The Effect of Disposable Personal Income and Housing Prices on the Personal Savings Rate

Abstract:


Some people are concerned with the recent decrease in personal savings in America. It has been suggested that factors such as increases in wealth, especially due to housing prices contributes to this decline $^{[1]}$. To explore this issue, this paper studies the relationship between personal savings and disposable personal income, taking into account the recent rise in housing prices.

FINAL REPORT - PERSONAL SAVINGS

Aaron Koga

Econ 425

11 December 2006

Introduction

Recently in America, personal savings has rapidly decreased. Savings is important because it provides future consumption for individuals as well as resources for investment in the nation as a whole.

Traditionally, the biggest factor in determing personal savings is disposable personal income (DPI). The portion of DPI which is saved is known as the personal savings rate. However, the recent decline in personal savings cannot be explained by changes in DPI alone. Thus, additional factors such as increases in wealth due to rapid rises in housing prices have been suggested to explain this discrepancy $^{[1]}$.

Fitting and Interpretation

Personal savings vs. time index Figure 1: Graph of personal savings versus Time Index (top), where the first index, 0 = Q1-1975 and the last index, 125 = Q2-2006; and graph of personal savigns versus DPI (bottom).
Using data from the St. Louis Federal Reserve $^{[2]}$ on personal savings and DPI (shown in FIG 1 and TABLE V) and the Office of Ferdal Housing Enterprise Oversight (OFHEO) on housing prices $^{[3]}$, Various regressions were run to examine the effects of DPI and housing prices on personal savings. The data on personal savings and DPI are given in billions of dollars. The data on housing prices is the Housing Price Index (HPI). This index is nominal and normalized to the year 1980. All data is available quarterly for the years 1975 through 2006.

Personal Savings vs DPI

Expected and Actual personal savings versus DPI.
Figure 2: Graph of Expected and Actual personal savings versus DPI. Expected savings is calculated according to (1).


Table I: Table showing the fit statistics for (1)
Coefficient Value Std Error t-value
$A_{0}$ 260.05 16.78 15.5
$A_{1}$ -0.010 0.0032 -3.13
$R^{2}$ 0.0732    
$\overline{R^{2}}$ 0.0656    
$F$ 9.79 for $R^{2}=0$  


A regression of the personal savings on DPI using the equation
\begin{displaymath} Savings_{t}=A_{0}+A_{1}DPI_{t} \end{displaymath} (1)

yielded the results listed in TABLE I and displayed in FIG 2. Although the fit is significant according to the F-statistic, as the low $R^{2}$ value of 0.0732 suggests, this fit to the data does not adequately explain the personal savings. Looking at FIG 2, there seem to be shifts in the savings rate, which (1) cannot take into account.

Graph of Expected and Actual personal savings versus DPI.
Figure 3: Graph of Expected and Actual personal savings versus DPI. Expected savings is calculated according to (2).


Table II: Table showing the fit statistics for (2)
Coefficient Value Std Error t-value
$B_{0,0}$ -33.82 41.7 -0.81
$B_{0,1}$ 0.12 0.02 4.76
$B_{1,0}$ 255.83 59.77 4.28
$B_{1,1}$ -0.1 0.03 -3.66
$B_{2,0}$ 625.81 66.29 9.44
$B_{2,1}$ -0.18 0.03 -6.76
$B_{3,0}$ 971.01 135.54 7.16
$B_{3,1}$ -0.22 0.03 -7.44
$R^{2}$ 0.743    
$\overline{R^{2}}$ 0.728    
$F$ 48.74 for $R^{2}=0$  


In 1982, America experienced a serious recession. As the data suggests, this recession probably had an impact on the savings rate. This type of assumption can be logically justified. During recessions people often experience hardships such as the loss of jobs. Due to these new budjet constraints, people are forced to change their spending and saving habits. After keeping these new habits for a certain period of time, people become used to them and when the recession eventually ends, they persist in their new habits. In addition to the 1982 recession, there may also have been effects from the 1991 and 2001 recessions on the savings rate.

To account for the changes in the savings rate due to the recessions, dummy variables ($E_{i}$) were used to form the following equation:


$\displaystyle Savings_{t}=$   $\displaystyle B_{0,0}+B_{0,1}DPI_{t}+B_{1,0}E_{1}+B_{1,1}E_{1}DPI_{t}$  
    $\displaystyle +B_{2,0}E_{1}+B_{2,1}E_{2}DPI_{t}+B_{3,0}E_{3}$  
    $\displaystyle +B_{3,1}E_{3}DPI_{t}$ (2)

where $E_{1}$=1 for 1982-1990, $E_{2}$=1 for 1991-2000, and $E_{3}$=1 for 2001-2006 (all $E_{i}$=0 otherwise). The fit statistics for (2) are displayed in TABLE II and graphed in FIG 3.

As can be seen from FIG 3 and the increased $\overline{R^{2}}$, (2) is an improvement over (1). Testing $B_{i,j}=0$ (i=1,2,3 j=0,1), yielded an F-value of 51.2558. Thus, allowing for changes in the savings rate during each period of recession seems justified. This can also be seen in the significance of the t-values for the coefficients $B_{i,j}$ in TABLE II. This fit says that while 12 cents was saved for every dollar of DPI before 1982, during and after the 1982 recession only 2 cents was saved for every dollar of DPI. In addition, the savings rate became negative after 1991.

Including HPI

Graph of Expected and Actual personal savings versus DPI. Figure 4: Graph of Expected and Actual personal savings versus DPI. Expected savings is calculated according to (3).


Table III: Table showing the fit statistics for (3)
Coefficient Value Std Error t-value
$C_{0,0}$ -33.82 29.87 -1.13
$C_{0,1}$ 0.12 0.02 6.64
$C_{1,0}$ 255.83 42.82 5.97
$C_{1,1}$ -0.1 0.02 -5.11
$C_{2,0}$ 625.81 47.49 13.18
$C_{2,1}$ -0.18 0.02 -9.43
$C_{3,0}$ -1781.88 276.64 -6.44
$C_{3,1}$ 0.48 0.07 6.97
$C_{3,2}$ -9.72 0.91 -10.63
$R^{2}$ 0.869    
$\overline{R^{2}}$ 0.860    
$F$ 97.22 for $R^{2}=0$  


To account for the recent negative personal savings, the HPI was taken into account. As suggested by others, the increase in housing prices may help to explain the recent decrease in personal savings. Personal savings was regressed on DPI and the HPI (only since 2001, to simulate a 'recent effect') according to the equation
$\displaystyle Savings_{t}=$   $\displaystyle C_{0,0}+C_{0,1}DPI_{t}+C_{1,0}E_{1}+C_{1,1}E_{1}DPI_{t}$  
    $\displaystyle +C_{2,0}E_{1}+C_{2,1}E_{2}DPI_{t}+C_{3,0}E_{3}$  
    $\displaystyle +C_{3,1}E_{3}DPI_{t}+C_{3,2}E_{3}HPI_{t}$ (3)

where $E_{1}$=1 for 1982-1990, $E_{2}$=1 for 1991-2000, and $E_{3}$=1 for 2001-2006 (all $E_{i}$=0 otherwise). The fit statistics for (3) are displayed in TABLE III and graphed in FIG 4.

The increase in $\overline{R^{2}}$ for (3) compared with (2) suggests that taking into account the HPI is justified. Also, as can be seen from the t-values and F-statistic in TABLE III, all coefficients are significant. The fit to the data for (3), like (2), says that while the 12 cents was saved for every dollar of DPI before 1982, during and after the 1982 recession only 2 cents was saved for every dollar of DPI. In addition, -6 cents was saved for every dollar of DPI for the period 1991-2001, and 58 cents was saved for every dollar of DPI after 2001. Also, as is expected, the negative value of $C_{3,2}$ indicates that increases in housing prices decreases personal savings.

Other regressions using the periods 1982-1990, 1991-200, and 2001-2006 as the base period were run. In each regression the coefficients $B_{i,j}$ corresponding to terms outside of the base year had significant t-values (see TABLE IV). So, each period (1975-1981, 1982-1990, 1991-200, and 2001-2006) has savings rates which are significantly different from one another. Thus, allowing for changes in the savings rate during each period of recession, as specified, is justified. Also, the insignificance of $C_{1,1}$ when running the regression with 1982-1990 as the base period suggests that the savings rate during that period of time was not significantly different from zero.


Table IV: Table showing the t-values for regressions using different periods as the base period. Base period is listed in parenthesis and the period corresponding to the coefficient is given for clarity.
Coefficient corresponding t-value t-value t-value
  period (1982-1990) (1991-2000) (2001-2006)
$C_{0,0}$ 1975-1981 -5.97 -13.18 6.44
$C_{0,1}$ 1975-1981 5.11 9.43 -6.97
$C_{1,0}$ 1982-1990 7.24 -7.71 7.36
$C_{1,1}$ 1982-1990 1.77 6.86 -8.66
$C_{2,0}$ 1991-2000 7.71 16.04 8.68
$C_{2,1}$ 1991-2000 -6.86 -9.34 -9.84
$C_{3,0}$ 2001-2006 -7.36 -8.68 -6.6
$C_{3,1}$ 2001-2006 8.66 9.84 8.98
$C_{3,2}$ 2001-2006 -10.63 -10.63 -10.63


Summary

It is apparent that when examining the personal savings rate, the effects of recessions on people's saving habits is important. Also, to explain the recent and rapid decrease in personal savings, taking into account housing prices (or potentially other types of wealth) is also important. Taking housing prices into account indicates that recent decreases in personal savings is at least partially justified.

On the other hand, a savings rate of 0.58 for the period 2001-2006 as suggested by this regression is too high to be believable. However, adding other variables to the model such as stock prices may prove useful.

References

[1] Garner, Alan. Should the Decline in the Personal Saving Rate Be a Cause for Conern. www.kc.frb.org/publicat/econrev/PDF/2Q06garn.pdf (2006).

[2] Data can be found at: http://research.stlouisfed.org/fred2/.

[3] Data can be found at: http://www.ofheo.gov/HPI.asp.

Table V: Table showing the raw data$^{[2],[3]}$.
Date Personal Savings HPI DPI
(M/D/Y) (Billion Dollars) (Billion Dollars)
1/1/1975 110.5 61.63 1126
4/1/1975 148.6 62.97 1193.2
7/1/1975 120 62.32 1199.1
10/1/1975 123.2 63.27 1231.5
1/1/1976 121.7 64.38 1263.5
4/1/1976 122.9 66.29 1284.5
7/1/1976 124.4 66.82 1315.8
10/1/1976 120.2 68.1 1346.1
1/1/1977 109.8 70.09 1372.5
4/1/1977 119.5 72.81 1411.3
7/1/1977 130.3 74.71 1454.3
10/1/1977 141.4 77.14 1504.6
1/1/1978 144 79.57 1538.9
4/1/1978 134.8 82.41 1589
7/1/1978 143.8 84.94 1630.5
10/1/1978 147.5 87.51 1674.8
1/1/1979 162 91.41 1725.8
4/1/1979 154.6 93.99 1760.2
7/1/1979 152.6 96.02 1813.9
10/1/1979 167.4 97.91 1874.2
1/1/1980 184.9 100 1944
4/1/1980 194 101.06 1955.2
7/1/1980 201.6 104.27 2021.2
10/1/1980 225.4 104.65 2115.5
1/1/1981 211.6 105.77 2161.9
4/1/1981 218.3 107.83 2202.8
7/1/1981 262.2 109.25 2289.6
10/1/1981 285.1 109.63 2330.1
1/1/1982 273.1 110.97 2359.7
4/1/1982 282.7 111.54 2399.1
7/1/1982 280.1 111.09 2447.2
10/1/1982 247.2 112.03 2478.7
1/1/1983 247.2 114.02 2521.2
4/1/1983 223.3 115.24 2564.3
7/1/1983 220.6 116.07 2635.1
10/1/1983 243.3 116.54 2712.9
1/1/1984 288.2 118.24 2805.3
4/1/1984 306.5 120.28 2885.4
7/1/1984 334.5 121.44 2955
10/1/1984 330 122.77 3002.4
1/1/1985 283.7 124.57 3032.2
4/1/1985 318.9 126.63 3117.5
7/1/1985 245.7 129 3115.4
10/1/1985 271.8 130.77 3172.2
1/1/1986 287.7 133.33 3233.4
4/1/1986 290.5 136.27 3269.1
7/1/1986 256.4 138.86 3307.2
10/1/1986 238.9 141.42 3330.7
1/1/1987 273 144.55 3397.1
4/1/1987 198.1 147.29 3389.4
7/1/1987 225.6 149.63 3484.5
10/1/1987 268.7 151.01 3562.1
1/1/1988 262.4 153.71 3638.5
4/1/1988 273.7 156.97 3711.3
7/1/1988 280 158.68 3786.9
10/1/1988 275.5 160.36 3858.2
1/1/1989 314 162.48 3954.9
4/1/1989 285.3 164.65 3993.4
7/1/1989 269.7 168.45 4038.8
10/1/1989 279.5 170.04 4099.5
1/1/1990 292.6 170.73 4198.2
4/1/1990 307.2 170.68 4268.1
7/1/1990 297.8 171.28 4325.7
10/1/1990 300 170.48 4351.3
1/1/1991 320.4 171.78 4387.1
4/1/1991 317.7 172.56 4441.8
7/1/1991 313.7 172.54 4483.7
10/1/1991 344.7 174.9 4544.5
1/1/1992 359.4 176.05 4651.4
4/1/1992 373.8 175.68 4716.1
7/1/1992 350.1 177.45 4768.6
10/1/1992 380.9 178.19 4869.6
1/1/1993 272.4 177.92 4801.6
4/1/1993 304.3 179.4 4901.1
7/1/1993 264.5 180.49 4924.3
10/1/1993 295.1 181.88 5020.8
1/1/1994 203.3 182.73 4998.7
4/1/1994 258.8 183.34 5118.1
7/1/1994 256.3 183.84 5197.5
10/1/1994 279.4 183.39 5293.1
1/1/1995 302.9 184.07 5350.9
4/1/1995 253 187.28 5376.3
7/1/1995 230.3 190.19 5427.1
10/1/1995 217.6 191.69 5478.6
1/1/1996 236.5 194.03 5574.5
4/1/1996 223 194.22 5656.6
7/1/1996 234.9 194.97 5727.5
10/1/1996 219.2 196.64 5795.3
1/1/1997 213.7 198.44 5877.4
4/1/1997 230.6 200.05 5936.7
7/1/1997 204.7 203 6020.8
10/1/1997 224.3 205.66 6120.5
1/1/1998 291.7 208.8 6255.9
4/1/1998 285.4 210.44 6357.7
7/1/1998 280.5 213.34 6448.1
10/1/1998 249.6 215.9 6522.1
1/1/1999 240.4 218.09 6586.7
4/1/1999 149.1 221.04 6638.6
7/1/1999 115 224.45 6708.2
10/1/1999 129.7 226.96 6846.2
1/1/2000 171.2 231.67 7059.2
4/1/2000 171.3 235.58 7141.2
7/1/2000 190.1 240.15 7266.4
10/1/2000 141.2 244.1 7309.3
1/1/2001 138.6 250.41 7392.1
4/1/2001 88.7 254.87 7407.6
7/1/2001 261.6 259.1 7622.8
10/1/2001 40.5 262.48 7524.8
1/1/2002 225.4 266.74 7751.5
4/1/2002 221.2 271.73 7841.7
7/1/2002 153 277.59 7845.4
10/1/2002 139.3 281.97 7881.7
1/1/2003 149.1 285.71 7975.5
4/1/2003 173.9 289.29 8087.6
7/1/2003 194 294.2 8261
10/1/2003 182.5 304.06 8326
1/1/2004 178.9 309.24 8481.6
4/1/2004 168.3 317.77 8607.1
7/1/2004 141.2 331.97 8706.3
10/1/2004 208.9 340.29 8931.2
1/1/2005 52.5 349.61 8890.9
4/1/2005 -30.8 362.38 8969.7
7/1/2005 -132.6 374.23 9047.7
10/1/2005 -28.5 385.76 9236.1
1/1/2006 -29.7 394.23 9388.8
4/1/2006 -54.6 398.85 9522.4