The Undoing Project

The Freakonomics episode The Men Who Started a Thinking Revolution from January this year induced me to get a copy of Michael Lewis’s latest book The Undoing Project. However, having read Daniel Kahneman and Amos Tversky’s papers on Prospect Theory and the Framing of Decisions, as well as Kahneman’s Thinking, Fast and Slow, I was not sure whether I would enjoy a re-iteration of their ideas from an outsider’s perspective. My concerns actually turned out to be unfounded. The book does not intend to be a pure summary of Kahneman and Tversky’s research. It has a distinct novel touch; Michael Lewis tells the story of Kahneman and Tversky’s partnership beyond what is recorded in their papers and the book. It provides one with the context when reading about their insights into the heuristics and biases in decision-making, and Prospect Theory. For me, especially the second chapter The Outsider (aka Kahneman), and the third chapter The Insider (aka Tversky) put another complexion on their academic works and accomplishments. Admittedly, the book has strengths and weaknesses. The introduction, for example, is not very interesting if (1) you are not a baseball fan or (2) you have not read Michael Lewis’s 2003 book Moneyball. The many quotes and memos from Kahneman and Tversky, however, make up for this mediocre introduction. They are plainly ingenious and I collected my favourites to not forget them. Here they are:

Amos Tversky’s notes on conversations with Danny Kahneman in Spring 1972

People predict by making up stories

People predict very little and explain everything

People live under uncertainty whether they like it or not

People believe they can tell the future if they work hard enough

People accept any explanation as long as it fits the facts

The handwriting was on the wall, it was just the ink that was

invisible

People often work hard to obtain information they already have

And avoid new knowledge

Man is a deterministic device thrown into a probabilistic

Universe

In this match, surprises are expected

Everything that has already happened must have been inevitable (p.197)

 

Amos Tversky’s memorable sentences (collection by Don Redelmeier)

A part of good science is to see what everyone else can see but

think what no one else has ever said.

The difference between being very smart and very foolish is

often very small.

So many problems occur when people fail to be obedient when

they are supposed to be obedient, and fail to be creative when

they are supposed to be creative.

The secret to doing good research is always to be a little

underemployed. You waste years by not being able to waste

hours.

It is sometimes easier to make the world a better place than to

prove you have made the world a better place. (p.230)

 

Amos Tversky’s note to Danny Kahneman on Loss Aversion (appeared also in a 1977 draft of Prospect Theory)

The greater sensitivity to negative rather than positive changes is not specific to monetary outcomes. It reflects a general property of the human organism as a pleasure machine. For most people, the happiness involved in receiving a desirable object is smaller than the unhappiness involved in losing the same object. A high sensitivity to losses, pains, and noxious stimuli also has adaptive value. Happy species endowed with infinite appreciation of pleasures and low sensitivity to pain would probably not survive the evolutionary battle. (p.269-270)

If these paragraphs sound interesting, you might want to give the book a chance. Overall, I can recommend The Undoing Project to anyone who would like to know more about how the heuristics-and-biases programme came to be, and how Prospect Theory was born. For this, it is a worthwhile reading.

Jasmin


References

Dubner, S. (2017). The Men Who Started a Thinking Revolution. Available at: http://freakonomics.com/podcast/men-started-thinking-revolution/

Lewis, M. (2016). The Undoing Project: A Friendship that Changed the World. London: Allen Lane.

 

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The Gender Gap in Economics

While preparing my applications for graduate studies in Economics, I noticed that most of the programmes are male-dominated. They tend to have a 70-30 (male-female) distribution or less. Considering that the majority of those enrolling at university nowadays are female (Royal Economic Society, 2014), this is a rather striking result. What is more, following the reasoning of Akerlof and Kranton in their 2011 book Identity Economics, such a gender dominance may take a long time to reverse if the minority group is deterred from entering the profession. A recent article also highlights why society would benefit from an increase in females choosing a career economics:

Economics has a serious gender problem – it needs more women

In the article, Victoria Bateman – a lecturer and fellow in Economics at the University of Cambridge – aptly notices:

While economists like to think of their discipline as being gender neutral, the reality is that economists have looked at the world around them through male eyes – and rather privileged male eyes at that.

While Economics investigates gender gaps in a variety of settings, our profession has yet to raise awareness of its own gender gap, taking more measures to encourage females to choose a career in Economics.

Jasmin


References

Akerlof, G.A., and Kranton, R.E. (2011). Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being. Princeton: Princeton University Press.

Bateman, V. (2016). Economics has a serious gender problem – it needs more women. Available at: https://theconversation.com/economics-has-a-serious-gender-problem-it-needs-more-women-67653

Royal Economic Society (2014). The gender gap in economics enrolment: where does it arise. Available at: http://www.res.org.uk/view/art1Oct14Features.html

Econometrics Refresher

It has been a bit quieter on my blog over the exam period and the Christmas break, but now university is back on again and I cannot wait to start my second semester! As we have our consolidation and development week this week, it seems like the perfect time to prepare for my classes and as the semester is going to be my last one before graduation, I can pick from a list of electives.

So, besides Behavioural Economics and Industrial Economics, I get the chance to do Applied Econometrics. The course builds upon the Econometrics component from my third-year classes in Micro- and Macroeconomics and introduces:

  1. Models with limited dependent variables
  2. Panel data sets
  3. Topics involving time series data (volatility and cointegration).

One of the class prerequisites is a change in notation to the matrix form of econometrics. This is a very useful step as many econometric problems have a multivariate character and for this, the matrix form is much more convenient. While I have studied matrices in my advanced mathematics course as well as through MITOpenCourseware, I have yet to relate it to econometrics and this is what I am up to this week! Ben Lambert has a great graduate course in econometrics on his YouTube channel which covers topics from the undergraduate course in matrix formulation:

It is an indispensable source for developing your understanding and getting a feel for this representation. In particular, the course starts with an introduction to the matrix formulation of econometrics, followed by an example of it. It then continues with the differentiation with respect to a vector as well as the derivation of OLS estimators in matrix form. So, if you want or need to refresh your econometrics skills or develop them to the next level, this is for you.

Many thanks for reading!

 Jasmin

Emotions and Economics

In today’s post, I want to review the role of emotion in economic behaviour as emotions used to play an important part in Economics. Jeremy Bentham, for example, who is regarded as the founder of modern utilitarianism, gave emotions a prominent role in the decision process and viewed the concept of utility as the sum of emotions. Yet neoclassical economics abstracts utility from its psychological foundations (Loewenstein, 2000). Undergraduate students of Economics, in particular, familiarise with the representative economic agent as a rational and self-interested individual who deploys pure logic to maximise her utility. Insights from behavioural research rarely make it into an Introductory Microeconomics course. Yet more descriptive realism – particularly at undergraduate level – might help to arouse the students’ interest in the field.

economics-and-emotions
Figure 1. Consequentialist model of decision-making (Source: Rick and Loewenstein, 2008, p.139)

So, let’s start with the neoclassical view on emotions in economic behaviour. Standard economic models are consequentialist in nature (figure 1), meaning that choice is modelled as a cognitive process of utility maximisation. This does not rule out the influence of emotions in the decision process as consequentialist models can account for expected emotions, i.e. emotions which the decision-maker anticipates to experience because of her decision. Emotions experienced at the point of decision-making, however, are difficult to capture in these models as the decision-process itself is some form of expectation-based calculus.

Type

When Scope

Expected emotions

After making the decision

Related to the decision

Integral emotions

At the point of decision-making

Related to the decision

Incidental emotions At the point of decision-making

Unrelated to the decision

Table 1 The different types of emotions in decision-making

In contrast, behavioural research has identified two types of immediate emotions which are important for understanding an individual’s choice but which are typically neglected in the neoclassical view (see table above). First, there are integral emotions. They are related to the decision at hand and arise from thinking about the decision’s consequences. As shown in figure 1, consequentialist models can, in fact, be extended to incorporate this type of emotions as there is a causal link between the decision and this type of immediate emotions. Second, there are incidental emotions which are also experienced at the point of decision-making but which are unrelated to the decision, arising from situational influences and visceral factors (Rick and Loewenstein, 2008). Yet because incidental emotions are irrelevant to the decision, they are difficult to capture in the consequentialist perspective. What is more, economists tend to refrain from incorporating visceral factors in their analyses as (1) “visceral factors often drive people to behave in ways that they view as contrary to their own self-interest” and as (2) “people tend to underestimate the impact of visceral factors on their own current and future behaviour” because these complications run counter to the view that decision-making is a cognitive process (Loewenstein, 2000, p.428). Fortunately, with the rise of behavioural economics, integral and incidental emotions re-enter economic analyses. Starting with counterfactual emotions such as regret, more realistic models of behaviour emerge which re-connect emotions and utility. In the last few years, in particular, one can see a rethinking in economic modeling, for example, with the risk-as-feelings hypothesis by Loewenstein, Weber, Hsee and Welch (2001).

In sum, expected, integral and incidental emotions play an important role in economic behaviour and with a shift towards more psychologically realistic assumptions, they re-enter economic models.

Many thanks for reading; I hope you enjoyed today’s topic!

Jasse


References

Loewenstein, G.F. (2000). Emotions in Economic Theory and Economic Behaviour. Preferences, Behaviour, and Welfare, 90(2), pp. 426-432.

Loewenstein, G.F., Weber, E.U., Hsee, C.K. and Welch, N. (2001). Risk as Feelings. Psychological Bulletin, 127(2), pp. 267-286.

Rick, S., and Loewenstein, G.F. (2008). The Role of Emotion in Economic Behavior. In: M. Lewis, J.M. Haviland-Jones, L.F. Barrett (Eds.). Handbook of Emotions (3rd ed.). New York: Guilford Press.

The Economic Approach to Human Behaviour

Economics is the study of society. It goes beyond the allocation of scarce resources in markets, examining how agents in society behave and how their behaviour influences their environment. This human factor makes the study of Economics both important and exciting. However, how to model it is an open debate in Economics. In today’s post, I want to look at the new classical Economist’s view on humans. It has been shaped by the works of Chicago Economist and Nobel Laureate Gary Becker. In particular, Becker’s book The Economic Approach to Human Behavior (1976) serves as a cornerstone for how one ought to model human behaviour in the economy and society. It argues for (1) maximising behaviour, (2) market equilibrium, and (3) stable preferences.

Maximising Behaviour

In the new classical view, humans are assumed to be utility maximisers. They act as if they maximise their intrinsic utility or wealth function. However, utility maximisation does not necessarily imply that humans act only in their own interest. Becker (1993, p.386) argues that “individuals maximize welfare as they conceive it, whether they be selfish, altruistic, loyal, spiteful, or masochistic”. Hence utility maximisation is consistent with the view that humans have some broader preferences and a wide range of constraints such as income, time, imperfect memory and abilities, limited resources or opportunities available to them (Becker, 1996).

Market Equilibrium

The second pillar is market equilibrium. Markets are in place to coordinate humans’ actions. Although they vary on their degree of efficiency, markets converge towards equilibrium because humans as utility maximising agents exploit all their profit opportunities.

Stable Preferences

The third pillar is not uncontroversial; it is assumed that humans’ preferences are stable over time and similar among people. Such preferences are not preferences regarding goods and services but preferences over the fundamental aspects that people have to deal with in life. Gary Becker (1976) names the areas of health, prestige, sensual pleasure, benevolence, and envy as examples. That humans should be modeled as agents with stable preferences over these fundamental aspects in life is explained as follows:

The assumption of stable preferences provides a stable foundation for generating predictions about responses to various changes, and prevents the analyst from succumbing to the temptation of simply postulating the required shift in preferences to “explain” all apparent contradictions to his predictions (Becker, 1976, p. 5).

It should also be noted that Becker has changed his view on humans’ preferences over the course of his works. In his early works, he advocates a radical version of preference stability with time-invariance and similarity of preferences among the poor and the wealthy as well as different countries and cultures (Becker, 1976). In later works, he reverts to a less radical view on preference stability in which preferences are shaped, for example, by parents during childhood, as well as the media through advertising, or “imagination” capital (Becker, 1996). This less radical view acknowledges that humans’ preferences are relatively stable but can evolve through practice, habituation and learning, and may therefore be heterogeneous (Heckman, 2015).

In sum, the new classical view argues that “all human behaviour can be viewed as involving participants who maximize their utility from a stable set of preferences and accumulate an optimal amount of information and other inputs in a variety of markets” (Becker, 1976, p.14). Hence utility maximisation, market equilibrium and preference stability serve as the three pillars for how to analyse human behaviour in the economy and society. They ensure that new classical Economists apply the same analytical framework because human behaviour “is not compartmentalized, sometimes based on maximizing, sometimes not, sometimes motivated by stable preferences, sometimes by volatile ones, sometimes resulting in an optimal accumulation of information, sometimes not” (Becker, 1976, p.14).

Lastly, I would like to stress that, while Becker’s works have greatly influenced the profession (especially standard economic theory), his arguments are not uncontroversial. For example, although utility maximisation allows for a broader set of preferences and constraints, it models humans in a very mechanical way. Lucas, a central figure in the new classical approach to macroeconomics, once admitted that “we’re programming robot imitations of people, and there are real limitations on what you can get out of that” (Lucas in Klamer, 1984, p.49). In my opinion, this is one of the main reasons why Behavioural Economics has been so successful in the last couple of years, especially after the global financial crisis of 2008. Behavioural Economics, unlike New Classical Economics, models humans as humans and not as robots. While this may complicate the analysis, it allows for descriptive models rather than normative models of human behaviour which are of superior predictive value.

I hope you enjoyed today’s discourse and many thanks for reading,

Jasse


References

Becker, G.S. (1976). The Economic Approach to Human Behavior. Chicago: University of Chicago Press.

Becker, G.S. (1996). Accounting for Tastes. Cambridge: Harvard University Press.

Heckman, J.J. (2015). Gary Becker: Model Economic Scientist. The American Economic Review105(5), 74–79. http://doi.org/10.1257/aer.p20151106

Klamer, A. (1984). The New Classical Macroeconomics: Conversations with New Classical Economists and Their Opponents. Brighton: Wheatsheaf.

The Economics of Deception and Manipulation

I recently finished George Akerlof and Robert Shiller’s latest book Phishing For Phools. While I also enjoyed their earlier book Animal Spirits I have to say that Phishing For Phools is a hidden gem. So I decided to devote today’s post to the book and why every student of Economics should have a copy of it.

What makes Phishing For Phools different?

Phishing for Phools is different because Akerlof and Shiller give the reader a new perspective on Economics. It is not a re-iteration of New Behavioural Economics because it addresses:

  1. The Role of Equilibrium in Competitive Markets,
  2. The Difficulties with ‘Revealed Preference’ and
  3. Story Grafting.

First, Akerlof and Shiller in their perspective on Economics endorse that economic systems converge towards a general equilibrium, albeit a phishing equilibrium. In contrast, work in Behavioural Economics tends to centre on shrouded markets and economic actors having certain weaknesses (e.g. present bias). While these assumptions make phishing undeniable, the results of these studies are not generalisable. Shiller and Akerlof level criticism at Behavioural Economics in its current form because it misses the generality of phishing for phools in our economy. They describe a range of examples in the book with their favourite probably being Cinnabon® bakeries in airports and shopping malls to show that when “people have informational or psychological weaknesses that can be profitably exploited” (p.170), then we can be certain that phishing for phools is going to happen. Hence phishing for phools is a general feature of our economy rather than an externality of shrouded markets or biases of non-rational economic actors.

phishing equilibrium.png
A Phishing Game

I am thinking of Akerlof and Shiller’s phishing equilibrium in the Cinnabon® example as a Pareto-inferior equilibrium in a simple two-player “Phishing Game” with a consumer (C) and a firm (F). Here the consumer, that is the row player, has some true preferences and some monkey-on-the shoulder tastes. Both preferences map into some choice. However, the choice based on the consumer’s true preferences yields a higher payoff for her than her choice based on her monkey-on-the-shoulder tastes (assuming that the firm simultaneously chooses to provide her with that specific good and not the alternative). The column player, that is the firm, has two profit opportunities. It can open a healthy shop or a sweet & tasty shop in the airport or shopping mall where the consumer can easily be phished for a phool. I have arranged the firm’s and consumer’s payoff similar to the Battle of the Sexes game with the modification that the consumer receives a payoff of 3 and not 2 in the optimal equilibrium. This allows us to distinguish the two equilibria into an equilibrium which maximises social welfare (Healthy Shop | True Preferences) and a Pareto-inferior one, i.e. a phishing equilibrium (Sweet & Tasty Shop | Monkey-on-the-Shoulder Tastes). Both the consumer and firm want to coordinate in the sense that the consumer wants to consume and the firm wants to sell. However, the firm wants to maximise profits by selling its sweet and tasty products rather than selling a healthy product (which might allow for a lower mark-up).

Crucially, Akerlof and Shiller argue that such a ‘general equilibrium’ perspective with phishing for phools as a general feature of the economy gives an answer to why economists did not see the financial crisis coming: they did not look for phishes stemming from the informational and psychological weaknesses of economic actors and the counterparts that profitably exploited them.

Moving on to the second argument; the book is also not a re-iteration of Behavioural Economics because it challenges Revealed Preference. The authors criticise this concept and the general acceptance of it in Behavioural Economics. As mentioned above, Akerlof and Shiller distinguish between what people really want and what they think they want, i.e. their monkey-on-the shoulder tastes (and hence the book’s caption The Economics of Deception and Manipulation). Akerlof and Shiller criticise that both standard economic theory and Behavioural Economics assume that people optimise and therefore make choices which maximise their utility. Both fields tend to assume that people reveal their preferences if free to choose and given all the necessary information. This allows for the simple assumption that, in theory and practice, people’s choices reflect their true preferences. However, this is not what we observe: Akerlof and Shiller give plenty of examples in their book which they call the NO-ONE-COULD-POSSIBLY-WANTs. They categorise them into the areas of (1) personal financial security, (2) the stability of the macroeconomy, (3) health, and (4) the quality of government in order to highlight how prevalent they are. The book therefore challenges both standard economic theory and Behavioural Economics for overlooking this subtle but important difference between true preferences and what people think they want.

Third, Story Grafting makes the book different from Behavioural Economics. Akerlof and Shiller make the case for a new variable in Economics, that is the story that people are telling themselves. While Behavioural Economics has come up with a choice menu of psychological biases to explain non-rational behaviours, it has often eschewed the underlying mental frames of decision-making. Daniel Kahneman (1999, in Kahneman and Tversky, 2000, p.xiv) once said that we

apply the label “frame” to descriptions of decisions at two levels: the formulation to which decision makers are exposed is called a frame and so is the interpretation that they construct for themselves.

New Behavioural Economics has very much focused on the latter. It is the frame which decision-makers have control about. In contrast, the frame which decision-makers are exposed to is much broader and in some sense out of their control. Akerlof and Shiller’s stories describe these broader frames which are shaped in great deal by the media and our environment and peers. Rather than having a choice menu of psychological biases, Akerlof and Shiller argue for recognising these broad mental frames that influence individuals’ decisions. Stories, like phishes, are a general feature of our economy. Economics as a study of society needs to go beyond the analysis of the exchange of scarce resources. It needs to become more inclusive. In particular, Akerlof and Shiller argue that “we should be inclusive of whatever thinking, conscious or subconscious, is the basis for people’s decisions” (p.172).

In my opinion, Akerlof and Shiller have crafted a hidden gem with their book Phishing For Phools because it really offers a new perspective on Economics which goes beyond recent work in New Behavioural Economics. It makes the case for phishes and stories as a general feature of our economy and makes the subtle but important differentiation between true preferences and monkey-on-the-shoulder tastes. This New Economic perspective is more inclusive and much needed to understand how people make decisions.

So I hope that my post today has inspired you to give the book a chance. Many thanks for reading,

Jasmin


References

Akerlof, G.A., and Shiller, R. (2015). Phishing For Phools: The Economics of Deception and Manipulation. Princeton: Princeton University Press.

Kahneman, D. (1999). Preface. In: Kahneman, D., and Tversky, A., eds. (2000). Choices, Values and Frames. Cambridge: Cambridge University Press, pp. ix-xvii.

Germany’s Beveridge Curve

Today’s blog post is all about the so-called Beveridge curve. It describes the negative empirical relationship between the unemployment rate and the job vacancy rate. It can be used to gauge the state of the labour market and generally indicates where an economy is in the economic cycle (Bleakley and Fuhrer, 1997). In recessionary times, the economy moves towards the lower right corner due to an increase in unemployment and a reduction in vacancies. In expansionary times, the economy moves towards the upper left corner due to a natural fall in unemployment and an increase in vacancies posted by companies (figure 1). The position of the Beveridge curve itself is dynamic over time. It can shift out- or inward due to changes in factors like matching efficiency. An example would be the implementation of effective training programmes by the government which reduce the skills mismatch between the readily available labour and the job openings in the country. Such policies would tackle structural unemployment, shifting the Beveridge curve to the left (figure 1).

beveridge-curve-1
Figure 1 – The Stylised Beveridge Curve (Own work)

While figure 1 represents a stylised Beveridge curve, one can obtain actual data from the OECD, Eurostat or other national databases to estimate the curve empirically. I plotted the empirical Beveridge curve for Germany over the period from 2006 to 2016 in figure 2. First, the job vacancy rate can be obtained from Eurostat and is represented on the y axis. To be more exact, it is the vacancy rate for industry, construction and services (except activities of households as employers and extra-territorial organisations and bodies). The unemployment rate can be obtained from the Deutsche Bundesbank and is represented on the x axis. They have seasonally adjusted unemployment data readily available but I used the quarterly unadjusted unemployment rate because the vacancy rate quoted in Eurostat is likewise unadjusted. Also, in order to distinguish between the different states of the economic cycle, I divided the empirical Beveridge curve into the expansionary and recessionary periods in the Euro area as defined by CEPR (2016). Since 2006 there have been two major downturns, namely the global financial crisis and the European debt crisis:

Start End Euro Area
1993Q4 2008Q1 Expansion
2008Q2 2009Q2 Recession (Global Financial Crisis)
2009Q3 2011Q3 Expansion
2011Q4 2013Q1 Recession (European Debt Crisis)
2013Q2 today Expansion

Having described my methodology, let’s look at the diagram in detail. First, we can compare the state of the labour market in the first quarter of 2006 with the second quarter of 2016 and it becomes obvious that the German economy has moved along its Beveridge curve from a low vacancy/ high unemployment state to a high vacancy/ low unemployment state over the last decade. In the second quarter of 2016, the job vacancy rate quoted by Eurostat was at 2.4 percent while unemployment was at a historic low of 6 percent in comparison to unemployment rates in the years before.

beveridge-curve-2
Figure 2 – Germany’s Beveridge Curve (Data source: Deutsche Bundesbank, 2016; Eurostat, 2016)

Second, we can look at the Euro area expansionary and recessionary periods sequentially and examine potential changes in the German labour market. In the run-up to the global financial crisis (dark blue section), we can see a significant movement along the curve to the left, indicating major improvements in the German labour market. Over the financial crisis itself (green section), we observe a significant temporary dislocation of the Beveridge curve in the first two quarters due to a reduction in the job vacancy rate. However, the vacancy rate jumped back up in the third quarter of the recession followed by an increase in the unemployment rate of 1.2 percent from the last quarter of 2008 to the first quarter of 2009. The subsequent expansionary period (grey section) has overall led to further increases in the vacancy rate and reductions in unemployment despite considerable temporary jumps. More recently, however, the German economy has appeared unimpressed by the weak European macroeconomic outlook (blue and orange section) and its labour market recovered quickly from the increase in unemployment of around 1 percent over the course of the European debt crisis at the end of 2012. Since the second quarter of 2013, its job vacancy/ unemployment rates cluster in the upper left corner, signalling a strong labour market and a relative resilient national economy compared to the rest of Europe. Lastly, one could argue that, according to the data, Germany has not experienced major permanent shifts in its Beveridge curve over the last decade but rather movements along the curve. This stands in contrast with economies like the US where economists debate over a permanent outward shift in the Beveridge curve over the global financial crisis with higher structural unemployment rates for a given job vacancy rate post-recession (Zumbrun, 2014).

So that’s me for today; my post looked at the Beveridge curve both theoretically and empirically for the case of Germany. I hope you enjoyed my work and many thanks for reading!

Jasse


References

Bleakley, H., and Fuhrer, J.C. (1997). Shifts in the Beveridge Curve, Job Matching, and Labor Market Dynamics. New England Economic Review, Sept./Oct. 1997, p.3-19.

CEPR (2016). Euro Area Business Cycle Dating Committee. Available at: http://cepr.org/content/euro-area-business-cycle-dating-committee [Accessed 01 November 2016]

Deutsche Bundesbank (2016). Time series BBDL1.Q.DE.N.UNE.UBA000.A0000.A01.D00.0.R00.A: Unemployment registered pursuant to section 16 Social Security Code III / Germany / Social Security Code III and Social Security Code II / Rate / Unadjusted figure. Available at: https://www.bundesbank.de/Navigation/EN/Statistics/Time_series_databases/Macro_economic_time_series/its_details_value_node.html?https=1&tsId=BBDL1.Q.DE.N.UNE.UBA000.A0000.A01.D00.0.R00.A [Accessed 01 November 2016]

Eurostat (2016). Job Vacancies Database. Available at: http://ec.europa.eu/eurostat/web/labour-market/job-vacancies/database [Accessed 01 November 2016]

Zumbrun, J. (2014). Peter Diamond Thinks the Beveridge Curve Might Not Tell Us Much of Anything. The Wall Street Journal Online. Available at: http://blogs.wsj.com/economics/2014/08/26/peter-diamond-thinks-the-beveridge-curve-might-not-tell-us-much-of-anything/ [Accessed 01 November 2016]