Introduction to Econometrics and Data Types

Causal Effects vs. Correlation

One of the most important distinctions in econometrics is the difference between correlation and causation. A causal effect occurs when a specific action or treatment directly results in a measurable change in an outcome.

The gold standard for measuring causality is the randomized controlled experiment. In such an experiment, subjects are randomly assigned to either a treatment group (which receives the action) or a control group (which does not). This randomness ensures that, on average, the two groups are identical in every way except for the treatment. The causal effect is then calculated as:

$$\begin{aligned} \text{causal effect} &= \text{average outcome (treatment group)} - \text{average outcome (control group)} \end{aligned}$$

Exam Tip: Remember that correlation is merely a description of how two variables move together in a dataset. It does not prove that one variable causes the other.

In the real world, we often rely on observational data—data collected by observing behavior as it naturally occurs without intervention. Because we cannot always run experiments, we run into the risk of mistaking correlation for causation due to three main issues:

• Omitted (confounding) factors: An unobserved variable influences both the supposed cause and the effect.
• Reverse causality: The direction of influence is the opposite of what was assumed; the "effect" is actually causing the "cause".
• Selection: The groups being compared are not similar because of how individuals "selected" themselves into a group (non-random assignment).

It is also important to distinguish causation from prediction. Prediction (or forecasting) involves using known variables to estimate the value of an unknown variable, such as predicting next year's GDP growth. While a good prediction model is highly useful, it does not necessarily explain the underlying causal mechanism.

Data Sources and Structures

Data in econometrics generally comes from two sources: experimental data, derived from designed trials to investigate causality, and observational data, obtained from real-world observations.

Regardless of the source, data is organized in a rectangular format where each row represents an observation and each column represents a variable. Economists categorize these datasets into three primary types:

1. Cross-sectional data: Observations of multiple entities (such as individuals, firms, or countries) at a single point in time.
2. Time-series data: Observations of a single entity (such as one country's GDP) over multiple consecutive time periods.
3. Panel data (also called longitudinal data): A combination of both, where multiple entities are observed over multiple time periods.

Visualizing and Describing Data

Before running complex regressions, economists must understand the "shape" and "center" of their data. For quantitative data, we often use a histogram to see the distribution of values. Common shapes include symmetric distributions and right-skewed distributions (where a long tail stretches to the right, common in wealth and income data).

To summarize a dataset, we look at measures of central tendency and variability:

• Central Tendency: The mean (arithmetic average), the median (the middle value), and the mode (the most frequent value). Note that the median is often more robust (resistant to outliers) than the mean.
• Variability: The range (difference between max and min), variance ($s^2_X$), and standard deviation ($s_X$) describe how spread out the data is.

Finally, to understand the relationship between two variables, we use a scatterplot. From this, we can calculate the sample correlation coefficient ($r_{XY}$), which measures the strength and direction of a linear relationship on a scale from $-1$ to $+1$.