[Sam Rickman]

\[ \begin{bmatrix}
\sigma^2_{u0} \\
\sigma_{u0,u1} & \sigma^2_{u1} \\
\sigma_{u0,u2} & \sigma_{u1,u2} & \sigma^2_{u2}
\end{bmatrix} \]

\[ \begin{bmatrix}
1.71368 & & & & & & & \\
0.756977 & 1.57591 & & & & & & \\
0.529473 & 0.786411 & 2.08232 & & & & & \\
0.491731 & 0.558595 & 0.933849 & 2.13161 & & & & \\
0.276758 & 0.342848 & 0.638271 & 0.821977 & 1.58599 & & & \\
0.170209 & 0.260075 & 0.510564 & 0.435605 & 0.899372 & 1.92696 & & \\
0.205027 & 0.248522 & 0.631041 & 0.556762 & 0.742223 & 1.02729 & 2.1866 & \\
0.060675 & 0.164207 & 0.300921 & 0.441473 & 0.58498 & 0.639033 & 1.20417 & 2.22011
\end{bmatrix} \]

[Xavier Pedros]

test test \[y_{it} = \mu_i + \theta y_{i,t-1} + \varepsilon_{it}\]

\[ln (Y_{i,t}) = \beta_0 + \beta_1 ln (Y_{i,t-1}) + \beta_2 ln(S_{i,t}) + \beta_3 ln(P_{i,t}) + \sum_{j=1}^{5} \gamma_j ln (EUF_{i,t-j}) + \mu_{i} + \tau_{t} + u_{it} \]

[Xavier Pedros]

\[\frac{dY_{i}}{dEUF_{i}} = \frac{\gamma}{\frac{EUF_{i}}{Y_{i}}} \]

[Chengmou Lei]

just trying:
\[TFPQ = \sum_{q=-3}^{+3}\delta_q\mathbb{I}\mathbb{I}\left \{ t-EventYear=q \right \}\times Treat+\theta+\epsilon \]

[Chengmou Lei]

trying within line math symbol:the treatment effect (\[delta_q\] in the following model).

[mariofiorini]

test \[ (e^{\beta}-1) = \frac{\mathbb{E}[Y_{it}(1)\mid \text{Treat,Post}]-\mathbb{E}[Y_{it}(0)\mid \text{Treat,Post}]}{\mathbb{E}[Y_{it}(0)\mid \text{Treat,Post}]} \]

[Stefan Kreisel]

\[ r = {\sigma^2_\text{Between} \over \sigma^2_\text{Between} + \sigma^2_\text{Error}} \]

[Stefan Kreisel]

`icc` test

[Romano Tarsia]

\[
\beta_1 T_{i,t} - \beta_1 T_{i,t-1} = \beta_1 (T_{i,t} - T_{i,t-1})
\]

[Aidan Sloyan]

test

\[ m_{it} = \sum\gamma_j . D_{i,t-j} + \alpha_i + \delta_t + \beta.X_{it} + \epsilon_{it} \]

Where
\[ m_{it}, D_{i,t-j}, \alpha_i, \delta_t , X_{it} \] are out-out-pocket spending, event time dummies, individual fixed effects, time (e.g., year-month) fixed effects, and other covariates, respectively.