How efficiently do U.S. cities manage roadway congestion?

Abstract

We estimate efficiency and TFP growth for two measures of congestion and two measures of the monetary value of congestion for the largest 88 contiguous cities in the U.S. over the period 1982–2007. Using stochastic frontier analysis we find that the efficiency scores for congestion and the associated ranking of cities is sensitive to the measure of congestion. In contrast, the efficiency scores and rankings are robust for the two measures of the monetary value of congestion. Most importantly, for the most valid measure of congestion and both measures of the monetary value of congestion, we find that average TFP growth over the study period is characterized by an upward trend. This is an encouraging sign even though in all three cases growth is only zero or slightly less than zero at the end of the study period. We therefore conclude that policies which have been used towards the end of the study period such as providing incentives to carpool and encouraging employers to offer flexi-time and telecommuting arrangements appear to have been effective and should be implemented more widely.

Appendix

See Table 3.

Table 3 Monotonicity properties outside the sample mean

1.1 Test of the concavity condition

Microeconomic theory assumes that the form of an input distance function, D _I , satisfies a particular curvature property i.e. D _I is linearly homogeneous and concave in inputs x. The symmetry property and homogeneity of degree one in x of D _I implies that only K(K − 1)/2 elements of the Hessian matrix, H(x), where $H(x)\equiv \frac{\partial ^{2}D_{I}}{\partial x\partial x^{\prime }}$, are linearly independent. Applying the arguments of Diewert and Wales (1987), the Hessian of the input distance function with respect to x can be calculated as follows:

$$ H(x)={\mathbf{B}}-\widehat{ex}+exex^{\prime }, $$

where: $\widehat{ex}$ is a diagonal matrix with estimated input elasticities, ex _k for $k=1,\ldots ,K-1$, on the leading diagonal and zeros elsewhere; ex is a vector of estimated input elasticities, $ex_{k}; \mathbf{B}$ is the matrix of second order coefficients on the input terms in the translog function.

Concavity of the input distance function in x requires that the Hessian matrix is negative semidefinite. Whether the Hessian matrix is negative semidefinite can be verified from the sign pattern of the principal minors of the Hessian. The necessary and sufficient conditions for D _I to be concave are as follows: all the odd-numbered principal minors of the Hessian must be non-positive and all the even-numbered principal minors must be non-negative. At the sample mean with mean corrected data, the Hessian is given by

$$ H(\overline{x})={\mathbf{B}}-\widehat{\beta }+\beta \beta ^{\prime }, $$

where $\widehat{\beta }$ is a diagonal matrix with estimated input elasticities, β _k for $k=1,\ldots ,K-1$, on the leading diagonal and zeros elsewhere, and β is a vector of estimated input elasticities, β _k . The Stata code for the concavity test is available from the corresponding author on request.

1.2 Efficiency scores

See Table 4.

Table 4 Efficiency scores