# The Effect of the SSI Program on Labor Supply: Improved Evidence from Social Security Administrative Files

by David Neumark and Elizabeth T. Powers
Social Security Bulletin, Vol. 65 No. 3, 2005

## Chart 1.Trade-off between preretirement work effort and postretirement unearned income with an SSI program

Chart 1 is an illustrative line chart showing the relationship between current work hours and possible unearned income after age 64. The horizontal axis represents hours worked before age 65, and the vertical axis represents unearned income after age 64. The axes converge in the lower right corner and extend upward and to the left. Three parallel lines ascend from points on the lower half of the vertical axis toward points in the upper left quadrant of the diagram.

The bottom of these three lines, representing the function  $Δ B ( h w ) ,$  originates where the axes meet in the lower right corner of the diagram. The middle line represents   and originates on the vertical axis at a point designated  $Y 0$ . The top line represents   and originates on the vertical axis at a point designated  .

The line that represents the trade-off between preretirement work effort and postretirement unearned income with an SSI program consists of the parts of the top and middle parallel lines. It begins as that part of the top parallel line that extends from the vertical axis to the point with coordinates  ; then it tracks horizontally on the   line until it meets the middle parallel line at the point with coordinates  , which it then tracks indefinitely.

## Chart 2.Optimal choice with lower (G) and higher (G′) guaranteed benefit

Chart 2 is an illustrative line chart showing the effects of alternative maximum SSI benefit amounts on the optimal relationship between current work hours and possible unearned income after age 64. The horizontal axis represents hours worked before age 65, and the vertical axis represents unearned income after age 64. The axes converge in the lower right corner and extend upward and to the left. Four parallel lines ascend from points on the vertical axis toward points in the upper left quadrant of the diagram.

The bottom of these four lines, representing the function  $Δ B ( h w ) ,$  originates where the axes meet in the lower right corner of the diagram. The lower middle line represents   and originates on the vertical axis at a point designated  $Y 0$ . The upper middle line represents  , and originates on the vertical axis at a point designated  . The top line represents  , and originates on the vertical axis at a point designated  .

The line that represents the optimal choice with the lower (G) guaranteed benefit consists of the parts of both of the middle parallel lines. It begins as that part of the upper middle parallel line that extends from the vertical axis to the point with coordinates  ; then it tracks horizontally on the   line until it meets the lower middle parallel line at the point with coordinates  , which it then tracks indefinitely.

The line that represents the optimal choice with the higher (G′) guaranteed benefit consists of the parts of both of the uppermost parallel line and the lower middle parallel line. It begins as that part of the uppermost parallel line that extends from the vertical axis to the point with coordinates  ; then it tracks horizontally on the   line until it meets the lower middle parallel line at the point with coordinates  , which it then tracks indefinitely.