Public Sector Output: Output Indicators and Welfare Indicators

1. Public Sector Output:Output Indicators and Welfare Indicators Martin Weale

2. The role of the adjustment to volume measures to reflect “increasing value put on public sector outputs” Broader issues • The distinction between output and income • The capacity of the national accounts to serve as welfare indicators

3. Current Prices Income=Expenditure=Output Constant Prices National accountants have always known there was a problem. Hence the need for the terms of trade effect. No agreed approach to the calculation of real national income

4. The basic theorem of constant price national income accounting (Samuelson and Swamy AER 1974) If output is produced with constant returns to scale and preferences are homothetic then, in an economy with no capital accumulation or foreign trade an index of output is also an index of welfare

5. Consider an economy with two sectors, public and private. Each sector produces only one output (hip replacements and corn) and both use homogeneous labour as the only input. The total labour force is L • Social preferences are Cobb-Douglas so the share of expenditure at current prices on public sector output is constant (=q). • Productivity growth takes place only in the private sector at rate g

6. The growth rate of the output index is (1-q)g • The basic theorem implies that this is also the growth rate of the welfare index. • If wages grow at rate w, then the price index of output grows at rate w- (1-q)g and real wages grow at rate (1-q)g • The share of real hip replacements in real GDP declines asymptotically to zero • But the contribution of each economic activity (public and private activities) to welfare is better indicated by the share of income attributed to each sector in total real income (Money income divided by the price index) and this is constant

7. Proposal • Leave real GDP figures and output indices as they are • Derive real income by deflating nominal income by the consumption deflator • Produce an additional table showing the value added in each industry deflated by the consumption deflator. • Real income equals real output only if the economy is closed and there is no capital accumulation • The output table shows contributions to output and the income table shows contributions to income.

8. If preferences are not homothetic (e.g. the value people put on health increases with income) a welfare index can be produced only by writing out the parameters of the utility function –e.g. AIDS or its relatives. • The link between aggregate output and aggregate welfare is broken and a single measure cannot serve both purposes.