Predicting  the  Impact  of  COVID-19  on  Australian

Abstract:

This article explores the impact of the novel corona- virus(COVID-19)upon Australia’s education in- dustry with a particular focus on universitics.With the high dependence that the revenue structures of Australian universities have on international stu- dent tuition fees,they are particularly prone to the economic challenges presented by COVID-19.As such,this study considers the impact to total over- all Australian university revenue and employment caused by the significant decline in the number of international students continuing their studies in Australia during the current pandemic.We use a linear regression model calculated from data pub- lished by the Australian Government’s Depart- ment of Education,Skills,and Employment(DESE) to predict the impact of COVID-19 on total Austra- lian university revenue,the number of internation- al student enrolments in Australian universities, and the number of full-time equivalent (FTE)posi- tions at Australian universities.Our results have implications for both policy makers and university decision makers who should consider the need for revenue diversification in order to reduce the risk exposure of Australian universities.

Key words:COVID-19,education,Australian uni- versities,revenue,international student enrolment, full-time equivalent employment

Introduction:
The tertiary sector of Australia’s education indus- try has been forced to rapidly respond to the out- break of COVID-19,which in turn has exposed it to new financial risks and its over-dependence on in- ternational markets.Australian universities in par- ticular are now dealing with the prospect of losing up to $19 billion in revenue by 2023 as a result of their reliance on tuition fees from international stu- dents,many of whom are currently unable to travel to Australia(Hurley,&Van Dyke,2020).This is re- flected in the way that the number of international student enrolments has decreased from 4,608,520 to just 626,052 in March,2020(DESE,2020b).As such,the immediate impact ofCOVID-19 is already bcing felt by Australian universitics and has the po- tential to cause long-term losses depending on howlong current international travel restrictions remain in place.Furthermore,Australian universi- ties act as a major source of the nation’s future productive human capital and therefore this sector takes on added significance given the extensive eco- nomic recovery required post COVID-19.In 2019, international education was Australia’s fourth largest export,contributing $40.4 billion to the economy(Ross,2020).As such,universities are key to both Australia’s current and future economic fortunes and in this way warrants the need for ex- tensive investigation into the potential impacts of COVID-19.
Existing research documents the challenges faced by Australia’s university sector in relation to gov- ernance issues and the dependence on internation- al students(Howes,2018;Goodwin,2018).Fur- thermore,recent literature has heavily detailed the initial outbreak and government responses to COVID-19 with a particular focus on the differing national responses and strategies to curbing the virus(Del Rio,&Malani,2020;Duckett,&Stobart, 2020).There has,however,only been limited re- search and modelling (eg.Hurley,&Van Dyke, 2020)released that details the impact of COVID-19 upon total Australian university revenue and inter- national enrolments.Furthermore,current esti- mates of the impact to university employment have been limited in scope as highlighted by the state- ment issued by Catriona Jackson,Universities Australia CEO,“Universities estimate that more than 21,000 jobs are at risk in the next six months, and more after that” (Universities Australia, 2020a).Therefore,a research gap exists to investi- gate the impact of COVID-19 on total Australian university revenue,employment,and international student enrolments.

This study aims to assess the changes caused by COVID-19 to total Australian university revenue, international student enrolments in Australian universities,and the number of FTE positions pro- vided by Australian universities.Previous data re- leased between 2016 and 2018 makes it possible to generate a correlation matrix between these vari- ables.This data was used as it was the most rereleased by the DESE prior to the impact of COVID-19 for the variables of total Australian uni- versity revenue and the total number of FTE jobs at Australian universities.We then use the actual number of current international student enrol- ments in Australian universities for 2020 to esti- mate the predicted effect that COVID-19 will have on total Australian university revenue and FTE jobs at Australian universities.This investigation conse- quently provides scholars,policy makers,and uni- versity decision makers with strategic foresight into the potential changes in Australia’s university sector caused by COVID-19.
As the major focus of this study is to assess the impact of COVID-19,it is first necessary to briefly review the state of coronavirus in Australia.Sec- ondly,an overview of the strategic importance of Australia’s education industry gives context to re- viewing the current governance and business models of Australian universities.This then pro- vides the basis for identifying ‘pressure points’ of Australian universities that are most likely to be impacted by COVID-19.
Literature Review and Hypotheses:
COVID-19 is a respiratory infection caused by the virus SARSCoV-2,and was discovered following an outbreak in Wuhan,China,in December 2019 (Desai,&Patel,2020).Australia’s first case of COVID-19 was recorded on 22nd January 2020 and at the time of writing (June 2020)there has been 7,391 confirmed cases and 102 related deaths (Australian Government Department of Health, 2020a).Modelling released by the Australian Gov- ernment’s Department of Health(2020b)high- lights that the government enforced shutdowns of economic activity and the implementation of strict social distancing measures have to this point been effective in suppressing community transmission of COVID-19.Consequently,there currently exists a trade-off between health-related risks,which have largely been prioritised,and economic risk which has greatly increased (Hedegaard,&Hodrick,2016; Chang,&McAleer,2020;White,2020).This creates higher risk exposure for all Australian industries, including education and more specifically the uni- versity sector,with economic growth contracting as a result of government enforced lockdowns(Wen, Ling,&Li,2020;OECD,2020).The continued shutdown of economic activity could result in Aus- tralia’s economic growth declining by 22%in the short-term with GDP decreasing at a rate of 2%per month for each month that strict containment mearemain enforced (Kehoe,2020;OECD,2020).At- tention should therefore be paid to industries such as education that hold the potential to accelerate Australia’s economic recovery from COVID-19.In particular,universities have an important part to play given their role as enablers of Australia’s cur- rent and future productive human capital.
Previous research has clearly demonstrated the link between Australian universities and higher economic growth(Deloitte Access Economics, 2015).Growth of international student enrolments has also facilitated the growth of education to become Australia’s fourth largest export in 2019 (Ross,2020).Benefits flow not only at a national level but are also apparent at the household level with higher educational attainment being associat- ed with numerous individual advantages including higher lifetime earnings(Chapman,&Lounkaew, 2015).More recently,studies have identified the clear role that universities must play to accelerate the process of economic recovery from COVID-19 (Majowicz,2020;Group of Eight Australia,2020). In particular,the continued investment in Austra- lian universities plays a key role in generating greater taxation revenue and overall economic ac- tivity in the future(Deloitte Access Economics, 2015).The challenges posed by COVID-19 to Aus- tralia’s universities therefore have far broader economic implications than just those directly re- lated to the financial health of the education indus- try.

Universities,both in Australia and around the world,have been forced to rapidly change the con- tent and delivery of their offerings to accommodate social distancing requirements and economic shut- downs caused by COVID-19(Watermeyer,Crick, Knight,&Goodall,2020;Fernandez,&Shaw,
2020;Araujo,de Lima,Cidade,Nobre,&Neto, 2020).The switch to online study and other remote learning programs has been acknowledged as plac- ing extensive strain on both university staff and ex- isting technological infrastructure(Houlden,& Veletsianos,2020).Issues with international stu- dents have also arisen with international travel bans imposed to slow the spread of COVID-19.In the case of Australian universities,travel restric- tions have impeded the ability of more than 100,000 international students from China to begin the 2020 academic year(Daley,&Mackey, 2020).Indeed,Jayasuriya(2020)identifies that the economic slowdown created by COVID-19 has ex- posed the reliance that Australian universities havehad on the tuition fees of international students and that this creates significant challenges for their future revenue base given the current ban on over- seas travel.We suggest that such reliance on inter- national students creates a pressure point for Aus- tralian universities that is directly exposed COVID-19 and increases risk.
With clear exposure to international markets,uni- versity governance in Australia takes on an added role of significance in managing external shocks. Structural changes that resulted in the creation of modern day enterprise universities can be traced back to the deregulation and funding cuts to Aus- tralian universities in the 1980s(Pietsch,2019; Howes,2018).Jayasuriya(2020)notes that the pri- vatisation of domestic student tuition fees through the Higher Education Contribution Scheme(HECS) and the extensive reliance on international student enrolments makes the current climate for Austra- lian universities very precarious.In 2020,58%of international students in Australia come from five countries with China being the single largest con- tributor at 27%(Australian Government DES&&E, 2020).Goodwin(2018)consequently concluded in his audit of New South Wales universities that the dependence on international students,particularly from China,was concerning given that total course fee revenue from international students was 54.5% greater than that of domestic students.The declin- ing nature of federal funding to Australian universi- ties accentuates the dependence on overseas stu- dents with the Commonwealth Grant Scheme (CGS),the main source of government funding for universities,being capped at 2017 levels(Universi- ties Australia,2020b).Universities have therefore been more pragmatic and acted like corporate enti- ties by prioritising international markets as their key source of growth (Loomes,McCarthy &Owens, 2019).With COVID-19 compromising the ability of international students to resume their studies in Australia,there are serious implications for the fi- nancial resilience and Australian universities.

Our research seeks to clarify the relationship be- tween international student enrolment and total Australian university revenue in the face of COVID-19.With the majority of Australia’s inter- national student population coming from five coun- tries any external shock,let alone one the size of COVID-19,will detrimentally impact Australian universities(DESE,2020).Moreover,the way in which international student enrolments have been the key driver of revenue growth for Australian universities suggests that the impact of COVID-19 on this sector will be severe.As such we propose the following hypotheses:
Hypothesis 1:COVID-19 negatively affects total Australian university revenue.
Hypothesis 2:COVID-19 negatively affects interna- tional student enrolment in Australian universities.
The impact on employment is a consequence of changes to overall revenue and student enrolment in Australian universities.Changes in work ar- rangements as a result of COVID-19 have been well documented with employees largely working from home with more flexible working hours(Spurk,& Straub,2020;Hodgson et al.,2020).In Australia, the federal government introduced a wage subsidy in March,2020 known as the JobKeeper program, enabling businesses who passed a ‘decline in turnover test’ to pass on fortnightly payments from the Australian Taxation Office to eligible em- ployees (Australian Government Federal Register of Legislation,2020).The wide scale use of short-term or fixed contracts at Australian universities has prompted concern for academics and other univer- sity staff who do not meet the JobKeeper eligibility criteria of having had worked with their current employer for at least twelve months(Harris,Smith- ers,&Spina,2020).Moreover,academic research output is estimated to be heavily affected by a de- cline in both public and private funding as a result of COVID-19(Larkins et al.,2020).Much like the situation with international student enrolments, COVID-19 has exposed the precarious nature of Australian university employment which has long shown signs of job insecurity (Broadbent,&Stra- chan,2016).Whilst there is extensive literature on the topic of job security and stress levels of Austra- lian university employees(eg.Langford,2010),this research remains outside the scope of our study. Our focus remains on the impact of COVID-19 on Australian universities with respect to total reve- nue,international student enrolment,and employ- ment.

With a decline in both the level of funding available for academic research and the ability of interna- tional students to resume their studies in Austra- lia,employment at Australian universities is likely to be severely impacted.As such,we identify the number of FTE positions at Australian universities as another pressure point that will be significantly affected by COVID-19.Based upon this,we proposethe following hypothesis:
Hypothesis 3:COVID-19 negatively affects the number of FTE positions at Australian univer- sities.
Methodology:
We tested our hypotheses using data pub- lished by the DESE.The DESE(2020a)exists to facilitate quality education,skills and em- ployment opportunities for all Australians and has numerous strategic objectives including creating a globally competitive tertiary educa- tion system.We sourced the data for the total revenue of Australian universities from the DESE’s annual ‘Finance Publication’for the years 2016 through 2018(DESE,2016a, 2017a,2018a).These publications compile in- formation from the financial reports,namely the statements of financial position,perfor- mance and cash flows,that have been pub- lished by Australian universities for the year ending 31st December for each year.At the time of writing,the 2019 Finance Publication had not been published and as such we used the most recent data available to include in our study.The data on international student enrolments was sourced from the DESE’s (2020b)international student data set with fig- ures used for enrolments in 2016,2017,2018, and March 2020,which was the most recently updated statistics at the time of writing.In re- gards to the FTE employment data for Austra- lian universities,it was retrieved from the ‘Staff Data’ statistics published by the DESE for the years 2016 through 2018(DESE, 2016b,2017b,2018b).The data includes inon the number of FTE staff employed by Aus- tralian universities as at 8th December for each year.Again,at the time of writing these were the most recently available statistics that could be used for our study.Sourcing the data published by the DESE for all our variables has the main advantage of using data from a reputable and reliable source.Furthermore, using data that is reported and consolidated by one body ensures consistency in the mea- surement across variables and hence,does not impact the validity of our study.
The causal research design for this study in order to assess the relationship between total Australian university revenue,international student enrolment,and the number of FTE employment positions provided by Australian universities.The analysis techniques that were conducted in this study include correlation analysis and linear regression analysis to assess the relationship between the variables under investigation.The correlation matrix was estimated to check for probability of multi- collinearity whilst the regression model was used to estimate how COVID-19 influences total Australian university revenue and the other auxiliary variables.By using the interna- tional student enrolment figures released in March 2020,we were able to predict the corre- sponding 2020 values for total Australian uni- versity revenue and FTE employment positions at Australian universities based on our analy- sis of their relationship between 2016 and 2018.This then enabled us to gauge the impact that COVID-19 has had on the variunder investigation for 2020.Whilst our analy- sis would have been made more accurate by the inclusion of 2019 data,it was not available at the time of writing.Furthermore,2019 data wil not reflect any of the changes caused by COVID-19 and in this way would not have fun- damentally changed the outcome of our analy- sis.Dependent Variable:
We use total Australian university revenue as our dependent variable to measure the effects of COVID-19,where total Australian university revenue is the cumulative sum of each univer- sity’s revenue within Australia in a given year.As such,we look to see the changes to total Australian university revenue that have occurred over time.Of particular interest is the change from the most recently reported figure by the DESE for total Australian university revenue in 2018 and our predicted value for this variable as it will show any change caused by COVID-19.

Independent Variables:
Our two independent variables for this study are the number of international student enrol- ments in Australian universities,and the number of FTE employment positions at Aus- tralian universities.We use these independent variables as we believe they will exert the big- gest influence on total Australian university revenue as a result of COVID-19.The number of international student enrolments is mea- sured by calculating the number of full fee paying university students in Australia thatwere born in a country other than Australia and that currently hold a student visa.FTE employment positions at Australian universi- ties is measured as the cumulative number of equivalent full-time positions across all Aus- tralian universities in a given year.This in- cludes staff who work full-time,fractional full-time,and casual based on their work con- tract.

Results:
Based on our data from Table 1,we produced a correlation matrix that can be seen in Table 2.Table 2 highlights that there is a linear rela- tionship between total Australian university revenue and FTE employment positions at Australian universities.This is informed by the positive correlation coefficient of 0.982 be- tween these two variables.Similarly,we show that there is a positive linear relationship be- tween total Australian university revenue and the number of international student enrol- ments in Australian universities,as highlight- ed by the correlation coefficient of 0.997 in Table 1.The p-value in Table 2 determines whether the relationship between the depen- dent variable and independent variables are statistically significant and as such can be used to test our hypotheses.

Table 1:Total Australian University Revenue, FTE Positions,and International Student En- rolment Data

Table 2:Results of Correlation Analysis

Significance level +p<0.1;p<0.05;*p<0.01

Based on our correlation matrix,we used a linear regression model to predict the values for the three variables for 2020 and hence, identify if there is any change as a result of COVID-19.For the relationship between total Australian university revenue and FTE em- ployment positions at Australian universities, we use the following regression model:
Revenue =-24382232698+434416.9397Em- ployment This model shows that when FTE employment positions at Australian universities is equal to zero,there will be a total revenue loss of $24,382,232,698.Furthermore,for every one additional FTE employee,total Australian uni- versity revenue will increase by $434,416.9397. For the relationship between total Australian university revenue and international student enrolments at Australian universities,we use the following regression model: Revenue =18475579453+3698.602658En- rolmentThis model shows that if there are zero inter- national student enrolments at Australian uni- versities,total Australian university revenue would be $18,475,579,453.Moreover,the model highlights that for every additional in- ternational student enrolment at Australian
This model shows that if there are zero inter- national student enrolments at Australian uni- versities,total Australian university revenue would be $18,475,579,453.Moreover,the model highlights that for every additional in- ternational student enrolment at Australianuniversities,there is a $3,698.602658 in- crease in total revenue.
We used the published figure from the DESE for international student enrolments in 2020 to predict the corresponding values for total Australian university revenue and FTE em- ployment positions at Australian universities based on the linear relationships we previously established.The number of international stu- dent enrolments in Australian universities in 2020 is $626,052(DESE,2020b).As such,we made the following calculations:
Revenue
18475579453+3698.602658*(626,052)
=20791097044
Employment
(20791097044+24382232698)/434416.9397
=103986.1148
As shown by these calculations,we predict that total Australian university revenue for 2020 will be $20,791,097,044 and that FTE employment positions at Australian universi- ties will be 103,986(nearest whole position). This therefore supports the notion that COVID-19 will have a severely negative impact on Australia’s universities.As shown by Chart 1,we predict that total Australian uni- versity revenue will decrease by $12,950,812,956 between 2018 and 2020. Given that total Australian university revenue is so heavily dependent on international stu- dent enrolment,we argue that the significant loss in revenue shown in Chart 1 can be large- ly attributed to the effects ofCOVID-19 rather than due to the influence of another variable. This is because COVID-19 is the single largest contributor to the significant drop in interna- tional students currently enrolled at Austra- lian universities.The results shown in Chart 1 consequently support Hypothesis 1.Chart 2 summarises the changes to international stu- dent enrolment reported by the DESE(2020b) and shows that enrolments decrease by
3,516,537 between 2018 and 2020.The DESE attributes the substantial drop in international student enrolments to current international travel bans which have discouraged interna- tional students in enrolling in Australian uni- versities for the 2020 academic year.As such this provides support for Hypothesis 2.Chart 3 demonstrates that we predict that 30,126 FTEpositions at Australian universities will be lost between 2018 and 2020.Considering the rela- tionship between total Australian university revenue and FTE positions at Australian uni- versities,we use the results from Hypothesis 1 to help explain the change witnessed in Chart 3.With total Australian university revenue sig- nificantly declining as a result of COVID-19, the follow-on effect is a substantial reduction in the number of FTE positions available at Australian universities.We therefore conclude that the change to FTE employment between 2018 and 2020 can be explained by the impact of COVID-19 which in turn supports Hypothe- sis 3.

Chart 1:Impact of COVID-19 on Total Austra-lian University Revenue

Chart 2:Impact of COVID-19 on International Student  Enrolments  in  Australian Universities

Chart 3:Impace of COVID-19 on FTE Positionsat Australian Universities

Discussion:
This study was motivated by the limited nature of current analysis and estimations of the impact of COVID-19 on Australia’s education industry.In our study,we have detailed the effect of COVID-19 on three key variables for Australian universities;total Australian uni-
versity revenue,international student ments,and FTE employment positions tralian universities.In this regard,we
gated the exposure of these variables to the impact of COVID-19 and consequently high- light that they are indeed pressure points that indicate the risk exposure of the broader ter- tiary education system.With the high level of uncertainty in the current COVID-19 climate, our research provides measurable results that are highly relevant to the present state of Aus- tralia’s education industry.
The empirical results of this study confirm the already known negative effects of COVID-19. Previous research only demonstrated the impact of COVID-19 on individual variables such as international student enrolment (eg. Hurley,&Van Dyke,2020)and as such pro- vided a limited analysis of the consequences of the pandemic.Our findings therefore extend upon this prior research by taking internation- al student enrolments and introducing the variables of total Australian university revenue and FTE employment at Australian universi- ties to demonstrate the severe effects that COVID-19 has had on the relationship be- tween these variables.Of particular note is the significant loss of total revenue that we predictfor Australian universities in 2020,declining from $33,741,910,000 in 2018 to $20,791,097,044 by the end of the current year.With a revenue loss of $12,950,812,956 faced by Australian universities,our results reveal the immediate financial challenge that confronts the tertiary education sector.Whilst existing research indicates that Australia’s universities face a cumulative loss of $19 bil- lion by 2023(Hurley,&Van Dyke,2020),we suggest that more than $12 billion of that could be realised in 2020.Moreover,we argue that the current business model of most Aus- tralian universities is over-dependent on income generated from international student enrolments and that this has been exposed and exacerbated by COVID-19.This conse- quently extends the discussion on the expo- sure of Australian universities to external shocks and questions the sustainability of the current practice of deriving a significant pro- portion of revenue from international markets. Furthermore,our results have implications for
Australia’s ability to sustain petitiveness in international in turn will affect the path of ery from COVID-19. its export com- education which economic recov-

With our research indicating severe effects of COVID-19 on Australian universities in the immediate term,it is also worth considering the long-term impact of the pandemic.The sig- nificant decline in total revenue,international student enrolment,and FTE employment that we predict for Australian universities in 2020 points towards a multi-year recovery effort to return to pre COVID-19 levels.In particular, international student enrolments are likely to remain significantly lower whilst international travel restrictions remain in place.Indeed,re- search released by the DESE(2020c)demon- strates that the year-to-date April 2020 defer- ments for international students was 53,075. This represents an increase in the number of deferments by 40,725 from the same period in 2019.The analysis conducted in our study therefore serves as a way of understanding the impact and relationship between the variables, and can be used to contextualise the implica- tions of newly released findings such as those published by the DESE.Additionally,we argue that the significant decline in international student enrolments not only has negative con- sequences for the revenue generated by individual universities but it is also problematic for the broader performance of Australia’s in- ternational education sector over the short to medium term.With international education being Australia’s fourth largest export in 2019,our findings suggest that the impact of COVID-19 will cause a significant decline in the performance of this sector.As shown by our results,FTE employment at Australian universities is an area that will be majorly af- fected by the loss of revenue and international student enrolments The prevalence of short-term or fixed contracts for many of these workers has made them particularly prone to layoffs resulting from COVID-19.Such layoffs raise concerns over the quality of tertiary edu- cation offered by Australian universities in the future as well as the impact to the output and rigour of academic research.The importance of tertiary educated workers to the productivity of Australia’s workforce and the guidance that current academic research provides to policy direction leads us to point out the importance of minimising the number of job losses in this sector.

Our research provides practical insights for policy makers and university decision makers in Australia.By demonstrating the significant decline in total Australian university revenue, international student enrolment,and FTE em- ployment at Australian universities we have been able to quantify the short-term impact of COVID-19.In particular,the over-dependence on international student enrolment for the growth of Australian university revenue is an area of deep concern given the high levels of uncertainty in the global economy.This not only places Australian jobs at risk but also has severe implications for one of Australia’s key exports.Our study consequently provides policy makers and university decision makers with real time findings that demonstrate the potential impact of COVID-19.From this it be- comes apparent that Australian universities and the education sector more broadly is set to face significant financial challenges that need to be carefully navigated to avoid further losses.

Limitations and Further Research:
Making predictions from our statistical analy- sis for total Australian university revenue and the number of FTE equivalent jobs at Australian universities in 2020 warrants the need to acknowledge the limitations of our study. Whilst making these predictions enabled us to clearly map out the impact of COVID-19 on in- ternational student enrolment,total Austra- lian university revenue,and Australian univer- sity employment,it ultimately limits the appli- cability of our study.For policy makers and university decision makers it is important to note that these predicted values are as accu- rate as current information and publications allow,but that they may differ from the actual values reported in subsequent time periods. Furthermore,this study being completed in June 2020 can only make a premature assess- ment of the relationship between the variables in the wake of COVID-19.For more accurate and extensive analysis,data for at least the entire 2020 academic year and ideally 2021 would be used to investigate the long-term im- pacts that COVID-19 has had on Australian universities.We therefore suggest that further areas of research could include the impact that COVID-19 has had on total student enrol- ments,both domestic and international,and the subsequent effect this has on funding for academic research.Also of relevance would be investigating the current role that Australian universities are playing in sustaining econom- ic growth whilst other industries are operating at below capacity.

Conclusion:
COVID-19 is set to severely impact Austra- lia’s universities and the broader education industry.Our research investigates the impact of COVID-19 on three key variables;total Aus- tralian university revenue,international stu- dent enrolment in Australian universities,and FTE employment at Australian universities. Through the use of correlation analysis and re- gression analysis we show that our three key variables will significantly decrease in 2020 due to the effects of COVID-19.More specifi- cally,we use the 626,052 international stu- dentenrolments reported by the DESE for 2020 to predict that there will be a loss of $12,950,812,956 in total Australian university revenue whilst the number of FTE employment positions at Australian universities will de- crease by 30,126.As such,we provide a dis- cussion on the significant exposure of Austra- lian universities to the effects of COVID-19 and point to their dependence on revenue coming
from the enrolments of international students as a key reason for such exposure.Our study therefore adds to the growing research on the effects of COVID-19 with a specific focus on demonstrating the adverse impact on Austra- lia’s universities.
Acknowledgements:All authors gratefully ac- knowledge the support provided by Dr Xue-Feng Shao.We would like to thank him for careful supervision and comments which greatly improved this paper.

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