Mikael Svensson
email: mikael.svensson@esi.oru.se

Economic Upturns are good for Your Heart but Watch out for Accidents: A Study on Swedish Regional Data 1976-2005

Keywords: E32 -Business Fluctuations|Cycles &lt, E3 -Prices, Business Fluctuations, and Cycles &lt, E -Macroeconomics and Monetary Economics, I12 -Health Production: Nutrition, Mortality, Morbidity, Disability, etc. &lt, I1 -Health &lt, I -Health, Education, and Welfare Determinants of Health, Mortality, Unemployment Determinants of Health, Mortality, Unemployment JEL codes: E32, I12

This paper explores the relationship between the regional unemployment rate and total and cause-specific mortality in Sweden during 1976-2005. Overall mortality is unrelated to changes in the unemployment rate, while the biggest cause of death (heart disease) decreases when the unemployment rate decreases. At the same time other accidents, including job-related accidents, increase when the unemployment rate decreases. Swedish evidence provides no support for the US research findings that short-term increases in the unemployment rate are bad for your health in general.

I. Introduction

In a series of papers in the 1970s [START_REF] Brenner | Economic changes and heart disease mortality[END_REF][START_REF] Brenner | Trends in alcohol consumption and associated illnesses. Some effects of economic changes[END_REF][START_REF] Brenner | Mortality and the national economy. A review, and the experience of England and Wales[END_REF] used time-series evidence and found that there was a fluctuation in the trend of decreasing mortality rates that could be explained by changes in the business cycle. He found that there was an even larger decrease in mortality rates during economic upturns. However, other authors' argued that Brenner had some flaws in his analysis. Correcting for these flaws, a time-series approach by [START_REF] Mcavinchey | A Comparison of Unemployment, Income and Mortality Interaction for five European Countries[END_REF] reached an opposite conclusion to Brenner.

More recently, there has been a growing series of papers that have studied the relationship between short-term changes in the unemployment rate and total and causespecific mortality, using mostly panel-data techniques. In the panel data approach different economic developments in each region are compared to changes in mortality rates in the same region. Hence, the effect of business cycles on the mortality rate is measured by exploring within-unit changes compared to other within-unit changes, an approach that in many cases is beneficial in attempts to control for omitted variable bias. It began with an important paper by [START_REF] Ruhm | Are Recessions Good for your Health?[END_REF] who used state level data in the US and found that mortality actually increased in economic upturns (pro-cyclical relationship). In a follow-up [START_REF] Ruhm | Good times make you sick[END_REF] used individual level data and confirmed the finding of the aggregate state-level study that good times make you sick (or make you die). Other authors have followed and using regional data the same pro-cyclical relationship has been documented for most causes of death in Germany [START_REF] Neumayer | Recessions lower (some) mortality rates: evidence from[END_REF], Spain (Tapia Granados, 2005) and France [START_REF] Buchmueller | Unemployment and Mortality in France, 1982-2002[END_REF]. In a more recent paper [START_REF] Ruhm | A Healthy Economy Can Break Your Heart: NBER Working Paper[END_REF] looked specifically at mortality in acute myocardial infarction (heart attacks), which is one of the main causes of death, and found that a one percentage point decrease in the unemployment rate increased heart attack mortality by 1.3%. The pro-cyclical relationship has also been documented using cross-country data from 23 OECD countries [START_REF] Gerdtham | Deaths Rise in Good Economic Times: Evidence From the OECD[END_REF].

These pro-cyclical trends were also found in recent time-series applications by Tapia Granados (2004) using Swedish data for the period 1800 to 1998 (even though he found that the effect faded over the last 50 years). In another paper Granados (2005), using time-series techniques again, found a pro-cyclical pattern on US data for the period 1900 to 1996. Most papers in the literature use the unemployment rate as the only proxy for the business cycle, but Granados (2005) argued that it cannot for certain be assumed to be true that the unemployment rate is the best proxy for the business cycle. Hence, he tested three other proxies for the business cycle, but found the same qualitative results as using the unemployment rate.

There are two exceptions to the consensus that is beginning to emerge from the literature cited above, but they also differ in some respects, making them difficult to directly compare with the pro-cyclical findings. One paper by [START_REF] Gerdtham | Business cycles and mortality: results from Swedish microdata[END_REF], using individual level data from Sweden, studied whether national business cycle indicators were related to the probability of death. In many cases they found no such relationship, but for males they found a counter-cyclical relationship for four business cycle indicators. 1 In a recent paper [START_REF] Svensson | Do not go breaking your heart: Do economic upturns really increase heart attack mortality?[END_REF] uses the same statistical approach as the papers that report a pro-cyclical relationship, but finds that there is no pro-cyclical relationship between incidence, mortality and lethality in heart attacks and the business cycle in Swedish regions.

Instead, a counter-cyclical relationship is found for individuals of prime-working age, i.e. between 20 and 49. There are also contrasting results regarding the association between the unemployment rate and some cause-specific mortality rates. As an example, in contrast to his overall findings, [START_REF] Ruhm | Are Recessions Good for your Health?[END_REF] found that suicides increased when the unemployment rate 1 The unemployment rate was not one of these indicators, but was rather insignificant in all estimations. increased. However, a paper by Andrés [START_REF] Rodriguez | Income inequality, unemployment, and suicide: a panel data analysis of 15[END_REF] specifically looking at determinants of suicide rates does not show a statistically significant effect in the full model.

The goal of this analysis is to further explore the relationship between mortality and the unemployment rate in Sweden, extending previous analyses to a longer time period and focusing on ten specific causes of death. The two Swedish studies finding contradicting results in the literature are not directly comparable to the studies documenting a pro-cyclical relationship. [START_REF] Gerdtham | Business cycles and mortality: results from Swedish microdata[END_REF] use business cycles that are national in scope and focus on initial surveys taking place from 1980 to 1986. [START_REF] Svensson | Do not go breaking your heart: Do economic upturns really increase heart attack mortality?[END_REF] uses the same regional fixed approach as [START_REF] Ruhm | Are Recessions Good for your Health?[END_REF][START_REF] Ruhm | Good times make you sick[END_REF], [START_REF] Neumayer | Recessions lower (some) mortality rates: evidence from[END_REF] and [START_REF] Gerdtham | Deaths Rise in Good Economic Times: Evidence From the OECD[END_REF], but instead concentrates on a more detailed study of heart attacks only.

The research field exploring links between health and economic conditions, lifestyles and socioeconomic status, is an important one with major public health interests. As an example, [START_REF] Thornton | Estimating a health production function for the US: some new evidence[END_REF] showed that lifestyles and socioeconomic status are far more important determinants of public health in the US compared to more medical care utilization.

Hence, health care policy should not only be about medical care provision.

The specific analysis in this paper is also important for at least three main public policy reasons. (1) To be used in a broader societal perspective on changes in the unemployment rate. Unemployment has direct financial effects, but also has indirect effects on e.g. property crime rates [START_REF] Edmark | Unemployment and Crime: Is There a Connection?[END_REF]. The latter type of effects, which could include health effects, are important to analyze so that public policy on, e.g. labour market issues may take all the relevant effects into consideration. (2) If it is found that mortality, or some cause-specific mortality, is closely associated with the business cycle, this can serve as an instrument in public health and health care planning, e.g. increasing resources for heart diseases in economic upturns or adjusting road safety regulations to different traffic demands etc. (3) To increased/decreased risk of heart disease related to the business cycle, and, as mentioned above, as a possible input in a broader health care policy.

The analysis in this paper reveals that no robust relationship can be found between total, age or gender-specific mortality and the business cycle. The ten specific causes of death indicate that this is reasonable, considering that the effects are different for different causes.

Two robust results are found in the cause-specific analysis. Primarily Other Accidents, including job-related fatalities, significantly increase in economic upturns, while Heart Disease mortality, the most common cause of death in Sweden as well as in many other developed countries, tends to decrease in economic upturns.

The rest of the paper is structured as follows. Section two provides a brief background to the expected mechanism between mortality and the business cycle. The third section describes the data and the methods used in the empirical analysis, which is conducted in the fourth section. The last section concludes the paper with a discussion.

II. Mechanisms through which the business cycle may affect mortality

There are several mechanisms through which the economy may affect the mortality rate and some of them are listed below.

Stress:

In good times unemployment decreases and this may imply less psychosocial stress due to less economic insecurity [START_REF] Fenwick | The Macroeconomic Context of Job Stress[END_REF]. However, stress may also increase in good times for the average individual if overtime becomes more frequent and jobstress increases. Hence, stress might increase in bad times for some and in good times for others. It is generally known that stress is a risk factor, especially for cardiovascular [START_REF] Black | Stress, inflammation and cardiovascular disease[END_REF][START_REF] Brenner | Unemployment and health in the context of economic change[END_REF][START_REF] Elisaf | The treatment of coronary heart disease: an update -Part 1: An overview of the risk factors for cardiovascular disease[END_REF][START_REF] Fenwick | The Macroeconomic Context of Job Stress[END_REF][START_REF] Krantz | EFFECTS OF PSYCHOLOGICAL AND SOCIAL FACTORS ON ORGANIC DISEASE: A Critical Assessment of Research on Coronary Heart Disease[END_REF][START_REF] Pickering | Behavioral Cardiology -Has Its Time Finally Arrived?[END_REF].

Unhealthy behavior:

Using a large individual level dataset over a period of 11 years in the US has helped to show that binge drinking increases in recessions [START_REF] Dee | Alcohol abuse and economic conditions: Evidence from repeated crosssections of individual-level data[END_REF]. The same result is found using regional data for Finland [START_REF] Johansson | Alcohol-related mortality, drinking behavior, and business cycles: Are slumps really dry seasons?[END_REF]. By contrast, Ruhm (2005) and [START_REF] Ruhm | Does drinking really decrease in bad times?[END_REF] have shown that binge drinking and smoking increase during economic upturns. [START_REF] Ruhm | Does drinking really decrease in bad times?[END_REF] argue that this is mainly due to heavy drinkers consuming less in recessions and not movements into and out of drinking in general.

They maintain that this is to some extent an income effect leading to less drinking in shortterm economic downturns when unemployment increases. That behavior such as binge drinking is important for mortality rates even in the short-run was documented as early as during WWII when alcohol-related mortality decreased quickly when alcohol consumption decreased, see e.g. [START_REF] Johansson | Alcohol-related mortality, drinking behavior, and business cycles: Are slumps really dry seasons?[END_REF] and [START_REF] Ruhm | Does drinking really decrease in bad times?[END_REF].

Health investments: Longer working hours in short-term economic upturns could make it more costly for individuals to invest in health enhancing exercises and to eat healthier food, which might be more time-intensive in preparation [START_REF] Chou | An economic analysis of adult obesity: results from the Behavioral Risk Factor Surveillance System[END_REF][START_REF] Ruhm | Does drinking really decrease in bad times?[END_REF]. However, once again there is some conflicting evidence; it has been found that better economic conditions produce a decrease in BMI in Finland [START_REF] Böckerman | Does a Slump Really Make you Thinner? Finnish Micro-Level Evidence 1978-2002[END_REF]. There is also an indication that economic upturns, and the longer working hours that result from them, lead to lower investments in sleep time [START_REF] Biddle | Sleep and the Allocation of Time[END_REF], which in turn is linked to higher levels of stress and increases in psychological illness [START_REF] Sparks | The effects of hours of work on health : A meta-analytic review[END_REF].

Further, in good economic times it is also possible that traffic intensity increases and hence the risk of traffic-related mortality. The same link could be argued to potentially exist between job-related fatalities and the business cycle. In good economic times there is more Given that the evidence above indicates that there are several mechanisms linking the business cycle and mortality, and they might move in opposite directions, it becomes an empirical issue to determine which effects dominate, if any. Finally, it should be noted that the effects described above primarily concern the health effects of short-term economic upturns or downturns. In the long-term economic growth and innovation are major causes of increased health and longevity. The difference compared to the short-term impact is that longterm growth is the result of technological improvements that are not associated with more intensive use of labor and health inputs. As an example it has been estimated that 50 to 70 percent of the increased survival in cardiovascular disease between 1984 and 1999 may be explained by improved medical technology [START_REF] Cutler | Intensive Medical Care and Cardiovascular Disease Disability Reductions: NBER Working Paper[END_REF]. Topel and Murphy estimate that the economic value of e.g. medical research, possibly due to long-term economic growth, is enormous. An example, the value of reduced heart disease mortality in the US was worth around $1.5 trillion per year over the period 1970 to 1990.

III. Data and Method

To estimate the short-term impact of business cycle fluctuations on mortality, I use aggregate data for all 21 Swedish regions, all of which are also independent providers of health care.

Data covers these 21 regions between 1976 and 2005, giving a balanced sample of 21 cross section units followed for 30 years and a total number of 630 observations. The main dependent variable of interest is the natural log of the mortality rate per 100,000 individuals in each region. In addition to exploring the mortality for males and females and for different age categories, I will also look at ten cause-specific mortality rates, for (ischemic) heart disease,

ln jt t jt jt j j jt y u R R T e = + + + + + x , (1)
where y jt is the mortality rate in region j at time t, and t is a year-specific effect and R j is the regional-specific intercept. R j •T is a regional specific time trend. The business cycle proxy is u, which is the regional unemployment rate from Statistics Sweden (SCB, 2005). The unemployment rate is measured as the unemployed as a share of the labor force. In contrast to most other developed countries, Sweden does not count students actively looking as unemployed. Using the unemployment rate as a business cycle proxy is most common in the literature [START_REF] Gerdtham | Deaths Rise in Good Economic Times: Evidence From the OECD[END_REF][START_REF] Neumayer | Recessions lower (some) mortality rates: evidence from[END_REF][START_REF] Ruhm | A Healthy Economy Can Break Your Heart: NBER Working Paper[END_REF]. Finally in equation ( 1)

x is a vector of other covariates and jt e is the error term.

Within-region changes in the variables are calculated in the fixed-effects panel data model and these are then compared region-wise to estimate the particular impact of the business cycle fluctuations on mortality. The main benefit of the fixed-effects model as described in equation ( 1) is that it can control for omitted variable bias in a way that a crosssection or time-series model is not capable of doing. In equation (1) R j controls for factors that differ among regions (such as lifestyles), but do not change over time, and t controls for factors that change over time in the same way in all regions, such as improved medical technology or new and more efficient pharmaceuticals. R j •T controls for changes over time, but allows these changes to be different, and/or occur at different times, e.g. if new medical technology is introduced earlier in some regions.

Finally in this section descriptive statistics of the variables and their sources are found in [Insert Figure 1 here] Other covariates included are the shares of the young and elderly, which are assumed to have negative and positive impacts on mortality respectively. This is included to control for different age-structures in the region, considering that the dependent variable is not ageadjusted. 2 Migration may be potentially important in these type of studies [START_REF] Ruhm | A Healthy Economy Can Break Your Heart: NBER Working Paper[END_REF] since regions that have a more positive business cycle impact may attract more individuals in pursuit of better employment opportunities that might be e.g. healthier than the average. The share of foreigners in each region may be important due to evidence of health gradients et al., 2006) even though they tend to be lower in Sweden compared to other countries [START_REF] Gerdtham | Measuring Income-Related Health Inequalities in Sweden[END_REF][START_REF] Van Doorslaer | Income-related inequalities in health: some international comparisons[END_REF].

IV. Results

Before studying cause-specific mortality rates, Table 2 below begins by showing the results of exploring the business cycle effect on total, male and female mortality rates.

[Insert Table 2 here] The results when using three different specifications are shown. The first specification includes year dummies and the unemployment rate as independent variables. The second specification adds the other covariates, and the third specification estimates the full equation

(1), including regional specific time trends as well. Generally, no robust relationship can be found. In the more simplistic specifications there are some indications that female mortality decreases when the economy weakens (a higher unemployment rate is related to a decrease in the mortality rate). But this is not significant in the full model. The age-variables behave as expected; an increasing share of young individuals decreases mortality, while an increasing share of elderly increases mortality. Somewhat surprisingly, a higher share of non-Swedish born individuals is associated with a decrease in mortality in some specifications, albeit not significant in the full model. As was discussed in section two, there are some mechanisms likely to increase mortality, and some likely to decrease mortality, in good times. Hence, the non-robust and weak relationships in Table 2 are not particularly surprising. Considering the weak results, I move on to age-and cause-specific mortality.

[Insert Table 3 For Heart Disease and Other Accidents I also perform some dynamic analysis, in which I use the average unemployment rate in each region 3 years prior to the year of interest regarding mortality. I also check for the very short-term impact in this model by calculating the deviation in the employment rate in year t compared to the average employment rate in year t-1 to t-3. This is similar to the approach to dynamic analysis in [START_REF] Ruhm | A Healthy Economy Can Break Your Heart: NBER Working Paper[END_REF], an argument for which is that changes in the business cycle will affect health in many respects and not only in the short-run. Further, there is a correlation between the unemployment rate in year t and the unemployment rate in the preceding years, which means that the analysis in Table 2 might pick up some of the medium-term trends.

[Insert Table 4 here] The results in Table 4 indicate that there is an impact of the average unemployment rate 3 years prior to the current year, and in addition to the short-term impact. that it is both a very short-term impact and a short/medium-term relationship.

Hence, the results in the paper indicate that the pro-cyclical results based on US, German and Spanish data cannot be taken to be universally true in other settings. A countercyclical result has also been documented regarding alcohol-related mortality in Sweden's neighbour Finland [START_REF] Johansson | Alcohol-related mortality, drinking behavior, and business cycles: Are slumps really dry seasons?[END_REF]. The same has been found regarding general health in Finland, where BMI increases during economic downturns [START_REF] Böckerman | Does a Slump Really Make you Thinner? Finnish Micro-Level Evidence 1978-2002[END_REF]. Other possible explanations for the contrasting results in Sweden might be that large parts of Sweden have a very low population density, and e.g. the strong effects of increased traffic fatalities due to economic upturns as documented in the US (Granados, 2005;[START_REF] Ruhm | Are Recessions Good for your Health?[END_REF], cannot be seen to be significant for Sweden in this paper. There are simply no congestion effects, with increased accidents, on most roads in Sweden in economic upturns. However, this cannot explain the opposite and significant effect on Heart Disease found in this paper.

A potential explanation can be found in the paper by [START_REF] Gerdtham | Deaths Rise in Good Economic Times: Evidence From the OECD[END_REF], who find that the pro-cyclical effect on OECD countries is weaker in countries with extensive social welfare systems and more rigid labor markets. Compared to the US, Sweden certainly has more of a social welfare system and rigid labor markets. However, the same results as found in the US have also been documented in Germany and France [START_REF] Buchmueller | Unemployment and Mortality in France, 1982-2002[END_REF][START_REF] Neumayer | Recessions lower (some) mortality rates: evidence from[END_REF], which are also countries with rigid labor markets and "social-democratic" Considering the magnitude of the results, a one percentage point lower unemployment rate decreases Heart Disease mortality by approximately 1% and increases Other Accidents by 13.9%. 4 An economic estimate of the effect may be obtained by monetizing this in terms of the number of fatalities and using the value of a statistical life year (VSLY), or the value of a statistical life (VSL) [START_REF] Mishan | Evaluation of Life and Limb: A Theoretical Approach[END_REF][START_REF] Schelling | The Life You Save May Be Your Own[END_REF][START_REF] Thédié | Economic Aspects of Road Accidents[END_REF]. 5 In frequencies the mean annual national number of deaths in (ischemic) heart disease between 1976 and 1996 was 28,705 (SCB, 2006a). A decrease of 1% corresponds to 287 reduced deaths. Monetizing 287 reduced deaths using a recent US estimate of VSLY of $100,000 [START_REF] Viscusi | The Value of a Statistical Life: A Critical Review of Market Estimates Throughout the[END_REF], as a lower bound estimate, puts this at $28.7 million. Using a recent estimate of Swedish VSL [START_REF] Hultkrantz | The value of improved road safety[END_REF] introduction, how a broader societal concept of unemployment may be calculated. With unemployment comes not only financial loss, but an increase in heart-related mortality and other effects as well, such as increased property crime rates [START_REF] Edmark | Unemployment and Crime: Is There a Connection?[END_REF]. This is important for public policy to take into consideration when evaluating the labour market and labour market policy.

It is also sometimes argued that national accounts should be extended to include environmental values that might be destroyed in economic production, e.g. called green national accounts, or that a total economic wealth of nations should include estimates of natural capital, see e.g. The World Bank (2006). However, taking such steps would logically also have to lead to including monetized health effects of long-term growth. As in the results reported here, or as e.g. [START_REF] Cutler | Intensive Medical Care and Cardiovascular Disease Disability Reductions: NBER Working Paper[END_REF] have shown, longevity is related to investments in medical care that has tremendous value in itself. This implies that we underestimate the true value of long-term economic growth, and monetized health improvements included in national accounts would indicate even larger growth rates than those reported in regular national accounts.

Reiterating further the policy relevance discussed in the introduction, the results can be summarized by saying that an increase in the unemployment rate may be regarded as being related to an increase in health care demand for heart-related problems. Hence, if budget issues are a concern in recessions, the results here indicate that it is important not to cut back on health care related to heart diseases; rather the opposite, to plan for higher demand in weaker economic times. Further, in good economic times it will be beneficial to improve jobrelated safety, or to increase monitoring of newly employed workers, who have less experience and might be a reason for some of the increase in job-related fatalities in economic upturns [START_REF] Breslin | Trial by fire: a multivariate examination of the relation between job tenuer and work injuries[END_REF]. (SCB, 2005(SCB, , , 2006c(SCB, , , 2006a)). Number of observations are 630 for all variables except cause-specific mortality rates where the observations number 441. Data on mortality rates are mean values among the regions and not weighted for population, which mean that the figures do not necessarily correspond to national data (which are in fact lower). -0.107 ** -0.088 ** Notes: Two-tailed tests significance levels: *** 0.01, ** 0.05, * 0.10, based on robust std. errors. Other covariates included in the model, but not shown here. The 3-year prior unemployment rate refers to the average unemployment rate in year t-3 to t-1 where t is the survey year. Short-term impact refers to the deviation of the unemployment rate during the survey year compared to the average for the 3-year priors to the survey year.

F

  element of knowledge for potential public health information, e.g.

  and potentially at a faster pace, so job-related accidents, also with fatal outcomes, might increase.

  , traffic accidents, influenza, cancer, two different alcohol-related mortality rates, falling accidents and finally "other accidents", including many types of jobrelated fatalities. The full model to estimate in the paper is:

  Exactly why the results differ in the Nordic countries (Sweden, and evidence of it in Finland as well) needs further research.

  Figures

Table 1 .

 1 The mean mortality per 100,000 individuals is 1,125 over the full time period. There was a decrease in the mortality during the time period 1976 to 2005. In 1976 the mortality was 1,101 per 100,000, which decreased to 1,060 per 100,000 in 2005. The mortality rate also varied significantly between the regions; in 2005 the mortality rate was 815 per 100,000 in the region of Uppsala, close to the capital region of Stockholm, compared to 1,263 per 100,000 in the rural and northern region of Västernorrland. The unemployment rate, on a national level, increased during the time period from 1.6% in 1976 to 6% in 2005. This time period is also of particular interest to study, since it also contains a time period with unusually large business cycle swings, e.g. from 1990 to 1996 the unemployment rate increased from approximately 1.6% to 8%. Figure1below shows the unemployment rate over the time period 1976 to 2005, as well as cause-specific mortality in heart disease and cancer, with data from 1976 to 1996.

	[Insert Table 1 here]
	F o r
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	e r
	R e v
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	9

  specific mortality the results in Table3tell a similar story to the one in Table2, and hence reveal no significant overall effect. Looking at cause-specific mortality, most causes show no significant correlation with respect to the unemployment rate. One of the main causes of death, cancer, is probably not likely to be affected by short-term changes in the business cycle. However, a non-significant effect on Traffic Accidents is perhaps more surprising. The non-significant effect on Suicides might intuitively be surprising, but is consistent with recent evidence based on European data[START_REF] Rodriguez | Income inequality, unemployment, and suicide: a panel data analysis of 15[END_REF].

	Regarding age-
	F o r
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	R e v
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	here]
	11

There are two major exceptions to the non-significant results regarding Heart Disease and Other Accidents. The results relating to Heart Disease are of major importance since this is the cause-specific category with most deaths. Considering that it is a semi-log model, the coefficients should be interpreted as that the exponent of the coefficient is the percentage increase in mortality from a one percentage point increase in the unemployment rate. In the full model, as in equation (

1

), this implies that a one percentage point higher unemployment rate increases ischemic heart disease mortality by approximately 1%. Other Accidents picks up different types of accidents, but they tend to be of the job-related sort. Hence, the procyclical result, a decrease in Other Accidents mortality when the unemployment rate decreases, is quite intuitive. The coefficient of the full model indicates that a one percentage point increase in the unemployment rate decreases Other Accidents mortality by 13.9%.

  is explained by the fact that of ten cause-specific mortality rates, the unemployment rate indicate a pro-cyclical relationship in some cases, and in other cases a counter-cyclical relationship. Two causes of death tend to be statistically significantly related to the unemployment rate. As mentioned above, the most common cause of death (ischemic heart disease), indicates a counter-cyclical relationship and other accidents, which includes job-related fatalities, indicate a pro-cyclical relationship. The dynamic analysis also indicates

	significant overall effect
	F o r
	P
	e
	e r
	R e v
	i e
	w
	13

The coefficients imply that a one percentage point higher unemployment rate during the last 3 years increases mortality in Heart Disease and decreases mortality in Other Accidents with approximately 2.7% and 11.3% respectively. Regarding the short-term impact the coefficients imply that a one percentage point increase in the unemployment rate during a given year, compared to the average unemployment rate during the last 3 years, increases mortality in Heart Disease by 1.7% and decreases mortality in Other Accidents by 9.2%.

  puts this at a higher bound of $832 million.6 Regarding Other Accidents there was an average of 843 annual fatalities between

	F o r
	P
	e
	e r 1976 and 1996 (SCB, 2006b). A one percentage point lower unemployment rate increases this by 13.9%, which corresponds to circa 117 increased fatalities, with a monetized value of $11.7 million and $340 million using VSLY and VSL estimates, respectively. R e v These are of course very crude estimates, but are meant as indications of the relevant i e economic values related to changes in health status. They also indicate, as stated in the w

  Where is the Wealth of Nations? Washington D.C.: The World Bank.

	o r F o r F o r F o r Table 1: Descriptive statistics Tables Variable name Description Mortality Mortality per 100,000 individuals Male mortality Male mortality per 100,000 men Female mortality Female mortality per 100,000 females Heart Disease Ischemic heart disease mortality per 100,000 Suicides Suicide mortality per 100,000 Homicides Homicide mortality per 100,000 Traffic Accidents Traffic accident mortality per 100,000 Influenza Influenza mortality per 100,000 Cancer Cancer mortality per 100,000 Alcohol Alcohol psychosis & addiction mortality per 100,000 Alcohol 2 Alcohol poisoning mortality per 100,000 Falling Accidents Falling accidents mortality per 100,000 Other Accidents Other accidents mortality per 100,000 Unemployment Unemployment in % WorldBank (2006). F Foreign Share of non-Swedish citizens in each region (%) Migration Net migration as share of population (%) o Young Share of population aged 0 to 20 Old Share of population aged 65+ r Notes: All data are from Statistics Sweden	Mean 1125.10 1184.80 1065.53 360.08 17.82 1.11 10.23 3.15 241.94 3.48 1.67 15.17 9.81 4.41 3.94 0.15 26.58 17.74	Std. Dev. 120.52 144.00 121.94 70.83097 4.01 0.77 3.70 3.56 22.01 2.59 1.47 5.23 3.22 2.48 1.92 0.35 1.47 1.73
	P P P P P
	e e e e e
	e r e r e r e r e r
	R e v R e v R e v R e v R e v
	i e i e i e i e i e
	w w w w w
			19 20

Table 2 : Business cycle effects on incidence and mortality: panel data fixed effects estimations Dep. Var.

 2 Two-tailed tests significance levels: *** 0.01, ** 0.05, * 0.10, based on robust std. errors. Estimations are based on equation (1) with region fixed effects and year dummies, and also including regional specific time trends in one model.

	Unemployment 3.86E-04 (0.002) -Foreign -Young -Old	Total mortality 0.003 * -7.51E-04 (0.002) (0.002) -0.001 -0.004 (0.003) (0.005) -0.004 -0.002 (0.004) (0.005) 0.038 *** 0.018 *** (0.004) (0.005)	-0.003 (0.003) ---	Male mortality -0.003 (0.003) -0.023 *** (0.004) -0.017 ** (0.006) 0.011 *** 3.99E-04 0.002 (0.003) 0.001 (0.005) -0.008 (0.007) (0.005) (0.006)	Female mortality -0.006 * -0.005 * -0.002 (0.003) (0.003) (0.004) --0.021 *** -0.008 (0.005) (0.006) --0.009 -0.010 (0.006) (0.007) -0.003 0.010 (0.005) (0.007)
	Migration	-	0.006 (0.005)	0.002 (0.005)	-	0.008 (0.007)	-0.006 (0.007)	-	0.010 (0.008)	-0.002 (0.007)
	Year dummies	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Region specific	No	No	Yes	No	No	Yes	No	No	Yes
	time trend
	N R 2	630 0.34	630 0.59	630 0.69	630 0.57	630 0.60	630 0.76	630 0.71	630 0.73	630 0.82

Notes:

Table 3 : Business cycle effects on age subgroups and cause-specific mortality: panel data fixed effects estimations Dep. Variable: Unemployment coefficient Unemployment coefficient

 3 Two-tailed tests significance levels: *** 0.01, ** 0.05, * 0.10, based on robust std. errors. Other covariates refer to those used in Table 2 except for the age-specific mortality regressions which do not use the variables Old and Young as covariates. For cause-specific mortality the panel data covers all regions for years 1976-1996, which implies 441 observations.

	Unemployment
	coefficient

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The magnitude of Heart Disease mortality is different from the results in[START_REF] Svensson | Do not go breaking your heart: Do economic upturns really increase heart attack mortality?[END_REF], but that study only focused on acute myocardial infarction (heart attacks), whereas in this paper heart disease refers to all cardiovascular-related mortality.[START_REF] Svensson | Do not go breaking your heart: Do economic upturns really increase heart attack mortality?[END_REF] was also based on a different time period and only on individuals aged 20-49.

If one life-year is assumed to be saved, VSLY is the appropriate estimate, which can be thought of as the willingness to pay to increase longevity by one year. If many life-years are saved, VSL, or something in between VSLY and VSL is the appropriate estimate. These estimates (VSL) can be considered as the willingness to pay to prevent one (unidentified) fatality. Hence, in a situation where e.g. 10 unidentified fatalities can be prevented, the total monetized value is the value per prevented fatality multiplied by 10.

This should only be interpreted as a very crude indication of how one may go about monetizing the effects, something that has not been discussed previously in the literature on business cycles and mortality rates. The VSL estimate from[START_REF] Hultkrantz | The value of improved road safety[END_REF] is translated to US dollars only using the exchange rate (not PPPadjusted). An effect of equal magnitude of reduced deaths in the US would render higher monetized effects, given the higher income in the US compared to Sweden (VSL is assumed to increase with income). It should also be noted that an assumption is that transferring values from the transport sector is OK (the VSL estimate is from the preventing fatalities in the transport sector, which may not necessarily be the same as preventing fatalities from heart disease).

Acknowledgments

The paper benefited of comments from two anonymous referees.

V. Discussion and Conclusions

This paper, using the same methods as Ruhm (2000), Neumayer (2004), Gerdtham and Ruhm (2006), finds approximately the same results with Swedish data as Gerdtham and Johannesson (2005) who used a different approach, namely a non-existent overall relationship between the unemployment rate and mortality, and a counter-cyclical result for heart disease. 3 It also points in the same direction as the results in Svensson (2007), who found that a one percentage point increase in the unemployment rate increases heart attack mortality by 7.8%.

This paper contradicts the results on Swedish data by Granados (2004), but he used timesseries data for almost 200 years, and the pro-cyclical effect faded after WWII. The non-3 This was found for men in Gerdtham and Johannesson (2005) for some of the business cycle indicators. Page 12 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Corrado Andini
email: andini@uma.pt

Within-Groups Wage Inequality and Schooling: Further Evidence for Portugal

Keywords: Endogeneity, Quantile Regression, Schooling, Wage Inequality Endogeneity, Quantile Regression, Schooling, Wage Inequality. JEL Classification: I21, J31, C29

published or not. The documents may come

Many authors agree on the argument that schooling has a positive impact on withingroups wage inequality in Portugal 1 . The evidence is generally based on the standard quantile-regression techniques due to [START_REF] Koenker | Regression Quantiles[END_REF] 2 , applied to several types of wage equations. As a matter of example, [START_REF] Hartog | Changing Returns to Education in Portugal during the 1980s and Early 1990s: OLS and Quantile Regression Estimators[END_REF], [START_REF] Machado | Earnings Functions in Portugal 1982-1994: Evidence from Quantile Regressions[END_REF] as well as [START_REF] Martins | Does Education Reduce Wage Inequality? Quantile Regression Evidence from 16 Countries[END_REF] use different specifications of a Mincerian model and find that the return to schooling is increasing along the conditional earnings distribution. Particularly, the return at the ninth decile seems to be significantly higher than the return at the first decile.

Apart from a recent contribution by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF], a common feature of the quantileregression studies on schooling and within-groups wage inequality in Portugal is that no one deals with the endogeneity of schooling which is, typically, a relevant issue in studies focusing on the impact of schooling on the mean of the conditional earnings distribution.

Likewise the ordinary-least-squares estimator, the estimator of [START_REF] Koenker | Regression Quantiles[END_REF] assumes residuals' orthogonality 3 . Therefore, disregarding the endogeneity of 1 This section partly borrows from [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF].

2 [START_REF] Kim | A Monte Carlo Comparison of Parametric and Nonparametric Quantile Regressions[END_REF] provide a Monte Carlo comparison between the Koenker-Bassett parametric estimator and the nonparametric approach due to [START_REF] Yu | Local Linear Quantile Regression[END_REF]. The results indicate that the nonparametric quantile-regression method is more appropriate, particularly when the underlying model is nonlinear or the error term follows a non-normal distribution. A further common feature of existing studies is that no one deals with the total impact of schooling on within-groups wage inequality in Portugal, meaning that previouslyestimated wage equations do not exclude schooling-dependent covariates, such as industry dummies 4 and labour-market experience 5 , from the list of regressors.

To be more precise about the meaning and the relevance of the concept of total return to schooling, let us present the following simple example. First, let us label the logarithm of hourly earnings as w ln , the number of schooling years as s, the so-called potential labour-market experience as 6 s age exp =

. Second, let us suppose that a wage equation includes potential labour-market experience as control-variable, i.e.

+ + + = exp s w ln 2 1 0 .
In the latter case, the coefficient of schooling years 1 does not capture the total effect of schooling on earnings for the simple reason that the total effect is given by 2 1 s w ln = .

Although in our simple example one can recover the total effect of schooling by subtracting the estimate of 2 from the estimate of 1 , it is worth stressing that, when 4 Jobs in some industries may require more years of schooling than jobs in other industries.

5 [START_REF] Pereira | Returns to Education and Wage Equations[END_REF] properly argue that in order "to obtain the full impact of education on wages, one should be careful not to include in the wage equation covariates whose value can depend on education. In the extreme case one should only regress the ln(wage) in education." (p. 526). See also [START_REF] Andini | Returns to Education and Wage Equations: a Dynamic Approach[END_REF]. 3 the mathematical law of the schooling-dependent covariate is unknown (i.e. the general case), the recovering exercise becomes impossible. Hence, if the objective of the empirical analysis is the total return to schooling, it is important to exclude schoolingdependent covariates from the wage equation.

Following [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF], this paper tackles a controversial issue. On the one hand, if the potential correlation between residuals and schooling is limited by the insertion in the wage equation of a large set of control-variables, standard quantile-regression techniques are likely to consistently estimate the coefficient of schooling along the conditional wage distribution but unlikely to recover the total returns to schooling due to the likely presence of schooling-dependent covariates among the control-variables.

On the other hand, if the set of control-variables excludes schooling-dependent covariates and only includes strictly exogenous regressors, then standard techniques may poorly estimate the total impact of schooling on within-groups wage inequality due to the likely correlation between residuals and schooling. This paper aims at presenting consistent estimates the total return to schooling along the conditional distribution of Portuguese wages and compares the results with previous findings by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF]. [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF] finds that the difference between the total return at the ninth decile and the total return at the first decile of the conditional earnings distribution in Portugal is likely to range between 4.2% estimated using the standard quantile-regression techniques due to [START_REF] Koenker | Regression Quantiles[END_REF] and 26.2% estimated using the instrumental-variable approach due to [START_REF] Arias | Individual Heterogeneity in the Returns to Schooling: Instrumental Variables Quantile Regression Using Twins Data[END_REF]. In this paper, we provide further evidence on the total impact of schooling on within-groups To explain the rationale behind our estimation procedure, let us suppose that a variable Y is explained by an exogenous variable X and an endogenous variable S. Further, let us assume that there is an interest in estimating the impact of S (not only on the mean but also) on the shape of the conditional distribution of Y, controlling for X and using quantile-regression techniques. The control-function approach due to Lee ( 2007) is a two-stage approach similar to the one adopted by Arias, Hallock and Sosa-Escudero (2001, AHS henceforth). The first-stage regression consists of an ordinary-least-squares regression of S on X and instrumental variables Z1, Z2, and so on. The difference between the estimator of AHS and the estimator of Lee is related to the second stage.

II. EMPIRICAL MODEL

The method of AHS replaces the actual values of S with first-stage predicted values of S. In contrast, Lee adds a polynomial function of first-stage residuals to the set of the second-stage regressors, formed by the actual values of S and X.

Both approaches aim at providing consistent estimates of the coefficient of the endogenous explanatory variable at several quantiles of the conditional distribution of the dependent variable, using the estimator of Koenker and Bassett (1978, KB henceforth) in the second stage. And, both approaches suffer from the typical loss of efficiency associated with the implementation of instrumental-variable techniques in finite samples, but the method of Lee turns out to be more efficient than the method of AHS, in our specific application, at both the first and the ninth decile of the conditional wage distribution. Note that the latter point has special relevance for the issue of recovering a reliable measure of the impact of schooling on within-groups wage inequality. Based on the empirical specification proposed by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF], the estimation procedure of this paper is as follows:

(1)

µ + + + + = j i c c i c ji j i i ŷb s w ln + + + = j k i ki k ji j i qb yb s ) qb , yb s ( E s ˆki ji i i = i i i s ŝ ˆ = with 0 ) , yb , s ( Quant i ji i i = µ
for each .

Our notation is as follows: letter i refers to the i-th individual in the sample, w ln stands for the logarithm of gross hourly earnings, s measures years of schooling, yb is an indicator-variable for year of birth with j going from 1937 to 1984 (year 1936 is the excluded category), qb is an indicator-variable for quarter of birth with k going from 1 to 3 (quarter 4 is the excluded category), is a quantile-indicator going from 5 to 95, c represents the order of the control-function.

Data are extracted from the latest available wave of the European Community Household Panel (ECHP), the 2001 wave, and are related to Portuguese male workers.

Summary sample statistics are reported in Table 1.

III. RESULTS

First-stage regression results are presented in the Appendix. Specifically, as already discussed by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF], the use of a full set of quarters of birth as instrumental variables is not entirely satisfactory because the F-test of excluded instruments does not This is particularly true when the Sargan test of over-identification is passed (p-value 0.1351), i.e. the model specification is not rejected. In addition, our results are consistent with the findings of [START_REF] Angrist | Does Compulsory Schooling Attendance Affect Schooling and Earnings?[END_REF] who argue that people born later in the year have slightly more schooling than people born earlier. Note, indeed, that the estimated coefficients for the first, the second and the third quarter of birth are negative and that the excluded category is the fourth quarter of birth. Further, robustness checks highlight that, if the model is just-identified using the fourth quarter of birth only, the estimated coefficient for the last quarter of the year has the expected positive sign and is statistically significant (p-value 0.055). Finally, if only the last two quarters of the year are used as instruments, the estimated coefficients are both positive and the F-test of excluded instruments is passed (p-value 0.096).

It is worth stressing that our estimation results for the wage equation are robust to the identification strategy. As a matter of example, the AHS method provides roughly the same results when one uses the fourth quarter of birth as single instrument for schooling years rather than a full set of indicator-variables for quarters of birth as in the Appendix.

Hence, for sake of comparison with our previous estimates of the total return to schooling along the conditional wage distribution, we adopt the same identification strategy as implemented by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF].

Figure 1 plots the estimates of the main parameter of interest, i.e. the estimates of in model (1) which are, in turn, reported in Table 2. Note that the last two columns of Regarding the choice of the order of the control-function, [START_REF] Lee | Endogeneity in Quantile Regresssion Models: A Control Function Approach[END_REF] does not suggest the existence of an optimal order because Monte-Carlo experiments in finite samples show that "the estimator is not very sensitive to the choice of the order of the polynomial approximations" (p. 15). Indeed, our empirical findings based on a number of different orders of the control-function are consistent with the simulation results. As a matter of example, we report estimates of based on c going from 1 to 4. The corresponding estimates of the total return to schooling along the conditional wage distribution are labelled as L1, L2, L3, L4.

Depending on the order of the control-function, the total impact of schooling on withingroups wage inequality varies from 5.1% to 7.4% and fits the interval provided by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF], who refers to the difference between the return at the ninth decile and the return at the first decile of the conditional earnings distribution. Therefore, one contribution of this paper consists of providing evidence on a smaller interval of impact than previously estimated, i.e. 5.1%-7.4% vs. 4.2%-26.2%.

Further, note that the standard KB techniques disregarding the endogeneity issue suggest a 4.1% gap and therefore underestimate the total impact of schooling on withingroups wage inequality in Portugal, as previously suggested by [START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF], although the magnitude of the downward bias is smaller than one predicted by the AHS method.

Remarkably, the estimator of Lee predicts a pattern of the schooling coefficient, along the conditional wage distribution, that looks very much like the one predicted by the method of AHS, with a peak around the eight decile and a drop around the second decile. Hence, the impact of schooling on within-groups wage inequality is higher when measured as difference between the 25 th quantile and the 75 th quantile, ranging from 7.6% to 12.2%. Again, this result is not captured by the standard quantile-regression estimator that only highlights a 3.0% gap. In contrast, the standard exogeneity-based techniques seem to perform relatively fine when considering the conditional average return to schooling. The ordinary-leastsquares estimator prospects a 5.7% coefficient, which lies within the interval of 4.7%-7.5% obtained using the control-function approach and the AHS method. The conclusion is that schooling has a positive impact on between-groups wage inequality in Portugal. The latter, however, is a well-known result and goes beyond the objective of this paper.

IV. FINAL REMARKS

This paper uses the control-function estimator for quantile regression due to [START_REF] Lee | Endogeneity in Quantile Regresssion Models: A Control Function Approach[END_REF] and provides further evidence of the total impact of schooling of within-groups wage inequality in Portugal. In our specific application, the estimator of Lee turns out to be more efficient than the estimator of Arias, Hallock and Sosa-Escudero ( 2001) at two key-deciles of the conditional wage distribution, thus providing more reliable measures of the corresponding total returns to schooling. Specifically, we find that standard exogeneity-based estimator of [START_REF] Koenker | Regression Quantiles[END_REF] underestimates the impact of schooling on earnings dispersion trough its within-groups dimension, although the magnitude of the bias is likely to be less than previously suggested.

The empirical research on the positive association between schooling and within-groups wage dispersion in Portugal is relatively rich in contributions. The finding of a positive association is also supported by several studies using the KB estimator with education levels rather than schooling years. The striking evidence that schooling/education is a strong source of the so-called residual earnings inequality should inspire an effort of understanding the reasons behind this stylized fact. 9 Some authors suggest that one possible explanation of the above-referred fact has to do with educational mismatches in the labour market. However, the existing empirical evidence is not necessarily consistent with this argument (see [START_REF] Budría | Can Over-Education Account for the Positive Association between Education and Within-Groups Wage Inequality? A Note[END_REF]. Our perception of the problem is that future research should pay more attention to the issue of school quality. The existing differences in the quality of Portuguese universities and secondary schools, which are well-known to everybody living in Portugal (although the academic research in this field is relatively scarce 6 ), are likely to play an important role in explaining the stylized fact that the wage returns for individuals with the same number of schooling years or the same level of education (and the same observed characteristics) are quite heterogeneous. However, an empirical evaluation of the latter hypothesis needs individual-level data on school quality, which are not currently available.

6 [START_REF] Oliveira | Assessing School Efficiency in Portugal using FDH and Bootstrapping[END_REF]

  of Koenker and Bassett is consistent at each quantile of the conditional distribution of Y if the orthogonality condition holds at each quantile, i.e. consistency of the ordinary-least-squares estimator requires that the conditional mean of regression residuals is null, i.e. ( ) inconsistent estimates of its coefficient along the conditional wage distribution, i.e. the estimated impact of schooling on within-groups earnings dispersion may be misleading.

  the latest available instrumental-variable technique for quantile regression, i.e. the control-function estimator due to[START_REF] Lee | Endogeneity in Quantile Regresssion Models: A Control Function Approach[END_REF].

  (p-value 0.1972; this result seems driven by the third quarter). It is also known, however, that passing the F-test should not be intended as a strict requirement due to the limitations of the test itself, i.e. low power (seeCruz and Moreira, 2005).

	reject the null
	F o r
	P
	e
	e r
	R e v
	i e
	w
	6

Table 2

 2

also report the AHS results and the standard KB results presented by

[START_REF] Andini | The Total Impact of Schooling on Within-Groups Wage Inequality in Portugal[END_REF]

.

10 of 15 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  find evidence of heterogeneity in efficiency among secondary schools in Portugal. To the best of our knowledge, a more comprehensive study on school quality in Portugal is not available.

	Page Submitted Manuscript
	F o r F o r
	P P
	e e
	e r e r
	R e v R e v
	i e i e
	w w
	11

Table 1 . Summary sample statistics

 1

	Variable	Obs.	Mean	S.E.	Min	Max
	Logarithm of gross hourly wage	1782	6.55	0.47	3.32	8.49
	Schooling years	1782	8.80	3.91	3.00	27.0
	Year of birth	1782	1965	11.5	1936	1984
	Quarter of birth	1782	2.45	1.11	1.00	4.00

Table 2 . Conditional Returns to Schooling

 2

	Quantile	L1	L2	L3	L4	KB	AHS
	5	0.1175	0.1296	0.1124	0.1103	0.0211	0.0550
		(0.0869)	(0.0933)	(0.0859)	(0.0909)	(0.0052)	(0.0828)
	10	0.0300	-0.0050	-0.0084	0.0096	0.0298	0.0000
		(0.0631)	(0.0674)	(0.0611)	(0.0728)	(0.0033)	(0.0782)
	15	0.0067	-0.0195	-0.0195	-0.0279	0.0352	0.0054
		(0.0452)	(0.0476)	(0.0455)	(0.0551)	(0.0025)	(0.0536)
	20	0.0111	-0.0194	-0.0207	-0.0228	0.0368	0.0028
		(0.0444)	(0.0516)	(0.0633)	(0.0533)	(0.0019)	(0.0376)
	25	0.0313	0.0177	0.0128	0.0164	0.0396	0.0000
		(0.0335)	(0.0369)	(0.0324)	(0.0494)	(0.0017)	(0.0155)
	30	0.0367	0.0115	0.0225	0.0152	0.0427	0.0000
		(0.0378)	(0.0373)	(0.0300)	(0.0421)	(0.0023)	(0.0151)
	35	0.0381	0.0066	0.0116	0.0069	0.0497	0.0000
		(0.0311)	(0.0357)	(0.0462)	(0.0400)	(0.0018)	(0.0108)
	40	0.0467	0.0314	0.0205	0.0184	0.0518	0.0214
		(0.0304)	(0.0371)	(0.0302)	(0.0310)	(0.0020)	(0.0526)
	45	0.0559	0.0540	0.0423	0.0401	0.0537	0.0329
		(0.0335)	(0.0289)	(0.0385)	(0.0391)	(0.0018)	(0.0329)
	50	0.0770	0.0925	0.0651	0.0535	0.0570	0.0221
		(0.0668)	(0.0389)	(0.0423)	(0.0501)	(0.0032)	(0.0398)
	55	0.0819	0.0594	0.0699	0.0501	0.0577	0.0549
		(0.0445)	(0.0472)	(0.0469)	(0.0563)	(0.0026)	(0.0613)
	60	0.0822	0.0651	0.0685	0.0340	0.0614	0.0977
		(0.0509)	(0.0547)	(0.0436)	(0.0517)	(0.0031)	(0.0473)
	65	0.0855	0.0711	0.0479	0.0371	0.0631	0.1312
		(0.0440)	(0.0523)	(0.0471)	(0.0522)	(0.0030)	(0.0489)
	70	0.0918	0.0727	0.0338	0.0488	0.0658	0.1541
		(0.0542)	(0.0650)	(0.0643)	(0.0647)	(0.0029)	(0.0567)
	75	0.1129	0.1401	0.0887	0.0934	0.0698	0.2195
		(0.0675)	(0.0414)	(0.0963)	(0.0632)	(0.0036)	(0.0397)
	80	0.1861	0.1626	0.1445	0.1556	0.0723	0.2473
		(0.0551)	(0.0657)	(0.0702)	(0.0589)	(0.0038)	(0.0729)
	85	0.1600	0.1360	0.0836	0.1103	0.0716	0.3029
		(0.0642)	(0.0576)	(0.0795)	(0.0797)	(0.0031)	(0.0795)
	90	0.0872	0.0695	0.0521	0.0606	0.0717	0.2624
		(0.0813)	(0.0735)	(0.0719)	(0.0680)	(0.0042)	(0.1123)
	95	0.0756	0.0834	0.1103	0.1329	0.0706	0.1808
		(0.0990)	(0.1046)	(0.1060)	(0.1105)	(0.0062)	(0.1073)
	Mean	0.0751	0.0643	0.0472	0.0479	0.0577	0.0751
		(0.0447)	(0.0447)	(0.0446)	(0.0445)	(0.0029)	(0.0534)
	90-10	0.0572	0.0745	0.0605	0.0510	0.0419	0.2624
	75-25	0.0816	0.1225	0.0759	0.0770	0.0302	0.2195
			Standard errors in parentheses

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Appendix. First-stage regression of schooling years

		Coeff.	Robust	t	P-value
			S.E.
	Quarter of birth
	1	-0.5303	0.2733	-1.94	0.053
	2	-0.5162	0.2780	-1.86	0.064
	3	-0.3004	0.2675	-1.12	0.262
	Year of birth
	1937	-0.1968	0.4193	-0.47	0.639
	1938	0.4486	0.8273	0.54	0.588
	1939	0.1668	1.1782	0.14	0.887
	1940	-0.2851	0.3714	-0.77	0.443
	1941	1.2821	1.2007	1.07	0.286
	1942	0.0151	0.7509	0.02	0.984
	1943	2.6175	1.3599	1.92	0.054
	1944	0.4641	1.3862	0.33	0.738
	1945	3.5350	1.1231	3.15	0.002
	1946	1.7825	0.9022	1.98	0.048
	1947	0.1080	0.5157	0.21	0.834
	1948	2.4706	1.2484	1.98	0.048
	1949	1.3233	0.7644	1.73	0.084
	1950	2.5171	0.9047	2.78	0.005
	1951	1.4911	0.6433	2.32	0.021
	1952	1.2574	0.6183	2.03	0.042
	1953	1.2702	0.4896	2.59	0.010
	1954	1.5278	0.8376	1.82	0.068
	1955	0.5447	0.4065	1.34	0.180
	1956	1.6778	0.6129	2.74	0.006
	1957	1.6236	0.6541	2.48	0.013
	1958	1.4677	0.5944	2.47	0.014
	1959	0.6664	0.4798	1.39	0.165

I gratefully acknowledge financial support from the European Commission (EDWIN Project, HPSE-CT-2002-00108). Budría, Joop Hartog, Pedro Telhado Pereira, Robert Wright and the participants at the 22 nd National Conference of the Italian Association of Labour Economists. The usual disclaimer applies.


Torben Schubert
email: torben.schubert@isi.fraunhofer.de

Hariolf Grupp

Tests and Confidence Intervals for a Class of Scientometric, Technological and Economic Specialisation Ratios

Keywords: specialisation, indicators, statistical inference, RPA, RLA

In economic, scientometric, and innovation research, often so-called specialisation indices are used. These indices measure comparative strengths or weaknesses as well as specialisation profiles of the observation units with respect to certain criteria, such as patenting and publication or trade activities. They allow question like: Is Germany specialised in the export of motor vehicles? Or is the UK specialised in biotech patents? Unfortunately, little is known about their statistical properties, which makes valid inferencing difficult. In this article we prove asymptotic normality for a certain class of scientometric, technological, and some economic, though non-monetary, specialisation indices. We provide asymptotic confidence intervals and demonstrate in an example how to obtain statistically sound results. We will also address the problem of normalisation of these indicators. All procedures proposed are provided in an add-on package for R statistical environment.

Introduction

Information about countries' scientific, technological, or economic performance is often required for various reasons. The specific strengths and weaknesses are commonly assessed by indicators.

Thus, for example, a country's patent count will be interpreted as a measure of its technological capacity (Blind andJungmittag, 2005, Jang et al., 2008). Other studies focus on scientific publications to assess a country's scientific performance [START_REF] Garcia-Castrillo | A World-Wide Assessment of Economics[END_REF]. Apart from using simple counts as performance measures, also specialisation ratios, describing a country's profile (e.g. specialisation in high-tech or low-tech patents; specialisation in natural science or social science publications; export and import profiles), are widely applied (e.g. [START_REF] Jensen | Foreign Direct Investment, Industrial Restructuring and the Upgrading of Polish Exports[END_REF][START_REF] De Benedictis | Semiparametric Analysis of the Specialization-income Relationship[END_REF] Originally specialisation ratios were introduced in the context of the analyis of trade flows.

Among the early indicators are the Revealed Export Advantage (RXA) and the Revealed Import Advantage (RMA) [START_REF] Keesing | Labor Skills and International Trade: Evaluating Many Trade Flows with a Single Measuring Device[END_REF]. Another example is the the Revealed Comparative Advantage (RCA) (see [START_REF] Balassa | Trade Liberalization and Revealed Comparative Advantage[END_REF], 1977[START_REF] Wolter | Factor Proportions, Technology and West-German Industry's International Trade Patterns[END_REF][START_REF] De Benedictis | A Note on the Balassa Index of Revealed Comparative Advantage[END_REF], for a discussion). Other indicators that describe trade flows emerge from the phenomenon of intraindustry trade (IIT). The earliest indicator measuring IIT is the Grubel-Lloyd Index (GLI) (Grubel andLloyd, 1971, 1975). Many more IIT indicators have been developed in this branch of research (an overview can be found in [START_REF] Brülhart | Marginal Intra-Industry Trade: Measurement and Relevance for the Pattern of Industrial Adjustment[END_REF]). 4 Later on, in technometric and scientometric research similar indicators originated from the methodogical ideas of the RMA, the RXA, and the RCA, such as the Revealed Patent Advantage (RPA) and the Revealed Literature Advantage (RLA) (Grupp, 1998, pp. 157 -158, 216 -219). Indicators also emerged in economic analysis, including the Revealed Trade Mark Advantage (RTMA) and the Revealed Norms and Standards 4 Note for now that the GLI and, related to it, other IIT indicators are not really specialisation ratios, as they are discussed in this paper. This will become clear later on. 3 Specialisation (RNSS). Additionally, the TRIS database containing national regulations of EUmembers has been used to calculate the Revealed Regulation Specialisation (RRS). 5 All these indicators have a neutral value which indicates neither above nor below average specialisation.

Values below the neutral value are a sign of under-specialisation, whereas values above the neutral indicate over-specialisation.

Due to their easy construction and interpretability they have awakened growing interest in various fields of research, as they provide information about the relative strengths of certain units in measuring specialisation without reference to size. Nonetheless, in a statistical sense, specialisation ratios are complex sample functions, for which the stochastic properties are largely unknown. While there is a formula to calculate some form of "parametric imprecision" [START_REF] Engelsman | The Netherlands in Modern Technology: A Patent-based Assessment[END_REF], the inability to determine their statistical distribution makes interpretation a cumbersome endeavour, often subjected to intuition or rules of thumb. In the following we will provide the asymptotic distribution for a specific class of specialisation ratios.

Commonly, though not exclusively, these specialisation ratios will be technometric or scientometric.

The rest of the paper is organised as follows. Section 2 presents the most common specialisation ratios, to provide an intuition for the interpretation of these indicators. In view of their importance we will also describe the trade-related monetary specialisation ratios, although they are not covered by the statistical analysis of this paper. Section 3 summarises the main statistical results.

The derivations may be found in the appendix. Section 4 presents an empirical example and some considerations of robustness with respect to classification decisions. Section 5 concludes.

Common Specialisation Ratios

In this section, we discuss the most common indicators and their meaning in order to provide the reader with a feeling for this type of indicators. We also discuss which indicators meet the conditions needed for the statistical analysis and which do not. Before we do so, we introduce a technical definition and the requirements formally:

Technical Definition: A specialisation ratio is a measure which divides a ratio describing some feature of unit under consideration by an identically constructed ratio corresponding to a reference unit.

Statistical Conditions: (a) The quantities concerned are measured on an absolute scale. 6 (b) The specialisation ratio can be interpreted as a fraction of fractions. 7 To begin with, any indicator adhering to the technical definition and the statistical conditions is a specialisation ratio that falls in the class of indicators for which we are able to determine the asymptotic distribution by the methodology used in this paper.

We start our review of the most common specialisation indicators with those that either fail the technical definition or the statistical conditions (or both). Among the earliest specialisation ratios is the Revealed Comparative Advantage (RCA) -a measure for comparative advantage -which is given by 8 ( ) ( )

/ / ik ik ik hk hk h h RCA E I E I = (1)
6 Note that quantities that can be measured on an absolute scale have a natural unit. In our context this will imply that the quantities can be counted (for example, patents).

7

The technical definition only requires it to be a ratio of ratios. where E and I denote exports and imports in a given product group and a given country. The RCA compares the export to import ratio of some country i for product group k to that of the reference group of countries. A value greater than 1 is indicative of a comparative advantage the country i has with respect to product group k, while a value below 1 is a sign of a comparative disadvantage. Concerning requirements (a) and (b), neither the numerator nor the denominator is assured to be between zero and one, so that none is a fraction. Further, the quantities of the RCA fail the condition of having a natural unit. This is easy to see, by considering the following idea: a count measure could be derived by taking each euro as an individual element. Unfortunately, though unit stepped, this is not unique since the imports or exports could also be measured in yen or dollars. By changing the scale we would also change the number of counts.

The Revealed Export Advantage (RXA) -a measure for export specialisation -and the Revealed Import Advantage (RMA) -a measure for import specialisation -are defined as 9

(

) ( )

/ / ik ik ij hk hj j h h j RXA E E E E = (2) and ( ) ( ) / / ik ik ij hk hj j h h j RMA I I I I = (3)
For instance, if the RMA is greater than unity, then country i imports more of product group k in comparison to own total imports than does the reference group of countries compared to its total imports. Country i imports more of product group k, relatively, than does the rest of the world.

Clearly, the fractions condition is met. Unfortunately, both the RMA and the RXA fail the natural unit condition for the same reason as the RCA does. Despite these more traditional trade indicators, many advances have been made in measuring intra-industry trade (ITT). The earliest indicator of this type is the Grubel-Lloyd-Index (GLI), which we will shortly discuss here. The GLI is defined by following formula:

( ) ( ) ij ij ij ij j j j ik ij ij j E I E I GLI E I + = + (4)
where the notation is the same as above. The index takes a value of unity whenever all trade is intra-industrial and zero if all trade is inter-industrial. In fact, the GLI is not a specialisation ratio, as this was defined previously (see the technical definition). The reason for mentioning it here is the problem of aggregation bias, which has a parallel in what will be discussed later in Section 4.2. For the sake of completeness, it shall be noted that neither condition (a) nor condition (b)

applies.

We now turn to indicators that meet the technical definition and the statistical requirements. The Revealed Patent Advantage (RPA) -a measure for technological specialisation proxied by patents -and the Revealed Literature Advantage (RLA) -a measure of science specialisation proxied by scientific publications -are defined very similarly to the RXA and the RMA. Take the RLA, for instance:

( ) ( ) / / ik ik ij hk hj j h h j RLA P P P P = (5)
where P denotes publications. A value of above 1 means that the fraction of publication in discipline k (e.g. biotechnology) of country i (say, the UK) is greater than the respective fraction of the reference region (e.g. the world). To put it in simple terms: the UK gives, in this hypothetical example, much greater relative emphasis to biotechnology compared to the rest of the world.

Thus the fraction condition is met, as with the RMA and the RXA. Also, the number of publications is a natural integer stepped unit. The same holds true for the RPA. Other measures with In summary, the procedures discussed subsequently work well, whenever quantity describing the feature can be (uniquely) counted and classified. This applies for example for the RPA, the RLA, the RTMA, the RNSS, and the RRS, but not for he RXA, the RMA or the RCA and not for any kind of monetary indicator such as the GLI. So the main restriction in an economic sense is that the indicators must be non-monetary.

Another issue concerns interpretability. The fact that all these indicators range between zero and infinity with neutral value at 1 makes interpretation a cumbersome endeavour. Symmetric and normalised indices are easier to understand. Therefore, often the symmetrifying second order Moebius transformation in the form ( )

2 1 r / ( ) 2 1 r + ,
where r is the respective specialisation index, is embarked upon (Grupp, 1994, pp. 187 onwards). The transformed index then ranges from -1 to +1 with a neutral value ("no specialisation") at 0. However, there is a large class of similar Moebius transformations, 10 and to our knowledge, there is no mathematical solution to determine the optimal transformation so far. 11 In the following analysis we adopt the second order version, for simplicity's sake. In any case, this is not a great problem in our context because our results hold for any differentiable transformation, which is true for any transformation common to the literature.

Asymptotic Results

In this section we briefly present the main theorems derived in this paper. The proofs are given in the Appendix. All of the procedures are implemented in the R-package SRinference (current version: 1.1) freely available under http://www.isi.fhg.de/p/mitarbeiter/tos.html, which does not require much statistical knowledge to use it. Additionally, a user guide is provided, which introduces the basic features of the package to the user. Therefore, for the application-oriented reader these derivations may be skipped as well as the theorems in Section 3. Instead, Section 4 gives an empirical example. This should help to make application and interpretation more accessible.

Let us first introduce some definitions. We will refer to 'unit' when we mean the unit having certain attributes. We will denote as 'objects' the attributes which may take certain values. For example, when we talk about Germany's strength in publishing reviewed articles in the field of natural sciences, Germany is the unit while a given reviewed article is the object (which either belongs to natural sciences or not).

The theorems only present the (asymptotic) distributions of the statistics under consideration. In any case, this is enough for our purpose because once their distribution is known to be normal, it is straightforward to define valid tests and confidence intervals, following the spirit of usual ttests or t-based intervals.

We define the following variates: During applied work it is often necessary to determine if a country is specialised e.g. in patenting activity in the chemical industry field. However, for values of the RPA close to zero, it is hard to maintain that the observed deviation is not just coincidental. Therefore a one-sample test is useful to determine whether the observed effect is not just noise. The result of Theorem 1 allows such inference, including, of course, the construction of confidence intervals. n -consistent with a variance that can be consistently estimated from the data.

Theorem 1 (One Sample Inference

): If i) j n is non-random for all j , ii) ij X is independent of
Especially assumption ii) is very strong. It essentially assumes away any kind of economic reasons for dependence. Taking the example of patenting activity, it means that regional clustering of industrial (and therefore innovative) activity is neglected, despite the fact that its existence is widely accepted in the literature [START_REF] Krugman | Geography and Trade[END_REF]. There are a multitude of reasons for that, including spill-overs, endowment with natural or human resources, demand and supply side externalities resulting from transportation costs, pathdependence, etc. Yet the independence assumption is unavoidable from a statistical point of view (see Appendix). The reader is encouraged to decide if in a specific application this assumption seems justified or if it is too strong. This will also depend on how strong regional interdependencies are believed to be.

Very often we would like to test whether two specialisation ratios are significantly different or not. For example, we might like to know if Italy's specialisation in astrophysical publications is significantly different from that of Portugal. This is also possible as indicated in Theorem 2.

Theorem 2 (Two Sample Inference): Under the conditions of Theorem 1, the difference of the transformed specialisation ratio is asymptotically normal and n -consistent with a variance that can be consistently estimated from the data.

Sometimes changing structures in time are relevant. We may, for example, want to know if the patent specialisation of the UK concerning biotechnology has significantly changed over time.

Theorem 3 gives conditions under which we can test for this. n n const , iv) the function used to transform the linear indicator is differentiable around the estimated value, v) (a) the objects have a natural unit and (b) the indicator has a fraction of fractions meaning, then the difference of the transformed specialisation ratios in time is asymptotically normal and n -consistent with a variance that can be consistently estimated from the data.

In essence, Theorems 1-3 define ways to construct confidence intervals and tests for the statistics discussed (let these be denoted as n T ) by approximating the finite sample distribution with its asymptotic counterpart. However, simulation studies have shown that this approximation may be quite imprecise if the sample size is small. We therefore provide a bootstrap procedure which has better rates of convergence [START_REF] Hall | The Bootstrap and Edgeworth Expansion[END_REF][START_REF] Horrowitz | The Bootstrap[END_REF]. In essence, this will make inference much more precise in small samples. The consistency results are summarised in Theorem 4.

Theorem 4 (Bootstrap Inference): Under the respective conditions of Theorems 1-3 the resampling bootstrap distribution of any of the statistics n T is a consistent estimate of the true distribution.

From a practical point of view, in small samples we recommend the use of the estimator described in Theorem 4 (function SRboottest in the R-package). However, with large enough samples

An Empirical Example and the Problem of Classification

In this section we present an empirical application and discuss the robustness of the procedure with respect to the definition of the classes.

A Short Empirical Example

To save space, we present only the case of one sample inference. We use the asymptotic test from Theorem 1. In any case, the other procedures work in very much the same manner.

For the empirical example we use patent data on 11 countries gathered for a study of the catchingup process of several of Germany's world market competitors in the context of the Technological Performance Report 2006 prepared for the German Ministry of Education and Research.

One task of this study was to describe the technological profile of these catching-up countries by their patenting profile. 13 The results for the profile of patenting activity are depicted in Figure 1. To do this, specialisation ratios as described above were used along with the second order Moebius transformation. The latter bounds the specialisation ratio to the interval -1 and 1. A zero indicates that the country average is identical with the reference group average (often the world average) while positive values indicate above average und negative below average specialisation. The main results can be summarised as follows. The eastern European countries (Poland, Czech Republic, Slovakia, Hungary, and Russia) have somewhat similar profiles, putting high weight on mechanics. This means that they are still, to some degree, in the production tradition of the Warsaw Pact. Slightly different profiles are apparent for Slovenia, Slovakia, Hungary, and Russia which are specialised in instruments. However, we also see that only the Russian specialisation in instruments is statistically significant, which indicates that the results for the other three countries are not overwhelmingly reliable. Though not applying to Slovenia, where none of the estimated specialisation ratios is statistically significant from zero, the similar profiles across the Eastern 'generalist' patenting strategy. Second, Slovenia's patent counts are very low. Therefore, the precision of the specialisation ratios is limited. The bands for India, on the contrary, are very narrow, because the total number of India's patents is relatively large (1202).

Analogous to the eastern European cluster there is definitely a South American cluster of Mexico and Brazil, which also share similar profiles. To some extent, Singapore and Taiwan also have similarities.

So the main conclusion of this analysis could be that in fact regional clusters of technological specialisation do exist, that are shaped by regional, technological or cultural proximity and possibly by comparable factor and human capital endowments.

However, knowledge about statistical confidence is still absolutely necessary, in order to separate real effects from purely random ones. The same applies to time change inference. This can help to detect significant changes in country profiles earlier or prevent researchers from interpreting noise as relevant changes.

Influence of the Classification

Motivated by the well-known aggregation bias inherent to the construction of the GLI, 14 it is worthwhile asking what is likely to happen, if the classes of the previous example (engineering, chemistry, instruments, and mechanics) were disaggregated. Intuitively, it can be expected that the significance of specialisation is likely to decrease, because estimations will become less precise. If this were true, then disaggregating patent classes would have a very similar effect to the 14 Aggregation bias in this context means that IIT is overestimated and vanishes after disaggregation The reason is the 'opposite sign effect'. [START_REF] Gray | Intra-industry Trade: The Effects of Different Levels of Data Aggregation[END_REF], Greenaway, 1983, Tharakan, 1984[START_REF] Balassa | Intra-industry Specialization: A Cross-Country Analysis[END_REF][START_REF] Doroodian | The J-curve Effect and US Agricultural and Industrial Trade[END_REF][START_REF] Bahmani-Oskooee | How sensitive are Malaysia's Bilateral Trade Flows to Depreciation[END_REF]. We will demonstrate that the asymptotic variance will increase with the number of the classes considered, implying a decrease of precision and significance. In any case, finding an analytical solution in the general case seems very hard. Therefore we consider only a special case in which, after still tedious calculations, an easy closed form expression pertains.

Taking the test of Theorem 1 along with the second order Moebius transformation, we assume that for a given class, no subject is over-or under-specialised and that each subject holds an identical number of objects. Further, we assume that all classes have the same probability that an object belongs to them both before and after disaggregation.

These assumptions result in the following simplifications:

1 2 ... 1/ J K = = = = = 1 2 / / ... / 1/ J n n n n n n J = = = = (6)
where K and J are the number of classes and the number of subjects. Taking the expression for the asymptotic variance of test in Theorem 1 15 , we see that

J j j dI K r J dr K = = 2 2 2 2 2 2 1 1 1 ( 1) ( 1) dI K J J J dr K J J = + 2 2 2 4 ( 1)( 1) ( 1) r K J r = + ( 1)( 1) K J = (7)
where the last line follows from the assumption of no specialisation, i.e. 1 r = . This indicates that the asymptotic standard error increases by the order 1/ 2 in the number of classes. Therefore, disaggregating too much will increase the asymptotic variance and for any given sample size will result in a drop in significance.

However, unlike the aggregation bias known from the GLI, this is not a measurement bias, but purely a statistical problem of finite samples, which vanishes asymptotically for any finite number of classes.

Still, it should be stressed that the definition of classes should follow an economically sensible understanding and should result in a manageable number of classes, because otherwise the precision of the specialisation ratios is lost.

Conclusion

Specialisation ratios are in wide use concerning science, technology and trade assessment. Up to now, little was known about their statistical reliability. In order to progress in this field, we proved asymptotical normality for a certain type of non-monetary specialisation ratios. We used this knowledge to provide asymptotic confidence intervals and tests for the one and two-sample problem and the two-sample time change problem, whose critical values converge at usual rates, obtained from first order asymptotics. We showed in an empirical example how this knowledge can be applied to obtain statistically sound results. As specialisation ratios are a widely accepted und frequently used tool in economics, scientometrics, and technometrics, we believe that these new inferencing techniques are extremely relevant to any user of such indicators. In order to guarantee fast dissemination, we implemented each method proposed in an add-on package for R

ik k E X = , ( ) (1 ) ik k k V X = (1)
as well as 1 ~( , )

j n ij j j i X B n = with 1 j n ij j j i E X n = = , 1 (1 )
j n ij j j j i V X n = = j (2)
Check that the true value of the linear specialisation ratio can be defined by:

1 1 1 1 1 1 j k j n n J k k k ik ij J n i j i j n j r E n X E n X = == = = (3)
This can be estimated by using the corresponding sample shares. To establish the asymptotics of the estimator / k r = $

, we first show that the estimated shares are normal.

We have:

1 1 (1 ) , j n d j j j ij j i j n X N n = (4)
which follows from the central limit theorem. The linear indicator is thus a function of J asymptotically normal variables. We use the mean value expansion (see [START_REF] Hayashi | Econometrics[END_REF][START_REF] Wooldridge | Econometric Analysis of Cross Section and Panel Data[END_REF] to derive the following statement: . We obtain:

( )

(1) p r n r r n o = + $ uv ( ) ' 0, cov d r r N n uv uv (6)
From independence stated in ii) we find that the covariance matrix is diagonal:

( )

1 1 1 cov (1 ),..., (1 )
J J J n n n V diag n n = (7)
Thus we conclude that is n -consistent when iii) holds. The variance can be calculated by straightforward matrix multiplication

( ) ( ) 2 ' 1 (1 ) / / J j j j j j r r V r n n = = uv uv (8)
Now, again by the delta method under iv) any of the transformed versions is also normal. Let The important point with ( 9) and ( 10) is that we can treat I $ as approximately normal with

( ) ( ) ( ) ( ) , , v k v v v k k k I I I I r I r = . It is easy to verify that: ( ) (1) p
I n I I n o = + ur ' 0, d I I N V uv uv (11)
where we obtain the gradient of I by: To compare indicators over time is conceptually very much the same. The proof follows along the lines of that of Theorem 2. We therefore omit most of it. However, since I consists of twice as many different estimators for the sample shares, the variance is slightly different:

1 1 2 2 2 2 ,..., ,..., v v n n n n v k v k v n k n v n k n v k v k dI dI dI dI I dr dr dr dr = + + uv 2 2 2 2 ,..., k k J J n n n n v k v k v n k n v n k n v k v

Proof of Theorem 4:

We will not discuss the testing problem explicitly because a confidence interval that entails the value of the null hypothesis is indicative of a non-ejection decision with the corresponding test.

First, we will define the bootstrap algorithm and then argue why it is consistent.

• Given ( ) 1 ,..., j j j jn X X X = for all j, calculate n , where n is one of the estimators described in Theorem 1-3.

• Draw from each vector responding standard deviation. The latter will be calculated by one of equations ( 10), ( 13) or ( 14). 16

• Repeat the last two steps very often. 17 10), ( 13) or ( 14) based on the original sample.

It should be noted that this approach follows a non-parametric re-sampling strategy, which might seem curious at first sight, because we have specified a parametric distribution. However, since the binomial distribution has only two outcomes (success and failure), both techniques have identical statistical properties, which is not the case with any other common statistical distribution.

Concerning consistency, it is shown by [START_REF] Beran | Trade and the Impact of Innovation and Standards: The Case of Germany and the UK[END_REF] that we need to meet three conditions:

• ( ) ( )

sup 0 p x F x F x
, i.e. that the EDF converges uniformly to the CDF.

• ( )

, G x F " , denoting the asymptotic CDF of the statistic, is continuous. 16 In fact, we could use a nested bootstrap to determine the variance. But this is computationally even more intensive. Since we are in the lucky situation of having an asymptotic expression for the variance it is better to use this for practical reasons (see e.g. Wassermann ( 2006)).

17 The precision increases with the number of bootstrap replications. Thus infinite replications would be ideal. Since this is impossible for reasons of finite computation time, a usual recommendation is to choose 1,000-5,000 replications. Thus all conditions are met and the bootstrap is consistent.

8

  Check that the technical definition applies.

9

  In this definition ij j E denotes total exports of country i.

  specialisation ratios based on trade marks (RTMA), norms and standards (RNSS), and technical regulation (RRS), which are certainly economic rather than scientometric or technological indicators.

  variable, which is 1, whenever object i for unit j belongs to the field under consideration and 0 otherwise 12 which counts the number of all objects for unit j which belong to the field under consideration When different times are concerned, the objects and their number will be denoted by k ij X and k j n where the superscript indicates the time period.

hlX

  whenever both variates denote different objects, iii) when n increases, also each j n grows, such that / j n n const , iv) the function used to transform the linear indicator is differentiable around the estimated value, v) (a) the objects have a natural unit and (b) the indicator has a fraction of fractions meaning, then the transformed specialisation ratio is asymptotically normal and

  all j), the analytical tests and confidence intervals from Theorems 1-3 give a reasonably good approximation (function SRtest in the R-package). Under these conditions time savings should outweigh the higher precision of the bootstrap method.

  13

Figure 1 :

 1 Figure 1: Patent Profile for 11 catching-up countries in 2003 (including 95%-confidence inter-

  European countries are largely real effects. The non-significance in the Slovenian case might have two reasons. First, it does not have a very sharp profile. So indeed, Slovenia might follow a rather

  though for a very different reason. This question is of special relevance, because classification is largely arbitrary. Referring to the empirical example of the previous subsection, the chosen level with only four classes is rather broad. Since the International Patent Classification (version 7) contains about 85,000 classes, we could have relied on a much more detailed analysis.

15

  Equation (10) of the Appendix.

  shares caught between the true and the estimated. Also, note that

  bootstrap point estimator and its cor-

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

We use either k or v throughout the text to denote the subjects under consideration. Also note that by defining an individual object we make use of the 'absolute scale' condition.

Acknowledgements

The research underlying this paper was partially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) in a project on "performance indicators for research groups" (SCHM 1719/1-2) which is part of a larger research group on "international competitiveness and innovation capacity of universities and research institutions -new forms of governance" (FOR 517). We would also like to thank two anonymous referees who with their comments helped significantly to improve the quality of this paper. We would especially like to thank them for the suggestions that gave rise to Section 4.2 and the discussion of intra-industry trade indicators in Section 2. Any remaining errors are of course the authors' responsibility.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Checking the second and third condition is absolutely standard. The second holds because we know that the distribution of the statistics under consideration are asymptotically ( )

in the one-sided interval and when we use the two-sided interval,

Turning to the third condition, we use Polya's Theorem which states that for any n X converging to X almost surely, if the corresponding distribution function

= , which implies the last condi- tion. Combining this with the first condition (if it holds), it follows that

The first condition requires ( ) ( )

, where ( ) F $ is vector of J distribution functions corresponding to the distribution of the objects in each of the j subjects. Because of the Glivenko-Cantelli Theorem we have component-wise convergence. However, with the Euclidean distance this is enough (see also [START_REF] Serfling | Intra-industry Trade between the Industrial Countries and the Developing World[END_REF]. Check that: 18 now denotes the circle constant.