• Use of statistical methods to analyze economic data
• Dealing with nonexperimental data
• Trying to make inferences from incomplete data
  • i.e. trying to estimate population-wide relationships based on sample data

• Estimate relationships between variables
• Test theories and simple hypotheses
• Forecast variables ("crystal balls")
• Evaluating gov't policy

1. Economic model (this can get complicated for difficult questions)
2. Econometric model

Examples: estimating demand curve, evaluating effects of minimum wage increase

“A planner is a gentle man, with neither sword nor pistol. He walks along most daintily, because his balls are crystal.” Mike Lynch, MIT

"Prediction is very difficult, especially if it's about the future." Nils Bohr, Nobel laureate in Physics

• Gary Becker, 1968
• Assume criminals are utility maximizers
• We could model criminal behavior as a function of the opportunity costs of crime and its benefits.

\[y = f(w_1,w_2,p_1,p_2,s,a)\]

• What functional form do we use?
• It depends…
  • Simple first step: throw together a bunch of variables and estimate a linear model.
  • Consider possible interactions (e.g. does schooling affect men differently than women?)
  • Some variables might need to be modified (e.g. \(p_1 \times p_2 \times s = E(s)\))

• Does extra training increase productivity?
• What factors are important to hold constant?
  • Education
  • Work Experience
  • Training
  • Others?

• How do we measure these?
  • Years of schooling
    • Does quality matter?
    • Subject?
    • Earnestness?
  • Years since leaving school
  • Weeks of training
• The data we have is always imperfect
  • Schooling \(\neq\) Education

• Econometric model:

\[ crime = \beta_0 + \beta_1 wage + ... + u\]

• This is a linear model

• We're looking at how the \(y\) variable changes as the \(x\) variables change

\[ y = \beta_0 + \beta_1 X + ... + u\]

• With multiple x variables, we're seeing how \(x_i\) changes, holding \(x_j\) constant.
• A lot of interesting things are happening in the \(u\) term
  • Factors that aren't included in the model affect this "error term"
  • We hope that the effects of these other factors balance out
  • We also hope their effects aren't too big

When the effects of all the things not in our model are small, it's relatively easy to see the relationship between our variables.

When the data is noisier (i.e. there's a lot of variation in \(y\) that isn't associated with \(x\)) the confidence interval (dark grey) expands and we're less certain that the relationship holds up.

• Cross-sectional
• Time series
• Panel/Longitudinal
  • Pooled cross-sections
• Different types of data call for different approaches

• Looking at different individuals at one point in time
  • e.g. countries, regions, people, firms, etc.
• Assumes observations are essentially independent

• Looking at one or more variables over time
  • e.g. GDP, stock prices, CPI, homicide rates
• Usually "serially correlated"
  • \(GDP_{2016} = GDP_{2015} + u\)
  • This will raise problems with statistical inference if we don't do something.

• Looking at cross-sectional variation and variation over time
  • Pooled: different (independent) cross-sections
    • e.g. random people from different states at different time periods
  • Panel (longitudinal): following the same people/firms/countries/etc. over different time periods
    • can account for unobservable differences ("fixed effects")

• What is the effect of \(x_1\) on \(y\)?
  • what if \(x_2\) changes at the same time as \(x_1\)?
    • We might face the problem of colinearity.
  • to the extent we can, we want to isolate the effect of interest.
• We need to be careful to include the right variables to avoid "model specification error"

What about when we think \(x_1\) and \(x_2\) work together to affect \(y\)? We can use interaction terms to understand the effect of both of them together.

https://www.xkcd.com/552/

Correlation doesn't imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing "look over there".

• The best way to determine causality is with an experiment.

• Most economists aren't able to run experiments, so figuring out causality is much harder.

• Good advice: imagine an experiment that would help you figure out causality.

• Effect of fertilizer on crop yield
  • how many extra pounds of soybeans can I get from an extra pound of fertilizer?
  • implicit assumption: other factors (e.g. weather, parasites, etc.) are held fixed

• Experiment
  • sort fields into grid (e.g. squared meters)
  • randomly put different amounts of fertilizer on different squares (why randomly?)
  • carefully keep track of everything (make sure computers/GPS are working well)
  • compare results, taking account of other variables
    • e.g. when comparing to last harvest, take account of differences in weather

• Measuring returns to schooling
  • what would happen to someone's wages if they'd spent an extra year in school?
  • implicit assumption: other factors (e.g. motivation, IQ, etc.) are held fixed

• Experiment
  • pry babies from their mother's arms
  • randomly assign them to different amounts of schooling at different schools
  • compare wage outcomes

• Econometrics
  • collect information on people, including demographics, wages, years of schooling, etc.
  • make and justify assumptions about what variables are included
  • look for natural experiments when possible

• Theories might be:
  • Causal: "good institutions cause economic growth"
  • Correlational: "short term and long term bonds should be roughly equivalent"