Consumer Confidence and Business Cycles
A case study for the Netherlands: are business cycles driven by animal spirits?
‘The only thing we have to fear is fear itself’ - Franklin D. Roosevelt -
A.F. Klein
University of Groningen
Abstract: In this paper, an attempt is made to explore the relevance of a consumer confidence index in forecasting business cycles in the Netherlands. Furthermore, the possible heterogeneity regarding the information content of individual questions is addressed, and it is investigated whether this information can be attributed to the information view or to the animal spirits view. This paper constructs a Bayesian VAR (BVAR), which includes a consumer confidence index, the unemployment rate, a composite leading indicator, producer confidence, and the Michigan consumer sentiment index. The results show that for the 24-month-ahead forecast and the 48-month-24-month-ahead forecast of unemployment, consumer confidence explains respectively 3.96% - 8.06% and 10.25% - 15.99% of the error variance. Moreover, there seems to be significant heterogeneity among the individual questions in the consumer confidence survey. Finally, it is concluded that the additional predictive power of consumer confidence can be attributed to the information view.
Keywords: Consumer Confidence Index (CCI), Bayesian VAR, Unemployment JEL Classifications: C11, D12, E37
1. Introduction
past 10 years was consumer confidence, which is measured by a consumer confidence index (CCI). Furthermore, the media generally presents the development of these CCIs in order to inform the public about the future state of the economy. Indeed, as you explore the development of consumer confidence in the Netherlands over the past 10 years, as shown in Figure 1 below, you see that consumer confidence resembles a recognizable pattern. In the earlier 2000s, the economy in the Netherlands was still recovering from the burst of the Dot-com bubble, and this is reflected in Figure 1 by a consolidated relatively low level of Figure 1 Consumer confidence in the Netherlands over the past 10 years
The graph depicted here shows the development of the consumer confidence index from February 2004 to February 2014 calculated by Netherlands Statistics. The horizontal line represents the zero-line where the percentage of optimists coincides with the percentage of pessimists.
technologies that induced low interest rates and gave a boost to investment and economic growth. However, once the realization sunk-in that this growth was fuelled by low-quality loans, investors massively pulled back their funds followed by a collapse of the financial system (see e.g. Eichengreen, et al. 2012). Again, Figure 1 presents a mirror image of this story; in the flourishing period, prior to the collapse, confidence among Dutch consumers peeked to its highest point on June 2007, directly followed by a steep decline in confidence once the public realized that bad financial products drove this growth. Furthermore, due to the collapse of the financial system, several leading financial institutions required funds from the government and as a result debt levels skyrocketed among EU member countries (see e.g. Afonso, Arghyrou and Kontonikas 2012). This process eventually developed in a sovereign debt crisis where the Netherlands is still recovering from. Once more, Figure 1 reflects this economic development with a consolidated negative value of consumer confidence, reaching its all-time low on February 2013. Though, the percentage of pessimist still exceeds the percentage of optimists, consumer confidence seems to be recovering from this trough1.
From Figure 1, and the story drawn above, it becomes evident that there is a strong correlation between consumer confidence and business cycles. In this paper, an attempt is made to explore the economic relevance of consumer confidence in forecasting unemployment. The following research questions are addressed: (1) Can a CCI be considered as an important variable in explaining business cycles in the Netherlands? (2) Does the additional predictive power comes from the fact that a CCI contains information about future economic activity, not captured by an econometrician, or is it due to people’s animal spirits? To answer these questions, a Bayesian vector autoregression (BVAR) is constructed which includes a set of common predictors of business cycles. Moreover, as a monthly proxy for business cycles the unemployment rate (UNEMR) will be used.
To answer the first question, the assumption is adopted that consumer confidence can be considered as an important variable for a professional forecaster of business cycles if, after
the inclusion of other predictors of future business cycles, consumer confidence remains to explain a substantial share of the forecast error variance of unemployment. This assumption is based on past research, which has revealed that the link between consumer confidence and economic activity might disappear once the researcher includes other predictors of economic activity. This would imply that consumer confidence simply mirrors information already captured by other variables and does not possess important unique information. On the other hand, if consumer confidence does capture additional predictive power regarding future business cycles, the literature suggests that there are two opposing beliefs about the nature of this extra information. First, there is the information view that postulates that people possess information about the future state of the economy that is not already captured by other financial variables. Second, there is the animal spirits view that states that the additional causing effect is due to people’s animal spirits2, i.e. people’s spontaneous urge to action rather than inaction. We can distinguish between both views by inspecting the impulse response figures (IRFs) of the unemployment rate to unexpected shocks in consumer confidence. The second assumption made in this paper states that the information view is valid when the IRFs show a permanent response to a one-time unexpected shock in consumer confidence. Contrarily, when a temporary response is observed, it can be concluded that the animal spirits view is valid.
What is the merit of the analysis done in this paper? First, for professional forecasters, it is important to know whether they should incorporate consumer confidence in their analysis or that they can simply ignore it. Current evidence for the Netherlands is scarce on this issue. Second, it is valuable to know whether this additional information comes from superior forecasting power of individuals about the future state of the economy or that it is induced by the emotions of individuals that have a causing effect. If the latter is true, this might be a justifiable reason for the Dutch government to intervene and to actively manage
people’s animal spirits3. Of course, this would be a hard task to perform, but I believe that properly informing people about economic matters and thereby enriching people’s information set is important. Third, this paper distinguishes from others in the sense that it provides an extensive literature review on both the concept of animal spirits and on consumer confidence. The past literature seems to suffer from several measurement errors. Moreover, animal spirits are structurally interpreted as some exogenous force while Akerlof and Shiller (2009) have shown that animal spirits can be described by 5 important drivers. To my knowledge, this is the first paper that extensively discusses these 5 dimensions of animal spirits. Fourth, past research seems to neglect the possible heterogeneity of individual survey questions and this paper will take this measurement error into account. Finally, by applying a BVAR instead of the more traditional general VAR, it is possible to impose less restrictive restrictions on the parameters. Moreover, I am able to deal with the fact that the link between the considered variables might not be constant over time.
The results for the 5-variable 7th-order BVAR model including CCI, UNEMR, CPI, MSCI, and a CLI4, which is comprised of manufactures’ order books, manufacturing production future tendency, AEX stock prices, finished manufacturing goods stocks, IFO business climate indicator for Germany, and inverted manufacturing orders inflow: tendency, show that CCI can be considered as an important variable in forecasting future business cycles. Depending on the setting of the overall tightness parameter, 𝜆1, 3.96% - 8.06% of the error variance of the 24-month-ahead forecast is explained by CCI, and 10.25% - 15.99% of the error variance of the 48-month-ahead forecast. Moreover, section 7 shows that there is significant heterogeneity among the individual questions. ECSITN12 explains most of the error variance (8.16% - 9.17%) for the 24-month-ahead forecast of UNEMR, and FINSITL12 is the most important variable (13.18% - 20.27%) for the 48-month-ahead forecast. Finally,
3 Especially since the Netherlands is a member of a monetary union, and the design of such a union is prone to asymmetric shocks and animal spirits might amplify these shocks (see De Grauwe 2012 p32), it is worthwhile to explore whether consumer confidence can be certified as an important source of these shocks. Of course thee results in this paper only relates to the Netherlands, hence, in order to draw any convincing conclusions a thorough analysis is required of all individual 27 EU members.
following assumption 2, I conclude that the additional predictive power is compatible with the information view and not with the animal spirits view.
In the next section, I will start with discussing the multidimensional character of animal spirits. Second, in the third section, I will present an accurate literature review on consumer confidence and economic activity, and how it can be related to animal spirits. Thereafter, in the fourth section, it is explained how consumer confidence can be linked to business cycles and how this can be formally presented in a theoretical model. Fourth, section 5 will be used to explain the data and the methodology applied. Fifth, in section 6 the BVAR model is discussed and the results of this model are presented in section 7. Thereafter, the heterogeneity of individual questions will be discussed. I will end with a conclusion summarizing the paper.
2. Multidimensionality of animal spirits
In the current empirical literature, animal spirits are taken as some exogenous force that might drive individual behavior. Besides mentioning Keynes' definition of animal spirits, i.e. as our spontaneous urge to action rather than inaction, researchers never explain what factors drive these spontaneous urges. Nonetheless, I believe that in order to understand why and how animal spirits might play a role in macroeconomics, you should at least have some idea of what animal spirits are. Fortunately, Akerlof and Shiller (2009) give us a good understanding of the theory on animal spirits. According to Akerlof and Shiller (2009), a complete theory on Animal spirits should incorporate the following five drivers of animal spirits: (1) Confidence, (2) Stories, (3) Fairness, (4) Corruption and bad faith, and (5) Money illusion. The key characteristics and implications of all five dimensions will be sequentially discussed below.
2.1 Animal spirits: confidence
matter whether an agent has confidence or not in his actions, he knows the underlying ‘truth’ and simply chooses the action that maximizes his utility. However, Akerlof and Shiller (2009) doubt that investors are really able to make their decisions in such a mechanical way. They stress that, in reality, decisions are ultimately made on the basis of whether someone has confidence or not in a good outcome. Note that the confidence dimension of animal spirits can only have a causing effect on economic activity if our animal spirits let us forego (undertake) investment or consumption opportunities that would (not) have been done under the standard neoclassical framework. Hence, our animal spirits can make us under-confident or over-confident. In the field of psychology, many research is done on overconfidence, and we know that it is observed in several professions, ranging from physicians and nurses (see e.g. Christensen-Szalanski and Bushyhead 1981; Baumann, Deber, and Thompson 1991) to managers and investors (see e.g. Barber and Odean 2001; Malmendier and Tate 2005). Furthermore, we know that people especially tend to be over-confident for tasks they have little experience with, that are difficult, hard to forecast and that give no clear and fast feedback (Lichtenstein and Fischhoff 1977; Barber and Odean, 2001). The interested reader is referred to box B1 in Appendix B where the market for over-confidence is defined and from which it will be clear by what motives over-confidence is driven and through which mechanisms overconfidence is achieved. Contrarily, far less is known about under-confidence, and the current literature is insufficient to explain why economic agents might be under-confident.
2.2 Animal spirits: stories
economy permanently. Moreover, when people start to believe and act on these stories, a contagious wave of optimism is created. As a result, the economy starts to grow faster and faster. Furthermore, those who are skeptic and question whether this period of rapid growth is sustainable, and refer to earlier crises were similar patterns emerged, are reminded that a ‘new era’ is born (Shiller 2005) and that ‘this time is different’ (Reinhart and Rogoff 2009)5. This self-fulfilling wave of optimism will hold on until reality reveals that this time was not different but that it was simply a result of a free-market process driven by positive stories and believes that contributed to an economic bubble. Once this realization has sunk in, the bubble bursts and an economic crisis arises. Despite the historical literature that has clearly identified the relevance of stories, to my knowledge, there is no formal theoretical model of stories yet. Nevertheless, I believe that in order to properly understand the welfare implications and the importance of stories in economics, a formal model is required. In the search for such a model, Akerlof and Shiller (2009) suggest that economists might use mathematical models of epidemics of infectious diseases as a guide in developing these models. However, the construction of such a model is behind the scope this paper but it would certainly be an interesting subject for further research.
2.3 Animal Spirits: fairness
Third, Akerlof and Shiller (2009) state that another factor that drives our urge to action rather than inaction is fairness. In the standard neoclassical framework without altruistic preferences, the representative agent is self-interested, knows how the model works and fairness is irrelevant in the decision-making process. In this setting, the invisible hand in the market determines whether prices or wages go up or down, and the representative agent simply anticipates to these market-induced changes by alternating his actions such that his utility is maximized again and market equilibrium is re-established. In other words, in the standard neoclassical framework, an individual will always undertake an action if the material value that he attaches to this action is higher or equal to the costs of this action
irrespective of the fact whether these costs are seen as fair or not. Despite of the valuable insights generated by the standard neoclassical framework, some psychologists and economists believe that in reality people do care about the fact whether they, or others, are treated fairly, and fairness plays an important role in an individual’s daily decision-making. Regarding the empirical evidence of the relevance on fairness in the decision-making process, experiments in the field of economics have revealed that people are typically not fully altruistic in the sense that they unconditionally want to help others, but that their willingness to help others depend on how fair the other individual behaves. Several psychologists have shown that people are willing to give up some of their own material welfare in order to reward others for fair behavior (see e.g. Marwell and Ames 1981, Kim and Walker 1984; Andreoni 1988a,b). Furthermore, other experiments have indicated that, besides rewarding fair behavior, people are also willing to give up some share of their own material welfare in order to punish unfair behavior of others (see e.g. Greenberg, 1978; Roth, Prasnikar, Okuno-Fujiwara, and Zamir 1991; Kahneman, Knetsch and Thaler 1994). Thus, these experiments show that people are willing to sacrifice material welfare out of fairness considerations, however, the existing empirical evidence points out that this willingness to sacrifice depends negatively on the costs of this sacrifice (see e.g. Leventhal and Anderson 1970; Thaler 1988). Besides the empirical evidence from psychology, several economists have incorporated the stylized facts from these experiments in a formal model of economic behavior based on fairness in order to get a broader understanding of its welfare implications6.
2.4 Animal spirits: corruption and bad faith
Fourth, Akerlof and Shiller (2009) state that our animal spirits might induce periods of corruption and bad faith. They argue that capitalistic economies produce one serious negative externality and that is, that it does not necessarily produce the goods and services
that people need, instead it produces the goods and services that people think they need. Hence, this feature of capitalistic economies might induce people, who are sensitive to their animal spirits that appeal to their dark-side (dark animal spirits), to take advantage of the gullibility of others in an attempt to make excessive profits. Moreover, the consequences of this negative externality are aggravated due to the common introduction of public limited liability companies (LLCs) in modern-day economies. LLCs are designed such that the owners of the firm, i.e. the stockholders, have limited liability and that these stockholders can sell their shares on the stock market and thereby handing-over their ownership to the buyer. Furthermore, these stockholders can be divided into two groups, the insiders (those stockholders who work at the LLC) and the outsiders (those stockholders that do not work at the firm). Typically, the insiders know more about the true value of the firm than the outsiders, however, it is generally restricted by law, and hence illegal to use this inside-information. Nonetheless, the design of these LLCs gives those insiders who cannot resist their dark animal spirits an incentive to deceive outsiders and obtain an excessive return by means of creative bookkeeping. Historical research on past financial and economic crises have pointed out that dark animal spirits have contributed significantly to past crises. Appealing examples are the Enron fraud in 2001 and the collapse of the Lehman Brothers in the fall of 2007 (see e.g. Akerlof and Shiller 2009).
2.5 Animal spirits: money illusion
distorted by inflation did not match well with the standard neoclassical framework that started dominating economic textbooks from the 1960s, and that evangelizes rational workers who are only interested in real wages, and rational buyers and sellers who are only interested in real prices (Akerlof and Shiller 2009). Despite the fact that this view still dominates current macroeconomic textbooks, empirical studies show that in reality nominal values do matter. The following stylized facts have been identified: (1) only few labor contracts are indexed against inflation (see e.g. Christofides and Peng 2006), (2) people do not seem to like nominal wage reductions, i.e. they seem to exhibit downward wage rigidity (see e.g. Altonji and Devereux 1999; Fehr and Goette 1999; Lebow, Saks and Wilson 2003), (3) buyers seem not to like nominal price increases (see e.g. Shafir, Diamond, and Tversky 1991), and (4) only few debt contract are indexed against inflation (see e.g. Akerlof and Shiller 2009). This evidence suggest that peoples’ economic decisions might deviate from the standard neoclassical framework and instead might be driven by animal spirits characterized by money illusion.
3. Consumer confidence
CCIs, and the measurement errors that these empirical applications seem to exhibit. Finally, the second part of this section explains how animal spirits can be filtered from a CCI.
3.1 CCI: construction, determinants, application and measurement errors
In order to measure the confidence of its citizens about the current and future state of the economy, most countries have a national statistical institute that carries out a survey among its citizens with questions regarding this issue. Each month, these bureaus gather the results of these surveys and construct a CCI7. Past research has indicated that, besides economic fundamentals, the level of a CCI is influenced by indicators for political stability/events (see e.g. Neisingh and Stokman 2013) and by major exceptional national and international events (Malgarini and Margani 2007). Although, the note must be made that the variables to proxy these political and exceptional events are sensitive to the adopted CCI (see e.g Golinelli and Parigi 2004), vary over time (see e.g. Neisingh and Stokman 2013) and depend on social-demographic characteristics (see e.g. Malgarini and Margani 2007). Furthermore, there is evidence that due to increased synchronization across business cycles, consumer confidence in the European Union (EU) is affected by consumer confidence in the US (see e.g. ECB Monthly Bulletin January 2013). To be more precise, confidence movements in the US might lead confidence movements in the EU in time.
The fact that these CCIs grasp individual’s expectations about the future state of the economy and about their own future financial situation, have attracted many economists’ attention over the past five decades to investigate what information these indices contain. The most addressed issue is whether CCIs contain information that affects future economic activity and that is not already obtained by other financial indicators such as stock prices, the inflation rate, and interest rates. Since CCIs are constructed based on specially designed questions to reveal an individual’s belief about the future state of the economy, it could be that these indices contain additional information about the future not already captured by
other financial indicators. Although there is no consensus yet on the exact information content of CCIs, nor is there consensus on the exact link between consumer confidence and economic activity, economist have agreed that the additional information of consumer confidence is especially relevant in periods of severe economic booms and recessions, and less relevant during ‘normal’ times8. As regards to the predictive power of CCIs on economic activity, research is done on consumer spending (see e.g. Mueller 1963; Mishkin 1978; Hutt, Eppright and Taube 1994; Ludvigson 2004), GDP/GNP growth (see e.g. Matsusaka and Shordone 1995; Batchelor and Dua 1997), the unemployment rate (see e.g. Leeper 1992), Industrial production (see e.g. Leeper 1992), and labor income growth (Carroll, Fuhrer, and Wilcox 1994; Ludvigson 2004). In order to give the reader a good understanding of the empirical application, the predictive power and significance of CCIs, Table C1 is constructed (see Appendix C). The interested reader is referred to this table, which contains an overview of a wide range of the most relevant literature on the forecasting power of CCIs. Most conclusive evidence is reported for the additional predictive power of a CCI regarding future consumer spending9. There exist three theoretical concept that can explain this link between consumer confidence and consumer spending: (1) the precautionary saving motive, (2) liquidity constrained agents or agents that consume a fixed fraction of their income, and (3) an agent’s willingness-to-buy. The interested reader is referred to Box C1 in Appendix C where all three concepts are shortly explained.
8 In general, these extreme periods are characterized by a high volatility of consumer confidence (see e.g. Garner 1991; Howrey 2001) and consumer confidence seems to granger cause these booms and crises, i.e. they lead them in time (see e.g. Matsusaka and Sbordone, 1995). Hence, this literature suggests that the relationship between consumer confidence and economic activity is non-linear. That is, in normal times CCIs seem simply to reflect the same information contained in other publicly available financial indicators. However, in periods of financial crises, economic crises, and periods of severe political instability as well (see Dées and Soares-Brinca 2013; ECB Monthly Bulletin Jan 2013), CCIs seem to exhibit significant additional information regarding the future state of the economy not already reflected by other financial indicators.
Finally, the four measurement errors that the literature on CCIs and economic activity seem to exhibit are discussed. First, past research has shown that there exists heterogeneity regarding the information content of different CCIs. For instance, Ludvigson (2004) finds that the two most popular CCIs in the US, the Conference Board Consumer Confidence Index and the Michigan Consumer Sentiment Index, reflect different information10. This makes sense since you should not see a CCI as some exogenous variable capturing consumer confidence, the information reflected by a CCI depends in full on the questions of the corresponding survey. Moreover, it could be that each individual question measures a different aspect of confidence. In my opinion, past research lacks proper attention to the possible heterogeneity of individual questions and this might lead to a measurement error. This issue will be addressed in section 8. Second, past research mostly deals with aggregate data and this might lead to biased results because the link between consumer confidence and economic activity might differ between idiosyncratic characteristics such as social class, education, wealth and income (Souleles 2004; Malgarini and Margani 2007). Third, another measurement error results from the fact that, in a consumer confidence survey, individuals are interviewed on a certain point in time, let’s say time t, and they base their answers on the information available on time t. Hence, when you want to empirically test the macroeconomic impact of some CCI, one should ideally use independent and dependent variables that were available at period t. In other words, for the most representative and accurate results, real-time data should be incorporated rather than the most frequently used revised data (historical data). Of course, the revised data issue is only relevant if revised data differs substantially from the real-time data or how Croushore (2005) puts it: ‘If data revisions were small and inconsequential, we would not worry about using real-time data, but instead could rely on data that have been revised many times. However, data revision may be large and may be systematic, so that our empirical results could be biased if we did not use time data’. [Croushore (2005), p440] However, the problem with
10 Ludvigson (2004) shows that the Conference Board Index reflects mainly changes in labor market conditions and the Michigan Index reflects especially recent changes in the economy. For the exact questionnaire see Ludvigson (2004) or go to
time data is that its availability is scarce. To my knowledge, there is only one paper concerned with consumer confidence that incorporates real time data, and that is the research of Croushore (2005)11. Finally, the last measurement error that a researcher on the subject of consumer confidence and economic activity should acknowledge is the fact that a CCI might possess a fourth measurement error due to the fact that some questions might be too qualitative or too ambiguous for the interviewed person (see e.g. Manski 2004). Unfortunately, this is an error that a researcher must take as given and the mitigation of this problem is a task for the statistical bureau constructing the CCI.
3.2 CCI: information view or animal spirits?
Now we have established that consumer confidence might contain additional information about future economic activity; it is time to evaluate how this additional information can be captured and how its nature can be identified. There is consensus that in order to obtain this additional information, you should include an extensive set of fundamentals and predictors of the variable that you want to predict. With such an approach, we are able to disentangle whether a CCI anticipates to some measure of economic activity or that it causes economic activity. If the former is true, a CCI will lose its predictive power after controlling for other fundamentals, and if the latter is true, a CCI will maintain its predictive power, even after controlling for other fundamentals (Matsusaka and Sbordone 1995). The fact that a CCI has additional predictive power implies not by definition that this additional power is induced by people’s animal spirits. There is still a possibility that there is some other underlying predictor of economic activity not accounted for in the model. Barsky and Sims (2009) introduced two concepts to define these two opposing possibilities. The first view is defined as the information view and implies that the additional predictive power reflects fundamental information about the future state of the economy that is not captured by other economic indicators. According to the information view, shocks in consumer confidence should have a permanent effect on the economy. Furthermore, the second view
is labeled as the animal spirits view and states that the additional information reflects people’s animal spirits that, in turn, have a causing, but temporary, effect on the economy. The empirical approach used in this paper to filter animal spirits from a CCI is based on the papers of Matsusaka and Sbordone (1995) and Barsky and Sims (2009). First, Matsusaka and Sbordone (1995) apply a VAR analysis in order to link consumer confidence to GNP, and they control for an extensive series of predictors used by professional econometricians in forecasting GNP. Their results show that, even after including these variables, still between 13 percent and 26 percent of the error variance of the 24-month-ahead forecast of GNP is due to shocks in consumer confidence. Furthermore, they state that, for the information view to be valid, consumers apparently possess more information about future economic activity than a professional econometrician. Contrarily, for the animal spirits view to be valid, this additional predictive power for GNP is driven by consumer’s sentiment. Matsusaka and Sbordone (1995) conclude that they find the second assumption not less plausible than the first.
Notwithstanding the importance of the insight generated here by Matsusaka and Sbordone (1995), they do not give a quantitative conclusion. They leave it up to the reader to decide whether to interpret the information or animal spirits view as more plausible. Fortunately, Barsky and Sims (2009) offer an intuitive solution to control with econometric tools whether the additional predictive power is driven by animal spirits or by information outside the econometrician’s information set. By estimating a VAR and simulating a shock in some CCI, the researcher can derive from the IRFs whether the shock contains animal spirits or additional information regarding economic fundamentals. When the effect of a shock in consumer confidence on economic activity is only temporary, the animal spirits view is valid. On the other hand, when the IRFs show permanent effects, the information view is valid. Barsky and Sims (2009) conclude that in their analysis for the US, using the Michigan Consumer Sentiment Index, the information view seems to be valid.
extensive set of plausible predictors of economic activity. Hence, it could be that their conclusion suffers from omitted variable bias. In this paper, this bias is minimized by following the approach of Matsusaka and Sbordone (1995). Moreover, the method of Barsky and Sims (2009) will be applied to distinguish between the information and the animal spirits view.
4. Theoretical framework: animal spirits and business cycles
In the previous sections it is clearly described what animal spirits are, what its dimensions are, and how they are commonly measured. We concluded that the most popular empirical method to capture the effects of animal spirits is via a CCI. Furthermore, it is shown that consumer confidence can, theoretically, be linked to future consumption spending through three concepts: (1) the precautionary savings motive, (2) liquidity constrained agents or agents who consume a fixed fraction of their income, and (3) a consumer’s willingness-to-buy. Nonetheless, the ultimate goal of this paper is to link animal spirits to business cycles. Hence, this section discusses the theoretical literature in which business cycles are driven by consumer confidence.
eventually the bubble bursts. As a result, a crisis is born. Hence, rather than real factors, as suggested by standard real business cycle models, people’s animal spirits seem to play a crucial role here. To quote Shiller (2002): ‘If I may interpret the model more broadly, I think we can say that investors have overconfidence in a complex culture of intuitive judgments about expected future price changes and an excessive willingness to act on these judgments. This overconfidence is a powerful force in the market; the intuitive judgments are ultimately behind both the upward feedback that underlies the bubble and the down-ward feedback that signals the end of a bubble.’ [Shiller (2002), p4] Hence, the statement of Shiller (2002), and the evidence presented above, suggests that non-economic fundamentals such as animal spirits and especially consumer confidence (two concepts which we elaborately discussed in section 2 and 3) may help us in understanding the magnitude of past economic crises. The popular textbook models of real business cycles and the new-Keynesian Dynamic Stochastic General Equilibrium (DSGE) models do not account for these non-economic fundamentals and fall-short in understanding the factors that lead to economic bubbles that often precede economic crises. Below, three types of models will be discussed that do account for these non-economic fundamentals.
expectations of future developments can play a role, it still does not account for the possible effect of consumer confidence driven by animal spirits.
In the second-range models on confidence and business cycles, waves of optimism and pessimism cause multiple equilibria (sunspots). Again, agents’ expectations are rational and they do not exhibit cognitive limitations. The waves of optimism and pessimism, that are the cause of sunspots in these models, are driven by agents’ animal spirits (see Azariadis 1981; Howitt and McAfee 1992; Farmer and Guo 1994; Benhabib and Farmer 1996; Ferreira and Dufourt 2005). In the sunspot literature, a boom or a recession can occur even in the absence of a real shock. That is, a positive (negative) shock in consumer confidence can bring the economy on the saddle path to a better (worse) equilibrium. For instance, Howitt and McAfee (1992) develop a model in which firms recognize when market confidence is positive or when it is negative. Hence, rational firms know when the economy starts to move on the saddle path from the old to the new equilibrium. Moreover, these paths of optimism and pessimism are self-fulfilling, in the sense that in the optimistic (pessimistic) period the hiring costs of a firm are lowered (increased) and more (less) profits can be made, hence, it is optimal for a firm to hire more (less) workers in the optimistic (pessimistic) period.
The theoretical models presented above all incorporate the standard neoclassical framework in which a representative agent understands the underlying ‘truth’. In these models, there is no room for the cognitive limitations earlier described (see section 2 and Box B1 in Appendix B). Therefore, De Grauwe (2011) argues that these models are not fully compatible with the concept of animal spirits. He states that animal spirits and the traditional rational framework do not mix well. To improve these models, De Grauwe (2011) developed a model, under bounded rationality12, that accounts for the fact that, due to the overwhelming complexity of the world and the cognitive limitations that people exhibit, people might not understand what the actual ‘truth’ is. Such behavior makes people not irrational, rather they are rational as far as their knowledge reach, and beyond this
point their animal spirits will be decisive. In De Grauwe’s (2011) model, people use heuristics13, which are simple rules that people use as a guideline for their economic decisions, and people know that their heuristics are biased due to their animal spirits. Moreover, the agents do not just take this bias as given; rather they try to reduce their bias by learning from their past mistakes via a trial-and-error learning mechanism. To my knowledge, De Grauwe (2011) is the only one in the theory on business cycles that accounts for the fact that people do not always know the complete ‘truth’ and recognizes the cognitive limitations that people might have.
From the three types of models presented here; the Pigou cycle model, the sunspots models, and the model of De Grauwe (2011), I believe that the latter incorporates animal spirits in the most accurate and intuitive way. De Grauwe (2011) is the only one who accounts for the fact that animal spirits are more than just exogenous shocks in consumer confidence. As discussed section 2, animal spirits are driven by the cognitive limitations that we have. Moreover, De Grauwe’s (2011) model contains the feature that the magnitude of people’s animal spirits becomes smaller as they learn by time from their mistakes. Note that this is exactly what is suggested by the theory presented in section 2.1 and Box B1 in Appendix B. In those parts, past research in both psychology and behavioral economics is discussed and suggests that our cognitive limitations are reduced when we have more experience with a certain task. In my opinion, the model of De Grauwe (2011) is the best theoretical model that is currently available to explain the purpose of this paper. Therefore, the last part of this section will be used to outline the model of De Grauwe (2011).
The main contribution of De Grauwe (2011) is that he models a basic aggregate-demand-aggregate-supply (AD-AS) model, and intuitively shows the macroeconomic implications of introducing a representative agent who exhibits cognitive limitations and whose animal
spirits might induce endogenous business cycles14. First, the AD equation can be denoted as:
(𝟏)𝑌𝑡= 𝛼1𝐸̃𝑌𝑡 𝑡+1+ (1 − 𝛼1)𝑌𝑡−1+ 𝛼2(𝑟𝑡− 𝐸̃𝜋𝑡 𝑡+1) + 𝜀𝑡
Where 𝑌𝑡 is the output gap in period t, 𝑌𝑡−1 is the output gap in period t-115, 𝑟𝑡 is the exogenous nominal interest rate16, and 𝐸̃𝑌𝑡 𝑡+1 denotes the representative agent’s expectations on period t about the output gap at period t+117. Similarly, 𝐸̃𝜋𝑡 𝑡+1 is the expectation on period t of inflation in period t+1, 𝜀𝑡 is the disturbance term, and the parameters have the following values: 0 ≤ 𝛼1 ≤ 1, and 𝛼2 < 0. The attentive reader would note that the (𝑟𝑡− 𝐸̃𝜋𝑡 𝑡+1) term represents an expectations augmented Fisher equation. Second, the AS equation in De Grauwe’s (2011) model can be represented as a New Keynesian Philips curve18:
(𝟐)𝜋𝑡 = 𝛽1𝐸̃𝜋𝑡 𝑡+1+ (1 − 𝛽1)𝜋𝑡−1+ 𝛽2𝑌𝑡+ 𝜇𝑡
Where 𝜋𝑡 is the inflation rate in period t, 𝜋𝑡−1 is the inflation rate in period t-1, 𝐸̃̃𝜋𝑡 𝑡+1 is the expectation formed on time t about the inflation rate at period t+1, 𝜇𝑡 is the disturbance term, and the parameters have the following values: 0 ≤ 𝛽1 ≤ 1, and 𝛽2 > 0. The composition of the AS curve is based on profit maximizing firms in a world of imperfect
14 I present the simplest model of De Grauwe (2011) here with the most basic set of beliefs, i.e. either optimistic or pessimistic. For an extension of this model the reader is referred to section 2.4 and section 5 of De Grauwe (2011) 15 The one-period lag of 𝑌
𝑡 is included because this is common practice in DSGE models in order to account for habit
formation. For more information on DSGE models and habit formation, see Bouakez, Cardia, Ruge-Murcia (2005), Smets and Wouters (2007), and Uhlig (2007).
16 Note that in De Grauwe’s (2011) original model, a Taylor rule is used to model the Central Bank’s interest rate setting behavior. Nonetheless, the country considered in this paper is the Netherlands and this country is a member of a monetary union and hence has no power of its monetary policy. Therefore, for simplicity reasons, I interpret changes in the inflation rate as exogenous and slightly altered the model.
17 Note that all expectations are modeled based on bounded rationality.
competition under the Calvo pricing rule, and under the assumption that the representative firm indexes his prices against aggregate inflation (represented by 𝜋𝑡−1)19.
Now we have derived the AD-AS model, we can explore the role of expectations. There are two variables that involve expectations, which are the inflation rate at period t+1, 𝜋𝑡+1, and the output gap at period t+1, 𝑦𝑡+1. De Grauwe (2011) argues that since previous research in psychology have revealed the cognitive limitation of people, and since individuals may find the complexity of the economy overwhelming, individuals set their expectations based on heuristics (simple rules). In De Grauwe’s (2011) model, individuals are aware of the fact that their heuristics are biased by their animal spirits and, by trial and error; they will try to improve the performance of their heuristics over time. To limit the complexity of the model, it is assumed that there exist two types of heuristics, one is optimistic and positively biased and the other is pessimistic and negatively biased. The optimists are defined as:
(𝟑)𝐸̃𝑌𝑡𝑂𝑝𝑡 𝑡+1 = 𝜃𝑡 (𝟒)𝐸̃𝜋𝑡𝑂𝑝𝑡 𝑡+1= 𝜌𝑡
Note that 𝜃𝑡 is the positive bias of the optimists in forecasting 𝑌𝑡+1at time t, and 𝜌𝑡 is the positive bias of the optimists in forecasting 𝜋𝑡+1 at time t. Furthermore, the pessimists are defined as:
(𝟓)𝐸̃𝑌𝑡𝑃𝑒𝑠
𝑡+1= −𝜃𝑡 (𝟔)𝐸̃𝜋𝑡𝑃𝑒𝑠
𝑡+1= −𝜌𝑡
Where −𝜃𝑡 is the negative bias of the pessimists in forecasting 𝑌𝑡+1at time t, and 𝜌𝑡 is the negative bias of the pessimist in forecasting 𝜋𝑡+1 at time t. Since the pessimists have exactly the opposite expectation relative to the optimists, the divergence between the optimists
and pessimist about their expectations of respectively 𝑌𝑡+1 and 𝜋𝑡+1 can be written as follows:
(𝟕)𝑑𝑦,𝑡 = 2𝜃𝑡 (𝟖)𝑑𝜋,𝑡 = 2𝜌𝑡
Moreover, De Grauwe (2011) accounts for the fact that when the volatility of the output gap and/or inflation is high, it becomes harder for an individual to form an accurate forecast. Hence, the divergence of the output gap, 𝑑𝑦,𝑡, and inflation, 𝑑𝜋,𝑡, is a function of the volotality of the variable to be forecasted:
(𝟗)𝑑𝑦,𝑡 = 𝛽 + 𝛿𝜎(𝑌𝑡) (𝟏𝟎)𝑑𝜋,𝑡 = 𝛽 + 𝛿𝜎(𝜋𝑡)
Note that 𝜎(𝑌𝑡) is the standard deviation of the output gap calculated over 50 past periods, 𝜎(𝜋𝑡) is the standard deviation of inflation calculated over 50 past periods, and 𝛽 ≥ 0 and 𝛿 ≥ 0. Furthermore, equation (9) and (10) show that when the volatility of respectively the output gap or inflation converges to zero 𝑑𝑦,𝑡 and 𝑑𝜋,𝑡 converge to zero as well.
Now we have specified the expectations of the optimists and pessimists, it is time to quantify the expectations of the market as a whole, i.e. the aggregate expectations of the pessimists and the optimists:
(𝟏𝟏)𝐸̃𝑌𝑡 𝑡+1= 𝛼𝑜𝑝𝑡,𝑡𝜃𝑡− 𝛼𝑝𝑒𝑠,𝑡𝜃𝑡 (𝟏𝟐)𝐸̃𝑌𝑡 𝑡+1= 𝛼𝑜𝑝𝑡,𝑡𝜌𝑡− 𝛼𝑝𝑒𝑠,𝑡𝜌𝑡
(𝟏𝟑)𝛼𝑜𝑝𝑡,𝑡+ 𝛼𝑝𝑒𝑠,𝑡 = 1
Of course, it is naïve to assume that the probability that an individual is optimistic or pessimistic is exogenous. A more realistic assumption would be that an individual learns from past performance and chooses accordingly to be optimistic or pessimistic. Before we can specify such a selection mechanism, we should define the utility functions of the heuristics regarding the output gap and inflation expectations. First, the utility function for respectively the optimistic heuristics regarding the output gap and inflation expectations can be specified as:
(𝟏𝟒)𝑈𝑜𝑝𝑡,𝑡= − ∑ 𝜔𝑘[𝑌𝑡−𝑘− 𝜃𝑡−𝑘−1]2 ∞ 𝑘=1 (𝟏𝟓)𝑈𝑜𝑝𝑡,𝑡 = − ∑ 𝜔𝑘[𝜋𝑡−𝑘− 𝜌𝑡−𝑘−1]2 ∞ 𝑘=1
Second, the utility function for respectively the pessimistic heuristics of the output gap and inflation expectations can be specified as:
(𝟏𝟔)𝑈𝑝𝑒𝑠,𝑡 = − ∑ 𝜔𝑘[𝑌𝑡−𝑘+ 𝜃𝑡−𝑘−1]2 ∞ 𝑘=1 (𝟏𝟕)𝑈𝑝𝑒𝑠,𝑡 = − ∑ 𝜔𝑘[𝜋𝑡−𝑘+ 𝜌𝑡−𝑘−1]2 ∞ 𝑘=1
Where 𝜔𝑘 can be defined as a geometrically declining weight, and the utility functions can be defined as mean squared forecasting errors of the optimistic and pessimistic heuristics. Finally, by applying discrete choice theory, De Grauwe (2011) specifies the probability that an individual will use the optimistic heuristic in equation (18) and the probability that someone adopts the negative heuristic in equation (19):
Where 𝛾 is a parameter that measures an individual’s willingness to learn from his mistakes and this willingness is increasing in 𝛾. Equation (18) and (19) give intuitive results, as the forecast error of the optimists decreases, 𝑈𝑜𝑝𝑡,𝑡 increases and it is more likely that someone becomes an optimist. Similarly, as the forecast error of the pessimists decreases, 𝑈𝑝𝑒𝑠,𝑡 increases and it is more likely that someone becomes a pessimist. Hence, equation (18) and (19) imply that individuals are willing to learn from their mistakes and will not consequently have wrong expectations; rather it tries to learn from his past mistakes that are fuelled by their animal spirits. To save space, the solution to this model is moved to Box D1 in Appendix D.
5. Methodology and data
The above sections have given us a clear idea what animal spirits are, how it can be filtered from a CCI, and how it can be linked to business cycles. This section explains the approach implemented in this paper to simultaneously derive the relevance of consumer confidence in predicting business cycles and to identify whether this additional predictive power can be attributed to the information view or to the animal spirits view. Section 5.1 will be used to present the research questions and the adopted assumptions. Furthermore, in section 5.2, the data, as well as the data limitations, will be discussed. Finally, the stationarity of the data is discussed in section 5.3.
5.1 Research questions and working assumptions
(1) Can a CCI be considered as an important variable in explaining business cycles in the Netherlands?
(2) Does the additional predictive power comes from the fact that a CCI contains information about future economic activity, not captured by an econometrician, or is it due to people’s animal spirits?
In order to answer these questions, the following two assumptions are adopted:
Assumption 1: When the linear-interdependency between CCI and UNEMR is still strong after including other economic fundamentals and predictors of business cycles, then we can conclude that a CCI contains additional predictive power regarding future business cycles. To measure this linear-interdependency, a BVAR model is constructed and the error variance decompositions of CCI and UNEMR are computed. When a CCI is able to explain a significant share of the error variance in UNEMR, then we conclude that a CCI can be considered as an important variable in explaining business cycles in the Netherlands. Note that a positive (negative) innovation in UNEMR is used to approximate a recession (boom). Assumption 2: Once established that CCI indeed contains additional predictive power in explaining business cycles, we simulate an autonomous shock in CCI, represented by an exogenous shock in CCI in my BVAR model. If we observe from the IRFs that the shock in the CCI has temporary effects we conclude that the animal spirits view is valid. Contrarily, if we observe that the shock in the CCI has permanent effects we conclude that the information view is valid.
5.2 Data and limitations
Before we construct the BVAR model, we have to discuss the variables and the data sources20. Since I want to link consumer confidence to business cycles, we need a variable measuring business cycles and a variable measuring consumer confidence, i.e. a CCI. Regarding the former, my first choice would be GDP growth, however, given that consumer confidence is measured monthly and GDP quarterly, I have to search for an alternative proxy. A variable that is on a monthly basis available, closely linked to GDP growth, and where consumers might contain additional predictive power over is the unemployment rate (UNEMR). An other alternative would be industrial production, which has a monthly frequency as well, but I consider unemployment as a better variable because the answers to the questions in the consumer confidence survey directly depends more on people’s employment perspectives than on future industrial production. The unemployment rate is denoted as UNEMR and is downloaded from the OECD database (see table E1 in Appendix E for all variables adopted in this paper and their sources).
Concerning the measure for consumer confidence, the monthly CCI constructed by Statistics Netherlands is used. The index is determined based on a monthly survey in which around 1600 households in the Netherlands are interviewed about their expectations regarding the current and future state of both the general economy and their own financial situation21. CCI is constructed based on five questions for which the answer can either be positive, negative or neutral. Furthermore, subtracting the percentage of pessimists from the percentage of optimists derives the value of CCI. See table E2 in Appendix E for the individual questions of the consumer confidence survey. From table E2 it becomes clear that the CCI consists of questions that exhibit heterogeneity in the confidence that each question measures. The first and the third question, ECSITL12 and FINSITL12, clearly deal with confidence about the past. Furthermore, the second and the fourth question, ECSITN12
20 All the data in this paper is from April 1986 – August 2013. April 1986 is chosen as the beginning period because the monthly CCI is only available from this period on. Furthermore, the endpoint is set on August 2013 because the Michigan Consumer Sentiment Index adopted in this paper is only available up to that point.
21 See
and FINSITN12, deal mainly with confidence in the future, and RIGHTTTP measures confidence in the present. Remarkably enough, the pairs that I have formed are not in particular the pairs that have the highest correlation (see Table 1 below).
Table 1 Correlation between CCI and PCI
ECSITL12 ECSITN12 FINSITN12 FINSITL12 RIGHTTTP
ECSITL12 1 0.71 0.77 0.70 0.78
ECSITN12 0.71 1 0.51 0.18 0.35
FINSITN12 0.77 0.51 1 0.84 0.77
FINSITL12 0.70 0.18 0.84 1 0.86
RIGHTTTP 0.78 0.35 0.77 0.86 1
The correlation between the different questions is quite strong. Only the correlation between ECSITN12 and FINSITL12 (0.18%), and between ECSITN12 and RIGHTTTP (0.35%) seems to be relatively weak.
Although some questions seem to mainly deal either with the past, future or present, the correlations in Table 1 clearly indicate that, in general, correlation between all questions is high (except for ECSITN12 and FINSITL12, and RIGHTTTP and ECSITN12) and it is not possible to identify pairs that clearly deal either with the past, future or present. Nonetheless, more attention will be spent to the possible heterogeneity of individual questions in section 8.
turning points, peaks and troughs in consumer confidence seem to precede turning points in time. This can be interpreted as some evidence that consumer confidence granger-causes business cycles. However, note that we only observe a correlation here, not necessarily causation.
Figure 2 depicts that there is a strong correlation between consumer confidence and business cycles; however, what we ultimately want to know is whether consumer confidence has any additional predictive power for business cycles after including other fundamental predictors. Therefore, following assumption 1, other variables used by econometricians to forecast GDP are included. In the most ideal scenario, a researcher wants to include all possible variables that could alter the transmission mechanism between CCI and UNEMR. Nonetheless, this is not feasible due to the restrictive dimensionality of VAR models. Although, a BVAR is constructed and such a restricted VAR loosens the constraints imposed on the parameters, it is still not possible to include a very large set of time-series. Hence, choices have to be made by the researcher.
First, a composite leading indicator (CLI) of business cycles is included. The CLI is an indicator developed by the OECD in order to provide early signals of business cycles, which are defined as fluctuations in the output gap. The selection of the component series comprising the CLI is based on both economic relevance and practical considerations22. To be more specific, the CLI for the Netherlands consists of: manufactures’ order books, manufacturing production future tendency, AEX stock prices, finished manufacturing goods stocks, IFO business climate indicator for Germany, and inverted manufacturing orders inflow: tendency. The choice for a CLI is motivated by the research of Matsusaka and Sbordone (1995) who incorporate a CLI as well.
22 As regards to economic relevance, the series must be a significant predictor of future economic fluctuations and the series must have a broad cover of economic activity. Second, concerning practical considerations, monthly series are preferred above quarterly (although quarterly data is not excluded by definition, some series are linearly
interpolated), real-time data is preferred that is not revised, and the OECD prefers long time series that do not exhibit breaks. For a detailed description on the methodology of the construction of CLI the reader is referred to:
Figure 2 Consumer confidence and business cycles in the Netherlands
The CCI is monitored from April 1986 until April 2014. The horizontal line represents the zero-line where the percentage of optimists coincides with the percentage of pessimists. The gray shaded areas mark business cycles peaks to troughs. All turning points before December 2008 are determined by the rules established by the NBER in the US. Furthermore, from December 2008 on, a simplified version of the original Bry and Boschan algorithm is used. Peaks: 1986M5, 1990M9, 1994M12, 1997M12, 2000M7, 2008M2, and 2011M4. Troughs: 1987M2, 1993M12, 1996M1, 1998M9, 2003M9, 2009M6, and 2013M3.
Second, the producer confidence index (PCI) calculated by Statistics Netherlands is included23. As you can see from table 2, CCI and PCI are strongly positively correlated (0.66) and this might imply that additional information regarding future economic activity might already be reflected in producer confidence.
Table 2 Correlation between CCI and PCI
CCI PCI
CCI 1 0.66
PCI 0.66 1
Correlation table between the consumer confidence index (CCI) and the producer confidence index (PCI) in the Netherlands. The correlation depicted in the table is for the period April 1986 – August 2013.
23 The PCI is constructed by the Statistics Netherlands based on a monthly survey among around 1700 manufacturing firms. The PCI is seasonally adjusted and can be split-up into three sub-indices: Opinion on the order book position, expectations of production in the coming six-months, and opinion about the stock of finished products. For the exact questions the reader is referred to Statistics Netherlands (CBS).
-50 -40 -30 -20 -10 0 10 20 30 86 88 90 92 94 96 98 00 02 04 06 08 10 12 C C I Years
Finally, the Michigan Consumer Sentiment index (MCSI) is incorporated in order to control for the possibility of synchronization between US business cycles and business cycles (see e.g. ECB Monthly Bulletin January 2013) in the Netherlands24. The Michigan MCSI serves as a proxy for these business cycles and it might be that consumer confidence in the US is an important driver of consumer confidence in the Netherlands. An initial (weak) support for this argument can be derived from Table 3, which shows that the correlation between the CCI and MCSI is positive and quite strong (0.63).
Table 3 Correlation between CCI and MCSI
CCI MCSI
CCI 1 0.63
MCSI 0.63 1
Correlation table between the consumer confidence index in the Netherlands and the Michigan consumer sentiment index (MCSI). The correlation depicted in the table is for the period April 1986 – August 2013.
Note that all the above-mentioned variables, except for CLI (which is amplitude adjusted), are seasonally adjusted. The reason to incorporate seasonally adjusted variables is that people and producers are generally more optimistic in the summer and less optimistic in the winter. Furthermore, measures for economic activity might significantly depend on the time of the year. Finally, Table E3 in Appendix E shows the descriptive statistics of all incorporated variables25.
This section is concluded with addressing the data limitations. First, as emphasized in section 3.1, in the most ideal scenario, a researcher wants to incorporate real-time data because consumer confidence is a snapshot of consumers’ contemporary believes about the current and future state of the economy based on their information set on that specific moment in time. Hence, for the most accurate results, and given that the discrepancy between revised data and time data is significant, a researcher should deal with real-time data. Unfortunately, these real-real-time databases are scarce, especially for the
24 The reader who is interested in the survey questions comprising the MCSI is referred to:
http://www.sca.isr.umich.edu/.
Netherlands, and incorporating such data would force me to drop too many observations. Hence, revised data is used, but it would certainly be worthwhile to replicate this research in the future based on a real-time dataset. Second, as discussed in section 3.1 as well, the effect of the link between consumer confidence and economic activity might be asymmetric depending on, inter alia, social demographic characteristics. Therefore, it is worthwhile to account for such characteristics, however, such data is only available from 2001. Nonetheless, for future research this might be a worthwhile extension. Finally, it is important to realize that the identified link between consumer confidence and future unemployment may be biased due to some omitted variable that both affects consumer confidence and future unemployment. Although the dimension of the BVAR analysis applied in this paper is above average compared to previous papers, it is possible that the results suffer from omitted variable bias. Therefore, for future research it would be a good extension to expand the set of time-series.
5.3 Stationarity
Now the data is known, it is time to explore a particular statistical property of the data that is crucial in BVAR models, and that is stationarity. In a standard BVAR, a necessary condition for valid interpretation of the model’s results is that the BVAR process is stationary. Therefore, this section will be used to test whether the variables considered in this paper are individually stationary.
as a motivation to use neither a deterministic trend nor an intercept in the formal test of stationarity of CCI and PCI, and to use a positive intercept but no deterministic trend for UNEMR, MSCI, and CLI.
Figure 3 Combined graphs of CCI, DLNCPI and UNEMR
All data shown here is from April 1986 – August 2013. The upper-left graph depicts CCI with on the vertical axis the value of the CCI represented by the percentage of optimists minus the percentage of pessimists. The upper-right graph represents the development of UNEMR over time. This middle figure represents MSCI, the figure in the left lower corner monitors PCI over time, and the graph of CLI is showed in the right lower corner.
6. Bayesian VAR model
times, i.e. during a recession or a boom. Since the estimated parameters in a VAR are not allowed to vary over-time, this might lead to biased results. Second, another general problem with VARs is its low dimensionality due to the fact that the restrictions to be imposed on the parameters increases quickly as the number of variables and lags in the VAR rises. A solution would be to impose hard restrictions. However, I do not consider these hard restrictions as desirable because it might force me to make arbitrary theoretical assumptions. Moreover, by setting coefficients a priori to zero you rule out spillover effects by assumption. In many cases, including this one, this is not desirable. A better solution would be to impose soft restrictions in a Bayesian VAR context (Del Negro and Schorheide 2010). In a BVAR, the parameters get an identical treatment to the disturbance terms, i.e. they are treated as random variables with a prior defined probability. By imposing a prior distribution it is possible to treat the parameters as a random walk centered at the desired restrictions set by the modeler. By applying Bayes’ theorem, the posterior distribution of each parameter is derived by updating the chosen prior with the information contained in the data:
(𝟐𝟎) 𝑃(𝐻|𝐸) =𝑃(𝐻)𝑃(𝐸|𝐻)𝑃(𝐸)
Where 𝑃(𝐻|𝐸) is the posterior probability, 𝑃(𝐻) is the prior, 𝑃(𝐸|𝐻) is the likelihood function, and 𝑃(𝐸) is a normalizing constant. What is important to note is that the researcher should choose the prior specification with care because a diffuse prior is highly sensitive to pure noise and as a result you end up with biased results. Whereas a well-specified prior can only be affected by sample variability that is systematic and such a prior is robust to pure noise (Felix and Nunes, 2002).
the Minnesota prior, consider the following general 5-variable kth-order reduced-form VAR:
(𝟐𝟏)𝑌𝑡 = 𝑐 + 𝐵(𝐿)1𝑌𝑡−1+ ⋯ + 𝐵(𝐿)𝑘𝑌𝑡−𝑝+ 𝑢𝑡
Where 𝑌𝑡 is a (5 × 1)-vector of 5-endogenous variables, consisting of CCI, UNEMR, CLI, PCI, and MSCI. 𝑐 is a (5 × 1)-vector of constants, 𝐵(𝐿)𝑘 is a (5 × 5)-matrix with the k-lag polynomials, also known as the autoregressive matrix. 𝑢𝑡 is a (5 × 1)-vector of reduced-form shocks, which has the following variance-covariance matrix: ∑ =𝑢 𝜏−1𝜏−1′26.
Now it is straightforward to show the implications of introducing the Minnesota prior. As earlier mentioned, the Minnesota prior postulates that the prior mean of each variable is centered around a random walk with drift:
(𝟐𝟐)𝑌𝑡 = 𝛼 + 𝑌𝑡−1+ 𝑢𝑡
Which is tantamount to setting the diagonal elements in 𝐵(𝐿)1 to 1 and all other elements in 𝐵(𝐿)1… 𝐵(𝐿)𝑘 to zero. Moreover, the modeler can fine-tune the expected value and the variance of the prior distribution via hyperparameters. That is, by setting the hyperparameters, the researcher can determine the expected value of the coefficients and by how much the coefficients are allowed to alter from their prior means. To be more specific, the researcher can, in principle, set in the equation of variable i the prior beliefs of the expected value and the variance of coefficient 𝐵(𝐿) associated with lag number l for variable j as follows:
(𝟐𝟑) 𝔼(𝐵(𝐿))𝑖𝑗,𝑙 = {𝜇, 𝑖𝑓 𝑖 = 𝑗, 𝑙 = 10, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
26 Note that we arrive at this equation by imposing orthogonality of the structural shocks 𝑒
𝑡. Originally, the
variance-covariance matrix is defined as ∑𝑢=𝜏−1∑ 𝜏𝑒 −1′. Nonetheless, by imposing orthogonality of the structural shocks, i.e. setting the off-diagonal elements of the variance-covariance matrix of the structural shocks, ∑𝑒., to zero, we
(𝟐𝟒) 𝑣𝑖𝑗,𝑙 = { ( 𝜆1,𝑖
𝑙 )2 𝑖𝑓 𝑖 = 𝑗
(𝜆1,𝑖𝜆2,𝑖𝑗𝜎𝑖/𝜎𝑗𝑙)2 𝑖𝑓 𝑖 ≠ 𝑗
Where 𝜇 is the autoregressive coefficient that is either 0 or 1, 𝑙 is the lag number, 𝜆1∈ [0, ∞) is the overall tightness parameter, 𝜆2 ∈ [0, 1) is the relative cross-variable weight, and 𝜎𝑖/𝜎𝑗 is a correction term to account for the different units of measurement of some variables.
The prior belief of the expected value of the coefficients is depicted in equation (23). The researcher has two choices regarding the value of 𝜇. If the researchers beliefs that there is a lot of persistence in the variables than he should set 𝜇 = 1. Contrarily, if the researcher beliefs that the variables are characterized by considerable mean reversion than he should set 𝜇 = 0. As showed in section 5.3, all variables seem to be mean reverting. Hence, I choose to set 𝜇 = 0.
In equation (24) the expected variance of the coefficient is expressed. Note that
