3  The link between the flow and stock measures of household saving

In this section we explore the link between the flow and stock measures of household saving. The link can be illustrated with a simple example of households’ choice problem. Households are assumed to value alternative streams of consumption and leisure over their lifetime according to some utility function, which they maximise subject to a budget constraint.

At the beginning of each period, households must decide how much to hold in demand deposits (), which they use for consumption during the period. Demand deposits consist of deposits with banks and other fixed interest. At the beginning of each period, households must also decide how to save for next period consumption. They can either purchase shares in firms (financial assets, ) or buy houses (real assets, ). Alternatively, households can “purchase” human capital () in the form of education or health care.

For simplicity, it is assumed that households don’t borrow. This implies that households’ liabilities are zero and household net wealth (assets minus liabilities) equals households’ wealth (assets). Moreover, it is assumed that there is no government sector. Households do not pay taxes and do not receive any transfer payments from the government.

The value of financial assets at time is given by , where denotes the market price of financial assets. The value of real assets and human capital is given by and respectively, where and denote the market price of real assets and education or health care at time .

During each period, households derive income from four sources. First, households earn wage income, , from supplying human capital to firms, where denotes the nominal wage rate. Second, households receive interest income, on demand deposits held with banks, where is the rate of interest paid on deposits. Third, they receive a return on financial assets , in the form of dividend payments from firms, where denotes the yield on financial assets. Finally, households receive a return on real assets, in the form of imputed rent for housing, i.e. , where is the yield on real assets.

Households use their income to purchase consumption, , where denotes the price of the consumption good . Households also purchase financial and real assets and human capital to provide income next period. The price they pay for financial and real assets and human capital depends on next period’s expected value of these assets and human capital. The household budget constraint can then be written as follows

(1)

where is the conditional expectation operator with respect to information available at time t.

Suppose for the moment that there is no uncertainty and that households have perfect information. Equation (1) can then be written as

(2)

Households’ budget constraint can be interpreted as follows. Each period, households receive a return on deposits and financial and real assets. They also receive income from their human capital in the form of wage income. Households then “sell” all their deposits, financial and real assets and human capital to purchase consumption, human capital and new financial and real assets. The budget constraint is binding and household expenditure equals household income.

The link between the stock and flow measures of saving becomes clear when re-writing equation (2) as follows

(3)

The left hand side of equation (3) is the change in household net wealth, or the stock measure of household saving. The right hand side measures saving in terms of flows as the difference between current income () and current expenditure (). Equation (3) then implies that, in the absence of uncertainty and under the assumption that households have perfect information, the stock measure of saving should be identically equal to the flow measure of saving. In reality, the two measures are not the same. There are several reasons for this.

In equation (3), it is the change in the market value of net wealth that should be equal to the difference between the flow of current income and expenditure. However, the Reserve Bank’s estimate of household net wealth does not include all components of net wealth at market value, like the stock of housing for example. This would lead to some discrepancy between the stock and flow measures of saving in New Zealand.

The two measures of saving can also differ because of mismeasurement. Most estimates of household net wealth do not include human capital. This means that measured changes in household net wealth are understated by , i.e.

(4)

The flow measure of saving will be understated relative to the measured stock saving rate that excludes human capital. This is because the flow measure includes expenditure on education and health care, but they are treated as consumption.

Saving measured in terms of flows will also be understated relative to the stock measure if expenditure on durables is treated as consumption rather than investment.

Another reason why the stock and flow measures of saving differ is because the assumptions of no uncertainty and perfect information do not hold in the real world. The (expected) cash flow of future earnings of financial and real assets, and hence their price, are subject to random, unforeseen shocks. In the above example, households must decide at the beginning of each period how much of their wealth to hold in bank deposits, financial and real assets and how much to add to their human capital. The prices paid depend on next period’s expected values of these assets and human capital. If assets are subject to random shocks that occur during the period and affect future earnings, then the value of assets at the beginning of the period will differ from the end of period value. Thus, ex post the change in household net wealth may not equal the flow measure of saving.

If the shocks affecting the price of financial and real assets are normally distributed, then asset prices are subject to positive and negative shocks, which, on average, are zero. This implies that the two measures of saving will diverge during some periods, but would tend to move together over time. However, they will not move together over time if shocks to asset prices are persistent. Generally, shocks to asset prices are persistent and the stock and flow measures of saving are likely to diverge. Tests for a unit root suggest that in New Zealand house and stock prices are non-stationary, i.e. shocks to asset prices have permanent effects.[6]