The ‘fragile five’ and the Taper Tantrum

The large scale bond purchase program (aka Quantitative Easing) started by the Federal Reserve in 2008 was an unprecedented move in the history of central banking. In the run up to the financial meltdown, the Federal Reserve Bank had increased the Federal Funds Rate to around 5% and started reducing the rate gradually when the crisis heightened in 2008. However, the policy rate reached its zero lower bound (the infamous ‘ZLB’ ) in 2009 and could not be reduced further to stimulate the economy.


As the markets panicked after the failure of the banking giant Lehman Brothers, the Federal Reserve Chairman, Ben Bernanke and Treasury Secretary, Henery M. Paulson Jr. presented their 700 billion dollar ‘rescue plan’ to the the Congressional leaders. These funds were going to be used to buy equity in troubled banks and to buy sub-prime mortgage backed securities which nobody was willing to buy. This was just the tip of the ice berg since the Federal Reserve eventually expanded its Balance sheet by more than 2 trillion dollars between 2008 and 2013. Such a massive inflow of liquidity ( purchase of long term government bonds and mortgage backed securities) lowered the yield on 10 year government bonds and investors flocked to emerging markets in search of higher yields. There were concerns among the policy makers that such a massive influx of capital can be destabilizing for the emerging market economies,especially if the investors pull out their money should the US begin to taper the asset purchases. The first announcement about tapering(reducing the amount of bond purchases) was made following the Federal Open Market Committee (FOMC) meeting on May 01, 2013 in which Ben Bernanke said that the pace of asset purchase would be reduced if the economic recovery is sustained. The minutes of the meeting were released on May 22, 2013 and financial markets in the emerging markets reacted sharply to the announcement. There were remarks made about tapering in the subsequent FOMC meetings and the in the FOMC meeting of December, 2013, it was announced that the Fed will reduce its bond purchases from $85 billion a month to $75 billion a month. This event can be considered as the actual tapering event. I conducted a simple event study analysis for select emerging market economies to see how the financial markets reacted to these tapering announcements and I want to share the simple yet instructive graphs that I have for the response of exchange rates and bond yields in these countries.

In August 2013, a research analyst at Morgan Stanley coined the term – ‘Fragile Five’ to refer to the emerging market economies, which had been affected severely by the tapering talks and were likely to be affected the most should the US begin to raise interest rates. India was one of the ‘Fragile Five’ along with Brazil, Turkey, Indonesia and South Africa. While India’s real economy was relatively unscathed by the crisis, its financial sector showed little resilience. Following the FOMC announcement of tapering (reduction in the amount of bond purchase by the Fed), the cumulative loss in INR/USD exchange rate between May 2013 and September 2013 was of the order of 14 percentage points.

I conducted the event study exercise for the fragile five and analyze the reaction of  exchange rates and bond yields in these countries. For the event study analysis, I conducted the following regression:

Δy_{m-1,m+1} = α + Β D_{m}

where the dependent variable is the change in the target variable (exchange rate and bond yields)  in a one day window before and after the event. One day window makes sure that we can isolate the effect of the event in question because no other event is likely to have happened in such a short window. D_{m} is the dummy variable for the event, which takes a value equal to 1 on the event date and zero other wise. I had 16 dummy variables for 8 FOMC meetings and 8 FOMC minutes in 2013 and I used daily data on exchange rates and bond yields.

The following figure graphs the exchange rate of the Fragile Five vs the US dollar from January 2013 to March 2014. The data is taken from Bloomberg. Increase in the exchange rate is depreciation. The exchange rate for 02 Jan, 2013 is normalized to 100. The vertical lines represent the FOMC dates which had a significant impact (using event study analysis) on exchange rates. The last vertical line – Dec 18, 2013 was not significant but is plotted to illustrate the actual tapering event.


We can see from the figure that all currencies started depreciating following May 01 FOMC. The depreciation for South Africa was particularly steep. In the next FOMC, on June 19, 2013 Ben Bernanke further reinforced the possibility of tapering. He said- “if the subsequent data remain broadly aligned with our current expectations for the economy, we will continue to reduce the pace of purchases in measured steps through the first half of next year, ending purchases around mid-year.” Following the June FOMC, markets reacted again and currencies depreciated further across the board. It can be seen form the graph that the increase was highest for India. Rupee reached a low of 68 to a dollar in August 2013. It is interesting to note that the actual tapering started in December 2013 when the Fed announced its plan to reduce its bond purchases from $85 billion a month to $75 billion a month however markets reacted very mildly to this announcement since they had already incorporated the information on FED’s intent to taper during the previous FOMCs. This event was found to be significant in the event study analysis.  A similar story appears when we look at the yield data on 5 year government bonds and 10 year government bonds. The following figure plots the 5 year government bond yield for the Fragile Five. Bond yields on Jan 01, 2013 are normalized to 100. The vertical lines represent the FOMC dates which were found to have a significant impact on bond yields ( except for Dec 18, 2013)


From January 2013 to May 2013, the bond yields on the 5 year government bonds were quite stable. Following the taper announcement in May 2013, the bond yields begin to rise as investors start pulling out their money from emerging markets as they anticipate higher return on US government bonds. Bond yields rise persistently from May 2013 to September 2013 and by December 2013, bond yields have risen by 50% on an average. Bond yields for 10 year bonds also exhibit a similar pattern.

Janet Yellen suggested on Friday, May 22, 2015 that  “an interest rate hike will be appropriate this year if the US economy improves”. It is highly likely that there will be a massive sell off of emerging market currencies if the US raises its interest rates and the emerging markets should brace themselves for a rate hike. India may have been the worst hit in the taper tantrum of 2013 but the recent efforts by the governor of RBI, Raghuram Rajan to accumulate forex reserves will make sure that India is not severely affected by volatile capital flows. India is no longer a member of the Fragile Five, it is replaced by Mexico. Hopefully, the rate hike, if it happens in the near future, will not cause immense distress to the financial sector.


Debt, war and slavery


While there is a burgeoning literature on business cycles – periodic episodes of booms and bust, work on debt cycles has largely remained in oblivion. In his magnum opus, Debt: The first 5000 years, David Graeber introduces the concept of debt cycles, which he also claims to be his greatest discovery. Contrary to the popular belief that barter was the first stage in the evolution of money, Graeber claims that there are no historical records to corroborate that ancient societies indeed operated on barter. The theory of debt cycles propounded by Graeber suggests that societies alternate through periods of virtual money(debt) and metal money(bullion). This theory postulates that bullion dominates debt during times of war while virtual money tends to dominate during periods of relative social peace. During periods of war, soldiers have access to loot and plunder, which is largely consisted of precious metals and hence they find it convenient to trade those metals for commodities of daily use. Graeber proposes the following breakdown of Eurasian history to illustrate the alternation between virtual and metal money:

1) The Age of first Agrarian Empires(3500 – 800 BC) – period of virtual credit money

2) Axial Age (800 BC – 600 AD) – rise of coinage and shift to metal bullion

3) The Middle Ages (600 – 1450 AD) – return to virtual credit money

4) The Age of Capitalist Empires (1450 – 1970) – shift to bullion ; Gold Standard scrapped by Richard Nixon in 1971

Graeber recounts that Mesopotamia, the earliest urban civilization operated on credit money. He writes, “in the great temple and palace complexes, money served largely as an accounting measure rather than physically changing hands, merchants and tradespeople developed credit arrangements of their own, which took the physical form of clay tablets, inscribed with some obligation of future payment”. Interest bearing loans were also offered to merchants by temples and palaces. The practice of debt peonage emerged during this period. Those who were unable to pay their debt had to work for their creditors and sometimes had to sell their family members to pay the debt. Hence, in order to keep the social order intact and to avoid severe debt crises, the ritual of ‘breaking of clay tablets‘ was observed from time to time where the temple would cancel all the outstanding debt and the debt peons would return to their families.

The Axial age is perhaps the most interesting since this was the period when “Pythagoras,the Buddha and Confucius were all alive at exactly the same time” and ” the three parts of the world where coins were first invented were also the very parts of the world where those sages lived : the Kingdoms around the Yellow river in China, the Ganges Valley in Northern India and the shore of the Aegean Sea.” It is interesting to note how Graeber links the invention of coinage to war. Silver, gold and other precious metals which would only be found in the treasuries of temples in the agrarian age were now being used as coins for daily transactions. Graeber suggests that it was possible because the precious metals were stolen. In Axial age, China, India and The Aegean saw the rise of an army of trained professionals. The armies were controlled by the state and as a way to provide for the armies the state converted precious metals (which were stolen) into coins which would be accepted for day-to-day transactions. Slavery, which was an outcome of this system,  also helped in reinforcing the system. War captives worked as slaves in the gold and silver mines and produced more gold and silver which was used to produce coins. Graeber calls this – “military-coinage-slavery” complex. This was the period when war was glorified and empire states were commonplace.

In the middle ages, the empire states, which were built on the bedrock of war, began to fall and religion took over the logic of war. People were beginning to ask questions about the existence of human life and religious debates were to be seen everywhere. The religious authorities started controlling the economic sphere and once again the concept of debt resurfaced. The temple treasuries again became the storehouses of precious metal and credit systems similar to those in the agrarian age became popular.

Around 1450, there was again a shift from virtual credit to gold and silver. The discovery of the New World(owing to the voyages of Christopher Columbus) and the colonization of the American continents led to  a massive influx of bullion into Europe from the Americas. This return to bullion was accompanied by “vast empires and professional armies, massive predatory warfare,  untrammeled usury and debt peonage, a new burst of scientific and philosophical creativity”. This was the time when a series of plagues and Black Death decimated large cities in Europe, commercial regions were destroyed and whole cities went bankrupt. Real wages fell as the inflation(price revolution) spurred by the inflow of bullion continued to erode the purchasing power and the region was trapped in endemic warfare. This set the stage for the emergence of capitalism. This phase also saw the emergence of the banking system. “The Bank of England was created in 1694 when a consortium of London and Edinburgh merchants offered the King William III a loan to help finance his war against France and in return asked for a monopoly over issuance of banknotes – notes for the money that the king owed them.” In 1690’s there was a severe shortage of silver coins and the wages and prices collapsed. It led to a series of debates on whether the coins should be debased or bullion should be abandoned in favor of pure credit money. The final outcome was that  various forms of credit money emerged alongside bullion but bullion was never abandoned and in 1717, Britain adopted gold standard.

Gold standard was vulnerable to fluctuations in the quantity of gold and countries kept suspending and adopting gold standard from time to time. For instance, Britain abandoned gold standard after the first world war and returned to it in 1925. It finally came to an end when in 1971, US President Richard Nixon announced that dollar was no longer convertible to gold. Since then, there have been a slew of innovations in the financial sector and various forms of credit money have emerged, marking the return to the phase of virtual credit money.

Graeber claims that modern money is based on government debt and governments borrow money to finance wars. He says that Nixon floated the dollar to pay for the Vietnam war and the debt crisis was a direct result of the massive military expenditure. In this light, Graeber says, US currency is fiat money backed by its military power. He concludes by presenting a paradox : If history holds true then a return to virtual money should mean a movement away from war, empire buildings and slavery but since 1971 what we have seen is the opposite. US debt has primarily been war debt and the credit arrangements are not mediated by interpersonal relations of trust(as was the case when credit systems dominated in history) but by profit seeking corporations. By eliminating all legal restrictions on the interest that these credit companies could charge, this system is actually making usury legal – which is the opposite of what one would expect in a society based on credit arrangements. US debt is monetized by the Fed which prints money to buy treasury bonds and then lends them to other commercial banks. The international organisations like IMF, World Bank, WTO work on the principle that “(unless one is the United States Treasury)one has to pay one’s debt “. Graeber claims that this “debt – imperialism” is not sustainable and the recent financial crisis was a manifestation of the strains that the system is experiencing.

Graeber’s book has garnered much praise in the intellectual sphere and has sparked off discussions on debt and the role of money as a social convention. Some commentators have critiqued  Graeber’s hypothesis including Noah Smith(here) and Brad DeLong(here). I feel that the book provides a fresh perspective on debt, war, slavery, politics and religion and debunks various myths surrounding money. Looking at the evolution of money through an anthropological lens, it touches upon concepts like gift economies, human economies, communism, hierarchy and exchange . While providing a background for the recent financial crisis, it raises many questions on the sustainability on the current system for which we still don’t have any concrete answers.


Communism as a moral principle


Those of us who have read or are interested in the history of economic thought identify communism as the last and the most advanced stage in the evolution of societies. It is considered to be the Utopian stage which is defined by collective ownership of means of production as opposed to capitalism where means of production are privately owned and there exists a class which does not have access to these means of production and is, therefore, forced to sell its labor to survive. As pointed out by Marx, Capitalism, which precedes communism, is rife with inherent contradictions which are responsible for the imminent collapse of the system. On the other hand, communism is supposed to be the panacea which will bring an end to social evils like inequality and poverty. One can find various debates in the intellectual sphere about which system is superior but one hardly witnesses discussions where communism can coexist with capitalism. David Graeber, in his book Debt – first 500 years, proposes one such theory which links capitalism and communism. Through this post I wish to share the main insights of his theory.

According to Marxist theory, every society has a base and a superstructure. The definition of base includes the economic relations between labor and capitalist, the division of labor, property rights etc whereas the superstructure includes the ideas and relations between individuals – culture, institutions etc compatible with the base. Base and superstructure of a society will depend on its stage of evolution. So economic relations in a society are formed on the top of moral relations in the superstructure. Graeber says that communism is one of the three moral principles on which economic relations can be founded (the other two being hierarchy and exchange). He calls the conventional definition of communism (collective ownership and management of resources) a myth and defines communism as ‘from each according to their abilities, to each according to their needs‘. According to this definition, communism can be looked at as a symbiotic relation between individuals; a system where people help each other (excluding their enemies) constrained by their own means. Examples of such communism can be seen in everyday life. Graeber gives the example of a worker who is fixing a broken pipe and asks his coworker for a wrench. His coworker will not ask what he would get in return for handing him over the wrench. Graeber emphasizes that communism is not mere cooperation, it is beyond that; it is the foundation of all human societies. All societies have witnessed how strangers become brothers and sisters in the wake of a disaster- floods, famines etc. This is communism. It explains why people are generous enough to give directions to strangers. It’s because they expect that others will also behave in the same way when they need help. Although the magnitude of such generosity might vary across societies. It is crucial to understand that communism does not imply a perfectly reciprocal system of exchange. Not all actions are reciprocated but it’s the expectation that one’s favors will be returned which defines the system.

Communism is also reflected in small courtesies like asking for a light or for a cigarette. He says ” if one has been identified as a fellow smoker, it’s rather difficult to refuse such a request. In such cases – a match, holding the elevator, a piece of information- the “from each” element is so minimal that most of us comply without even thinking about it. Conversely, the same is true if another person’s need is extreme – if he is drowning, for example. In such cases, we assume that anybody who is capable of helping will do so.” Graber calls this baseline communism. He says that in impersonal urban communities this might go no further than asking for a light or directions whereas in smaller communities it goes much beyond small courtesies. In small communities it is impossible for people to refuse a request for food. The obligation to share food becomes the basis of everyday morality. He cites examples where mothers would scold their children if they receive a gift and do not share it with their siblings.

This system can also explain why small communities do not have formal credit markets. People generally take credit form their relatives in such societies, which is often interest free because it is expected they will also lend to others when others are in need. In such societies, sharing is one of the greatest pleasures of life. People share not only in bad times but also in times of plenty. As Graeber writes – “the more elaborate the feast, the more likely one is to see free sharing of some things (for instance, food and drink)…the giving and taking often takes on a distinctly gamelike quality. The shared conviviality could be seen as a communistic base on top of which everything else is constructed”.  In communism, sharing is not only a moral value but also brings pleasure to human lives. For most human beings, the most pleasurable activities involve sharing something – music, food, liquor etc. There is communism in all the fun things that we do. We can also find traces of communism in commerce as well. In small communities, shopkeepers often do not keep accounts and find it difficult to ask money for things sold to the people in their community.

Although the kind of communism described by Graeber might not exist in contemporary world, we do find shades of it in our everyday life. The exchange of gifts which sounds so innocuous in a small community might take an evil shape in a hard core capitalistic society. It is also not surprising that festivals like Diwali, Holi, Id or Christmas go hand in hand with a surge in economic activity. The tradition of giving each other gifts on such occasions has now become intertwined with the contours of capitalism and is often responsible for pushing the deprived section of the society into a spiral of debt.

A Comparison of Programming Languages in Economics..

Good post for graduate students in economics. Interesting to note that R is almost 500 to 700 times slower than C++ whereas Matlab is only 9 to 11 times slower than C++.

Mostly Economics

Keynes once famously said of the desired qualities for a top economist:

The master-economist must possess a rare combination of gifts …. He must be mathematician, historian, statesman, philosopher — in some degree. He must understand symbols and speak in words. He must contemplate the particular, in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man’s nature or his institutions must be entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood, as aloof and incorruptible as an artist, yet sometimes as near to earth as a politician.”

We did not have computers then otherwise he would have added computer programmer to the list as well! Moreover, his quote anyways talks about things like abstract, flight of thought etc..which programmers do have…

View original post 419 more words

The religious angle to debt

Currency Image Finally, after having finished a grueling year at Cornell, I was all set to begin reading the book that everybody has been talking about – Capital in the Twenty – First Century. However, before I could start reading Piketty’s grand book, David Graeber’s Debt – The first 5000 years came my way and it has been keeping me occupied ever since. It is a book about the history of debt, the origin of money – something which I find really fascinating. David Graeber has tried to explain the origin of money and debt by emphasizing on the anthropological aspect of money – its relationship with religion, society, state, humanity. In the second and third chapter of the book, he talks about various theories of origin of money.  What caught my attention in the third chapter was the primordial debt theory which links the origin of money/debt with religion and I wish to share the main insights of this theory through this post.

Graeber starts the chapter on Primordial Debt with the following lines from Satapatha Brahmana :

In being born every being is born as debt owed to the gods, the saints, the Fathers and to men..If one recites a sacred text, it is because of a debt owing to the saints..if one wishes for offspring, it is because of debt owed to fathers form birth..And if one gives hospitality, it is because it is a debt owing to men.

The background for this theory is set by invoking the debate on creation of a common European currency. The author remarks that the core argument against a common Euro currency is that it separates fiscal policy from monetary policy. Primordial-debt theorist argue that these two have always been the same thing. Governments are able to tax people(fiscal policy) to create money(monetary policy) because government is the guardian of all the debt that citizens owe to one another and this debt is the essence of the society. It exists long before money and markets. Graeber says that this sense of debt was first expressed through religion. The Vedic poems(composed between 1500 and 1200 BC) show a constant concern with debt – which is synonymous with guilt and sin. There are numerous prayers pleading with the gods to liberate the worshiper from the shackles of debt. Graeber says that in these hymns, to be in debt, to be under any sort of unfulfilled obligation, any unkept promise, was to live in the shadow of death. In the sacred texts, debt seems to represent the broader concept of inner suffering, from which, one begs the gods(particularly Agni – the god of fire) for release. The conclusion of this philosophy is that : human existence is a form of debt.

A man, being born is a debt; by his own self he is born to Death, and only when he sacrifices does he redeem himself from Death

Graeber then asks – “If our lives are on loan, who would actually wish to repay such a debt? To live in debt is to be guilty, incomplete. But completion can only mean annihilation. In this way, the “tribute” of sacrifice could be seen as a kind of interest payment, with the life of the animal substituting temporarily what’s really owed, which is ourselves – a mere postponement of the inevitable.” If this theory is true, then can we use it to explain the debt crisis of Eurozone and the recent financial crisis? The debt level had increased to such a level that it could be repaid only by complete annihilation in that a collapse of the system was required for the system to continue. The primordial debt theorist also use this theory to explain why kings always imposed taxes on their subjects – ” if the king has simply taken over guardianship of that primordial debt we owe to society for having created us, this provides very neat explanation for why the government feels it has a right to make us pay taxes. Taxes are just a measure of our debt to the society that made us.” If taxes represent our absolute debt to the society then the first step towards creating real money comes when we start calculating how much we owe to the society, system of fines, fees, penalties and debt owed to specific individuals. This is how this theory explains the origin of money.

Graeber also presents the flaws associated with theory. His first argument is that the choice of the Vedic material by the primordial debt theorists plays a very important role. He says, for instance, we know nothing about the people who composed these texts and the society which created them. It is not even certain that interest bearing loans existed in Vedic India – which has a bearing on whether the priests really saw sacrifice as an interest on the loan we owe o Death(Yama – the god of death). Some theologians also found this idea ridiculous as they believe that Gods have everything they want and hence there is no reason why they would be interested in any exchange with man since exchange implies equality and exchange between man and God can never be equal.

Graeber also notes that the primordial debt theorists have nothing to say about the Sumer or Babylonia(Mesopotamian empires) despite the fact that the practice of loaning money at interest was first invented in Mesopotamia, 2000 years before the Vedas were composed.

Another problem with this theory is its initial assumption that everybody begins with an infinite debt to the society which gets taken up by the kings and national governments which then justifies the taxes imposed on the subjects by the kings. Graeber, however, questions the concept of society. He claims that it is very difficult to define modular units which can be called societies. He asks – what is society for a Christian American living under the reign of Genghis Khan. He beautifully wraps up his arguments by raising a broader question: Even if we owe a debt to the society, humanity, nature or the cosmos, who has the authority to tell us how should we repay this debt? He says that almost all systems of established authority – religion, politics, morality, economics and the criminal justice system tell us how this debt ought to be repaid. Hence theories of existential debt end up becoming ways of justifying such structures of authority.

Interesting trivia

While it is widely believed that Keynes founded the discipline of modern macroeconomics, the first national macroeconomics model was developed by Jan Tinbergen, a Dutch economist who won the first Nobel Prize in the field of economics.  He had developed the model for Netherlands and later applied it to the economy of US and UK. In his Nobel Prize Lecture, Christopher Sims talks about the model developed by Jan Tinbergen. He says that the macroeconomic model that Tinbergen developed was a statistical model with multiple equations and error terms trying to explain the economy. This model was criticized by Keynes and he was of the opinion that any model with error terms can not be used as a testing ground for theory since error terms are random and can explain any random theory. But Haavelmo(who won a Nobel Prize in economics in 1989) defended Tinbergen against Keynes. He argued that an economic system can be seen as a probability model where the observed data are realized outcomes form some probability distributions and hence it is possible to test the theories using a statistical model.

It is interesting to note how close-knit the economics community was at that time. Jan Tinbergen had shared his Nobel Prize with Ragner Frisch who is known for having founded the discipline of Econometrics. In 1933, he coined the term ‘microeconomics/macroeconomics’ and was the first person to formally acknowledge the difference between macroeconomics and microeconomics. Haavelmo, who defended Tinbergen against Keynes was Ragnar’s research assistant and he also won a Nobel Prize in 1989 for his work on probability theory and analysis of simultaneous economic structures.

A very interesting summary of the debate between Keynes and Tinbergen (famously known as the Tinbergen debate) can be found here :


Brief analysis of Indian Macro Economic time series

Macro economic time series are known to display trend growth. For example, if we look at a country’s GDP, it rises over time, i.e. it has a trend growth which can be categorized as a long term feature of GDP, however, in the short term we observe that the GDP fluctuates around the deterministic trend. A substantial literature in macro economics deals with the properties of these business cycles and how the government can come up with policies to counter these business cycles – also know as counter cyclical policies. Whether or not such policies are effective in containing the business cycles is a bigger question and there are different schools of thought (Freshwater and saltwater) which feel differently about this issue. There is a class of models known as RBC (Real Business Cycle) models which addresses questions such as: what causes business cycles, how persistent is the deviation of any time series from its steady state, what accounts for co-movement between various time series(such as consumption and income). RBC model conjectures that business cycle fluctuations are due to real factors (such as shock to technology) as opposed to monetary factors(such as change in money supply/monetary policy). The macro economic course taught in the spring semester at Cornell revolves around RBC theory which also happens to be my area of interest. In the first lecture of this course I learnt how to extract the cyclical component from any given time series and some stylized facts about GDP, consumption-income ratios, investment-income ratios, their correlations and persistence. In this post I endeavor to conduct the same analysis for Indian data. I take data on GDP and its components from RBI’s website.The first step is to extract the business cycles from the series of GDP. I use annual data from 1950 to 2012 for this analysis.

Log level(real per capita)

The above figure plots time series for real per capita output(GDP), real per capita consumption expenditure and real per capita expenditure for the period 1951 – 2012. We can see that there is a trend growth in output, consumption and investment. The y axis measures the log levels which makes it easier to get the growth estimates of the variables just by looking at the graph (log differences can be interpreted as growth rates so the slope of these lines/curves at any given point can be seen as the growth rate at that point). We can notice fluctuations around the trend at frequent intervals in all the series. The fluctuations in the output series around the trend are called business cycles. By eyeballing the graph, we can also say that the series of output and consumption move together. This will become more obvious when we extract the cyclical component from both the series and plot them.

Extracting cyclical component:

Any economic time series can be considered as having two components: the trend component and the cyclical component. For instance, if y(t) is a time series, it can be expressed as follows:

y(t) = y(t)_x  + y(t)_c

where  y(t)_x  is the trend component and  y(t)_c is the cyclical component. In the RBC model we are interested in the cyclical component of output.  There are various methods which separate the trend component from the cyclical component and in the literature detrending and filtering are often used interchangeably. However, the two processes are not the same. While detrending is used to make the time series covariance stationary, filtering is a broader concept. A filter can be used to extract cycles at specified frequencies. In this post, I have used the Hodrick-Prescott(HP) filter to extract the cyclical component of the time series. The following figure plots the fitted trend of output along with the original series of output.

Real GDP Trend

The red line in the above graph corresponds to the fitted trend and the green line is the original series of real output. The deviations from the trend are called business cycles. When the output is above the trend line and is rising, it reaches a peak and starts falling from there until it reaches the trough of the next cycle. The part of business cycle from the trough of one business cycle to the peak of next business cycle represents expansion while the part from the peak to the trough represents recession.

The following figure plots the cyclical component of Real GDP:

Real GDP -- Cyclical component

We can see that in the late 70’s there was a severe downturn . Again around 2000-01 we can see another downturn. This was also the time when the dot com bubble had burst. The high growth rate of GDP in 2006-07 can thus partly be attributed to the low base effect.

We had earlier pointed out that the series of consumption and output tend to move together. The following figure corroborates this fact:

RealGDP and Real cons- Cyclical comp

As can be seen from the figure, the cyclical component of output and consumption mirror each other. It can thus be inferred that whenever there is a decline in economic activity, consumption expenditure is hit severely(not implying any causal relationship here, just the co-movement of two series). The following figure examines the investment and output series:

RealGDP and Real Inv- Cyclical comp

Note that the correlation between investment and output is not as clear as between consumption and output, however, there does exist some correlation between the two. It can probably be inferred that investment affects output with a lag. The output series follows investment at a lag which sounds reasonable since the investment alters output by altering the productive capacity of a firm which takes effect only after some time. Next figure compares the consumption and investment series:

Real Cons and Real Inv- Cyclical comp

Although it is hard to say much about the correlation between the two just by looking at the graph, it can be said that investment is much more volatile than consumption – which is also a stylized fact for US data.

So the following stylized facts emerge from this analysis:

1) Consumption is contemporaneously correlated with output.

2) Investment is correlated with output at a lag

3) Consumption is less volatile than output

4) Investment is much more volatile than output and hence consumption

The Matlab code used for this analysis can be found at :