ECN 102: Analysis of Economics Data
Chapter 1: Introduction to Data
Chapter 1: Introduction to Data
Population vs. Sample Data
We will now begin our discussion of data. Data can be a powerful tool to answer important questions in Economics and beyond, but we must be sure we are understanding and using our data correctly. Today we will go over different types of data we will encounter in this class.
- If we can collect data for every possible individual, we call this population data. Descriptives based on these are called population parameters.
- If we can collect data for only a subset of the population, we call that sample data. Descriptives based on these are called sample statistics.
To be able to make assertions about the broader population, our typical goal, we want our sample data to be representative. We will talk more about what this means later.
Types of Data
There are many types of data we may encounter as well:
- Categorical data encodes which of many categories something belongs to, e.g. are you employed?
- Numerical or quantitative data encodes numerical information about something, e.g. income level
Furthermore, continuous numerical data can take any real number as a value, e.g. GDP, while discrete numerical data can take only separate, countable values (often whole numbers), e.g. number of classes taken in a quarter
Finally, we may need or want to transform our data in some way for analysis, e.g. calculating a growth rate
Observational vs. Experimental Data
The method we use to obtain our data also matters:
- Observational data comes from studying an uncontrolled environment, e.g. UCD enrollment. While this type of data is typically easier to obtain, it often makes it challenging to determine cause and effect in a relationship between variables.
- Experimental data comes from a randomized experiment specifically designed by a researcher, e.g. strategic economic behavior in a lab setting. This type of data is harder to obtain but may yield much easier interpretation of cause and effect.
Data Structure: Cross-Section, Time Series, Panel
We can further classify our data by thinking about how many units of observation and points in time it covers:
- Cross-sectional data covers many units at a single point in time
- Time-series data covers one unit over multiple points in time
- Panel or longitudinal data covers multiple (repeated) units over multiple points in time
- Repeated cross-sectional data covers multiple sets of non-repeated units over multiple points in time
Variable Subscript Notation
We denote a variable \(x_{...}\) with its necessary subscripts depending on the kind of data it contains:
The \(i\) subscript corresponds to units of observation
The \(t\) subscript corresponds to points in time
What kind of variable would \(x_i\) be? \(x_t\)? \(x_{it}\)?
\(x_i\) would be a cross-sectional variable, \(x_t\) would be a time-series variable, and \(x_{it}\) would be a panel variable.
Correlation vs. Causation
The main goal for a field like Economics is ultimately causality, or the robust determination that x causes y. Experimental and quasi-experimental methods speak to this concern, but are often unfeasible or impractical to implement. For this class, we will restrict our discussion to correlational variable relationships, where x and y are covarying but we cannot claim causality.
We cannot say: x going up causes y to go up
We can say: x going up is associated with y going up as well
Chapter 2: Summary Statistics
Summation Notation
Summation notation: how we add across observations
\[x_1+x_2+x_3+x_4 = \sum_{i=1}^4x_i\]
“Add up the first four observations of a variable \(x\)”
Summation Notation: General Form
Generally for a variable \(x\) with sample size \(n\) we write:
\[\sum_{i=1}^nx_i\]
“Sum up all observations in our sample from 1 to \(n\)”
Summation Notation: Operations
We can also add/subtract and multiply/divide elements within a summation:
\[\begin{align*} X &= \sum_{i=1}^{3} 2x_i+7\\ &= \underbrace{2x_1+7}_{i=1} + \underbrace{2x_2 + 7}_{i=2} + \underbrace{2x_3 + 7}_{i=3} \\ &= 2(x_1+x_2+x_3) + 7(3)\\ &= 2\sum_{i=1}^3(x_i) + 21 \end{align*}\]
Summation Notation: Properties
For a constant \(c\) with sample size \(n\):
\[\sum_{i=1}^n c = nc\text{ and } \sum_{i=1}^n c(x_i) = c\sum_{i=1}^nx_i\]
Summation Notation: Practice
What do the following sums add to?
\[\sum_{i=5}^6 i\]
\[\sum_{i=1}^3(2i + 1)=2\sum_{i=1}^3 (i) + 3(1)\]
\[\sum_{i=1}^3 2^i\]
Summation Notation: Solutions
What do the following sums add to?
\[\sum_{i=5}^6 i=5+6=11\]
\[\sum_{i=1}^3(2i+1)=3+5+7=15\]
\[\sum_{i=1}^3 2^i=2+4+8=14\]
End of Lecture Material
Knowledge Check 1
What types of data are the following examples and why?
Quarterly data on average US mortgage rates 2005-2015
Data on the mode of transit used to commute around Davis from a sample of 200 students
Data on the number of students attending each elementary school in Yolo county this year
Results from a double-blind medical trial of a new drug on immediate patient outcomes