The document discusses the complexities of relationships in agricultural economics, focusing on the 'blame' game surrounding treatment outcomes, such as crop insurance and disaster payments. It emphasizes the importance of understanding causal effects and outlines statistical methods like propensity score matching and regression to assess treatment impacts. The text highlights the challenges of selection bias and the need for well-defined causal models to analyze population average treatment effects.

1. It’s all about relationships:
The “blame” game
Dr. Phil Barrett Kirwan
University of Illinois

2. Relationships
• Difficult
• Complicated
• Never deterministic
• The “blame” game—Who/what caused the
outcome we are concerned about

3. Which relationships?
• Yi – outcome of interest
• Wi – “treatment”
• Xi – covariates (control variables)
• Conditional Expectation Function (CEF)
• E(Yi|Wi, Xi)

4. Treatments & outcomes in ag econ
Treatments
• crop insurance
• disaster payments
• CRP
• GMO crops
• payment limits
• no-till practices
• pesticide regulation
Outcomes
• profitability
• revenue
• production
• survival
• land values
• farm size

5. Mutual understanding of
the ultimate goal
• Billiard balls
• Potential outcomes =
• Realized outcome, Yi = Y0i + (Y1i - Y0i) Wi
• Causal effect for individual i: Y1i - Y0i
Y1i when Wi=1
Y0i when Wi=0

6. The road less travelled
• Not clinicians
• interested in the population average
treatment effect: E(Y1i - Y0i)
• population average treatment effect on the
treated: E(Y1i - Y0i |Wi = 1)
• E(Yi |Wi = 1) – E(Yi |Wi = 0) =
E(Y1i|Wi = 1) - E(Y0i|Wi = 1) +
E(Y0i|Wi = 1) - E(Y0i|Wi = 0)
(ATT)
(Selection Bias)

7. Advantages of this approach
• well-defined causal model
• no distributional assumptions
• no functional form assumptions
• allow for heterogeneous responses

8. The assignment mechanism
• Randomization
• “Selection on observables”
• The conditional independence assumption:
{Y1i , Y0i} || Wi | Xi
• E(Yi |Wi = 1) – E(Yi |Wi = 0) =
E(Y1i|Wi = 1) - E(Y0i|Wi = 1) +
E(Y0i|Wi = 1) - E(Y0i|Wi = 0)

9. Tools
• Matching
• Regression
• Propensity score matching
• Combination

10. Matching
• Pair a treatment obs with an identical looking
control obs.
• Take the difference in their outcomes
• Average these differences across all Xi
• Straightforward
• Nonlinear
• Inefficient

11. Regression
• Best linear approx of the CEF
• Extrapolates where there might be missing
data L
• Problem arises when the covariate
distributions are substantially different
between the treatment & control groups.
• Compare w/ normalized differences
• > 0.25 causes problems

12. Regression & Matching
• dX = E(Yi |Xi ,Wi = 1) – E(Yi |Xi ,Wi = 0)

13. Propensity Score Matching
• “An ongoing discussion concerns the role of
the propensity score … and indeed whether
there is any role for this concept”
– Imbens & Wooldridge (2009)
• The conditional probability of receiving
treatment
• e(Xi) = E(Wi | Xi) = P(Wi = 1|Xi)

14. Propensity Score Matching
• If CIA holds then {Y1i , Y0i} || Wi | e(Xi)
• Non parametric (kernel) regression
• Two steps:
– Estimate the propensity score
– Use it to match, or
– Use it to weight regression

15. PSM Weights