just saying...
eststo: reg lnc lnp lny, cluster(state)
Results can be seen in Table 1
quietly tab year, gen(period)
eststo: xtreg lnc lnp lny period*,fe cluster(state)
eststo: reg d.lnc d.lnp d.lny d.period*, cluster(state)
xtserial lnc lnp lny
\[\begin{align*}
lnC_{it}= \alpha + \beta_{1}lnP_{it} + \beta_{2}lnY_{it} + \gamma_{2} D_{2i}+... + \\ \gamma_{46} D_{46i}+ \delta_{1} T1_{t} + ...+ \delta_{29} T29_{t}+u_{it}\end{align*}\] - Model of interest
In order to account for time effects dummy variables (T1-T29) for each but one year are included.
Equivalently, a fixed effect within transformation can be applied to get rid of unobserved state-specific effects.
If the state-specific effects can be argued to be uncorrelated with the included regressors, a random effects model can be estimated.
Since the RE model yields very similar estimates we will stick with the FE model for comparative purposes.
I guess it is okay to make the presentation a bit shorter than the normal file
\[\begin{align*} & E[y_{i} | a^{l}_{i}=0, s_{i}=0] = \alpha - \gamma \frac{\pi_{0}}{\pi_{2}}\\ & E[y_{i} | a^{l}_{i}=0, s_{i}=1] = \alpha - \gamma \frac{\pi_{0}}{\pi_{2}} + \beta - \frac{1}{\pi_{2}} (\gamma \pi_{1} + \tau (\pi_{0}+\pi_{1}) ) \\ & E[y_{i} | a^{l}_{i}=1, s_{i}=0] = \alpha - \gamma \frac{\pi_{0}}{\pi_{2}}+\frac{\gamma}{\pi_{2}}\\ & E[y_{i} | a^{l}_{i}=1, s_{i}=1] = \alpha + \beta - \frac{1}{\pi_{2}}(\gamma (\pi_{0}+(\pi_{1}-1)+\tau(\pi_{0}+\pi_{1}-1))\\ \end{align*}\]
\[\begin{align*} & E[y_{i} | a^{l}_{i}=0, s_{i}=1] - E[y_{i} | a^{1}_{i}=0, s_{i}=0] = \beta - \gamma \frac{\pi_{1}}{\pi_{2}}-\frac{\tau}{\pi_{2}}(\pi_{0}+\pi_{1}) \\ & \text{If }\pi_{0} = \pi_{1} = 0, \\ & E[y_{i} | a^{l}_{i}=0, s_{i}=1] - E[y_{i} | a^{1}_{i}=0, s_{i}=0] = \beta - \gamma \frac{0}{\pi_{2}}-\frac{\tau}{\pi_{2}}(0+0) = \beta \\ \end{align*}\]
Partial derivatives of the expenditure function with respect to prices
\[\begin{align*}
&h_{1}(p,u) = \frac{{\partial}e(p,w)}{{\partial}{p_{1}}} = \frac{u}{2} \\
&h_{2}(p,u) = \frac{{\partial}e(p,w)}{{\partial}{p_{2}}} = u \\
&\rightarrow h(p,u) = \left(\begin{array}{c} \frac{u}{2} \\ u \end{array} \right)\end{align*}\]
Because figures are fun.
Checkout the different width's ;)
I hope we did not have to contruct a presentaiton which makes completely sense
I keep the following to know the codes for an easy copy and past:
pandoc -s --mathjax --slide-level 2 --toc --toc-depth=1 -t revealjs presentation.md -V theme=solarized -o index.html
pandoc --slide-level 2 --toc --toc-depth=1 -t beamer presentation.md -V theme:Montpellier -o presentation.pdf