Lecture 1 : the main empirical tools

what types of data exist

• cross sectional data

• time series

• panel data

cross sectional data

covers a cross section of observations (eg individuals, firms ext)

information is collected from this cross section for a given time

→ rows are units of observations and columns are variables

time series data

data indexed by time only

panel data

repeated observation of the same unit

the same unit is followed over time

→ the survey takes information about individuals

→ time-invariant information (eg race)

→ time varying information (eg employed last week)

Regression Discontinuity design RD

the treatment assignment rule : we know the rules for the treatment affected by cutoff’s

arounf the discontinuity :

• for observations very close to the discontinuity we effectiverly have an experiment

• we have a control group and a treatment group, assigned as good as random

Regression Discontinuity design RD : two types

Sharp RD

and Fuzzy RD

Sharp RD

• is used when treatment status is a deterministic and discontinuous function of a covariate Xi, = running variable

Fuzzy RD

instead of a deterministic assignment rule there may only be a change in the probability of treatment at the cutoff

RD : identification assumptions

1) the running variable is not fully manipulable around the threshold

• randomness around the cutoff

2) all observable covariates and unobsservables that might be correlated with our outcome variables should show continuity across the RD threshold

Instrumental variable : what makes a valid instrument

a variable Zi is a valid instrument for the endogenous regressor Xi if it satisfied the conditions

• relevance : corr (Zi, Xi) ≠ 0

• Exogeneity : corr (Zi, ei) = 0, so that Zi is as good as random, and Z only affects the outcome Y through affecting X

The Instrumental Variable (IV) estimation

most common estimation method : two stage least squares 2SLS

1) decompose Xi into the component that can e predicted by Zi and the problematic component

2) use the predicted value of Xi form the first stage regression to estimate its effect on Yi

Difference in difference DID

two dimensions

• group dimension : two groups (control and treatment)

• time dimension : two periods (pre and post treatment period)

→ came from john snow’s investigoation about water

Difference in difference DID validity depends on

the parallel trend assumption : trends would have been the same between the control and the treatment groups, in absence of the treatment

how can we have have some confidence in this assumption ?

• given both groups are iwthout treatment during the pre-period, the DID estimate shoud be 0