Personal Savings as a Personal Savings as a PercentagePercentage

of Disposable Personal Incomeof Disposable Personal IncomeTake Home IITake Home II

June 4June 4thth, 2009, 2009Marissa Pittman Morgan Marissa Pittman Morgan Hansen Hansen

Eric Griffin Chris Eric Griffin Chris StroudStroud

Yao WangYao Wang

Personal SavingsPersonal Savings

• Personal SavingsPersonal Savings• The difference between household income (after taxes) The difference between household income (after taxes)

and consumption expenditures. and consumption expenditures.

• Negative number implies debtNegative number implies debt• Positive number implies savingsPositive number implies savings

Household Income-Spending

Personal SavingsPersonal Savings

• As recently as April 2008, personal savings in the US totaled only 1.4 billion dollars

• In conjunction with the rapid collapse of the Economy in  September 2008, personal savings has increased dramatically

• The latest number from April 2009 showed personal savings at $620.2 billion, the highest value in history.

Disposable IncomeDisposable Income

• Disposable IncomeDisposable Income• Income (after taxes) that is available to you Income (after taxes) that is available to you

for saving or spendingfor saving or spending

Expected ResultsExpected Results

Personal Savings (Semi-linear)

Disposable Income (Exponential)

• Expect similar trends compared to the Personal Savings because decreasing and income is increasing

Savings as a Percentage of Disposable Savings as a Percentage of Disposable IncomeIncome

Why percentage and not net Why percentage and not net savings?savings? Normalizes the data setNormalizes the data set

• Different people make Different people make different amounts of moneydifferent amounts of money

• It is safe to assume It is safe to assume someone making someone making $100,000/year will be $100,000/year will be saving more than someone saving more than someone making $30,000/yearmaking $30,000/year

100Income

Savings

Savings/IncomeSavings/Income

• This brings up our series, personal savings as a percentage of  disposable income

• This ratio is also taken in order to account for inflation and the fact that incomes have been rising over time

Personal Savings as a Percentage of Personal Savings as a Percentage of Disposable Personal Income Disposable Personal Income

• Until the mid 1980s, people had been saving about 8-10 percent of their disposable income

• Starting in 1986 this number began trending downward due to easily obtainable credit (credit cards, lower mortgage rates, etc) 

Personal Savings as a Percentage of Personal Savings as a Percentage of Disposable Personal Income Disposable Personal Income

• After the collapse of the economy  in September this number began to shoot upward in conjunction with the increase in personal savings

• In April 2009 people were saving 5.7  percent of their disposable income which is the highest percentage  since February 1995.

Trace of Personal Savings as a Percentage of Trace of Personal Savings as a Percentage of Disposable Personal Income Disposable Personal Income

• Appears to be Appears to be random walkrandom walk

• Hit peak in 1975 Hit peak in 1975 at 14.6%at 14.6%

• Has been steadily Has been steadily declining sincedeclining since

• Hit low in 2005 at Hit low in 2005 at -2.7% which -2.7% which meant people meant people were spending were spending more than they more than they hadhad

Histogram of Personal Savings as a Histogram of Personal Savings as a Percentage of Disposable Personal Income Percentage of Disposable Personal Income

• Multi-peakedMulti-peaked• Large Jarque-Bera statisticsLarge Jarque-Bera statistics

Further evidence the data set is random walkFurther evidence the data set is random walk

Correlogram of Personal Savings as a Correlogram of Personal Savings as a Percentage of Disposable Personal IncomePercentage of Disposable Personal Income

The The correlogram correlogram shows a slow shows a slow decay in the decay in the autocorrelationautocorrelation

The PACF The PACF value at lag 1 is value at lag 1 is close to oneclose to one

Both further Both further indicators of a indicators of a random walkrandom walk

Unit Root Test of Personal Savings as a Unit Root Test of Personal Savings as a Percentage of Disposable Personal IncomePercentage of Disposable Personal Income

• The unit root test The unit root test returns a returns a negative value negative value that is not that is not sufficiently more sufficiently more negative than the negative than the critical valuescritical values

• Can’t reject null Can’t reject null hypothesishypothesis The time The time

series series is notis not stationary. stationary.

Differenced Trace of Personal Savings as a Differenced Trace of Personal Savings as a Percentage of Disposable Personal Income Percentage of Disposable Personal Income

• The trace of the differenced values looks to be white The trace of the differenced values looks to be white noise noise

• The peaks indicate some periods of heightened The peaks indicate some periods of heightened variance. variance.

Differenced Histogram of Personal Savings Differenced Histogram of Personal Savings as a Percentage of Disposable Personal as a Percentage of Disposable Personal

IncomeIncome

• The histogram of the differenced values is The histogram of the differenced values is kurtotic kurtotic

• It is single peaked which is a sign of stationarity It is single peaked which is a sign of stationarity but still not acceptable but still not acceptable

Differenced Correlogram of Personal Savings Differenced Correlogram of Personal Savings as a Percentage of Disposable Personal as a Percentage of Disposable Personal

IncomeIncome

• Differencing the Differencing the time saving has time saving has removed the removed the autocorrelation autocorrelation trendstrends

• The PACF at lag The PACF at lag 1 value is no 1 value is no longer close to 1longer close to 1

• The spikes in The spikes in PACF at lag 1 PACF at lag 1 and lag 3 are and lag 3 are evidence that an evidence that an ARMA model of ARMA model of a AR(1) and a AR(1) and AR(3) would be a AR(3) would be a good initial good initial model estimation model estimation

Differenced Unit Root Test of Personal Differenced Unit Root Test of Personal Savings as a Percentage of Disposable Savings as a Percentage of Disposable

Personal IncomePersonal Income

• The unit root test The unit root test of the differenced of the differenced series returns a series returns a negative value negative value that is that is sufficiently more sufficiently more negative than the negative than the critical valuescritical values

• Reject the null Reject the null hypothesishypothesis Time series Time series isis

stationarystationary• Dsaving does not Dsaving does not

contain a unit contain a unit root. root.

ARMA Model 1ARMA Model 1

• ARMA Model ARMA Model 1 returns 1 returns significant t-significant t-stats on both stats on both terms. terms. • AR(1)=-AR(1)=-

7.287.28• AR(3)=-AR(3)=-

4.464.46• The constant is not The constant is not significantsignificant• C=-0.23C=-0.23

Correlogram of ARMA Model 1Correlogram of ARMA Model 1

• The ARMA The ARMA terms have terms have removed the removed the PACF spikes at PACF spikes at lags 1 and 3 but lags 1 and 3 but the Q stats are the Q stats are still high. still high.

• The spike at lag The spike at lag 2 may be 2 may be eliminated with eliminated with a MA(2). a MA(2).

ARMA Model 2ARMA Model 2

• ARMA Model 2 ARMA Model 2 returns significant returns significant t-stats on all 3 t-stats on all 3 terms. terms. • AR(1)=-8.97AR(1)=-8.97• AR(3)=-4.43AR(3)=-4.43• MA(2)=-6.04MA(2)=-6.04

• The constant is The constant is not significantnot significant• C=-0.37C=-0.37

• Durbin-Watson Durbin-Watson statistic is statistic is approximately 2.0, approximately 2.0, indicating no indicating no serial correlation serial correlation

Correlogram of ARMA Model 2Correlogram of ARMA Model 2

• All spikes have now All spikes have now been eliminated and been eliminated and Q-stats are now lowQ-stats are now low

• L looks orthogonal, L looks orthogonal, with fairly low Q-with fairly low Q-statistics and high statistics and high probabilitiesprobabilities

• Model has now Model has now proven to be proven to be stationary and an stationary and an accurate estimationaccurate estimation

Serial Correlation Test of Model 2Serial Correlation Test of Model 2

• The low F-statistic also confirms that there’s no serial correlation.• Probability

is less than critical at 0.28

Actual, Fitted and Residual Plot of Actual, Fitted and Residual Plot of Model 2Model 2

• The residuals are orthogonal

• Tracking the actual trace well

• Peaks still implicated heightened variance

Histogram of Residuals for Model 2Histogram of Residuals for Model 2

• The residuals are still single peaked • Although highly kurtotic with afat tail• Could suggest existence of conditional heteroskedasticity

Trace of Squared Residuals for Model 2Trace of Squared Residuals for Model 2

• The episodic variance shows some spikes

• This indicates that residuals are not homoskedastic

Heteroskedasticity is present

Correlogram of Squared Residuals for Correlogram of Squared Residuals for Model 2Model 2

• The correlogram of squared residuals shows high Q-statistics

• There are some significant lags

ARCH Test of Model 2ARCH Test of Model 2

• The F-statistic is significant enough to reject the null hypothesis of homoskedasticity

• Consistent with former evidences

Heteroskedasticity exists

ARCH GARCH Estimation of Model 2ARCH GARCH Estimation of Model 2

• Added ARCH GARCH to account for heteroskedasticty of the residuals

• Z-statistics of coefficients showed the model to be significant

ARCH GARCH Correlogram for Model ARCH GARCH Correlogram for Model 22

• Correlogram is orthogonal

• Lower Q-stats were achieved

• Probabilities are above 0.05

GARCH Actual, Fitted, and Residual Plot for GARCH Actual, Fitted, and Residual Plot for Model 2Model 2

• The residuals are orthogonal

• Tracking the actual trace well

• Still some variance but tracking is better

Histogram of Standardized Residuals for Histogram of Standardized Residuals for Model 2Model 2

• Histogram is single peaked• Kurtosis is still an issue but all other problems

are resolved

Trace of GARCH for Model 2Trace of GARCH for Model 2

• Estimate of h(t) Estimate of h(t) by making by making GARCH GARCH variance series variance series

ARCH GARCH Test for Model 2ARCH GARCH Test for Model 2

• The F-statistic now is not significant to reject the null hypothesis of homoskedasticity

• The model we estimated above seems to be a good fit

Heteroskedasticity no longer exists

Forecast of Model 2Forecast of Model 2 Non-recoloredNon-recolored

• In sample forecast to test for accuracy

Forecast of Variance for Model 2Forecast of Variance for Model 2

• In sample variance

• Variance is increasing over time

• Leveling off

Forecast of Model 2Forecast of Model 2 In Sample In Sample

• Recession causing shocks to data set

• People would continue to spend at high rates or save at low rates

Project PurposeProject Purpose

• As said before there is an increase in saving due to our recent recession

• Purpose of the project is to answer is if people will continue to save as the economy comes out of the recession

Forecast for Model 2Forecast for Model 2Non-recoloredNon-recolored

• Out of sample forecast for the next year

Forecast of Variance for Model 2Forecast of Variance for Model 2

• Out of sample variance

• Variance is decreasing over time

• Leveling off

Out of Sample Forecast for Model 2Out of Sample Forecast for Model 2

• Stops going up and steadies

• Current trend of rising is going to cease

Final ResultsFinal Results

• The results of our forecast indicate that in fact people will continue to save as the recession subsides

• This makes sense intuitively because credit conditions will remain tighter

• People will need to save more for larger down-payments on homes, cars, and other loans that are now required due to more stringent loan requirements.

Thank You!Thank You!