4  Estimating income gains: A growth accounting approach

To identify the contributions made by specific factors to economic growth, standard growth accounting suggests it is necessary to focus on key factor inputs. Conventionally, the domestic labour force, the capital stock and multifactor productivity, inclusive of technological change, have been identified as the key sources of economic growth. In open economies however, a further distinction can be made between domestic capital accumulation that is funded via domestic saving, and domestic capital accumulation funded via external borrowing. In this section, we use a growth accounting approach to estimate the national income gains attributable to the capital accumulation in New Zealand that is made possible through external borrowing.

Using extended growth accounting, it is possible to estimate the net contribution of foreign capital in real terms for each of the variables in the following expression:

( f_K* - r^* ) dK^* - dr* K^*    (4.1)

where f_K* is the marginal product of foreign capital, r^* is the real foreign interest rate, dK^* is foreign capital inflow, dr^* is the change in the foreign interest rate from the previous period and K^* is that part of the domestic capital stock financed by foreign saving[8].

Since foreign borrowing is largely intermediated through commercial banks, we assume the productivity of capital in use domestically is invariant to the source of its funding. Therefore,

    (4.2)

Next, we assume output is generated by a Cobb-Douglas function[9] of the form

(4.3)

where K = K^d + K^* and α is the share of capital in national income.

This form of the production function is appropriate if the division of national income between capital and labour has been relatively stable, as indeed it has been for New Zealand over the past decade. A useful property of the Cobb-Douglas function is that the marginal product of capital is given by the share of capital in national income multiplied by the ratio of national output to capital. The marginal product of capital can therefore be estimated using national accounts data as

(4.4)

The net marginal product is then simply the difference between the marginal product of capital and the estimated rate of capital stock depreciation (Table 1).

Notes:

1. Productive capital stock data in 1995-96 prices from nvpcs series nat.bak from Aremos.
2. Expenditure base GDP data in 1995-96 prices from ngdp series nat.bak from Aremos.
3. The ratio of the real capital stock to real gross domestic product.
4. The ratio of gross operating surplus to the sum of compensation of employees (nysc series nat.bak) and gross operating surplus (nosg series nat.bak).
5. The product of the output-capital ratio and the capital share of income.
6. Estimated as the ratio of chain volume measures of consumption of fixed capital (ndep series nat.bak) to end-year capital stock.
7. The difference between the marginal product of capital and the estimated depreciation rate.

Next, using balance of payments flow and stock data it is possible to estimate the real effective cost of foreign capital and the annual national income gain attributable to the first term of equation (4.1), as shown in Table 2.[10]

Notes:

1. Measure of net foreign liability based on data in current price from tiin.a series (known as Net Investment Position) tra.bak from Aremos.
2. Current price data recorded in tbii.a series (known as Investment Income Balance) tra.bak from Aremos.
3. Ex post real cost of foreign capital is the ratio of net income payments to net foreign liabilities less annual inflation rate which is derived from pcpi series pri.bak from Aremos.
4. The difference between the net marginal product of capital from Table 1 and the real cost of foreign Capital.
5. Data recorded in tbc.a series tra.bak from Aremos; deflated to 1995-96 prices.
6. The product of the net marginal product of foreign capital less real servicing cost and the external imbalance in 1995-96 prices.

The fact that the marginal cost of capital is below the estimated marginal product may at first blush be taken as an indication of under investment. However it is more correctly seen as a reflection of a disequilibrium state. It is this disequilibrium that is the driving force behind foreign capital inflow. When the equilibrium point was reached, at which marginal costs and benefits were equated, capital inflows would cease. Here we are concerned with measuring the transitional net income gains as the economy gropes toward (but never reaches) an equilibrium state.

It is now possible to estimate the variation in real national income due to fluctuations in world interest rates that raise or lower the servicing cost of external liabilities as implied in the last term of equation (4.1). This is shown in Table 3 which combines this data with Table 2 results to yield the real cumulative national income gains that have resulted from past capital inflow.

1. Due to lack of data for net foreign debt and net income payments on foreign debt data before 2000, the proxy for implicit foreign interest rate is derived by equally weighted 10 year government bond rates from Australia, USA and UK. This is justified on the grounds that foreign investments in NZ from these countries account for over 50% of total foreign investments since 1995 and the amount from each is approximately the same.
2. The product of net foreign debt and the change in the implicit foreign interest rate. As the stock of net foreign debt changes through the year, a weighted value should be used. The Australian Bureau of Statistics recommends a weight of two-thirds for the beginning of year value and a weight of one-third for the end of year value. The net foreign debt and net equity debt data for NZ go back to 2000. Prior to that year, we use estimated values. The net foreign debt before 2000 is estimated by subtracting net equity debt from net foreign liability, where net equity debt from 1995 to 1999 is estimated by its average value from 2000 to 2006. The reason for doing so is that the net equity debt has remained at a relatively constant level ($13 to $18 billion) from 2000 to 2006.
3. The value of the income gain from interest rate changes deflated by the GDP deflator.
4. The sum of the real national income gain from annual foreign capital inflow from Table 2 plus the real annual net gain from interest rate movements.
5. The number of “Full Time Equivalent” workers in New Zealand in 2006 was 1.9 million, which yildss (5 /1.9*10^-3 = $2612) NZ per worker extra accumulated income from the contributions of CAD.
6. Calculated by dividing (5) by number of full time equivalent workers from lhfte.q series.

Hence New Zealand’s cumulative national income gain from net foreign capital inflow over the period was around $5.9 billion. Since the New Zealand workforce on a “full time equivalent” basis was 1.9 million in 2005-06, the extra accumulated income attributable to the use of foreign capital was around $2,600 per worker, or $3,300 when converted to 2007 prices.

However, the annual income gains estimated on this basis most likely understate the total contribution of foreign capital and should be considered minimum values. This is because part of capital inflow is direct foreign investment which entails the transfer of technology, work practices and management techniques that boost multifactor productivity. Hence, part of the multifactor productivity improvement over this time would be attributable to foreign capital rather than exclusively to domestic sources as assumed in the estimation method employed.