Old World vs. New World: Evolution of Nobel Prize Shares

Transcription

1 Old World vs. New World: Evolution of Nobel Prize Shares Wolfgang Jank Bruce L. Golden Paul F. Zantek Department of Decision & Information Technologies The Robert H. Smith School of Business University of Maryland College Park, MD December 2, 2004 Abstract We study current and past trends in the geographic distribution of Nobel Prize awards. A polynomial-smoothing-spline analysis reveals trends that correlate with major events of the 20th century. The results demonstrate the rise of North America and the fall of Europe since the 1930 s. There is an indication that North America s share of Nobel Prizes will continue to increase in the near future whereas Europe s will continue to decline. Differences among European countries are discussed. Key words and phrases: Nobel Prizes; smoothing splines; curve-fitting Corresponding author. address: bgolden@rhsmith.umd.edu 1

2 1 Introduction The Nobel Prize is awarded to individuals who have made outstanding contributions to the benefit of humankind. The prize recognizes major achievements in chemistry, economics, literature, peace, physics, and physiology or medicine. The prize is an international recognition, as the founder of the prize, the late Alfred Nobel of Sweden, stipulated that in awarding the prizes no consideration be given to the nationality of the candidates, but that the most worthy shall receive the prize, whether he be Scandinavian or not. Nobel Prizes have been awarded in nearly every year since Crawford (1998) notes that during most of their existence Nobel Prizes have been regarded as the supreme reward for scientific achievement. Modis (1988) points out that countries and institutions pride themselves on the number of Nobel Laureates they can count, and some countries and individuals fiercely compete for the Nobel Prize. For instance, the goal of the Japanese government s Science and Technology Basic Plan adopted in the year 2000 is to strengthen investment in basic research so that Japan will win at least 30 Nobel Prizes in the next 50 years (European Commission (2003)). The United States currently leads the world in number of Nobel Prizes received. As of 2004, Americans have received 283 (or 36.8%) of the 770 prizes that have been awarded. A logistic growth model estimated by Modis (1988), however, forecasts that the number of prizes awarded to Americans will decline from 4.9 per year in the 1980 s to 2.9 per year in the year 2000 and just 0.2 per year in the year In addition, the model forecasts that the total number of prizes to be received by Americans throughout all of time is 283. Golden and Zantek (2004) use more complete data ( ) to show that this model systematically forecasts too few prize awards to Americans. A generalized-logistic-substitution analysis, also conducted by Modis (1988), concludes that America s annual share of Nobel Prizes reached its maximum of 50% in the 1970 s and will decrease monotonically in subsequent years. For instance, by the year 2000, the U.S. annual share is forecasted to be approximately 41%. In reality, America s share has increased, essentially continuously, over the past 100 years and exceeded 50% in each year during the period 2000 to Clearly, recent history illustrates that Modis s study forecasts too small of a share for the U.S. The U.S. has not always received such large annual shares. In the early twentieth century, most of the prizes were awarded to Western Europeans. In this article, we study recent and past trends in 2

3 the geographic distribution of Nobel Prizes. Our retrospective analysis reveals trends and changes in dynamics that correlate with major events of the twentieth century, such as World Wars I and II. 2 Nobel Selection Process The process of selecting Nobel Prize recipients is international in scope. The European Commission (2003) Third European Report on Science and Technology Indicators points out that the institutions responsible for evaluating and selecting Nobel Prize winners are entirely independent of the Swedish and Norwegian governments as well as the Nobel Foundation. This same report also suggests that the autonomy of the prize-awarding institutions is of crucial importance to the objectivity of their prize decisions, and hence also to the prestige of the Nobel Prize. Each year, thousands of individuals from around the globe are invited to nominate candidates for the Nobel Prize. The merits of the nominees are evaluated by Nobel Committees with the assistance of international experts. As such, the nomination and evaluation of candidates are international assessments. After the Nobel Committees select the prize recipients, their recommendations are presented to the prizeawarding institutions for a final vote. 3 Nobel Prize Shares We use the Nobel Foundation website ( to obtain the nation of citizenship of each of the 758 individuals who received a Nobel Prize during the period We compare the success of the five groups of nations listed in Table 1. Of these five groups, three are comprised of strong economies separated by geographic location (North America, Europe, and the Asia-Pacific); the remaining two groups consist of economies in transition and developing economies, respectively. Investigating trends in the distribution of Nobel Prizes is complicated by the fact that the annual number of prizes awarded varies over time. For instance, only six prizes were awarded in 1901 whereas 11 prizes were awarded in To facilitate comparison across time periods, we measure each group s success by its share of prize awards (defined as the percentage of the Nobel Prizes that the group received) as opposed to the number of prizes it received. Figure 1 displays the annual shares of Europe and North America, the groups with the two largest shares. The annual share varies substantially from one year to the next, making it somewhat difficult to view trends. An alternative is to consider the cumulative share of prizes. To define 3

4 this measure, let N(t) denote the total number of Nobel Prizes awarded by time t (for instance, N(1901) = 6 and N(2003) = 758), and let N i (t) be the cumulative number of Nobel Prizes awarded to group i (= 1, 2,..., 5) by time t. Then, group i s cumulative share of Nobel Prizes as of time t is y i (t) = N i (t)/n(t) t = 1901, 1902,..., (1) The cumulative share in (1) measures group i s performance up through time t. Figure 2 presents the cumulative shares of the two largest share groups. We model each group s cumulative share of Nobel Prizes, y i (t), by a polynomial smoothing spline. The Appendix discusses the smoothing-spline model and the methodology for fitting it to the observed cumulative shares y i (1901), y i (1902),..., y i (2003). One of our goals is to study changes over time in the Nobel Prize shares. Notice that y i (t) gives the position of the cumulative share but does not describe how fast this share is changing. Attributes that we may associate with a change in position are velocity (or speed) and acceleration. Velocity and acceleration, respectively, are the first and second derivatives of y i (t) (with respect to t), which may be estimated from the fitted smoothing spline model. The polynomial smoothing splines provide excellent fits to the observed cumulative shares of each of the five groups of nations. Figure 2 displays the fitted splines for each of the groups. We see from Figure 2 that the cumulative shares have changed substantially over the past century; in particular, the geographic diversity of the Nobel Laureates has increased. In 1901 (the first year of the prize), all of the prizes were awarded to Europeans. Europe s cumulative share has decreased substantially since then, reaching 49% at the end of Figure 2 also shows that much of Europe s share has been captured by North America. North America s share has steadily increased over time, growing from less than 10% in the early 1900 s to 36.4% in A smaller portion of Europe s share has been taken by the three remaining groups: developed Asian-Pacific economies, economies in transition, and developing economies. The shares of these latter three groups have increased only gradually in recent years. Figure 2 also reveals that the shares of the groups have changed at nonconstant rates. This is perhaps not surprising, given the changes these nations have experienced. Major events such as wars are certain to have affected the ability of many nations to compete for Nobel Prizes. The rate at which the cumulative share has changed can be determined vaguely from Figure 2, but it is approximated more objectively by the first derivative of the fitted smoothing spline. Figure 4

5 3 presents the first derivatives (velocities) of each of the five groups. Consistent with Figure 2, Figure 3 illustrates that the velocity of Europe s cumulative share was negative for the entire 20th century while North America s velocity was always positive. The velocities have changed noticeably over time. Europe experienced a sustained decrease in velocity during the period Explanations for this decrease might be the impact of World War I, the subsequent rise of the nationalistic party and the Third Reich in Germany, the Holocaust, and World War II. These events emptied Europe, in general, and Germany, in particular, of many prominent minds. During this same time period ( ), North America experienced an increase in velocity. Possible explanations for this increase include the growth of the U.S. economy, population, and the fact that the U.S. was less devastated by the world wars than was Europe. After the end of World War II, Europe enjoyed a very flourishing time. The start of the Marshall Plan and the rebuilding of the individual countries is typically associated with the beginning of a very prosperous time for Europe. We observe from Figure 3 that Europe s share velocity increased beginning in the 1950 s. While Europe was re-gaining ground, its gain came naturally along with a loss for its competitors, especially North America. Figure 4 presents the second derivatives (accelerations) of each of the five groups. During the late 1980 s, the share acceleration of Europe in Figure 4 changes sign (from positive to negative) and faces downward into the early 21st century. This, of course, is accompanied by a decrease in Europe s share velocity. Since a change in the velocity s sign from negative to positive must be preceded by a change in the acceleration s sign from negative to positive, it appears that Europe s cumulative share will continue to decline in the near future. Similar reasoning suggests that North America will continue to enjoy an increase in its cumulative share. 3.1 Comparison of European Countries Of course, Europe is hardly monolithic. In Figures 5, 6, and 7, we display the fitted smoothing splines, velocities, and accelerations for France, Germany, the U.K., as well as the U.S. The recent trends and near-term forecasts are more upbeat for the U.K. than for France and Germany, although they are bleak in comparison to the U.S. Figure 5 shows that, consistent with the overall trend in Europe, the cumulative shares of France, Germany, and the U.K. have been falling over the last two decades or so. However, it is interesting to note that these three countries started the 20th century quite differently. While France 5

6 and Germany held the majority of shares at the beginning of the 20th century and experienced a decrease from there, the U.K. s share increased from zero throughout the first half of the century. We may further differentiate among the three countries when considering recent trends. While the velocities of France and Germany are negative and face downward into the early 21st century (accompanied by negative and downward-sloping accelerations), the U.K. s velocity and acceleration face upward. In fact, the U.K. s positive share acceleration, seen in Figure 7, suggests that some cautious optimism might be justified with respect to near-term success for Great Britain and Northern Ireland. This mild optimism is in stark contrast to the near-term expectations for France and Germany. Why has Europe lost so much of its share? Several sources, including the European Commission (2003), Liu et al. (2003), and The Economist (2002), make the connection between Nobel Prizes and world-class universities. This connection may be illustrated by reviewing the recent past. From 1991 through 2003, there have been 73 U.S. Nobel Prize recipients. About 50 of these were affiliated with doctoral universities in the U.S. at the time of the award announcement. Approximately 75% of these universities are listed as Top 30 doctoral universities by U.S. News & World Report (2003); nearly all of them are listed in the Top 50. A recent ranking of top world universities is provided by Liu et al. (2003). Of the top 10 universities world-wide, eight are in the U.S. and two are in the U.K. Cambridge is fifth and Oxford is ninth. Of the top 20 universities worldwide, 15 are in the U.S., four are in the U.K., and one is in Japan. In a report prepared by the European Commission (2003), European universities that achieve the greatest impact with respect to citation impact scores are ranked. In Table 2, we combine the results from this ranking with those from Liu et al. (2003). For each of the two rankings of European universities, the number of universities in the top 20 from each of the three countries (the U.K., Germany, and France) is presented. In both rankings, Cambridge and Oxford are at the very top. Given that both rankings are current, Table 2 might help explain why the U.K. has outperformed Germany which, in turn, has outperformed France in the last decade or so. In addition, it may be that the U.K. outperformed other European nations because a common language connects the U.K. with the U.S. 6

7 4 Concluding Remarks Writing in The Washington Post, Josef Joffe (2003), publisher and editor of the German newspaper Die Zeit, argues that it is brains... that have catapulted the United States to the top of the Nobel Prize roster and turned Harvard et al. into the world s greatest universities. Joffe contends that the United States s openness to researchers from all over the world has attracted considerable brainpower over the last decades, which is in contrast to many European countries where origin often still matters more than achievement. Following the events of September 11, however, the U.S. raised its barriers to legal entry in an attempt to improve homeland security. One result is that the number of student visas issued by the U.S. has declined in recent years, decreasing from 293,357 in academic year to just 214,331 in academic year (a 27 % decline). Joffe suggests that this shift may have a negative impact on future U.S. intellectual output. In light of this, the U.S. should examine its current policies with a view toward granting entry to talented individuals while simultaneously ensuring the security of the U.S. homeland. Acknowledgements The authors thank Alexander H.G. Rinnooy Kan for pointing out the second reference. 7

8 Appendix: Smoothing Spline Model Suppressing the group identifier i, the polynomial smoothing spline model of cumulative share y(t) for any particular group is f(t) = β 0 + β 1 t + β 2 t β p t p + 12 l=1 β pl [(t τ l ) + ] p, (2) where τ 1,..., τ 12 are constants placed every ten years (τ 1 = 1901, τ 2 = 1911,..., τ 11 = 2001) and at τ 12 = 2003, and u + = ui [u 0] denotes the positive part of the function u. Although the coefficients β 0, β 1,..., β p, β p1, β p2,..., of (2) can, in principle, be estimated by ordinary least squares, Ruppert et al. (2003) point out that this leads to a very rough fitted function f. To avoid this, define the following roughness penalty to measure the extent of departure from a straight line: P m = {D m f(t)} 2 dt, (3) where D m f(t) denotes the mth derivative (with respect to t) of the function f(t). When m = 2, for instance, P m is the integrated squared second derivative of f(t), which is sensitive to curvature in the function f(t). Fitting a polynomial smoothing spline to the observed cumulative shares y(1901), y(1902),..., y(2003) involves finding the coefficients β 0, β 1,..., β p, β p1, β p2,... of (2) that minimize the penalized residual sum of squares Q λ,m = λp m t=1901 {y(t) f(t)} 2, (4) where the smoothing parameter λ 0 controls the trade-off between the data-fit, as measured by the summation on the right-hand side of (4), and the local variability of the function f, measured by the roughness penalty P m in (3). Using m = 2 in (4), for instance, leads to the commonly-used cubic smoothing spline, a polynomial of degree three. More generally, a smoothing spline of order m is a polynomial of degree p = 2m 1. Notice that the order m of the roughness penalty P m in (3) controls the smoothness of the derivatives of f. For instance, while using m = 2 controls the curvature of the function f, it only controls the slope of its first derivative, D 1 f. Thus, Ramsay and Silverman (1997) recommend using m = q + 2, where q denotes the order of the highest derivative that is desired. In our application, we are interested in derivatives of order up to q = 2, so we use m = 4. The smoothing parameter λ is typically chosen to achieve a good data fit. We use λ = 50, and Figure 2 shows that the resulting models fit the data very well. We fit the smoothing splines using the software R (2003). 8

9 References Crawford, E. (1998). Nobel: Always the Winners, Never the Losers. Science, 282: European Commission (2003). Third European Report on Science and Technology Indicators. Directorate-General for Research, Luxembourg. (Available online at Golden, B. and Zantek, P. (2004). Inaccurate Forecasts of the Logistic Growth Model for Nobel Prizes. Technological Forecasting and Social Change, 71(4): Joffe, J. (2003). Locking Out the Brainpower. The Washington Post, November 23, Liu, N., Liu, L., Cheng, Y., and Wan, T. (2003). Academic Ranking of World Universities. Retrieved November 21, 2003 from Shanghai Jiao Tong University, Institute of Higher Education Web Site:(ed.sjtu.edu.cn/ranking.htm). Modis, T. (1988). Competition and Forecasts for Nobel Prize Awards. Technological Forecasting and Social Change, 34(2): R (2003). The R Project for Statistical Computing. Ramsay, J. O. and Silverman, B. W. (1997). Functional Data Analysis. Springer-Verlag, New York. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003). Semiparametric Regression. Cambridge University Press, Cambridge. The Economist (2002). The Ruin of Britain s Universities. November 16, 2002: U.S. News & World Report (2003). America s Best Colleges: Best National Universities - Doctoral. September 1, 2003:

10 Table 1: United Nations Grouping of Nations According to Economic Strength* Group Countries 1 Developed North American Economies US and Canada 2 Developed European Economies all of Europe except for European transition economies (see below) 3 Developed Asian-Pacific Economies Japan, Australia, and New Zealand 4 Economies in Transition Central and Eastern European transition economies (Albania, Bulgaria, Czech Republic, Hungary, Poland, Romania, Slovakia, and successor states of the Socialist Federal Republic of Yugoslavia), the Baltic States (Estonia, Latvia, and Lithuania), the Commonwealth of Independent States (Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kyrgyzstan, Republic of Moldova, Russian Federation, Tajikistan, Turkmenistan, Ukraine, and Uzbekistan) 5 Developing Economies Africa, Asia and Pacific (excluding any countries mentioned above), Latin America, and the Caribbean * List of Country Groupings and Sub-groupings for the Analytical Studies of the United Nations World Economic Survey and other UN Reports. Retrieved November 2003 from the United Nations Online Network in Public Administration and Finance Web Site: ( 10

11 Table 2: Where are the Top European Universities? Study U.K. Germany France #1 #2 Liu et al Cambridge Oxford European Commission Report Cambridge Oxford 11

12 Annual Shares North America 2 Europe Figure 1: Annual Shares: Annual Shares of Europe and North America. 12

13 Cumulative Shares North America 2 Europe 3 Asia Pacific 4 Transitional 5 Developing Figure 2: Polynomial Smoothing Splines Fitted to Cumulative Shares: The graph displays the smoothing spline for each group of nations identified in Table 1. For Europe and North America, the figure also presents the observed cumulative shares. 13

14 Share Velocity North America 2 Europe 3 Asia Pacific 4 Transitional 5 Developing Figure 3: Velocity of Cumulative Share: The graph displays the first derivatives (velocities) of the smoothing splines in Figure 2. 14

15 Share Acceleration 1 e 03 5 e 04 0 e+00 5 e 04 1 e 03 1 North America 2 Europe 3 Asia Pacific 4 Transitional 5 Developing Figure 4: Acceleration of Cumulative Share: The graph displays the second derivatives (accelerations) of the smoothing splines in Figure 2. 15

16 Cumulative Shares US 2 France 3 Germany 4 UK Figure 5: Polynomial Smoothing Splines Fitted to Cumulative Shares of Selected Nations 16

17 Share Velocity US 2 France 3 Germany 4 UK Figure 6: Velocity of Cumulative Share for Selected Nations: The graph displays the first derivatives (velocities) of the smoothing splines in Figure 5. 17

18 Share Acceleration 4 e 04 2 e 04 0 e+00 2 e 04 4 e 04 1 US 2 France 3 Germany 4 UK Figure 7: Acceleration of Cumulative Share for Selected Nations: The graph displays the second derivatives (accelerations) of the smoothing splines in Figure 5. 18