to resonate with MacLeod and Nuvolari (2009), who conjectured that, in the ﬁeld of machinery,

8The possible role played by high wages in precipitating the breakthrough of the Industrial Revolution was also considered by Habakkuk (1962, pp. 132-137 and 144-151) and Crouzet (1983, pp. 37-43 and 92-96).

12 the inventive eﬀorts of professional machine makers typically generated small incremental inventions; in this account, machine users facing actual industrial bottlenecks were responsible for the more radical inventions.

The Bibliographic Composite Index permits to operationalize empirically the distinction between micro- and macroinventions. In particular, we follow the literature on breakthrough patents and use the distribution of our quality indicator to single out the upper tail of macroinventions (Kelly et al.,

2018). The absolute value of the BCI drops rapidly when one moves away from the best inventions, thus we considered the very top patents (top 0.5% percentile) as the threshold for deﬁning the set of macroinventions (Table 22 in the Appendix B).9

4.1 Time dynamics of invention

Mokyr’s view is that micro- and macroinventions are actually the outcome of diﬀerent generating processes (Mokyr 1990, p. 295). In particular, macroinventions are conceptualized as the unfolding of an essentially serendipitous arrival process. On the contrary, microinventions are the systematic and cumulative improvement of new technologies and as such should display strong temporal persistence.

To investigate this conjecture, we test whether the arrival process of macroinventions shows any kind of time clustering. This kind of exercise is common in the classic literature that has investigated the

Schumpeterian hypothesis according to which basic inventions (a concept analogous to macroinventions) tend cluster overtime (e.g. Sahal 1974, Kleinknecht 1990). Assuming that innovations are count data generated by a point process, we follow Silverberg and Verspagen (2003) and employ Poisson and negative binomial regressions with time trends to predict the yearly number of macroinventions and microinventions (see Appendix C for technical details). In particular, the Poisson process is the statistical description of a process characterized by complete randomness (Cameron and Trivedi, 1998).

The negative binomial model is a generalization of Poisson distributions because it permits to model overdispersion, that is a situation where the variance of the distribution is not equal to the mean.

We generalized this framework by controlling whether the arrival rate of the distributions follows time trends of various orders. Finally, we also carried out a Box-Ljung test of autocorrelation of the standardized residuals to further test the explanatory power of the models (Silverberg and Verspagen,

2003).

9Our findings are robust to other definitions of the set of macroinventions, such as taking the first 100 patents or the top 1% of them (whose results we also report). Although there is no exact cut-off point to determine breakthrough innovations, it is standard in the literature adopting a rather arbitrarily high threshold (for instance, Ahuja and Lampert (2001) use the top 1% patents).

13 Our results (Tables 9 and 10) show that macroinventions neither display over-dispersion nor autocorrelation in the residuals of the model.10 This basically suggests that the occurrence of macroinventions does not display clustering in the sense of random spells of high and low innovation activity. On the contrary, for microinventions the hypothesis of equidispersion is rejected, favouring the negative binomial speciﬁcation. The series of microinventions shows strong time autocorrelation, suggesting that their generating process is driven by some mechanisms that induces time persistence.11

[Tables 9 and 10 about here]

Furthermore, we ﬁnd that microinventions are positively correlated with the economic cycle. The

Pearson’s correlation coeﬃcient between the growth rates of microinventions and the annual change in the GDP series (Broadberry et al., 2015) is equal to 0.1715 and it is signiﬁcant at a 5% level, while no such correlation exists in the case of macroinventions. All in all, the dynamics of macroinventions appears to be described well by a simple Poisson point process. Figure 6 shows that the

Poisson regression model that we estimated is able to almost perfectly reproduce the pattern of the observed data.12 Indeed, in Figure 7 we oﬀer an impressionistic graphical representation of the different processes governing micro- and macroinventions, as deﬁned using the Bibliographic Composite

Index.

[Figure 6 about here]

[Figure 7 about here]

Figure 8 charts the cumulative distribution of patents over time. The black in each subfigure represents the cumulative distribution of macroinventions vis-á-vismicroinventions for a different set of patents (textiles, engines, machinery, and all sectors together). More specifically, the curve in each sub-figure shows the proportion of macroinventions over the period 1700-1850 that already occurred when a certain proportion of microinventions is reached. For instance, the upper-left quadrant shows

10Results are robust to alternative definitions of macroinventions (e.g. first 100 patents, top 1% inventions) and to the inclusion of sectoral dummies in these regressions. One might fear that the procedure through which we cleansed the raw indicators might mechanically lead to this absence of time clustering. However, this is not the case, because the ranking of the most relevant inventions of the Industrial Revolution is extremely robust even if we do not control for time or if directly build the BCI using the raw indicators (Table 20 in the Appendix). As a further proof that this result is not due to the way we accounted for time trends in the raw indicators, note that one would symmetrically expect a similar absence of concentration of macroinventions across industries, given that we controlled for industry dummies in the same way we did for time decades. However, in unreported results we find that macroinventions show remarkable sectoral concentration, and three sectors alone (engines, textiles, metallurgy) account for half of them. 11In their sample of important inventions, Silverberg and Verspagen (2003) find instead time clustering in the form of overdispersion, a difference possibly due to the later time period they consider (second half of XIX century and XX century). An alternative way to analyze the difference between micro- and macroinventions is by means of time series analysis. In unreported augmented Dickey-Fuller tests, we found that the test strongly rejects the null hypothesis of presence of a unit root in the macroinventions series. Macroinventions follow a stable mean reverting process, a clue of the exogenous nature of the arrival of macroinventions first suggested by Crafts (1977 and 1995). 12Our finding echoes the early study of Sahal (1974), who also showed how this result is not simply due to a statistical artifact of rare events.

14 that by the year 1800, over half of all the macroinventions that spurred the Industrial Revolution had already appeared, while only 16% of the ensuing microinventions were there. In a sense, these graphs represent Lorenz curves of the “time inequality” in the distribution of micro- and macroinventions: a perfectly equal time distribution of the two arrival processes would be depicted by a straight line with a 45 degrees slope. The ﬁgure suggest that the majority of macroinventions occurred in the

ﬁfty years between 1750 and 1800, consistently with the traditional chronology of the Industrial

Revolution (Landes 1969; Sullivan 1990). Overall, the cumulative distribution of macroinventions tends to anticipate the cumulative distribution of microinventions. This is again consistent with

Mokyr’s suggestion that the two processes are complementary features of technological progress, with macroinventions prompting cumulative streams of microinventions, albeit with varying lags. Note also that this ﬁnding is robust across sectors: if anything, for the more technological dynamic sectors of steam engines and textile machinery this pattern is even more pronounced, possibly because the potential of prototype macroinventions required a longer period to be fully exploited.

[Figure 8 about here]

4.2 Characteristics of micro- and macroinventions

Allen (2009, p. 136) has argued that macroinventions radically changed factor proportion by substituting capital and energy for high-wage labour. In this account, the high wages prompted the search for labour-saving new technologies; microinventions, on the contrary, were the result of cumulative learning processes and thus they are not biased in any speciﬁc directions. In other words, microinventions were a stream of continuous productivity improvements that increased overall eﬃ- ciency of both capital and labour (Allen 2009, p. 148). This point of view is in contrast with the interpretation of Mokyr (1992, 2010), who argues that macroinventions were not sensitive to economic inducements (Crafts, 2011). To check these conjectures, we exploit the summary description of the patents contained in Woodcroft’s Titles of Patents of Invention Chronologically Arranged, 1617-1852

(1854), which is an excerpt of the speciﬁcation ﬁled by the inventor: for many patents granted before

1800, it is possible to surmise from this description the stated aims of the inventor (see Table 11 for three examples).13

[Table 11 about here]

We follow the approach of MacLeod (1988) and from the description of each invention we identify

13Obviously this exercise neglects inventions that consisted in entirely new products or services, like canned food, and that as such did not entail any kind of bias per se (Kelly et al., 2014). However, more than 85% of our set of macroinventions pertain to improvements in production processes, mostly ways to improve quality or reduce costs.

15 two main goals. If only one aim is clearly described, we count this goal once and mark as unspeciﬁed the second aim. This ensures comparability between our results and the original assessment that

MacLeod carried out for the entire sample of patents. Table 11 presents the results of this approach for three representative patents.

Table 12 compares the stated aims of invention for our selection of macroinventions with the results of MacLeod on all patents in the period 1700-1799. We find that microinventions were indeed mostly concerned with saving capital, raw materials and other inputs. Interestingly enough, among macroinventions the share of inventions with the same goal is significantly smaller, while the incidence of other motivations is very similar. However, the results of Table 12 must be interpreted with care: not surprisingly, in this period, inventors were reluctant to explicitly boast the labor saving potential of their inventions (MacLeod 1988, p. 166). Hence, it is likely that the share of labour saving inventions in Table 12 underestimates the actual phenomenon. Therefore, following again the approach of MacLeod (1988), we try to discern from the patent description also the actual labour saving effects of the inventions (beyond what is explicitly stated in the specification).14 Table 13 compares the labor-saving potential (defined in this broader meaning) of micro- and macroinventions.

In this case, we find a much stronger labour-saving character for macroinventions (38% of top 0.5% patents) than for microinventions (15% of all patents). The reason of this difference is that a large share of macroinventions consisted of machines: they account for almost half of the highest quality patents, while little more than 20% of microinventions was related to machines. Overall, these findings appear consistent with Allen’s view of a structural difference in the factor-saving biases between macro and micro-inventions and, in particular, with the notion that macroinventions displayed a significant labour saving bias (Allen, 2009).15

[Table 12 about here]

[Table 13 about here]

Allen (2009) has also suggested that microinventions resulted from local learning eﬀorts of inventors who were “insiders” to trade, while true breakthroughs were largely due to “outsiders” who

14More precisely the approach of MacLeod is the following: labour saving inventions are classiﬁed as “[. . . ] those labour-saving machines and technique which contemporaries generally identiﬁed as such, e.g. spinning, carding, or threshing machines and power looms”. However, in the labour-saving category are not included “[. . . ] machines and techniques whose labour saving potential was commonly overlooked by contemporaries, unless a particular invention would increase its labour productivity further. Thus, wind, water, horse and steam engines were excluded as were e.g. handlooms, the majority of stocking frame attachments, sugar mills, the printing press (but not mechanical textile printing)” MacLeod 1988, p. 257). 15Our evidence, however, does not allow to discriminate whether the impetus towards mechanization in macroinventions was actually prompted by high wages or by the limitations of traditional techniques and production systems, which is one of the issues currently debated by Humphries and Schneider (2019) and Allen (2019).

16 could rely on insights originating from “outside the immediate industrial experience” (Allen 2009, p. 149). According to the data on the occupations of the patentees reported in Woodcroft (1862),

Allen’s hypothesis is not corroborated: the results of Table 14 show that the share of macroinventions actually ascribable to outsiders is always below 30%.16 In terms of differences between macro- and microinventions, the first two columns of the table highlight a higher incidence of outsiders in patents for the former: especially after 1760, around a quarter of macroinventions was invented by people with an “outsider” background, whereas for total patents this share is around 17%. However, this difference disappears almost entirely if one removes Cartwright’s patents from the computations, showing that the results are actually sensitive to this specific case. Indeed, Cartwright is the outsider for excellence: a clergyman with a penchant for poetry, he started his quest for for the mechanization of weaving out of intellectual curiosity (O’Brien, 1997).17 His inventions are among the most important breakthroughs of the Industrial Revolution, and are rightly classified by our BCI among the most valuable patents. To sum up, our evidence suggests that macroinventions required specialized skills and competences (Mokyr, 2010), rather than simple insights outside the prevailing trade practices.

[Table 14 about here]

We expand the analysis by concentrating on machinery patents. Following von Hippel (1988),

MacLeod and Nuvolari (2009) suggested that macroinventions in machinery were mostly made by machine users, with professional machine-makers being responsible of incremental improvements. The reasons to expect a pattern in which the user-inventor made the initial technological breakthrough are at least two, rooted in the different incentives of users and makers (MacLeod, 1992). First, there was a differential in the risk factor: besides the technical challenges, makers incurred the commercial uncertainty involved in selling radically new inventions. On the contrary, users were the ones profiting in first person from riskier technical advances. Second, and relatedly, building one’s own machinery offered the opportunity for its deployment in secret, arguably an appropriation strategy more effective than the imperfect patent system of the time.18

We explore the merits of this hypothesis in Table 15. Contrarily to the prediction, the most important patents covering machinery were due to professional engineers and millwrights, while users

16Note however that the data reported in Table 14 should be considered a conservative approximation of the true incidence of outsiders in patenting during the Industrial Revolution (since doubtful cases of outsiders are not counted). 17In the reconstruction of O’Brien (1997), Cartwright started his quest for the mechanization of weaving after a dinner in Manchester where businessmen warned him on the impossibility of doing so. After years of work and huge investments in R&D, he eventually tried to open a business based on his invention, but the venture immediately failed because his main interests were purely technical and not commercial. Indeed, Cartwright himself was aware of the potential eﬀects on jobs of his new inventions (to the point that he even proposed to the Parliament to self-contain sales of his new machine). 18Of course, we cannot assess this second argument because our data comprises only patented inventions.

17 of industrial machinery were mostly active in microinventions. Again, this ﬁndings points towards the critical role of specialized competences in macroinvention.

[Table 15 about here]

4.3 A tentative interpretation

Crafts (2011) has provided a perceptive analysis of the different conceptualizations of macro- and microinventions proposed by Allen (2009) and Mokyr (1990). In Craft’s view, Allen and Mokyr focus on different stages of the innovation process, which runs “linearly” from ideas (1), to R&D efforts (2), to incremental improvements (3). Mokyr considers macroinventions as pertaining mostly to the first stage, hence he stresses the role of individual creativity and serendipity (Yaqub, 2018). For Allen, macroinventions encompass both the first and the second stage, and in particular, the role of the large investment outlays required to transform the original idea into a fully-fledged prototype.19 From this perspective, clearly, economic inducements come to play an important role.

In our interpretation, which is actually somewhat similar to the one sketched by Crafts, the evidence presented in this section suggests that Allen and Mokyr are actually focusing on two diﬀerent complementary dimensions of inventive activities. Figure 9 illustrates our attempt of summarizing

Allen and Mokyr’s perspective on macroinventions in a uniﬁed framework.

[Figure 9 about here]

On the horizontal axis of Figure 9 there is the principal dimension considered by Allen, namely investment in R&D activities, whereas on the vertical axis there is degree of serendipity surrounding the search activity of inventors which is the feature highlighted by Mokyr. Our framework makes clear that Mokyr and Allen are pointing to necessary but not suﬃcient conditions for the emergence of macroinventions. In terms of Figure 9, both serendipity and extensive investment in search activities are actually distinguishing and complementary features of macroinventions.

This fits well with the findings of this section on the different patterns of macro- and microinventive activity. The occurrence of macroinventions can be accounted for by a homogeneous Poisson process and this is in line with the notion of a significant role of chance and serendipity, which on the other hand remains somewhat impervious to economic factors. Economic factors instead seem to shape the actual character of macroinventions. One can imagine that economic factors will determined which areas of the space of technological opportunities will be searched, while serendipity will condition the success of the search process in this preselected domain. The findings concerning the role of insiders

19In this respect, Allen cites approvingly Edison’s quip that “invention is 1% inspiration and 99% perspiration”.

18 and of specialized engineers and mechanics point to the key role of specialized skills and competences together with other resources for a successful search of the space of technological opportunities.20

5 Conclusions

In this paper, we have introduced a new composite indicator of the quality of English patents in the period 1700-1850. Our Bibliographic Composite Index (BCI) synthesizes two different but complementary assessments of patent quality: the technical and economic importance perceived by contemporaries and measured by the number of references in Woodcroft (1862), and the historical significance as assessed by the modern history of technology literature with the benefit of hindsight.

We have carried out a thorough examination of the properties of BCI and tested its ability to identify the most important patents of the Industrial Revolution. The results are rather encouraging and it would seem that this new composite indicator may represent a very useful proxy for the quality of English patents in the 1700-1850 period, improving the WRI* index introduced by Nuvolari and

Tartari (2011).

Next, we have employed the new composite indicator of patent quality to study the patterns of innovation during the British Industrial Revolution. In particular, we have focused on the distinction between micro- and macroinventions. Our findings provide robust evidence in favor of the existence of two related but different processes governing the occurrence of macro- and microinventions. Fur- thermore, we have found limited incidence of outsiders or machine users in macroinventions, but we have confirmed the existence of a significant labour-saving bias in macroinventions, a conjecture that is one of the key points of the high wage interpretation of the Industrial Revolution proposed by Allen

(2009).

Our ﬁndings resonate with Crafts’ (2011) assessment of the Allen-Mokyr debate who found that the two accounts of the Industrial Revolution actually pointed to distinct but complementary features of innovation processes of that period. An intriguing research agenda for the immediate future would be to consider whether the tentative characterizations of the patterns of innovation proposed in this paper can actually be developed in a new synthesis as adumbrated by Crafts (2011).

20This perspective is reminiscent of the interpretation originally put forward by Crafts (1977, p. 437) who regarded macroinventions as the outcome of a “stochastic search processes in which both economic inducements and scientiﬁc, supply-side considerations play a part.”

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24 6 Figures and Tables

Figure 1: Entry in Woodcroft’s Reference Index for James Watt’s patent of the separate condenser (1769)

Note: the entry gives references to technical and legal literature where the patent is mentioned, while the last line of the table indicates in which oﬃce the speciﬁcation was lodged (in this case Rolls Chapel). The Index also notes of the Fire Engines Patent Act (1775) that extended the patent to 1800.

Figure 2: Entry in Woodcroft’s Reference Index for William Watts’ patent for making better small shots (1782)

Note: Not surprisingly, Watt’s separate condenser received a much higher number of citations than the incremental improvements patented by William Watts.

25 (a) Average number of references per patents in Woodcroft (1862), yearly (b) Average number of references per patents by decade. and by decade.

Figure 3: Average number of references per patents over time

P atent Quality

WRI P AT EM INV EM

ε1 ε2 ε3

Figure 4: Structural equation model used to extract a latent common factor from the residuals of Poisson regressions that control for time and industry eﬀects.

Figure 5: Empirical distribution of the Bibliographic Composite Index; the box in the top-right of the ﬁgure reports the upper-tail of the distribution for visual clarity.

26 Figure 6: Frequency of years characterized by a certain number of macroinventions, actual vs predicted by the Poisson model.

Note: the unit of observation is the year and the graph shows the frequency of years with zero to three macroinventions. The Poisson model is estimated using a quadratic time trend.

Figure 7: Number of micro- and macroinventions per year

Note: dots plot the yearly number of macroinventions (patents in the 99.5th percentile of quality) while the line shows the number of microinventions patented each year.

27 (a) All patents (b) Textile sector

Figure 8: Lorenz curves of microinventions vs macroinvention shares over time.

Note: patents related to engine and textile sectors are taken from the classiﬁcation of Nuvolari and Tartari (2011); machines are identiﬁed from the title of the patent in Woodcroft (1854).

Table 1: Summary of the sources consulted to construct the variables on Patent and Inventor Eminence

Patent Eminence Inventor Eminence Source Inventors Patents Source Inventors Patents Baker (1976) 123 150 Oxford DNB 291 893 Carter (1978) 201 266 Allen (2009) 76 234 Desmond (1987) 128 157 Day and McNeil (1996) 240 708 Inkster (1991) 27 44 Abbott (1985) 57 246 Dudley (2012) 33 55 Murray (2003) 54 199 Challoner (2009) 41 49 De Galiana (1996) 102 333 Bridgman (2002) 33 38 Mokyr and Meisenzhal (2010) 536 1519 Bunch and Hellemans (2004) 71 93 Benson (2012) 59 206 Ochoa and Corey (1997) 23 24 Gergaud et al (2016) 179 595 Lilley (1948) 28 33 Note: This table reports the number of patents and inventors mentioned in each source. The left side pertains sources grouped into the indicator of Patent Eminence, while on the right side there are those concerning Inventor Eminence.

28 Serendipity

Macroinventions Macroinventions High (Mokyr, 1990, 2010) (our interpretation)

Macroinventions Low Microinventions (Allen, 2009, 2018)

Low High Investments in R&D

Figure 9: Macro- and microinventions: a suggested interpretation

Table 2: Spearman’s rank correlation coeﬃcients of the raw quality indicators

Woodcroft Patent Eminence Inventor Eminence Woodcroft 1 Patent Eminence 0.0710*** 1 Inventor Eminence 0.0645*** 0.3001*** 1 Note: *** denotes signiﬁcance at 0.1% level.

Table 3: Comparison of references for Kay and Hulls’ patents

Patent N° Year Inventor Invention Woodcroft References Patent Eminence Inventor Eminence 542 1736 John Kay Flying shuttle 1 10 8 556 1736 Jonathan Hulls Steam-propelled ship 9 0 5

Table 4: Comparison of references for two of Arkwright’s patents

Patent N° Year Invention Woodcroft References Patent Eminence Inventor Eminence Patent case 931 1769 Water frame 3 10 9 0 1111 1775 Carding machine 15 3 9 1

29 Table 5: Factor loadings of the Bibliographic Composite Index (BCI) resulting from the SEM estimation

Residuals WRI Residuals PAT EM Residuals INV EM λ 1 1.1746*** 1.8698*** - (0.1401) (0.2619)

Note: *** denotes signiﬁcance at 0.1% level. λk are the factor loadings on the common factor q, representing the BCI. Standardized root mean squared residual= 0.000; Coeﬃcient of determination= 0.698.

Table 6: Fligner-Policello tests of stochastic equality

Extended to Scotland Extended to all UK Time Extension Litigated Patents Entire sample (1700-1850) Fligner-Policello statistics 17.166*** 11.072*** 15.292*** 35.430*** Year>1734 Fligner-Policello statistics 16.910*** 10.905*** 16.539*** 35.310*** Year>1778 Fligner-Policello statistics 14.503*** 9.267*** 19.045*** 34.158*** Note: *** denotes significance at 0.1% level. The Fligner-Policello test determines whether for two random variables X and Y it is statistically significant that P rob[X > Y ] > 0.5. The test resembles the widely used Mann-Whitney-Wilcoxon test of median equality, but entails less restrictive hypotheses on variance and shape of the distributions. In all cases, the null hypothesis of stochastic equality is rejected at a high significance level. Data for geographical coverage are taken from Bottomley (2014a) (3504 patents extended to Scotland and 1247 extended to the entire United Kingdom), while the lists of patents that were litigated (355 cases) and for which a time extension was petitioned (95) are taken from Woodcroft (1862). All the results hold if we employ Mann-Whitney-Wilcoxon median test.

Table 7: Fligner-Policello tests of stochastic equality, comparison between WRI* and the Bibliographic Composite Index

Perpetual Motion “Impossible” Engines BCI WRI* BCI WRI* Entire sample (1700-1850) Fligner-Policello statistics -5.062*** -0.887 -2.765** 1.822 Year>1734 Fligner-Policello statistics -5.088*** -0.890 -2.808** 1.793 Year>1778 Fligner-Policello statistics -5.305*** -0.857 -3.200** 1.685 Note: *,**,*** denote signiﬁcance at 5%, 1% and 0.1% level. Data for perpetual motion machines are taken from Dircks (1861) (23 patents), while the lists of 83 engines that were not technically feasible is the same employed by MacLeod et al. (2003). A negative sign of the Fligner-Policello statistics indicates that patents in the list considered are of lower average value than the excluded remainder. All the results hold if we employ Mann-Whitney- Wilcoxon median test.

Table 8: Selection of very important patents for which the Bibliographic Composite Index addresses limitations of Nuvolari and Tartari’s WRI*

Patent N° Inventor Invention N°Woodcroft Refs WRI* Percentile WRI* BCI Percentile BCI 542 John Kay Flying shuttle 1 0.578 20 5.006 99.5 550 John Hadley Octant 1 0.578 20 2.783 99.5 962 James Hargreaves Spinning jenny 2 1.140 68 5.221 99.5 1063 John Wilkinson Boring machine 2 1.165 69 4.700 99.5 1351 Henry Cort Rolling of metals 2 1.072 67 4.525 99.5

30 Table 9: Regression results, Poisson and negative binomial models with arrival rate for macroinventions as a function of time.

2 Model Patents c β1 β2 β3 α LR test logL Wald test Pseudo R Q test

Poisson Top 0.5% -0.8429*** -131.402 50.936*** (0.1319) Neg Bin Top 0.5% -0.84292*** 0.3107 NOT reject -130.869 50.936*** (0.1321) Poisson Top 0.5% -1.809*** 0.011*** -124.187 19.13*** 0.055 30.1501* (0.2879) (0.0026) Neg Bin Top 0.5% -1.8285*** 0.0114*** 0.1280 NOT reject -124.071 13.60*** 0.052 30.1211* (0.3307) (0.0032) Poisson Top 0.5% -3.689*** 0.064** -0.030**a -118.626 14.07*** 0.097 23.0980 (0.8409) (0.0193) (0.0104)a Neg Bin Top 0.5% -3.689*** 0.064** -0.030**a 0.0048c NOT reject -118.626 24.49*** 0.094 23.0985 (0.8013) (0.0185) (0.0101)a Poisson Top 0.5% -3.045* 0.0312 0.0144a -0.0178c -118.381 21.08*** 0.099 25.8504 (1.1938) (0.0505) (0.0628)a (0.0024)b Neg Bin Top 0.5% -3.045** 0.0312 0.0143a -0.0179c 0.0001a NOT reject -118.381 24.98*** 0.095 25.8504 (1.129) (0.0485) (0.0633)a (0.0025)b

Note: *,**,*** denote significance at 5%, 1% and 0.1% level. c, β1, β2 and β3 are the coefficients on the constant and the polynomials of time (first, second and third degree, respectively). Estimated coefficients are sometimes multiplied by the following factors: a=100, b=1000, c=10000. α is the parameter for overdispersion in the negative binomial model for which a likelihood-ratio test (LR test) of H0 : α = 0 (i.e. no overdispersion) is carried out. The last column give the Box-Ljung Q statistics on the standardized residuals of H0: no time autocorrelation. In this case, a significant value of the test statistics means that we reject H0. Following Silverberg and Verspagen (2003), we set k = 20 (see Appendix C). The period considered is 1700-1850 (151 observations).

Table 10: Regression results, Poisson and negative binomial models with arrival rate for microinventions as a function of time.

2 Model Patents c β1 β2 β3 α LR test logL Wald test Pseudo R Q test

Poisson All -4.4608*** -10950.859 1091.1466*** (0.1211) Neg Bin All 4.461*** 1.827 reject -803.643 1091.1466*** (0.1103) Poisson All 0.4222*** 0.038*** -824.490 1993.45*** 0.9247 159.5699*** (0.0957) (0.0009) Neg Bin All 0.641*** 0.036*** 0.0585 reject -572.144 463.00*** 0.2881 193.2231*** (0.0724) (0.0006) Poisson All 1.127*** 0.023*** 0.073***b -789.415 3047.81*** 0.9279 122.4661*** (0.1468) (0.0034) (0.0018)a Neg Bin All 0.851*** 0.030*** 0.034*b 0.0565 reject -570.130 467.03*** 0.2906 146.7201*** (0.1249) (0.0030) (0.0016)a Poisson All 0.310 0.059*** -0.037**a 0.016**c -765.420 2777.19*** 0.9301 92.4250*** (0.2766) (0.0114) (0.0001) (0.0054)c Neg Bin All 0.795*** 0.033*** -0.001a 0.0018c 0.0559 reject -570.047 467.19*** 0.2907 135.6694*** (0.1875) (0.0086) (0.0115)a (0.0045)c

Table 11: Examples of stated aims of invention for three macroinventions.

Patent N° Year Inventor Invention Excerpt from Woodcroft (1854) Stated aims “[. . . ] making an engine [. . . ] to be managed by one person only, which will spin, draw, and Save labour; 962 1770 James Hargreaves Spinning jenny twist 16 or more threads at a time by a motion save time of one hand and a draw of the other” “[. . . ] manufacturing iron and steel into bars Save capital and [. . . ] of purer quality, in larger quantity, by a 1420 1784 Henry Cort Puddling process raw materials; more effectual application of fire and machinery, improve quality and with greater yield” “[. . . ] the corn is thereby separated from the Save time; 1645 1788 Andrew Meikle Threshing machine straw in less time, and in more effectual manner improve quality than by threshing or any other manner” Note: Data are taken from Woodcroft (1854) and stated aims are classified using the methodology of MacLeod (1988).

31 Table 12: Patentees’ stated aims of invention, 1700-1799.

Stated aim Top 0.5% Top 1% Top 2% All patents Create employment 0 1.7 1.2 1.9 Improve working conditions 0 0 2.3 1.4 Save labour 2.9 3.4 4.7 4.2 Save time 11.8 8.5 7 5.2 Save capital and raw materials 8.8 5.1 7 30.8 Reduce consumer price 5.9 5.1 3.5 3.7 Improve quality 32.4 27.1 25.6 29.3 Import substitution 0 1.7 1.2 3.6 Government revenue 0 0 0 1 Other government beneﬁts 5.9 3.4 2.3 2.1 Note: Columns 2, 3 and 4 report the share of patents in that percentile of quality that mention each of the listed aims of invention. Figures are expressed as a percentage of the 34, 59 and 86 patents respectively granted for macroinventions in the period 1700-1799 (see text for details). The last column is taken from MacLeod (1988), Table 9.1 p. 160, who considered 2240 patents in the period from 1660 to 1799. This means that unfortunately the data are not strictly comparable, but given the low number of patents granted before 1700 (on average, less than four per year) and that the only major macroinvention that we excluding is Thomas Savery’s steam engine of 1698, the comparison presented remains informative.

Table 13: Patents for inventions intended to save labour, 1700-1799.

Patent aim Top 0.5% Top 1% Top 2% All patents Labour-saving stated 2.9 3.4 4.7 3.9 Effectively labour-saving 38.2 38.9 38.4 15.3 Note: The last column is taken from MacLeod (1988), Table 9.2 p. 170. Unfortunately, the data are not strictly comparable because MacLeod considered the entire period from 1660 to 1799 (see the note to Table 12). The methodology used to find patents covering inventions effectively labour saving is described in the text and is the same of MacLeod (1988, pp. 170 and 257).

Table 14: The incidence of “outsiders” in macroinventions

Including Cartwright Excluding Cartwright 1700-1850 1760-1850 1700-1850 1760-1850 All patents 17.4% 17.4% 17.3% 17.3% Top 0.5% 24.6% 28.6% 19.7% 23.1% Top 1% 22.1% 24.2% 17.1% 18.8% Note: the variable has been constructed in such a way to consider only the cases in which the invention was clearly not connected with the occupation of the patentee. When this dummy variable takes a value of 0 this does not mean that the inventor in question is an insider; this is also the case for all those inventors listed as “esquire”, “gentleman” or “baronet”. We also excluded from the count of outsiders patent agents and inventions imported from abroad, thus we should consider these ratios as very conservative estimates.

32 Table 15: Number of patents covering inventions in machinery and their share granted to users or makers.

Machines Users Makers Others Period considered: 1700-1850 Top 0.5% 30 (46.2%) 3.3% 63.3% 33.3% Top 1% 64 (48.9%) 14.1% 54.7% 31.3%

Period considered: 1780-1850 Top 0.5% 22 (47.8%) 0% 63.6% 36.4% Top 1% 54 (50.5%) 11.1% 55.5% 33.3% All patents 2649 (21.7%) 40.5% 26.8% 32.7% Note: the first column displays the total number of machinery patents at different percentiles of patent quality, and in parentheses their share over the total. The remaining columns are the shares of the machinery patents of the first column that were assigned to users or makers (thus they sum to 100%). The figures for the last row are taken from MacLeod and Nuvolari (2009), and are available only for the period from 1780 to 1850.

33 A Appendix: Sources used for constructing the patent quality in-

dicator.

Sources used for the Patent Eminence (PAT EM) indicator:

1. Baker, R. (1976): New and Improved... Inventors and Inventions that Have Changed the Modern

World, London: British Library.

2. Carter, E. F. (1969): Dictionary of Inventions and Discoveries, London: F. Muller.

3. Desmond, K. (1987): The Harwin chronology of inventions, innovations, discoveries: From pre-

history to the present day, London: Constable.

4. Inkster, I. (1991): Science and technology in history: an approach to industrialisation, London:

Macmillan.

5. Bridgman, R. (2014): 1000 inventions and discoveries, New York: Dorling Kindersley Ltd.

6. Bunch, B. H. and A. Hellemans (2004): The History of Science and Technology, New York:

Houghton Miﬄin.

7. Ochoa, G. and M. Corey (1997): The Wilson chronology of science and technology, New York:

HW Wilson.

8. Dudley, L. (2012): Mothers of innovation: How expanding social networks gave birth to the

Industrial Revolution, Newcastle upon Tyne: Cambridge Scholars Publishing.

9. Lilley, S. (1948): Men, machines and history: a short history of tools and machines in relation

to social progress, London: Cobbett Press.

10. Challoner, J. (2016): 1001 inventions that changed the world, Sydney: Pier 9.

Sources used for the Inventor Eminence (INV EM) indicator:

1. Matthew H. and B. Harrison (2004): Oxford Dictionary of National Biography, Oxford: Oxford

University Press (www.oxforddnb.com).

2. Allen, R. (2009): The British Industrial Revolution in Global Perspective, Cambridge: Cam-

bridge University Press.

34 3. Day, L. and I. McNeil (1996): Biographical dictionary of the history of technology, London:

Routledge.

4. Abbott, D. (1985): The Biographical Dictionary of Scientists, Engineers and Inventors, London:

F. Muller.

5. Murray, C. (2003): Human accomplishment: The pursuit of excellence in the arts and sciences,

800 BC to 1950, London: Harper Collins.

6. Benson, A. K. (2012): Inventors and inventions. Great lives from history, Pasadena: Salem

Press.

7. De Galiana, T. and M. Rival (1996): Dictionnaire des inventeurs et inventions, Paris: Larousse.

8. Meisenzahl, R. R. and J. Mokyr (2011): “The rate and direction of invention in the British

Industrial Revolution: Incentives and institutions,” in The rate and direction of inventive activity

revisited, ed. by J. Lerner and S. Stern, Chicago: University of Chicago Press, pp. 443-479.

9. Gergaud, O., M. Laouenan, and E. Wasmer (2016): “A Brief History of Human Time. Exploring

a database of ‘notable people’,” LIEPP Working Paper, Sciences Po.

The following tables show the highest ranking patents and inventors according to Patent Eminence and Inventor Eminence indicators. Next, we show the relative overlapping between patents and inventors mentioned in the sources we considered. Finally, in Figure 10 we plot the empirical distribution of the resulting indicators.

Table 16: Patents achieving the highest scores of Patent Eminence

Patent N° Year Inventor Invention Patent Eminence 542 1733 John Kay Flying shuttle 10 913 1769 James Watt Separate condenser 10 931 1769 Richard Arkwright Water frame 10 962 1770 James Hargreaves Spinning jenny 10 7390 1837 Charles Wheatstone Telegraph 10 1063 1774 John Wilkinson Boring machine 9 1351 1783 Henry Cort Rolling of metals 9 1470 1785 Edmund Cartwright Power loom 9 2599 1802 Andrew Vivian, Richard Trevithick High pressure steam engine 9 1298 1781 Jonathan Hornblower Compound steam engine 8 1565 1786 Edmund Cartwright Power loom 8 1645 1788 Andrew Meikle Threshing machine 8 2045 1795 Joseph Bramah Bramah’s lock 8 9382 1842 James Nasmyth Steam hammer 8

35 Table 17: Inventors achieving the highest score of Inventor Eminence

Inventor Inventor Eminence Andrew Vivian 9 Edmund Cartwright 9 Henry Bessemer 9 Henry Maudslay 9 James Hargreaves 9 James Nasmyth 9 James Watt 9 John Kay 9 Richard Arkwright 9 Richard Trevithick 9 Thomas Savery 9 William Murdock 9

Table 18: Overlap between the sources used for Patent Eminence

Source (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1) Baker (1976) 150 (2) Carter (1978) 48 266 (3) Desmond (1987) 45 68 157 (4) Inkster (1991) 21 29 20 44 (5) Dudley (2012) 29 37 26 27 55 (6) Challoner (2009) 31 28 29 14 20 49 (7) Bridgman (2002) 22 26 24 16 18 18 38 (8) Bunch and Hellemans (2004) 39 52 31 19 27 23 23 93 (9) Ochoa and Corey (1997) 16 15 17 12 13 10 11 15 24 (10) Lilley (1948) 21 24 17 21 21 14 15 17 12 33 Note: This table shows the number of patents cited in every sources along with the number of these that are also mentioned in each of the other sources used. The diagonal cells contain the total number of patents in each of these lists, while cells outside the diagonal show the number of patents mentioned simultaneously in both sources.

(a) Patent Eminence (b) Inventor Eminence

Figure 10: Empirical distributions of the quality proxies Patent and Inventor Eminence

36 Table 19: Overlap between the sources used for Inventor Eminence

Source (1) (2) (3) (4) (5) (6) (7) (8) (9) (1) Oxford DNB 292 (2) Allen (2009) 45 77 (3) Day and McNeil (1996) 105 50 241 (4) Abbott (1985) 41 29 48 58 (5) Murray (2003) 32 29 35 28 55 (6) De Galiana (1996) 60 36 66 40 35 103 (7) Mokyr and Meisenzhal (2010) 153 55 178 45 39 75 538 (8) Benson (2012) 38 28 38 26 27 37 45 60 (9) Gergaud et al (2016) 86 22 66 29 25 45 84 36 135 Note: This table shows the number of inventors cited in every sources along with the number of these that are also mentioned in each of the other sources used. The diagonal cells contain the total number of inventors in each of these lists, while cells outside the diagonal show the number of inventors mentioned simultaneously in both sources.

Table 20: Overlap between Top 0.5% patents when changing the time and industry controls employed in Poisson regression.

(1) (2) (3) (4) (5) (6) (1) 65 (2) 63 65 (3) 62 63 65 (4) 63 64 62 65 (5) 62 63 62 63 65 (6) 62 63 62 63 63 65 Note: This table shows the number of top 0.5% patents (65 patents) that overlap when the Bibliographic Composite In- dex is constructed using residuals of the raw proxies coming from diﬀerent sets of regressions. In particular: (1) preferred speciﬁca- tion, controls for time decade and industry (2) control for time windows of 50 years and industry (3) control for time windows of 25 years and industry (4) control for time decades only (5) control for industry only (6) no controls at all.

37 Table 21: Descriptive statistics of quality indicators, detailed by sector of economic activity as deﬁned by Nuvolari and Tartari (2011)

Industry Patents Woodcroft Reference Index Patent Eminence Inventor Eminence Mean Median Std Dev Min Max Mean Median Std Dev Min Max Mean Median Std Dev Min Max

Agriculture 432 2.5717 2 1.3433 1 7 0.0856 0 0.5655 0 8 0.2152 0 0.8300 0 7 Carriages 812 2.8140 2 1.6593 1 15 0.0615 0 0.3384 0 4 0.3645 0 1.1752 0 9 Chemicals 1118 2.9758 3 1.6713 1 19 0.0286 0 0.2009 0 2 0.2504 0 0.9759 0 9 Clothing 322 2.3074 2 1.3814 1 13 0.0465 0 0.3879 0 6 0.2732 0 0.9952 0 6 Construction 640 2.8687 3 1.6238 1 16 0.025 0 0.2078 0 3 0.3078 0 1.1135 0 9 Engines 1637 2.7874 3 1.5135 1 21 0.0989 0 0.6136 0 10 0.5534 0 1.5464 0 9 Food 716 2.6955 2 1.6118 1 17 0.0488 0 0.3873 0 7 0.1955 0 0.8743 0 9 Furniture 659 2.4962 2 1.5021 1 18 0.0515 0 0.3313 0 4 0.1638 0 0.8124 0 9 38 Glass 123 2.8130 2 1.5436 1 9 0.0569 0 0.3213 0 3 0.5934 0 1.7547 0 9 Hardware 834 2.6163 2 1.5798 1 13 0.0611 0 0.3948 0 7 0.2170 0 0.8385 0 8 Instruments 598 2.5953 2 1.4642 1 13 0.1371 0 0.6833 0 10 0.5083 0 1.3815 0 8 Leather 218 2.6559 2 1.3799 1 9 0.0137 0 0.1511 0 2 0.1605 0 0.7840 0 6 Manufacturing 685 2.6087 2 1.6064 1 16 0.0701 0 0.3797 0 4 0.2919 0 1.0328 0 8 Medicines 288 2.1527 2 1.1404 1 10 0.0243 0 0.1754 0 2 0.1423 0 0.6443 0 7 Metallurgy 682 3.1568 3 1.9808 1 23 0.1114 0 0.6520 0 9 0.6436 0 1.6546 0 9 Military 252 2.4603 2 1.2944 1 11 0.1111 0 0.7221 0 9 0.4246 0 1.2264 0 7 Mining 81 2.9876 3 1.9202 1 14 0.0987 0 0.5149 0 4 0.4691 0 1.0849 0 5 Paper 480 2.9041 3 1.6648 1 14 0.1 0 0.4266 0 4 0.5812 0 1.3683 0 9 Pottery 277 2.8483 3 1.5738 1 12 0.0649 0 0.4030 0 4 0.2454 0 0.9465 0 9 Ships 590 2.8932 3 1.8280 1 17 0.0355 0 0.3302 0 7 0.3067 0 0.9935 0 9 Textiles 1626 2.5645 2 1.6636 1 19 0.0805 0 0.6451 0 10 0.5405 0 1.3496 0 9

Total sample 13070 2.7223 2 1.6161 1 23 0.0695 0 0.4797 0 10 0.3774 0 1.2031 0 9 B Appendix: Ranking of Macroinventions (Top 0.5% Patents) ac-

cording to the Bigliographic Composite Index

Rank Patent number Year Patentee Invention 1 913 1769 James Watt Separate condenser 2 7390 1837 Charles Wheatstone Telegraph 3 931 1769 Richard Arkwright Water frame 4 962 1770 James Hargreaves Spinning jenny 5 542 1733 John Kay Flying shuttle 6 2599 1802 Andrew Vivian, Richard Trevithick High pressure steam engine 7 1470 1785 Edmund Cartwright Power loom 8 1063 1774 John Wilkinson Boring machine 9 1351 1783 Henry Cort Rolling of metals 10 9382 1842 James Nasmyth Steam hammer 11 2045 1795 Joseph Bramah Hydraulic press 12 1565 1786 Edmund Cartwright Power loom 13 1645 1788 Andrew Meikle Threshing machine 14 1298 1781 Jonathan Hornblower Compound steam engine 15 1876 1792 Edmund Cartwright Wool-combing machine 16 1430 1784 Joseph Bramah Bramah’s lock 17 5701 1828 James Beaumont Neilson Hot blast furnace 18 7104 1836 Francis Pettit Smith Screw propeller 19 3372 1810 Peter Durand Tin cans 20 8842 1841 William Henry Fox Talbot Calotype 21 3887 1815 George Stephenson Locomotive 22 4804 1823 Charles MacIntosh Macintosh waterproof cloth 23 1321 1782 James Watt Double acting steam engine 24 2772 1804 Arthur Woolf Improvements in steam engines 25 5990 1830 Edwin Budding Lawnmower 26 550 1734 John Hadley Octant 27 1306 1781 James Watt Rotary crank 28 4136 1817 David Brewster Kaleidoscope 29 4081 1816 Robert Stirling Stirling air engine 30 1420 1784 Henry Cort Iron puddling 31 6909 1835 Samuel Colt Revolving ﬁrearm 32 722 1758 Jedediah Strutt Stocking rib 33 380 1707 Abraham Darby Iron casting 34 4067 1816 George Stephenson Half-lap joint for railways 35 562 1738 Lewis Paul Spinning machine 36 2196 1797 Joseph Bramah Beer pump 37 6159 1831 William Bickford Safety fuse 38 5803 1829 Charles Wheatstone Concertina 39 2708 1803 John Gamble Paper making machine (Foudrinier) 40 5949 1830 Richard Roberts Self-acting mule 41 636 1748 Lewis Paul Spinning machine 42 939 1769 Josiah Wedgwood New method for decorating earthenware 43 1111 1775 Richard Arkwright Carding machine 44 6733 1834 Joseph Hansom Hansom cab 45 1105 1775 Alexander Cumming Flush toilet 46 5022 1824 Joseph Apsdin Portland cement 47 1177 1778 Joseph Bramah Watercloset 48 2202 1797 Edmund Cartwright Steam engine 49 6014 1830 Andrew Ure Thermostat 50 395 1714 Henry Mill Typewriter 51 3611 1812 Joseph Bramah High-pressure hydraulic mains 52 3105 1808 William Newberry Scroll bandsaw 53 2652 1802 Joseph Bramah Making gun stocks 54 6675 1834 Henry Shrapnel Fire-arms 55 5138 1825 Richard Roberts Self-acting mule 56 721 1758 John Dollond Lenses for telescopes 57 8447 1840 George Richards Elkington Electroplatingprocess. 58 1478 1785 Joseph Bramah Screw propeller 59 896 1768 Andrew Meikle Machine for dressing grain 60 1112 1775 Jesse Ramsden Astronomic telescope 61 734 1759 Jedediah Strutt Derby patent rib machine 62 10990 1845 Robert William Thomson Carriage wheel (pneumatic tyre) 63 3032 1807 Alexander John Forsyth Fulminate-primed gun ﬁring mechanism 64 3041 1807 William Cubitt Self-regulating windmill sails 65 1833 1791 John Barber Gas turbine

39 C Appendix: Testing the Diﬀerences between Micro- and Macroin-

ventions

The count nature of patent data requires the adoption of ad hoc statistical methods. A commonly used way to deal with this kind of data is given by the Poisson process, with probability mass function given by:

e−µµy P rob(Y = y|µ) = (1) y!

where y ∈ N and µ is the rate parameter (i.e. the arrival rate of the Poisson process). The ﬁrst two moments of the Poisson are exactly equal to the rate: E(Y ) = V ar(Y ) = µ. This shows the equality of mean and variance, the well-known equidispersion property of the Poisson distribution (Cameron and Trivedi, 1998).

The parameter µ can be set as a function of a vector of independent variables x, for instance

µ = ex0β. In this way, one derives the Poisson regression model which uses the exponential mean parametrization to ensure that µ > 0. Following Silverberg and Verspagen (2003), we estimated

2 3 ln(µ) = c + β1t + β2t + β3t , where t is a time trend. This approach allows us to test the hypothesis that the Poisson process is time-homogeneous by imposing β = 0 (i.e. all its element equal to zero,

β1 = β2 = β3 = 0), and then gradually inserting the higher-order time trends. This is done starting from the ﬁrst rows of Table 9 and 10, where the rate of the Poisson is ﬁxed equal to the constant c

(Silverberg and Verspagen, 2003), and gradually inserting time trends in the subsequent rows.

The Poisson regression model is usually too restrictive for count data since the assumption of equidispersion is often rejected in practice. A simple adjustment that leads to a more ﬂexible model may be obtained by adding an unobserved random eﬀect υ to the mean of the Poisson distribution, hence y ∼ P oisson(y|µυ). It is easy to show that the addition of υ allows to model overdispersion, that is V ar(Y |x) > E(Y |x). In the special case in which υ is gamma distributed, υ ∼ Gamma(1, α), one obtains the negative binomial distribution whose probability mass function is:

−1 Γ(α−1 + y) α−1 α µ y P rob(Y = y|µ, υ) = (2) Γ(α−1)Γ(y + 1) α−1 + µ α−1 + µ

Where Γ(.) speciﬁes the gamma integral and α is the variance parameter of the distribution

(Cameron and Trivedi, 1998). A test of the Poisson against the negative binomial distribution can be implemented by means of a Likelihood Ratio test of the null hypothesis α = 0.

40 Beside overdispersion, we also analysed the correlation structure of the residuals. Raw residuals from Poisson regression are inherently nonstationary (Cameron and Trivedi, 1998), so they need to be standardized before performing the test of serial correlation. This problem can be avoided by employing the standardised residuals: z = yt√−mt where y is the observed value, m is the residual t σt t t from a regression model such as Poisson, and σt is equal to the sample variance. If zt is standardized to have constant variance, at least asymptotically, we can apply the Box-Ljung statistics to test the null hypothesis that all autocorrelations of the residuals up to lag k are zero.