Notes: Model was simulated for \input \ParmDir/NumPeriodsToSimTime.tex
periods (quarters); to generate results comparable to the roughly
40 year span of U.S. empirical data, the table reports mean outcomes across 
nonoverlapping \input \ParmDir/MonteCarloSubsampleSize.tex
period subsamples.  Bars indicate the sticky
expectations model data, and $\sim$ indicates the presence of
introduced measurement error as discussed in the text.
`IV\%(all)
' indicates instruments that include lags of $\Delta
\log \mathbf{C}_{t},\Delta
\log \mathbf{Y}_{t}, A_{t}$ and $\Theta_{t}$ (resp. $\Delta \log
\bar{\mathbf{C}}_{t}, \Delta \log
\bar{\mathbf{Y}}_{t}, \bar{A}_{t}$ and $\bar{\Theta}_{t}$).  %'IV($\Theta_{t}$)' indicates that only the lagged value of $\Theta$ was used as an instrument.  
The average robust standard across the simulations is presented in 
parentheses.  The penultimate column reports
the $\bar{R}^{2}$ from a regression of the dependent variable on the
RHS variables (instrumented, when indicated); the final column reports
two tests of instrument validity: The $p$-value from the
\cite{shea:iv} test of first-stage instrument validity (top), and the
$p$-value from the Sargan overidentification test (bottom).

