ow-drafting-fx-event-study-estim

Using COVID-19 non-drafting response policies (2020–2022) to estimate the magnitude of swim drafting benefits (~20% improvement in outcomes according to sports literature).

Research Questions

1. Does the literature's ~20% drafting benefit $\implies$ 20% better mean outcomes for drafters in drafting races?

2. Optional control for drafting groups/robustness: Calculation of an event-specific clustering-based DraftingGroupCriteria (based on "Out"-Times).
3. Effect heterogeneity: Which groups (e.g., percentiles) benefit the most from drafting? Estimate marginal effects.

Research Design (Draft, Event-Study, Staggered-DiD Approach)

Event-Study Model with Three Periods:

$$ Y_{it} = \gamma_0 + \gamma_1 \mathbf{1}{t \in \text{covid}} + \gamma_2 \mathbf{1}{t \in \text{postcovid}} + \gamma_3 X_{i} + \gamma_4 \mathbf{1}{i \in \text{leader}} + \gamma_5 \mathbf{1}{t \in \text{covid}} \cdot \mathbf{1}{i \in \text{drafter}} + \gamma_6 \mathbf{1}{t \in \text{postcovid}} \cdot \mathbf{1}{i \in \text{drafter}} + \mu_i + \nu_j + \delta_t + \theta_t \text{trend} + \varepsilon_{it} $$

Where:

• $Y_{it}$: outcome of athlete $i$ at time $t$.
• $\gamma_0$: intercept term.
• $\mathbf{1}{t \in \text{covid}}$: indicator for the COVID period (2020–2022) when drafting was not allowed.
• $\mathbf{1}{t \in \text{postcovid}}$: indicator for the post-COVID period (after 2022) when drafting restrictions were lifted.
• $X_i$: additional covariates for athlete $i$.
• $\mathbf{1}{i \in \text{leader}}$: indicator for athletes who are the fastest in their cluster (leaders who do not benefit from drafting).
• $\mathbf{1}{i \in \text{drafter}}$: indicator for athletes who are eligible to draft.
• $\gamma_5$: interaction effect of the COVID period and drafting eligibility for drafters.
• $\gamma_6$: interaction effect of the post-COVID period and drafting eligibility for drafters.
• $\mu_i$: Athlete fixed effects (FEs).
• $\nu_j$: Event and event-type fixed effects (FEs).
• $\delta_t$: Month FEs (seasonality, weather, etc.).
• $\theta_t \text{trend}$: time trend to capture long-term performance improvements.
• $\varepsilon_{it}$: error term.

Structural Break Test / Parallel Trends Assumption (PTA):

Endogeneity:

Three Periods:

1. Pre-COVID (Baseline): No restrictions on drafting, this serves as the baseline period (no indicator is needed).
2. COVID Non-Drafting (2020–2022): No drafting allowed, represented by $\mathbf{1}{t \in \text{covid}}$.
3. Post-COVID (Post-2022): No restrictions on drafting, represented by $\mathbf{1}{t \in \text{postcovid}}$.

DraftingGroupCriteria

The DraftingGroupCriteria is based on hierarchical clustering of swim times, which is used to define drafting groups:

1. Swim Times ($T_i$): Let $T_i$ represent the swim time for athlete $i$. All athletes in an event are clustered based on their times.

2. Clustering: Using hierarchical clustering, athletes are grouped based on the proximity of their swim times, forming a cluster $C_k$ for each group $k$. The optimal choice of $k$ for each event $j$ will depend on the distribution of swim times. (->measure open)

$$ C_k = { i \mid d(T_i, T_{i'}) \leq d_{\text{threshold}}, \forall i, i' \in C_k } $$

Where:

• $C_k$ is the set of athletes in cluster $k$.
• $d(T_i, T_{i'})$ is a distance metric between the swim times $T_i$ and $T_{i'}$.
• $d_{\text{threshold}}$ is a pre-defined threshold that determines the proximity needed to form a cluster (->literature).

3. Leader and Drafters:
   • The athlete with the fastest time in the cluster,

$$ L_k = \underset{i \in C_k}{\arg \min} , T_i $$

is assigned to Leader.

• All other athletes in the cluster are assigned as Potential Drafters:

$$ D_k = C_k \setminus {L_k} $$

The leader $L_k$ cannot draft, but the potential drafters $D_k$ are considered to benefit from drafting effects within their respective cluster.

Data Requirements

1. Swim outcome times from multiple events, from different event types on multiple athletes across 2 drafting and 1 non-drafting periods.
2. COVID-19 policy period indicators (e.g., event-specific restrictions on drafting).
3. Athlete information (ID, performance history).
4. Event data (group starts, waves, etc.).
5. Fixed effect controls: athlete FEs, event FEs, and seasonality FEs.

Estimated Effects