Using equations (11), (12), (13) and (14) and dividing through by Ne, (15) may be expressed in terms of the initial proportions as:

It is possible to derive specific cases from this general expression. For example, equation (2) is equivalent to the assumption that both supply elasticities are infinite (completely elastic) since union labor shifts freely into the nonunion sector. This means that A, and λ are zero and (16) becomes

Since c

C

1u, this is the same expression as (2). At another extreme, one might assume that the union accepts whatever wage cut is necessary to maintain union employment at the pre-shift level N1. In this case, "" = 0 so λu = −1/ŋä and (16) becomes

Equation (18) is more complex than (17) because there are changes in nonunion. employment (and hence total employment in construction) and because there are wage changes in both sectors. One must use some caution with (18) because if it is interpreted in a strictly mechanical manner it would be possible in some cases to have the union wage rate drop below the nonunion rate. Since this is nonsense from an economic point of view it would be necessary to drop the assumption of complete inelasticity of union supply if it implies a "negative" differential in the empirical estimates.

This raises another, more realistic, question, however. One might wish to think of the union supply curve as a function of the difference in union and nonunion wage rates, as well as the union rate itself. No attempt is made here to build this possibility into a formal model but it is worth keeping this idea in mind when interpreting the results of equation (18). In particular, if the differential between union and nonunion rates gets very small, it is probably best to drop the assumption of complete inelasticity of supply.

A major advantage of equation (18) is to focus attention on economic variables that play a key role in determining the effect of the Davis-Bacon Act. It is

very difficult to get any good data on the parameters-we need to have values for four elasticities; the proportion of man-hours in union, government, and nonunion construction work; and the differential between union and nonunion wages, the theoretical and empirical questions involved are noted on page 23 of the text.

Appendix B

The Ehrenberg, Kosters and Moskow Analysis

This appendix briefly summarizes the preliminary work by Ehrenberg, Kosters, and Moskow to estimate the effect of Davis-Bacon type contracts on the relative wages of construction workers. The basic statistical model they examined is 1

R =ao + a1 U + a2 PUB + a3 G.

R is a measure of the relative wage.of unionized construction workers, U is the extent of unionization in nonresidential construction, PUB is the proportion of nonresidential construction that is publicly financed or assisted and G is a measure of recent growth in construction activity. All of these variables are logarithms of the basic data.

The coefficients a1, a2, a-measuring the relationship of U, PUB, and G to relative union wages R—are unknown and must be estimated. For example, if a2 is found to be positive it implies that increases in the proportion of nonresidential construction that is publically financed increase union wage rates relative to other wages.

It is difficult to get precise data on the relevant variables in this equation and the authors provide a detailed discussion of the conceptual difficulties inherent in the measures they used. The reader who is interested in a detailed discussion of these problems is referred to the Ehrenberg-Kosters-Moskow paper. We provide a brief description of the data here.

The data for all variables were obtained from a cross-section of 62 metropolitan areas with populations of over 100,000. The authors used three measures of relative union wage rates, but we will focus on only one of them here. The variable R is the average union wage scale of journeymen in the building trades divided by the average hourly earnings of local production workers in manufacturing. These wage data were obtained from Bureau of Labor Statistics publications and were averaged over a three year period (1967, 1968, and 1969) in an attempt to avoid the effects of different timings of contract expirations over the 62 metropolitan areas. The geographical coverage of the two wage series is not identical (city vs. Standard Metropolitan Statistical Area).

1 Ronald G. Ehrenberg, "The Economic Impact of Davis-Bacon Type Legislation: An Econometric Study," unpublished paper, March 1971.

2 The authors also used (a) the ratio of building trade helpers average union wage scales to average hourly earnings of manufacturing production workers, and (b) the ratio of building trade helpers average union wage scales to journeymen average union wage scales in other regressions.

The measure of unionization in each area, U, is the ratio of building trade union membership in each area to average nonresidential construction employment in the SMSA. Details on the construction of this variable can be found in the Ehrenberg-Kosters-Moskow paper. PUB is the proportion of the value of nonresidential construction in the SMSA which appeared to be either publicly financed or assisted. This variable is obtained from unpublished data of the F. W. Dodge Company on the value of construction contract awards by city and type of construction. The variable is defined to include construction activity defined as public by F. W. Dodge and transportation-related building (such as airplane hangars) and also utilities and transportation-related nonbuilding construction. The authors believe that the bulk of these additional construction activities are covered by legislation that contains Davis-Bacon type prevailing wage determination clauses. In order to get a measure of the "permanent" impact of Davis-Bacon determinations, these data were averaged over the three year period 1965-67.

G is the growth of construction in the area and is measured as the percentage change of the average value of construction in 1965-67 over the average value of construction in 1961-64.

Using standard statistical regression techniques, the authors estimated several equations. The following equation is a typical example of the results,3

4

This equation may be interpreted as follows: When the proportion of publicly financed construction in an area (i.e., PUB) rises by 10 percent, union wages of journeymen in construction rise by about 6.8 percent relative to wages of production workers in manufacturing. The effect of increases in the fraction of publicly financed construction appears to be stronger than the effect of increases in construction activity-a 10 percent increase in G raises relative union wages of journeymen in the building trades by about 2.4 percent.

Among the other regressions reported by Ehrenberg, Kosters, and Moskow is the following,"

RW3 = -.182.118 PUB + .002 U+.065 G, where RW3 is the ratio of building trade helpers' average union wage scales to building trade journeymen in each area. The coefficient on PUB in this equation, .118, indicates that a 10 percent increase in the fraction of publicly financed or assisted construction raises the average wages of helpers by about 1.2 percent relative to journeymen in the building trades. This increase probably results from the tendency of Davis-Bacon determinations to set very high relative wage rates

3 The t-ratios are 5.01, 2.44, 1.19, and 2.52 for the constant, PUB, U, and G respectively. The squared multiple correlation coefficient is .259. The authors' other regressions provided generally similar kinds of results.

4 The coefficients of PUB, U, and G are elasticities, since all variables are measured in logarithms.

5 The t-ratios are 1.78, 1.78, .06 and 2.83 for the constant term, PUB, U and G, respectively. The squared coefficient of multiple correlation is .195.

for workers in apprenticeship training programs as was noted by Professor Brozen in the paper mentioned earlier."

The preliminary findings of Ehrenberg, Kosters, and Moskow have to be interpreted with some caution. The authors note that their estimates are only tentative given the crude nature of the data and the limited geographic coverage of the sample. They also point out that there is no presumption that their model contains all the relevant variables. Indeed, the squared multiple correlation coefficients of between 2 and 4 suggest that additional explanatory variables might successfully be incorporated into the model.

It is not easy to ascertain the precise impact of Davis-Bacon determinations from these results, since it is possible that increases in public construction per se (i.e., in the absence of prevailing wage determinations) may lead to somewhat similar results. This problem is handled in part by the use of the control variable G, but there is some danger of multicollinearity between PUB and G (and also PUB and U). There is also the danger, as the authors point out, that any "spillover" of wages in construction to wages in other industries (such as manufacturing) can result in a downward bias in the estimate of the relative impact of PUB, U, and G.

Despite such ambiguities, these initial findings are in accordance with the studies of the General Accounting Office and the work of Professor Gujarati and the accumulated evidence points quite strongly in the direction that Davis-Bacon determinations (and determinations of related legislation) exert a powerful upward pressure on relative wages in the construction industry. This upward movement appears to take place directly in public construction and indirectly in private construction through the increased bargaining power which unions derive from the prevailing wage laws.

6 Yale Brozen, "The Davis-Bacon Act: How to Load the Dice Against Yourself," op. cit.