Random Thoughts

Seeing the sun shining

• Why do I not enjoy the sun, while sitting in the library?
• I mean, I have to work and cannot enjoy the sun.
• Maybe, because I have an aim I follow and there is not much which can actually distract me from that aim.
• Based on the fact that I have to work on the library, it is nicer to see the sun shining.
  • Clear reason to get a spot at a window btw.

More Cheese = Less Cheese

• More Chesse = More Holes
• More Holes = Less Cheese
• More Cheese = Less Cheese

just saying...

Question 1

subquestion a

eststo: reg lnc lnp lny, cluster(state) Results can be seen in Table 1

subquestion b(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

subquestion b(2)

• In order to account for time effects dummy variables (T1-T29) for each but one year are included.

• To include state effects there are several options.
• Firstly dummy variables (D2-D46) for each state can be added to the regression.

• 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.

• In fact, the Hausmann test does no reject the RE model.

• Since the RE model yields very similar estimates we will stick with the FE model for comparative purposes.

subquestion b(3)

• Given that smoking is an addiction it is plausible that there might be serial correlation.
  • confirmed by a test for serial correlation in the residuals obtained from the FD regression.
• Given substantial serial correlation, the FD regression should generally be preferred.

I guess it is okay to make the presentation a bit shorter than the normal file

Question 2

Some Math

\[\begin{align*} & E[y_{i} | a^{l}_{i}=0, s_{i}=0] = \alpha - \gamma \frac{\pi_{0}}{\pi_{2}}\\ & E[y_{i} | a^{l}_{i}=0, s_{i}=1] = \alpha - \gamma \frac{\pi_{0}}{\pi_{2}} + \beta - \frac{1}{\pi_{2}} (\gamma \pi_{1} + \tau (\pi_{0}+\pi_{1}) ) \\ & E[y_{i} | a^{l}_{i}=1, s_{i}=0] = \alpha - \gamma \frac{\pi_{0}}{\pi_{2}}+\frac{\gamma}{\pi_{2}}\\ & E[y_{i} | a^{l}_{i}=1, s_{i}=1] = \alpha + \beta - \frac{1}{\pi_{2}}(\gamma (\pi_{0}+(\pi_{1}-1)+\tau(\pi_{0}+\pi_{1}-1))\\ \end{align*}\]

More Math

\[\begin{align*} & E[y_{i} | a^{l}_{i}=0, s_{i}=1] - E[y_{i} | a^{1}_{i}=0, s_{i}=0] = \beta - \gamma \frac{\pi_{1}}{\pi_{2}}-\frac{\tau}{\pi_{2}}(\pi_{0}+\pi_{1}) \\ & \text{If }\pi_{0} = \pi_{1} = 0, \\ & E[y_{i} | a^{l}_{i}=0, s_{i}=1] - E[y_{i} | a^{1}_{i}=0, s_{i}=0] = \beta - \gamma \frac{0}{\pi_{2}}-\frac{\tau}{\pi_{2}}(0+0) = \beta \\ \end{align*}\]

Even More Math

Partial derivatives of the expenditure function with respect to prices\[\begin{align*} &h_{1}(p,u) = \frac{{\partial}e(p,w)}{{\partial}{p_{1}}} = \frac{u}{2} \\ &h_{2}(p,u) = \frac{{\partial}e(p,w)}{{\partial}{p_{2}}} = u \\ &\rightarrow h(p,u) = \left(\begin{array}{c} \frac{u}{2} \\ u \end{array} \right)\end{align*}\]

Figures

Because figures are fun.

Checkout the different width's ;)

Figure 1

Figure 2

• we can also do a figure from the web
  • But I actually prefer a funny meme
    • Because I like them
• Cool, different types of points for nested bullets
  • Nice

Figure 3

Conclusion

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:

• to get the html, type the following on one line:

pandoc -s --mathjax --slide-level 2 --toc --toc-depth=1 -t revealjs presentation.md -V theme=solarized -o index.html

• if you want a beamer/latex pdf, type:

pandoc --slide-level 2 --toc --toc-depth=1 -t beamer presentation.md -V theme:Montpellier -o presentation.pdf