Why is there serial correlation in panel data?

Question

I want to know the reason of serial correlation in panel data.

Is it because the data is drawn from a single person? If that's the case, why the very fact should cause serial correlation?

Answer 1

For the same reason that there is serial correlation in a longitudinal series. Recall that panel data is nothing more than a collection of observations over time, for several units/individuals/countries/etc. As such, it the data generation process is such that, for a unit of observation serial correlation, a process suffers from serial correlation, then other units will also have serial correlation.

For example, consider the study of the determinants of inflation for one country. Normally, such a study would test (and many times not reject) serial correlation in the error term.

Now, extend the analysis to a selection of countries. The nature of the process has not changed. The aim of panel data is not to get rid of serial correlation, but to make use of within (longitudinal) and between (cross-section) variation of variables. This is particularly useful to account for endogeneity, by means of a fixed-effect model. Yet, serial correlation remains there.

Answer 2

The intuition breaks down into three parts:

1. Positive Correlation. This is expected in most time series, since many things tend to be relatively smooth in how they change and things that change them tend to also change relatively smoothly. For example, think of the temperature in a particular city over the course of a year. Temperatures in July (in the northern hemisphere) are more likely to be above the average, and will tend to be more like each other than to be like temperatures in December.

2. Negative Correlation. This is less common in the real world, since it implies that if something was above average last time, it will tend to be below average this time. This can happen in a situation where there is a control of some sort that compensates -- and perhaps over-compensates. For example, if you eat a huge meal at lunch, you might well eat a much smaller meal at dinner because you're so full.

3. Zero correlation. What happened last time doesn't affect what happens this time. Think a roulette wheel, or "random noise". It's not like temperature: even if you live in a place that talks about how often the weather changes, you will rarely have an extremely hot day followed by an extremely cold day, with no clue which it might be. It's not like negative correlation, either.

Of course, the serial correlation value is continuously variable from -1 to 1. You can have a small positive correlation or a large one, so my three examples are more to illustrate what it means rather than saying it will firmly fall into one category or another.

In the case of your panel data, the common factor is an individual, as you say. And a particular aspect of an individual will tend to be similar (or different) to that aspect of themselves from time period to time period rather than randomly changing.

This applies to an individual time series. As Michael Chernick points out in his comment, panel data consists of several time series -- each tracking a different aspect of the individuals -- and each of these time series will tend to be autocorrelated, but there need not be any particular correlation between them.