infrastructure, based on utility maximizing consumers, such that: where Ij<sup>Cdenotestheconsumptionofinfrastructurebyindividualj,Yjdenotesj0sincome,andqI</sup> the price of infrastructure. Profit maximization on the production side of the economy provides the standard order condition: where Yi denotes the i0th firm’s output, wi the i0th firm’s output price, and Ii<sup>P</sup> the production use of infrastructure.

This framework leads Fay (2001) and Fay and Yepes (2003) to the formulation of a reduced form demand for infrastructure in per capita format: where P denotes population, Yag and Yind the output of the agricultural and industrial sectors respectively,<sup>44</sup> and A denotes technology. In estimation, Fay (2001) and Fay and Yepes (2003) employ fixed effects estimation, in which fixed effects are to control for the unobservable aggregate infrastructure price,<sup><u>q</u></sup> w<sup><u>I</u>,andtechnologydimensions.ApplicationistoLatinAmerica,aswellasa</sup> wider set of countries.<sup>45</sup> Empirically we proceed with two instrumentation strategies. The first instruments only on per capita output,<sup>46</sup> the second also controls for the share of the agricultural and industrial sectors in aggregate South African GDP. Tables 3 and 4 report deviations between the conditional mean predicted demand for the infrastructural stocks employed for this study, and the actual stock of infrastucture reported for South Africa, for decade averages in absolute and percentage terms, for estimation results derived under the time series methodology described under section 4.3.<sup>47</sup> In Table 5A and 5B we report the correlations between the two alternative instruments and original regressors, and the two alternative dependent variables used in this paper as measures for productivity, output per worker and the Solow residual. For both instruments, correlations with the original regressors is relatively high, while correlations with the productivity measures is low, strengthening confidence in the use of the two instruments. In general, we note that the instrument which loads on sector shares (agriculture, industry), is more highly correlated than the instrument loading only on per capita GDP. Exceptions emerge for a number of the railways-related measures (LOCO, COACH, GOODS, CCAP, RPASS), and one roads infrastructure measure (VEHP). Given this evidence, we proceed with estimation using instruments.

# 5.1.3 Results in the Presence of Instrumentation

Estimation is again of equation (14) by means of the PMG panel estimator for South African manufacturing sectors, with the exception that the infrastructure measure is now replaced by the instrumented measure. Results are reported in Tables 6A and 6B.

> 44 These are admittedly somewhat ad hoc proxies that substitute for the aggregation issues that arise from developing industry demand from firm level demand functions.

> 45 An alternative approach to establishing an appropriate level of infrastructural expenditure, is provided by Randolph, Bogeti ́c and Hefley (1996). The conditional mean of infrastructural expenditure in their model is determined by a wide range of regressors, including the existing stock of infrastructure, population density, the urbanization rate, the urban-rural balance, the labour force participation rate, per capita GDP, the internal and external balances, size of the foreign sector, terms of trade shifts, debt obligations, the level of institutional development, level and mix of foreign funding, and the degree of anti-poverty commitment on the part of government.

> 46 We employ the aggregate per capita GDP measure from Fedderke and Romm (2006).

> 47 Full estimation results and diagnostics available on request.

15