Technological convergence among US regions and states

Abstract

This paper employs unit root tests that allow for two endogenously determined structural breaks to study whether or not invention activities are converging across US regions/states. Using US patent data from 1929 to 1997, we find technological β-convergence in six of the nine Census regions, in 11 of the 14 leading states and in 28 of the 34 lagging states. Stochastic convergence, on the other hand, is found in three regions, in four leading states and in 17 lagging states. Carlino and Mills (1993) point out that both β- and stochastic convergence are necessary conditions for convergence. Putting these results together, we find convergence (both β- and stochastic) in invention activities in three regions, in three leading states and in 16 lagging states.

Keywords:

• Patent
• US regions and states
• β-Convergence
• Stochastic convergence
• Unit root test

Acknowledgement

We would like to thank Ke Yang for invaluable research assistance, David Rapach for programming assistance and two anonymous referees whose comments and suggestions have greatly improved this paper. The first author is also grateful to Junsoo Lee and Mark Strazicich for helpful discussions on unit root tests. All errors are our responsibility.

Notes

¹The former is referred to as the fertile technology hypothesis and the latter is referred to as the friendly court hypothesis.

²For brevity, we refer to patent per 100,000 inhabitants as patent per capita. If a region's patent per capita is above (below) the average annual US national rate in 1929–1935, it is considered a leading (lagging) region. We take the seven-year average to mitigate annual fluctuations in patenting. The average annual US national rate is 34.89 per 100,000 inhabitants in 1929–1935.

Figure 1a

Figure 1b

³Suarez-Villa (2000) refers to this process as regional inversion.

⁴Per capita income convergence was initially tackled using cross-section data (see e.g., Barro and Sala-i-Martin, 1992). Convergence (β-convergence) in this context is defined as a negative relation between the initial levels of per capita income and the growth rates of per capita income. This approach has received much criticism. One criticism is its use of only the initial and terminal values (in calculating growth rates) of the data series under investigation. This led to the use of time series data, which uses a stochastic definition of convergence. In this approach, convergence is achieved when income disparities between economies follow a zero mean stationary process or shocks to relative per capita income are temporary. Results using cross-section and time series data are often contradictory. This led Carlino and Mills (1993) to develop a test that incorporates these two notions of convergence. They point out that both β- and stochastic convergence are necessary conditions for convergence.

⁵It should however be pointed out that policy can impact long-run growth rates in endogenous growth models. This suggests that technology oriented policies such as research and development (R&D) subsidies can be put in place to close technology gaps among regions thereby leading to per capita income convergence.

⁶As reviewed in Section 1, there is strong empirical evidence that knowledge diffusion is geographically mediated.

⁷As Smith (1999, p. 350) points out, “…interstate knowledge spillovers are contained within industries and that the geographic proximity of states is more important than technological similarity for transmitting knowledge spillovers.”

⁸This is related to the argument put forth by Abramovitz (1986) that lagging regions need to have the necessary “social capabilities” (e.g., a well-educated workforce) to catch up.

⁹This is another reason why regions with patent per capita above their compensating differential exhibit slower patent growth. Co (2002) provides some examples.

¹⁰It should be pointed out that policy induced shocks may also emanate from within the region/state (e.g., the creation of a research park in state i).

¹¹Patent counts prior to 1963 include utility, design and plant patents. Data from 1929 to 1962 are from the US Patent and Trademark Office, Technology Assessment and Forecast, Seventh Report. US Department of Commerce, Arlington, VA: US Dept. of Commerce, Patent and Trademark Office, Office of Technology Assessment and Forecast, March 1977. Data from 1963 to 1997 are from the US Patent and Trademark Office, Information Product Division, Patenting Trends in the US, 1998, State/Country Report – All Years, 1963–1998. CD-Rom issued July 2000.

¹²To mitigate the effect of annual fluctuations in patenting, we use a seven-year initial (1929–1935) and terminal (1991–1997) period to calculate the growth rates.

¹³For example, using data from the Bureau of Economic Analysis, between 1969 (the earliest year for which this data is available) and 1997, the average wage per job in the Middle Atlantic region was higher than the US average wage per job in every year. The differential ranged between 5% (in 1981) and 17% (in 1996). Although average wage in the East North Central region has been below the US average since 1987, between 1969 and 1986, wages are 5% higher in the region. Average wage in New England (Pacific) is 9% lower (3% higher) than the US average.

¹⁴For example, using patent data from 1963 to 1997, Co (2002) presents evidence that states in New England and the Pacific region experienced significant changes in their patent specialization between 1963–1969 and 1991–1997 while state patent specialization in the Middle Atlantic and the East North Central regions did not change drastically.

¹⁵As one referee points out, this approach although appropriate is not without limitations. For example, it does not account for the relationships among cross-sectional units. That is, “…estimating individual time series models – one for each state, say, to permit differences across Maine and Oklahoma (e.g., Carlino and Mills, 1993) – leaves undetected the co-movements across states.” Quah (1996, p. 147) Bernard and Durlauf (1995; 1996) provide an alternative time series approach that accounts for relationships among countries. In their formulation, convergence is found when the log of real per capita output differences between countries i and s is a mean zero stationary process. Since this approach analyzes pairwise differences in output, it has a nice feature in that all countries may not be converging but they are able to identify subgroups that are. Quah (1992) extends standard unit root test procedures to account for possible dependence in the cross-section dimension. He considers whether income differences between countries i and s (a benchmark country) is a mean stationary process. Quah (1992) finds non-convergence of per capita income using various countries as benchmarks.

¹⁶Another factor is locational amenities that tend to attract skilled workers or high-tech industries (see e.g., Davelaar and Nijkamp, 1997; Markusen et al., 1986). Also see Gallup et al. (1999) who emphasize the role of geography in economic growth using cross-country data and Bloom et al. (2002) who point to geography as a contributing factor to the persistent differentials in total factor productivity across countries.

¹⁷Alfred Marshall makes a contrary observation. He observes that increased production specialization is conducive to greater inventive output. The evidence in favor of diversity though is quite compelling (see e.g., Feldman and Audretsch, 1999)

¹⁸Also see Loewy and Papell (1996) and Carlino and Mills (1996).

¹⁹Congress passed the Bayh-Dole Act in 1980. Universities are able to retain the rights to inventions emanating from federally funded research with this law. This is believed to be one of the important contributory factors in the development of the biotechnology industry (see e.g., Evenson, 2002; Pisano, 2002). In 1982, the CAFC was created to hear patent cases. This regime change created a patent friendly environment and may be one reason for the significant increase in the number of patents taken out by firms in the semiconductor industry (see e.g., Hall and Ziedonis, 2001).

²⁰ Equation (8) is Lumsdaine and Papell's (1997) model CC which is based on the sequential Dickey-Fuller test procedure of Zivot and Andrews (1992).

²¹Ng and Perron (1995) demonstrate that an overly parsimonious model can have large size distortions, while an over-parameterized model may have low power. But the size problem is more severe than power loss. They show that methods based on sequential tests have an advantage over both the Said and Dickey (1984) fixed-rule and information-based rules such as the Akaike information criterion and the Schwarz information criterion, because the former have less size distortions and have comparable power. The procedure adopted in this paper falls into this category of the general-to-specific sequential procedures.

²²As we point out previously, if leading regions/states are not able to reinvent themselves, they can lose their leads, and/or exhibit slower patent growth. This is one potential explanation for our findings of β-convergence in leading regions/states. Regions need to constantly attract R&D activities related to emerging technological fields to keep their leads. As Suarez-Villa (2000, p. 175) points out, “[e]xisting knowledge [in an area] must… be supplemented with new ideas and creativity in order to come up with new discoveries and to sustain the pace of invention over the long term.” Log relative patent per capita is also found to be diverging in some states, e.g., Connecticut prior to 1941; Kansas after 1972.

²³The results indicate that shocks have permanent effects in over half of the regions and states. One limitation of the method we use is that if an incorrect number of breaks dates are included, wrong conclusions can be reached. For policy purposes, under rejection of the unit root null hypothesis is more problematic as an incorrect conclusion of a permanent impact (of a policy-induced shock) can lull policymakers into not taking actions to support state infrastructures for technology development, for example. Too few rejections (under rejection) of the unit root null hypothesis (conclude that shocks have permanent effects) will be reached if the true data generating process is a series containing only one break and two breaks are assumed in the estimation. To ensure robustness of our findings, we also performed unit root tests assuming one break in the intercept and trend. With the exception of Idaho, the results confirm those allowing for two breaks.

²⁴Knowledge spillover is typically measured using patent citation data. However, patent citation data are currently available only for patents granted starting 1975 (see Hall et al., 2001). Several papers have established that knowledge spillover is geographically mediated. For example, Jaffe et al. (1993) find that for patents issued in 1975 (1980), about 6–11% (10–14%) of the citations received up to 1989 are from the same state as the originating patent.

²⁵Each state's capital is used to measure (as the crow flies) distance and the location quotient is used for patent specialization (see e.g., Co, 2002; Feldman, 1994). The location quotient measures the concentration of state i's patent activity in industry j relative to the national level. The industry with the highest location quotient is state i's top patent specialization. Patents granted beginning 1963 are also classified according to “industry of use”. This USPTO data are used to tabulate each state's patent specialization between 1963 and 1997 (see Co, 2002 for details).

²⁶Note that R&D data are available according to funding and performing sectors. These sectors are the federal government, industry, colleges and universities, non-federal government, federally funded R&D centers and other non-profit organizations. We consider only the first three major sources below.

²⁷These data pertain to R&D performed by industry and are available every year starting 1963 (see http://caspar.nsf.gov/nsf/srs/IndRD/start.htm). This data set has the widest temporal coverage at the state level; the breakdown for the other three sectors is not available for this length of time (it is available every two years since 1987) so we use aggregate information below.

²⁸According to NSF (1999), state governments funded only 1% of total US R&D in 1965 and about 1.18% in 1995. Although state governments' direct financial contributions to R&D is insignificant, they play an important role in the invention catch-up and growth process via their investments on education, workforce training, infrastructure, etc.

²⁹The possibility that state i intensively engages in activities to attract invention-intensive activities during the same period is not ruled out. In fact, states have instituted technology-oriented economic development policies since the late 1970s; and we do not rule out the possibility that these also contributed to some of the structural breaks in log relative patent per capita identified in the 1980s.