1. Methods of Economic Investigation Lecture 2
Data Structures
Methods of Economic Investigation
Lecture 2

2. Why are we doing this?
Thus far: Most of econometrics teaching has been theory based
Type of data can drive what you can do
Type of data affects credibility and problems with analysis
Can be hard to translate equations into applications and even into reading papers
Rest of this course based on applications: this lecture will help with both lectures and exercises

3. Choosing your data..
Suppose interested in causal effect of X on y: How would you test this?
If you could choose the way in which X is determined in your sample—what would you do
may seem fanciful but field experiments becoming more common in economics
Good thought experiment: If you could have any data in the world, is this question answerable (if not, move on!)
Good reason to choose to do randomized controlled experiment 3

4. Where does data come from?
Surveys
Response Rate
Stratification/Clusters
Reporting Error/Measurement Error
Administrative Records
Lots of different places
Often kept real-time (so addresses “reporting” or “recollection” errors)
May be missing, and that might not be random…
Researchers (and you!)
Often collected for specific project—so be careful what it has
More “unique” with different types of data (e.g. content analysis)

5. Who Collects Data Government Service providers Third Parties
Official Statistics: Unemployment, GDP, etc
Surveys: Labor Force, Consumption, etc.
Records: Justice System, Social Programs
Service providers
Often this may be administrative (e.g. hospital records)
Sometimes, internal surveys or evaluations which can be useful if you can get them
Third Parties
Critical for places with limited capacity (e.g. World Bank is a big source of this for developing countries)
University or Survey Research Programs
Newspapers and Media sources compile LOTS of things

6. Different Types of data
Cross-Sectional Data
Time Series Data
Panel Data
Repeated Cross-Section

7. Cross-Sectional Data
Cross section data covers a cross section of population and information is collected from this cross section during a given period of time.
What does this look like
Rows are units of observations (e.g. individuals)
Columns may be variables

8. Cross-Section Data
Simple descriptive statistics across individuals: can get sample mean and variance of various X’s
Regressions: The standard formulas

9. AlgebraReality: Outcome Variables
Try to get a sense of data, to translate the matrix algebra into reality.
What is the effect of education on income?
We have an Outcome “y”, for example income

10. AlgebraReality: RHS Variables
There may be several (labeled by k) different X’s. So usually we think of this as meaning that:
X is of dimensionality kxn
We will estimate k coefficients
Our X variables looks like:

11. Our Data Looks like: ID Income Race Sex Education 1 y1 x11 x21 x31 24 y4
x14
x24
x34 5 y5
x15
x25
x35
Our Data Example
N=5
k=3
We can index our individuals by ID (useful later)

12. What does a regression tell us?
Remember, it’s minimizing the errors and will pick the 3 coefficients (one on race, one on sex, and one on education) to do that
We are interested in the coefficient on education to tell use the “effect of education on earnings”
We might still care about the effect of race and gender as “control” variables

13. Stata Output

14. AlgebraReality: Stata Output
Using our “data” if we regress y on our X’s
To do this in stata we would tell stata:
regress income race sex education
Output:
Coefficients
Standard errors
R-squared

15. Limitations… Lots of things vary over time
Can’t control for these issues in cross-section data
Only source of variation is across individuals (or whatever the unit of observation)
Identification: Need observations similar time characteristics (because we can’t control this) but different on some variable of interest

16. Now to time series data
Pretty similar to panel data except data indexed by time instead of individual
Year
Income
Inflation
Growth
Unempl
2000 y1
x11
x21
x31
2001 y2
x12
x22
x32
2002 y3
x13
x23
x33
2003 y4
x14
x24
x34
2004 y5
x15
x25
x35

17. Why is time series different?
Correlation between different observations
Violates OLS assumptions (estimates ok but can’t do inference)
More on this later…
Lots of things about individuals are time-invariant so they don’t make sense in this context.
Other things, often in time series data, are common across individuals (e.g. macroeconomic trends)
Limits what we can do with these variables—we CAN’T “control” for time-invariant characteristics so all variation comes from time variation…

18. Estimating with Time Series Data
Two critical issues:
Stationary: Mean and Variance not changing over time
Stronger conditions sometimes required which is that distribution (e.g. all moments) same over time/space
May need to do something to make your data stationary (e.g. de-mean, detrend, difference, etc.)
Ergodic
Given a sufficiently long set of realizations, can estimate statistical properties
Worry about Unit roots (more on this later)

19. Panel Data Repeated observation on individuals
Common example: Labor Force Surveys
Take information about individuals
Usually contains time invarying for any individual (race, sex, education level)
Usually contains time varying for any given individual (employed last week)
Can contain or link to time varying but same across groups of individuals (local unemployment rate)

20. Example of Panel Data
Multi-dimensional—so indexed by time & individual ID
Year
Income
Employment
Sex
Education 1
2000
Y1,2000
X11,2000
X21,2000
X31,2000
2001
Y1,2001
X11,2001
X21,2001
X31,2001 2
Y2,2000
X12, 2000
X22,2000
X32,2000
Y2,2001
X12, 2001
X22,2001
X32,2001
2002
Y2,2002
X12,2002
X22,2002
X32,2002

21. Panel Data Regressions
Regressions need to be indexed by all dimensions (our example is time and individual but it could be time, state, and individual)
May allow intercept shift (e.g. add a dummy for each year)
May allow a slope shift (e.g. allow different coefficients for men and women)

22. What’s so great about Panel Data?
We can control for individual specific factors (e.g. error component models)
ECM may solve some of our omitted variable bias issues (individual controls)
Can use both “within” (for an individual over time) and “between variation (across individuals in a given time)
Can be rare to have long panels
Tend to span very short periods of time
May make it difficult to study trends—can only see “breaks” at big changes

23. Repeated Cross-Section Data
More common—Annual or Frequent Surveys—not always same people
Get repeated cross-section, of different cohorts of individuals
Can do several things:
Construct panel at more aggregate level
Use time-series aspects to compare cohorts

24. Example of Cross-Section Data
Multi-dimensional—so indexed by time & individual ID
Year
Income
Employment
Sex
Education 1
2000
Y1,2000
X11,2000
X21,2000
X31,2000 2
2001
Y2,2001
X12,2001
X22,2001
X32,2001 3
Y3,2000
X13, 2000
X23,2000
X33,2000 4
Y4,2001
X14, 2001
X24,2001
X34,2001 5
2002
Y5,2002
X15,2002
X25,2002
X35,2002

25. Repeated Cross-Section Regressions
Index by time and whatever “group” you want to use—for example: group 1 is men and group 2 is women, then you estimate:
Use similarities between groups but can’t control of individual specific issues
Cohort specific changes—selection issues, e.g.
Can allow ‘fixed effects’ for time or group—but not as believable to control for unobservables

26. Next Steps: Using data can we:
Describe the data to understand what we’ve got
Develop some “questions” to answer
Test our hypotheses
Application based class—will use Stata examples