## Thursday, January 10, 2008

### Volatility of Output, Consumption, and Investment

This is a graph of the standard deviations of the annualized quarterly growth rates for real values of GDP, C, and I for rolling ten year time periods. That is, the first point shown on the diagram for the blue line is the standard deviation of the growth rate of output for the period 1947:Q2 through 1957:Q1. The second point is for the period 1947:Q3 through 1957:Q2, the third for the period 1947:Q4 through 1957:Q3, and so on, and the last point is for the period 1997:Q4 through 2007:Q3. Thus, one observation is added and one is dropped as you move from one point to another. The observations are indexed by the last observation in the sample, so the first point is labeled 1957:Q1.

Standard Deviations of the Growth Rates of GDP, C, and I
Ten Year Rolling Window [Excel File with the raw data (from the St. Louis Fed) and calculations.]

The left-hand vertical axis shows the annualized values for output and consumption. The right-hand scale, which is on the order of five times larger, shows the values for investment (yellow line). Interestingly, the pattern for I is very similar to the pattern for GDP. This reflects the large influence of the volatility of investment on the volatility of output.

As you move from left to right along a line, a new observation is added and one is dropped, so if the line falls that means that the new observation contributes less to the variance than the observation ten years earlier that was dropped (there is a small complication in this interpretation because the measured mean changes as the sample changes).

By this measure, volatility was falling until somewhere near the sample ending in 1970. However, as observations from the 70s are added and observations from the 1960s dropped, the standard deviation increases again reaching a peak around 1984.

The decline in the standard deviations that begins around 1984 is the Great Moderation (podcast on the Great Moderation I did awhile back). This is well known. But I hadn't noticed how constant the variance has been recently. The observation labeled 1994:1 is for the time period 1984:2 through 1994:1, and it's noteworthy how constant the standard deviation has been since that time period (1984:2 is widely regarded as the beginning of the Great Moderation). For the ten year sample ending in 1994:1 until the ten year sample ending in 2007:3, the standard deviation of output hardly moves at all - it's very close to 2.0 - and the measures for C and I and fairly constant as well.

Given recent events in financial markets, it will be interesting to see if the standard deviations for these variables remain this constant, decline further, or increase.

Posted by on Thursday, January 10, 2008 at 12:15 AM in Economics | Permalink  TrackBack (0)  Comments (21) You can follow this conversation by subscribing to the comment feed for this post.