Home Equity, Household Savings and Consumption

In Choi et al. (2006) households respond to capital gains in their pension 401 k accounts by short-term saving, and they reduce consumption. That is attributable to a feedback effect to increase saving to follow positive returns, but may also be attributable to the difficulty of consuming from capital gains in 401 k accounts, or if they are viewed as transitory.

Borrowing against housing equity includes first and second mortgages, refinancing with cash out of equity, and home equity lines of credit. The housing asset is deemed illiquid for sales, but not for borrowing. For those with a mortgage, each dollar increases liabilities and cash equally, initially leaving net wealth unchanged. This situation occurs for homeowners with a loan. Bucks et al. (2006) report that for the 2004 Survey of Consumer Finances 69.1% of families own a home. Of homeowners, 69.3% reported a home loan, so 30.7% of homeowners had no mortgage debt. In addition, the 30.9% families are renters. Nevertheless, the remaining households represent a large contribution to debt and aggregate wealth. Overall mortgage debt was 44% of gross assets from the Flow of Funds of the Board of Governors of the Federal Reserve System (2006) in the first quarter of 2006. For those with any mortgage balance, the average loan-to-value ratio is 63% or 0.44/0.693.

Flavin (1981) and many other researchers note that household consumption changes due to changing expectations about future income. During 1991–1994 from the Panel Survey of Income Dynamics, Hurst and Stafford (2004) find that households with housing equity but limited other assets convert two-thirds of cash-out financing proceeds into consumption. An intertemporal consumption model in Buist and Yang (2000) allows households to make choices between adjustable and fixed-rate mortgages. Agarwal et al. (2005) show that home owners refinance their mortgages when the present value of interest saved is equal to the refinancing cost.

Laitner (2002) discusses this concentration of wealth, while Deaton (1991) and Bertaut (2002) estimate the low median financial holding at less than $1,000.

The possible linkage of housing prices to consumption has implications for monetary policy. However, Bernanke and Gertler (2001) argue that the central bank should not pay attention to asset price changes.

In Carroll et al. (2006), the short-run marginal propensity α _S in changes is estimated from consumption and wealth as ΔC _t  = α _S ΔW _t . Then wealth has ΔW _t  = γ _L ΔW _{t −1}, and the long-run marginal propensity to consume from wealth is \( \frac{{\alpha _{S} }} {{1 - \gamma _{L} }} \). The estimate of the housing first-order coefficient is sluggish, indicating the higher long-run marginal propensity to consume.

There is a spurious regression if the variables are not cointegrated. A cointegrating relationship between the variables involves a stable relationship such as lnC _t  − δlnY _t  − (1 − δ)lnW _t as the consumption disturbance in consumption C _t , income Y _t and wealth W _t . The geometric weights invested in human and nonhuman capital are, respectively δ and (1 − δ). That is a weighted lagged average of logarithms of income, consumption and interest rates.

Vesting provisions reward employees for loyalty and longevity, so the retirement accounts are part of incentive compensation. In exchange for tax and incentive benefits, the employee must accept illiquidity on most of its financial assets. Funds in defined-benefit accounts cannot be withdrawn prior to retirement, nor can they serve as loan collateral. Funds in defined-contribution accounts have restrictions and sometimes prohibitions on withdrawal. Hall and Murphy (2003) review the incentive aspects of pension compensation.

There may be a nonzero covariance between mortgages and financial assets. However, the financial assets are in restricted accounts, and the mortgage is more subject to separate timing issues on refinancing.

The family could hold other unsecured debt such as credit cards, but this is neglected in the analysis.

Utility can exhibit non-additive separability in consumption. For one specification as in Sundaresan (1989), consumption is relative to a reference level \( \overline{c} _{t} {\left( {c_{{t - 1}} ,...,c_{0} } \right)} \) depending on the past sequence. At the current date, utility is \( u{\left( {c_{t} - \overline{c} _{t} } \right)} \), a supernumerary level analogous to the Stone–Geary form of demand functions. In equilibrium, consumption is not homothetic in wealth. Consumption remains linear in wealth, the underlying structure required for estimating the wealth effect.

The unit root test is for ρ = 1 against the alternative of ρ < 1 in \( \Delta x_{t} = \alpha + \varsigma t + {\left( {\rho - 1} \right)}x_{{t - 1}} + {\sum\limits_{j = 1}^r {\varphi _{r} \Delta x_{{t - r}} } } + \varepsilon _{t} \). Here x tested is sequentially from (c, s _t , h, q _m ) relative to income. All exhibit unit roots in levels. When first-differenced, these time series are stationary. The test statistics on ρ are −7.51 for consumption Δc, −5.13 for income Δy, −5.01 for housing Δh, and −6.90 for mortgage balances Δq _m against a critical value of −2.86 at 1%. The data should be first differenced to create stationary time series. The Engle–Granger test statistic for a unit root on the residuals of Δx _t is −3.21 (−4.86) with a 5% critical value in parentheses, indicating no cointegrating relationships. Multiple cointegrating relationships are tested using the Johansen rank test. To correct for the autocorrelation of residuals, ARMA terms AR(L) up to lag L are included in the regression models. Serial correlation is tested using the Breusch–Godfrey Lagrange multiplier (LM) test. The null hypothesis of the LM test is that there is no serial correlation up to a lag order k where k is a pre-specified integer. The LM test statistic is asymptotically distributed as \( \chi ^{2}_{k} \), chi-squared with k degrees of freedom. There is no evidence of autocorrelation using orders for k as high as 5.

The test statistics are on insignificance of the trace and largest eigenvalue of a matrix of a Gaussian vector autoregressive representation of the time series. For testing all four time series on consumption, financial assets, housing and mortgage balances, the rank is four and the trace is 18.42 (47.18) while the largest eigenvalue is 18.42 (27.20). Critical values at a 5% significance level are in parentheses. Further, there is no evidence of autocorrelation of residuals.