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 :


Why Marx was right : A brief review

I was recently gifted a book by a friend who is cognizant of my deep interest in Marx. This book – ‘Why Marx was right’ by Terry Eagleton is about ten major criticisms against Marxism. Terry Eagleton has done more than justice to the writings of Marx by taking each criticism case by case and building a chapter around each wherein he tries to reason out why Marx was right and his claims were misunderstood. As each chapter unfolds I am astounded by the ingenuity and the aesthetic quality of Marx’s work. I am thus sharing some of the beautiful insights from this book which, I think, every historian/economist/philosopher should be aware of.

One of the major criticisms against Marx was that he reduced every aspect of history to economics, a phenomenon known as economic determinism. Marx was a proponent of the fact that a civilization cannot exist without ‘productive forces’ or ‘material production’ and that these forces are the prime movers of history. Those who oppose this idea contend that history can not be reduced to ‘material production’ and culture, science, religion and politics play an equally important role in shaping society and history. Although it it can be argued that the ideas, culture, religion and politics, which form the superstructure of a society, are to some extent driven by its economic base. For example, under slavery, it would be unnatural to think of the idea of freedom. For slaves, the act of performing their duties for their masters was as natural as is the idea of working 10 hours a day under capitalism or the idea of paying rent to the feudal lords under feudalism. Hence our ideas, culture and religious beliefs are to some extent dependent on the economic order prevalent in a given time period. But this is not to undermine the intrinsic importance of politics, culture or religion. If today we were to ask ourselves whether politics is a reflection of economics or economics is driven by politics, it would be difficult to find an answer to this question.

Marx, on the other hand, believed in a broader concept of material production. Under capitalism, material production is a means to a greater end, which is to keep oneself from starving. Marx, however, suggested that material production is important for its own sake and not because it serves as a means to an end. He believes that people should engage in an activity because they find it fulfilling to do so, not because they have to do it since they have no other option to sustain themselves. Against this backdrop,when Marx talks of material production, he is pointing towards the broader objective of emancipation of men and women. He is pointing towards the ‘Nature and human agency, the body and its needs,the nature of the senses, ideas of social cooperation and individual self fulfillment’. Marx believes that human labour has always been coerced in capitalism, even if the coercion in question is simply the need not to starve. He believes that good life consists of things done for their own sake. As Terry Eagleton beautifully puts it – “the best things are done just for the hell of it”.

So when Marx speaks of production as the prime mover of history, he does not mean production in its literal sense. He sees labour as a wonderful way of transforming reality. He sees intrinsic value in the process by which man uses natural resources and transforms them into ‘commodities’ and in the process of transforming them he transforms his own self and his own capabilities. This is how societies are transformed.

The following excerpt from the book elegantly summarizes the above arguments:
“The good life for him(Marx) is not one of labour but one of leisure. Free self- realization is a form of “production”, to be sure; but it is not one that is coercive…It is thus surprising that Marxism does not attract more card-carrying idlers and professional loafers to its ranks. This, however, is because a lot of energy must be expended on achieving this goal. Leisure is something you have to work for”Image