PP402 Model
RTC (Randomize test trial)
Concepts
Framework
Benchmark
General Concepts
Equation
Dependent
Control
Treatment
Independent variable we want to analize (Xi)
Contrafactual of the independet variable
(\neg Xi) + ceteris paribus
Outcome of the experiment (Y(x,g))
Results
Selection Bias
Causal Efect
Difference in the dependent variable under the effect of a tratment or independent variable
Y(1,i) - Y(0,i)
Difference in the dependent variable between groups
Y(0,G1) - Y(0,G2)
Selection bias can arise from un-observed variables
Process
Assigment
Random assignment to the treatment
(No selection Bias)
Large enough groups are comparable (LLN)
The model we have of an experiment is a RTC
The experiment is compare to a RTC
How to analize experiments
Samples
The treatment and control groups indeed look similar?
(checking for balance)
E(X1,1)-E(X1,2) / se(X1,1-X1,2) greater than 2
Yes
No
OK
Bias?
Is the Size of the group big enough to be statistically meaningful
¿?
Yes
OK
No
Is posible to create bigger group or consolidate?
Regressions
Results
Compare the mean difference on treatment and control group
Is the difference statistically meaningful?
Bi/se(Bi) greater than 2
Yes
No
Regect that X is uncorrelated with Y
Posible causal effect
No evidence of causal effect
Concepts
Compares treatment and control subjects who have the same observed characteristics.
We hold constant the other most obvious and important variables than affect the dependent variable
Matching estimator that controls for C
weighted averages of multiple matched comparisons
The effect of treatment when controlling/fixing the variable C
We must control the variables that affect selection and outcomes (bias and causal effects)
Inperfect but useful mimic of a randomized control trial
Variables
Is the variable treatment or the control?
Depends on the research question and theories considered
Parameters
The effect of treatment and control variables on the dependent variable Y
Residual
Random or sampling error
Process
Ordinary Least Square (OLS)
minimize the sum of squared residuals
Omitted variable bias (OVB)
We know other importat variable missing?
No
Yes
Is posible to include?
No
Yes
OK
No
If Pi =0, B_p is consistent and unbias, but incomplete
If Pi !=0, B_p is inconsistent, bias and incomplete
Parameters
Are the parameter estimation robust?
Quasi-experiments
Concept
external circumstances sometimes produce what appears to be randomization
many of the methods developed for analyzing randomized experiments can be applied
Threats to
Validity of Experiments
Internal Validity
External Validity
Causal effects are valid for the population being studied
Inferences and conclusions can be generalized
Failure to randomize
Failure to follow
the treatment protocol
Bias estimators
Can we produce an instrumental
variables regression
Yes
Include the instrumental variable
No
Bias
Attrition.
Is random
Yes
OK
No
Bias
Experimental effects.
Bias
Small samples
causal effect is estimated imprecisely
assumption of normality is typically as dubious
Nonrepresentative sample
Nonrepresentative program or policy.
General equilibrium effects
Prediction
Predictions far outside the data set are not reliable
Measures of FIT
R^2 imeasure of the fraction of Y explained by X
Standar Error: Yi typically is from its predicted value
Similar values while adding control variables
Test stadistical significance of B
the p-value is the probability of obtaining a statistic, by random sampling variation
Two sides hypotesis
One sides hypotesis
Reject with t greater that 1,96
Reject with t greater that 1,64
Confidence Interval for b1
Estimator are unbiased, consistent and efficente under assumptions
X is IID Independently and Identically Distributed
Large outliers are unlikely
Can we use instrumental variables to solve this problem?
Spillover (No in the books)
Understimation of the causal effect
Are the parameters concistent
Y=B1x1+B2X2+e
Selection Bias
Failure to include enough controls or the right controls generates selection bias
Include and calculate bias
Observable?
Endogeneity
COV (e,x) =0
No, because x% of the variables will have this difference
Look for great unbalance problems
Coefficient of variation
The lower bound suggests that one standard deviation in enfranchisement led to an increase in electrification of at least 3.5 percentage points, more than one-third of the sample mean: a substantively large effect.
Primero ver el efecto de la variable omitida en Y, luego ver el efecto sobre las X, para así usar la fórmula de abajo
Fix effects apply if we have panel(longitudial data
Change in LN(X) = (%) change in X
In LN(Y)=B+B1*LN(X) el B1 es la elasticidad
Joint hipotesis testing, both are zero
F-Test
Cambio porcentual del fit, ajustado por los grados de libertad
Problems with the estimation of the OLS standard error
Autocorrelation
Heteroskedastacity