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.

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.

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:

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:

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:

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:

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 : https://www.dropbox.com/s/ol0fcp03g4fwyb5/National_income_annual.m