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Using the parameters estimated above, we perform the same basic analysis for the years 1981-1991. We first examine the descriptive statistics similar to those in Table 4 for the years 1981-91. In general, the pattern of input shares, growth rates of output and costs and changes in inputs follow similar patterns to those depicted in Table 4. However, there are several noticeable changes in the trends of these variables. The estimates for total and internal scale elasticities Mathematical Formula are larger than 1 for most of the industries. The cost elasticity of output is close to unity in almost all of the industries. The average elasticity of cost with respect to highway capital is lower in 1981-91 than the average reported for the entire period.

Table 14 lists some of the more critical estimates for the period 1981-91. The aggregate output elasticities with respect to private sector inputs and highway capital shown in this table trace the same pattern and are basically of the same magnitudes as the averages for the entire period as shown in Table 11. The elasticity with respect to materials (Mathematical Formula0.50) followed by that of labor, Mathematical Formula, and that of private capital stock Mathematical Formula. The elasticity of output with respect to highway capital, Mathematical Formula, for 1981-1991 is much smaller than that during the previous sample period. It is about 0.039, and as noted earlier, declines over time. In 1991, the output elasticity of private capital stock is nearly 7 times as high as that of public capital stockMathematical Formula. The average net rate of return to highway capital Mathematical Formula for the period 1981-91 is about 0.16. This rate declines over time and in 1991 the estimate for Mathematical Formula is approximately 0.09.

However, the patterns of the distribution of the benefits across industries for the 1981-1991 subperiod are similar to those for the entire period. The effects of an increase in highway capital investment on demand for inputs are similar to the those observed for the earlier period. As seen in Table 14, the conditional demand for employment and materials (output held fixed) decreases when highway capital increases. Furthermore, private capital and highway capital are complements, i.e., the demand for private capital increases when the investment in highway capital rises.

Table 14: Aggregate Output and Input Elasticities
Output Elasticities
  Mathematical Formula Mathematical Formula Mathematical Formula Mathematical Formula  
  0.36 0.51 0.17 0.039  
Input Elasticities
    Mathematical Formula Mathematical Formula Mathematical Formula  
  Conditional: Output level held constant -0.054 -0.057 0.056  

Output level varies
-0.013 -0.016 0.080  

When we account for the output expansion effect induced by the productivity gain from highway capital, we see ostensibly similar results to those noted earlier for the entire period that are shown in Table 11. When output expands in response to the cost decline induced by the increase in highway capital, demand for all inputs increase. This induced cost increase is of approximately of the same magnitude, at the aggregate economy level, as the cost reduction or "productivity effect" of the initial increase in highway capital. This phenomenon, which is observed at both the industry and aggregate levels, is due to the magnitudes of the output cost elasticities(the reciprocal of the degrees of scale). These elasticities are about 0.97 to 0.98, which suggest that a 1% increase in output generates almost the same increase in cost. The productivity gain of highway capital offsets the increased cost due to the induced increase in output at the aggregate economy level as well. The effect of induced output expansion is to increase demand for all inputs at the aggregate economy level as noted before at the industry level. The total effect of an increase in highway investment is to decrease demand for materials and labor but to increase demand for private capital.

The most significant change in the analysis of the 1981-91 period compared to the entire period is that the elasticities of cost, output, and factors of production with respect to increase in highway capital have declined considerably. The results in Tables 11 and 14 indicate that a percentage increase in net investment in highway capital has a much smaller percentage effect on output and input demands at the aggregate and industry level in the 1981-1991 period than in the previous periods. Also, the rate of return to highway capital investment is, as shown in Table 12, much lower in the recent period and is less than 10% in 1991. Therefore, using average elasticities for the entire period to calculate benefits and rates of return of highway capital for recent years will be misleading.

Chapter 8 | Chapter 10

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