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\title{Are We Providing Enough to Those  Who Have Too Little?  \\  Measuring Poverty Relief \\\quad \\ Supporting Materials} 
\date{\today}
\author{Karen Long Jusko\footnote{Corresponding author.  Comments most welcome: kljusko@stanford.edu.}   \\ Department of Political Science\\ Stanford University \\\quad\\ and  \\\quad\\
Katherine Weisshaar\\Department of Sociology\\University of North Carolina at Chapel Hill}

\begin{document} 
\maketitle

\appendix 
\renewcommand{\thesection}{Appendix \Alph{section}.}

\section{Data Processing Notes}
\begin{itemize}
	\item All income amounts are reported in thousands of 2016 US dollars. 
	\item In an effort to generate the most inclusive measure of poverty relief, we follow the example of \citeasnoun{Tiehen_Jolliffe_Smeeding_2013}, and treat Supplemental Nutrition Assistance Program benefits (i.e., food stamps), and other near-cash benefits (energy assistance), as income support. 
	\item We restrict the analysis to households in which the head of the household is over the age of 25, and under the age of 60, to avoid the inclusion of households whose low levels of market income may not reflect their true levels of resources (i.e., students, seniors). We also exclude social security income, SSI, disability insurance, and education assistance. 
	\item We use reported, simulated estimates of EITC and CTC payments. 
	\item The parameters $\alpha$, $\beta_1$, and $\beta_2$ are estimated using Stata SE 12.1's \verb nl \rm program with starting values of $\alpha=1$, $\beta_1=2$, and $\beta_2=-.1$. The parameter $\tau$ is estimated using a line-search strategy. Standard errors for $\tau$ and $\mathcal{R}$ are calculated from simulated draws, based on the parameters and variances of $\alpha$, $\beta_1$, and $\beta_2$. 
\end{itemize}

\pagebreak 
\section{The General Relationship between Market Income and Social Transfers}

NOTE.  In the following panels, each data point represents one percent of the pooled 2010-2014 state sample. Error bars report the interquartile distribution at each income level. All currency amounts are reported in thousands of 2016 US dollars. The solid line reports predicted values for Eq. (2). The dashed line reports predicted values for Eq. (3). 
\bigskip

\centering\includegraphics[width=.77\textwidth]{20161021_Appendix_1.pdf}
\pagebreak

\centering\vspace{1in}\par\quad\par
\includegraphics[width=.77\textwidth]{20161021_Appendix_2.pdf}
\pagebreak

\noindent\includegraphics[width=.77\textwidth]{20161021_Appendix_3.pdf}
\pagebreak	


\section{State-Level Parameters} \singlespacing \footnotesize 
\begin{longtable}
	{lcccccc} \caption{Estimates of $\alpha$, $\beta_1$, $\beta_2$, $\tau$, and $\mathcal{R}$} \\
\toprule & N & $\alpha$ & $\beta_1$ & $\beta_2$ & $\tau$ & $\mathcal{R}$ \\
\midrule 
\endfirsthead
		
\caption{Estimates of $\alpha$, $\beta_1$, $\beta_2$, $\tau$, and $\mathcal{R}$ (continued)} \\
\toprule & N & $\alpha$ & $\beta_1$ & $\beta_2$ & $\tau$ & $\mathcal{R}$ \\
\midrule 
\endhead
			
\bottomrule \\
\multicolumn{7}{r}{(Continued on next page)} 
\endfoot
				
\bottomrule \\
\endlastfoot


Alabama	&	2,881	&	0.675	&	3.932	&	-0.026	&	16.500	&	0.354	\\
	&		&	(0.150)	&	(0.220)	&	(0.003)	&	(0.104)	&	(0.000)	\\ \addlinespace[5pt]
Alaska	&	3,041	&	0.604	&	4.497	&	-0.018	&	15.767	&	0.404	\\
	&		&	(0.196)	&	(0.261)	&	(0.003)	&	(0.149)	&	(0.000)	\\ \addlinespace[5pt]
Arizona	&	3,199	&	0.415	&	4.999	&	-0.022	&	15.817	&	0.414	\\
	&		&	(0.158)	&	(0.214)	&	(0.002)	&	(0.109)	&	(0.000)	\\ \addlinespace[5pt]
Arkansas	&	2,581	&	0.357	&	4.302	&	-0.019	&	16.202	&	0.369	\\
	&		&	(0.220)	&	(0.233)	&	(0.003)	&	(0.108)	&	(0.000)	\\ \addlinespace[5pt]
California	&	22,557	&	0.786	&	6.194	&	-0.024	&	14.590	&	0.517	\\
	&		&	(0.066)	&	(0.116)	&	(0.001)	&	(0.068)	&	(0.000)	\\ \addlinespace[5pt]
Colorado	&	5,402	&	0.636	&	5.144	&	-0.026	&	15.665	&	0.433	\\
	&		&	(0.101)	&	(0.210)	&	(0.002)	&	(0.110)	&	(0.000)	\\ \addlinespace[5pt]
Connecticut	&	5,132	&	0.496	&	5.157	&	-0.018	&	15.297	&	0.444	\\
	&		&	(0.143)	&	(0.226)	&	(0.002)	&	(0.139)	&	(0.000)	\\ \addlinespace[5pt]
Delaware	&	3,554	&	0.503	&	5.251	&	-0.022	&	15.479	&	0.440	\\
	&		&	(0.152)	&	(0.223)	&	(0.002)	&	(0.122)	&	(0.000)	\\ \addlinespace[5pt]
Florida	&	9,904	&	0.426	&	4.418	&	-0.025	&	16.375	&	0.369	\\
	&		&	(0.080)	&	(0.126)	&	(0.002)	&	(0.066)	&	(0.000)	\\ \addlinespace[5pt]
Georgia	&	5,653	&	0.625	&	5.068	&	-0.028	&	15.859	&	0.422	\\
	&		&	(0.099)	&	(0.168)	&	(0.002)	&	(0.086)	&	(0.000)	\\ \addlinespace[5pt]
Hawaii	&	3,463	&	0.723	&	6.953	&	-0.025	&	14.132	&	0.557	\\
	&		&	(0.177)	&	(0.349)	&	(0.003)	&	(0.195)	&	(0.000)	\\ \addlinespace[5pt]
Idaho	&	2,766	&	0.538	&	5.719	&	-0.020	&	14.942	&	0.479	\\
	&		&	(0.246)	&	(0.297)	&	(0.003)	&	(0.160)	&	(0.000)	\\ \addlinespace[5pt]
Illinois	&	7,642	&	0.723	&	5.542	&	-0.025	&	15.203	&	0.469	\\
	&		&	(0.105)	&	(0.182)	&	(0.002)	&	(0.097)	&	(0.000)	\\ \addlinespace[5pt]
Indiana	&	3,675	&	0.710	&	4.928	&	-0.025	&	15.672	&	0.428	\\
	&		&	(0.152)	&	(0.223)	&	(0.003)	&	(0.113)	&	(0.000)	\\ \addlinespace[5pt]
Iowa	&	4,256	&	0.557	&	4.761	&	-0.020	&	15.714	&	0.415	\\
	&		&	(0.156)	&	(0.210)	&	(0.002)	&	(0.117)	&	(0.000)	\\ \addlinespace[5pt]
Kansas	&	3,358	&	0.547	&	4.492	&	-0.020	&	15.935	&	0.395	\\
	&		&	(0.185)	&	(0.244)	&	(0.003)	&	(0.129)	&	(0.000)	\\ \addlinespace[5pt]
Kentucky	&	3,298	&	0.633	&	4.352	&	-0.023	&	16.093	&	0.386	\\
	&		&	(0.174)	&	(0.217)	&	(0.003)	&	(0.106)	&	(0.000)	\\ \addlinespace[5pt]
Louisiana	&	2,870	&	0.605	&	4.705	&	-0.031	&	16.275	&	0.390	\\
	&		&	(0.124)	&	(0.223)	&	(0.003)	&	(0.103)	&	(0.000)	\\ \addlinespace[5pt]
\pagebreak
Maine	&	3,545	&	0.536	&	5.834	&	-0.023	&	15.098	&	0.477	\\
	&		&	(0.165)	&	(0.254)	&	(0.002)	&	(0.139)	&	(0.000)	\\ \addlinespace[5pt]
Maryland	&	5,617	&	0.513	&	4.737	&	-0.021	&	15.855	&	0.406	\\
	&		&	(0.105)	&	(0.206)	&	(0.002)	&	(0.118)	&	(0.000)	\\ \addlinespace[5pt]
Massachusetts	&	3,552	&	0.832	&	6.026	&	-0.027	&	14.886	&	0.501	\\
	&		&	(0.128)	&	(0.313)	&	(0.003)	&	(0.169)	&	(0.000)	\\ \addlinespace[5pt]
Michigan	&	5,268	&	0.921	&	5.797	&	-0.030	&	15.139	&	0.487	\\
	&		&	(0.109)	&	(0.208)	&	(0.002)	&	(0.111)	&	(0.000)	\\ \addlinespace[5pt]
Minnesota	&	5,560	&	0.544	&	4.781	&	-0.019	&	15.661	&	0.417	\\
	&		&	(0.127)	&	(0.189)	&	(0.002)	&	(0.113)	&	(0.000)	\\ \addlinespace[5pt]
Mississippi	&	2,417	&	0.497	&	4.151	&	-0.021	&	16.289	&	0.365	\\
	&		&	(0.227)	&	(0.249)	&	(0.003)	&	(0.112)	&	(0.000)	\\ \addlinespace[5pt]
Missouri	&	3,741	&	0.564	&	4.149	&	-0.021	&	16.246	&	0.370	\\
	&		&	(0.133)	&	(0.186)	&	(0.002)	&	(0.099)	&	(0.000)	\\ \addlinespace[5pt]
Montana	&	2,390	&	0.525	&	3.902	&	-0.019	&	16.371	&	0.353	\\
	&		&	(0.221)	&	(0.254)	&	(0.003)	&	(0.122)	&	(0.000)	\\ \addlinespace[5pt]
Nebraska	&	3,629	&	0.889	&	4.578	&	-0.034	&	16.187	&	0.399	\\
	&		&	(0.088)	&	(0.250)	&	(0.003)	&	(0.111)	&	(0.000)	\\ \addlinespace[5pt]
Nevada	&	3,772	&	0.961	&	5.823	&	-0.031	&	15.159	&	0.488	\\
	&		&	(0.144)	&	(0.277)	&	(0.003)	&	(0.137)	&	(0.000)	\\ \addlinespace[5pt]
New Hampshire	&	4,475	&	0.207	&	3.913	&	-0.013	&	16.390	&	0.341	\\
	&		&	(0.191)	&	(0.219)	&	(0.002)	&	(0.137)	&	(0.000)	\\ \addlinespace[5pt]
New Jersey	&	4,788	&	1.178	&	6.068	&	-0.030	&	14.674	&	0.522	\\
	&		&	(0.124)	&	(0.325)	&	(0.003)	&	(0.171)	&	(0.000)	\\ \addlinespace[5pt]
New Mexico	&	2,555	&	0.577	&	4.185	&	-0.020	&	16.143	&	0.376	\\
	&		&	(0.216)	&	(0.255)	&	(0.003)	&	(0.121)	&	(0.000)	\\ \addlinespace[5pt]
New York	&	10,212	&	0.662	&	5.145	&	-0.024	&	15.542	&	0.439	\\
	&		&	(0.091)	&	(0.150)	&	(0.002)	&	(0.083)	&	(0.000)	\\ \addlinespace[5pt]
North Carolina	&	4,890	&	0.598	&	5.089	&	-0.028	&	15.891	&	0.420	\\
	&		&	(0.109)	&	(0.193)	&	(0.002)	&	(0.093)	&	(0.000)	\\ \addlinespace[5pt]
North Dakota	&	3,195	&	0.531	&	2.848	&	-0.017	&	17.085	&	0.280	\\
	&		&	(0.152)	&	(0.188)	&	(0.003)	&	(0.102)	&	(0.000)	\\ \addlinespace[5pt]
Ohio	&	6,100	&	0.524	&	5.028	&	-0.021	&	15.586	&	0.428	\\
	&		&	(0.142)	&	(0.184)	&	(0.002)	&	(0.098)	&	(0.000)	\\ \addlinespace[5pt]
Oklahoma	&	3,058	&	0.403	&	4.272	&	-0.020	&	16.257	&	0.368	\\
	&		&	(0.176)	&	(0.215)	&	(0.003)	&	(0.108)	&	(0.000)	\\ \addlinespace[5pt]
Oregon	&	3,326	&	0.337	&	6.672	&	-0.019	&	14.300	&	0.529	\\
	&		&	(0.241)	&	(0.293)	&	(0.002)	&	(0.167)	&	(0.000)	\\ \addlinespace[5pt]
Pennsylvania	&	6,830	&	1.091	&	5.896	&	-0.035	&	15.175	&	0.494	\\
	&		&	(0.089)	&	(0.223)	&	(0.003)	&	(0.115)	&	(0.000)	\\ \addlinespace[5pt]
Rhode Island	&	3,554	&	1.073	&	6.275	&	-0.028	&	14.495	&	0.532	\\
	&		&	(0.154)	&	(0.316)	&	(0.003)	&	(0.170)	&	(0.000)	\\ \addlinespace[5pt]
South Carolina	&	3,189	&	0.725	&	4.923	&	-0.035	&	16.235	&	0.403	\\
	&		&	(0.119)	&	(0.236)	&	(0.003)	&	(0.109)	&	(0.000)	\\ \addlinespace[5pt]
South Dakota	&	3,428	&	0.791	&	3.813	&	-0.026	&	16.444	&	0.356	\\
	&		&	(0.117)	&	(0.201)	&	(0.003)	&	(0.101)	&	(0.000)	\\ \addlinespace[5pt]
Tennessee	&	3,335	&	0.332	&	4.341	&	-0.019	&	16.204	&	0.370	\\
	&		&	(0.223)	&	(0.244)	&	(0.003)	&	(0.116)	&	(0.000)	\\ \addlinespace[5pt]
Texas	&	14,736	&	0.366	&	4.725	&	-0.019	&	15.869	&	0.400	\\
	&		&	(0.087)	&	(0.106)	&	(0.001)	&	(0.061)	&	(0.000)	\\ \addlinespace[5pt]
Utah	&	2,982	&	0.827	&	5.525	&	-0.021	&	14.861	&	0.485	\\
	&		&	(0.173)	&	(0.274)	&	(0.002)	&	(0.162)	&	(0.000)	\\ \addlinespace[5pt]
Vermont	&	3,131	&	0.519	&	5.401	&	-0.023	&	15.429	&	0.448	\\
	&		&	(0.167)	&	(0.271)	&	(0.003)	&	(0.150)	&	(0.000)	\\ \addlinespace[5pt]
Virginia	&	5,257	&	0.504	&	4.080	&	-0.023	&	16.426	&	0.357	\\
	&		&	(0.080)	&	(0.163)	&	(0.002)	&	(0.091)	&	(0.000)	\\ \addlinespace[5pt]
Washington	&	4,261	&	0.765	&	6.769	&	-0.024	&	14.131	&	0.552	\\
	&		&	(0.163)	&	(0.299)	&	(0.002)	&	(0.167)	&	(0.000)	\\ \addlinespace[5pt]
West Virginia	&	2,530	&	0.543	&	4.180	&	-0.018	&	16.074	&	0.377	\\
	&		&	(0.267)	&	(0.282)	&	(0.003)	&	(0.131)	&	(0.000)	\\ \addlinespace[5pt]
Wisconsin	&	4,467	&	0.587	&	5.259	&	-0.022	&	15.387	&	0.447	\\
	&		&	(0.141)	&	(0.213)	&	(0.002)	&	(0.119)	&	(0.000)	\\ \addlinespace[5pt]
Wyoming	&	3,251	&	0.443	&	3.652	&	-0.016	&	16.500	&	0.335	\\
	&		&	(0.208)	&	(0.229)	&	(0.003)	&	(0.124)	&	(0.000)	\\ \addlinespace[5pt]

\end{longtable}
				\begin{quote}
					NOTE.  This Table reports estimated parameters for pooled 2010-2014 state samples, for Eq. (2). See Appendix A for more information. 
				\end{quote}
				
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\section{Replication with Equivalent Households}

\begin{figure}[h!]
\begin{center}
	\caption{Poverty Relief in Equivalent Households} 
		\includegraphics[width=.7\textwidth]{20161021_Comparison_EH.pdf} 
	\end{center}
	\begin{quote} NOTE.  This Figure offers a comparison of estimates of the poverty relief ratio, estimated ``as reported'' to estimates of poverty relief for equivalent households.  To generate equivalent household estimates, market income and social transfer amounts are divided by the squareroot of the number of people in each household.
	\end{quote}
\end{figure}


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