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\begin_body

\begin_layout Standard
\begin_inset Formula $pr'$
\end_inset

 has today down and tomorrow across, so 
\begin_inset Formula $pr$
\end_inset

 has the transpose of this.
 Note what we've written the elements of the matrix 
\begin_inset Formula $pr'$
\end_inset

 and not 
\begin_inset Formula $pr$
\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula \[
pr'=\left[\begin{array}{cccc}
gg11 & gb11 & gg10 & gb10\\
bg11 & bb11 & bg10 & bb10\\
gg01 & gb01 & gg00 & gb00\\
bg01 & bb01 & bg00 & bb00\end{array}\right]\]

\end_inset


\end_layout

\begin_layout Standard
Forming the transpose:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
pr=\left[\begin{array}{cccc}
gg11 & bg11 & gg01 & bg01\\
gb11 & bb11 & gb01 & bb01\\
gg10 & bg10 & gg00 & bg00\\
gb10 & bb10 & gb00 & bb00\end{array}\right]\]

\end_inset


\end_layout

\begin_layout Standard
so 
\begin_inset Formula $pr$
\end_inset

 now has tomorrow down and today across.
 In our expected value calculation, therefore, 
\end_layout

\begin_layout Standard
\begin_inset Formula \[
pr=\left[\begin{array}{cccc}
0.8507\\
\\\\ &  &  & 0.5250\end{array}\right]\]

\end_inset


\end_layout

\begin_layout Standard
Using the parameters and restrictions given in the paper, the probability
 that you are in a good state today, a good state tomorrow, employed today
 and employed tomorrow is 
\begin_inset Formula $0.85$
\end_inset

.
 The probability you move from bad unemployed today, to bad unemployed tomorrow
 is 
\begin_inset Formula $0.52$
\end_inset

.
 his
\end_layout

\end_body
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