# Transportation Economics/Productivity

Productivity

## What is Productivity?

The question of what is productivity in transportation has several interpretations. One line of research, beginning with research by Aschauer (1988) and continuing through Boarnet (1998) and Nadiri (1996) examines how transportation investment affects the economy at large. These papers tend to treat transportation (or highways) as a black box, and make no distinctions between different kinds of transportation investment.
The input is state or national investment in transportation, and output is gross domestic product. While this research, which we refer to as macroscopic productivity provides useful rhetorical tools (transportation investments provides an X% return, compared with Y% for other investments) important for large budget debates, it provides no assistance in actually making management decisions, which requires an understanding of microscopic productivity.

## Macroscopic Productivity
### Theory

$GDP=f(K,L,T)$ Where:
* $GDP$ - Gross Domestic Product
* $K$ - Kapital
* $L$ - Labor
* $T$ - Transportation Investment

### Evidence

Nadiri's research claims that "the average cost elasticity with respect to total highway capital for the U.S. economy during the period 1950- to 1991 is about -0.08. " That is, increasing highway investment by 1% will reduce costs by -0.08%. The average net rate of return from highway capital fell from 54% in the 1960 to 27% in the 1970s to 16% in the 1980s, the last number is close to the private rate of return, indicating a near optimal level of highway investment. Does this indicate declining productivity  or an infrastructure shortfall? Nadiri suggests declining productivity of new investment. Aschauer argues that we are dramatically underinvested.

### Thought Questions

* Which one is right?
* What do what we know about S-Curves have to say about this?

## Microscopic Productivity

(based on Levinson, D. (2003a) Perspectives on Efficiency in Transportation. International Journal of Transport Management. 1 pp.145-155)
Firms try to maximize profit, society attempts to maximize overall welfare. In determining whether to build a project, select a policy, implement a system, or provide a service, it is possible to estimate the net present value of the future stream of profit or welfare with a cost/benefit analysis. However, those estimates depend on assumptions about demand and supply that may or may not pan out. For instance, the number of customers (passengers or trips, for example) depends on the money and time costs of a service, user preferences, competition or alternatives available, the availability and quality of complementary services, and other quality attributes. Money and time costs themselves depend in part on demand. User preferences and attitudes can be shaped for the better or worse depending on the service quality and number of alternatives. Competitors will emerge to provide services that replace previous needs with new ones, depending on the market strength of existing services.
Imagine a world where the only instrument your doctor had was a thermometer. He could diagnose fever, but not much else. Would you stay with him or change doctors? This is analogous to having only one Measure of Effectiveness (Consumers surplus, Benefit/Cost ratio, Volume/Capacity ratio, etc.) to understand a complex system like transportation.

### Beyond Benefit/Cost

So while a benefit/cost analysis may be necessary to make good decisions, it may not be sufficient to manage a complex system such as a transportation network. Thus there is a desire to monitor the transportation network on multiple dimensions, to understand how well it is performing (and how thus accurate were previous projections), and to steer future decisions. These measures can be made at the level of a road segment or a particular transit route, or they can be appraised at the level of the local highway or transit network or technology deployed systemwide, or they can even be assessed statewide or nationally.
These metrics might assess how efficiently labor or capital is employed and change in the system (to gauge where future labor or capital will be employed). They might consider market share against competitors, the state of complementary services (for instance, access to transit or parking in the case of a transit system) or the satisfaction of customers and vendors (to gauge future market share and the price and quality of inputs).

### Gauges

All of these gauges are important to monitor, but transportation in the public sector is only at the early stages of implementing such a complete management system. The most basic efficiency criteria are not routinely collected or analyzed, much less used for decisions or process improvements. While the ultimate objective in the public sector is to improve overall welfare, the difficulty is in its measurement. Things that are easily measured (flow and speed on isolated links) do not provide an unambiguous indicator of overall welfare. Better measures require much more complete (and expensive data), or models to estimate them. These better data include travel surveys, typically undertaken at most once a decade.

### Definition

Productivity is a measure of output divided by input.
The larger this ratio, the more productive the system is. So either increasing output or decreasing input can increase productivity. This performance measure that can indicate the direction in which welfare is moving.
All else equal, if productivity is increasing, welfare should be improving.

### Example Measures

Looking at productivity in other industries may provide some guidance. Industrial productivity is an output divided by an input, for instance labor productivity would be measured as widgets per hour of labor. All else equal, a firm that produces more widgets per hour of labor will be more profitable than one which produces less. In examining a trucking firm, we may look for miles (kilometers) moved per driver-hour, basically a speed measure. Or we may want to multiply the miles (kilometers) by tons (ton-miles (kilometers)) or value (dollars). Or we may want a different denominator to get a measure of capital rather than labor productivity (number of vehicles operated).

### Defining Inputs and Outputs

So the key question in measuring productivity are determining the outputs and inputs. This differs depending on what is examined. For instance, if we are considering a private bus system, then the cost of highways is paid for in taxes and fees. However if we are considering highways, we must examine the infrastructure more closely.

#### Inputs

Beginning with the inputs, we have, broadly, capital and labor.
* Labor includes all the workers required to produce a service paid directly by the agency, which produces that service. So when considering the productivity of transit service, labor inputs are the employees of the transit agency, including bus drivers, mechanics, managers, and accountants among others.
* Capital includes all the buildings and equipment needed to operate the service (buses, garages, offices, computers, etc).
While labor may go into each of the capital components, to the agency it is viewed as capital (the labor required to build the bus is considered in the labor productivity of the manufacturer of the bus, but not the operator).
Labor productivity ($P_{L}$) can be measured with hours of labor input (H) and an output measure (O) as:
$P_{L}={\frac {O}{H}}$
A related measure, unit labor costs (ULC) is calculated using dollars per hour, or labor compensation (C) per unit of output, represented as:
$U_{LC}={\frac {({\frac {C}{H}})}{({\frac {O}{H}})}}$
For instance, the annualized labor productivity would measure output over the year divided by total hours worked per year. The appropriate timespan depends on the case analyzed and the available data.
Similarly, capital productivity (PK) can be defined as output measure divided by the capital (K) in money terms that is required to produce that output.
$P_{K}={\frac {O}{K}}$
Capital is somewhat trickier than labor in that capital is often a stock, while output and labor are flows. For example, if it costs one million dollars to build a road section with a multi-year life, we can’t measure the productivity of capital as simply annual output divided by that one million dollars. Rather, that stock needs to be converted to a flow, as if the highway department were renting the road. This conversion depends on the interest rate and the lifespan of the facility.
Looking at either the productivity of labor or capital to the exclusion of the other is insufficient. Some investments can improve labor productivity at the expense of capital productivity. Total factor productivity measures can be used to combine labor and capital productivity. These require weights for each measure (and any submeasures which comprise a measure) proportional to the share of that measure in total costs. This issue becomes more complex when examining changes in productivity between time periods, as both inputs and outputs (and thus shares) change.

### Outputs

To this point, we have been intentionally vague as to what is output in our productivity measures. What happens when a particular investment is made in transportation that actually increases overall output?
In freight, output is typically measured by something like ton-miles (kilometers) shipped. So an improvement which increases the number of ton-miles (kilometers) which can be shipped with the same resources increases productivity.
These improvements are usually timesavings (cutting distance or increasing travel speed) which enable the same truck to be used on more shipments. But they may also be the ability to ship more weight per trip or driver (for instance hauling two trailers with one tractor, or the elimination of a weight restriction because of a bridge strengthening).

#### Paradox  ?

It might be noted that a link that shortened the network distance traveled might not increase productivity when output is defined as ton-miles (kilometers) shipped on the network. Two effects take place. First, there is a shortening of distance, reducing ton-miles (kilometers). But there is also a shortened travel time, which may induce more trips (and thus more ton-miles (kilometers)). This paradox can be obviated by looking at point to point distance rather than network distance as the basis.
A firm relocating to be nearer its suppliers will reduce point-to-point distances. A consequence is that while total travel time may reduce, it may not reduce as fast as distance (i.e. speed may drop). Again productivity (user speed in this case) may drop, though the system is better off. Examining accessibility may be useful in this case.

### Behavioral Shifts

In passenger travel, when travel times are reduced, people either travel more (either more trips or longer trips or both) or do something else with the time saved, or some combination of both. Furthermore, activity patterns may shift so trips can be taken at more convenient times of the day or by more suitable modes. Over the medium to long term, the locations of those activities may shift as well as individuals change first where they perform non-work, non-home activities such as shopping, and later may switch jobs or move homes. Trips are not goods in and of themselves, but they indicate the activities at their ends. So a new link, for instance, may increase or decrease total vehicle miles (kilometers) traveled, or total vehicle minutes of travel, but will surely result in more or different and better activities being pursued. In general, more activities can be correlated with more trip ends, though trip chaining may complicate this.

### Transit

From the point of view of a transit operator, output can be measured by passenger trips or passenger miles (kilometers) carried. Which an operator desires depends on its fare structure (flat or distance based). An operator with a flat fare structure may wish (to maximize revenue, at least in the short run) to have many short trips, while with a distance-based fare structure, the operator is rewarded for longer trips. Transit operators are in many ways similar to freight haulers in the productivity sense.

### Highway

A highway, on the other hand, is not so similar. Especially in the absence of link based road pricing, it is ambiguous as to what a highway operator wants to encourage to maximize overall social welfare. However, from the point of view of a link, maximizing throughput, person trips using a link or flow past a point, seems a reasonable output measure. All else equal, a link is more productive if it can serve more person trips or do so at a lower cost. Throughput cannot be maximized if service quality (travel speed) deteriorates as congestion sets in. Since the link is of a fixed length, for a given link, flow and person miles (kilometers) traveled are equivalent.
However it is important that the input and output be measured consistently. It is very hard to determine the labor required for a given link, as many services are provided network wide. If we want to consider a network, then an output measure of person miles (kilometers) traveled is necessary to allow for aggregation. An input measure of person hours traveled is useful for private time productivity. . However one element of labor that is often not considered is the time of the driver and passengers. This is especially important when we realize that the time costs to drivers and passengers dwarf those of the highway agency

### Partial Productivity

Four basic partial productivity measures can thus be considered for transportation (only the first three are meaningful for transit).
Productivity of Public Labor (PGL) $P_{GL}={\frac {T}{H}}$
Productivity of Private Labor (PPL) $P_{PL}={\frac {T}{D}}$
Productivity of Public Capital (PGK) $P_{GK}={\frac {T}{K}}$
Productivity of Private Capital (PPK) $P_{PK}={\frac {T}{V}}$
Transportation planning models, such as those used by metropolitan planning organizations and others, provide data that can be used to measure productivity. In particular, over a given network, person distance traveled, person hours traveled, and dollars spent for vehicle operating costs can be estimated. Agency labor and capital costs will still need to be collected separately. But the network data can be aggregated to give us the partial private productivity measures ($P_{PL}$ and $P_{PK}$), and with the other agency data, the partial public productivity measures ($P_{GL}$ and $P_{GK}$).
Productivity of Public Labor ($P_{GL}$) $P_{GL}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{H_{l}}}}$
Productivity of Private Labor ($P_{PL}$) $P_{PL}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{D_{l}}}}$
Productivity of Public Capital ($P_{GK}$)$P_{GK}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{K_{l}}}}$
Productivity of Private Capital ($P_{PK}$)$P_{PK}={\frac {\sum \limits _{l}{T_{l}}}{\sum \limits _{l}{V_{l}}}}$

### Partial Factor Productivity

PFP is defined as total output / factor i. For example, a measure of PFP for labor would be Q/L where Q is total output and L is some measure of labor input such as person-hours or number of workers [note that the former measure is better since the latter assumes an equal number of hours per worker as well as equal quality of worker].
Use of PFP The PFP measure is used quite frequently in business, particularly to measure the productivity or contribution of labor. A glance through Annual Reports from any number of industries will yield lots of evidence including those of airlines. Airports will, for example, provide measures of labor productivity of # of aircraft movements/employee or # of passengers/employee. This, perhaps, provides an excellent example of why the PFP measure is flawed; it fails to take into account other inputs such as capital which are used in the production process.

### Total Factor Productivity

Total Factor Productivity (TFP) was developed to overcome the problems associated with the PFP measure. TFP takes all factor inputs into account in calculating productivity. TFP is defined as the aggregate of output over the aggregate of input. It differs from PFP in two important respects; first, it recognizes that there may be more than one output and, it recognizes all inputs in the production process.
TFP has been defined as:
$\ln \left({\frac {TFP_{K}}{TFP_{L}}}\right)=\sum \limits _{i}{\left({\frac {R_{ik}+R_{il}}{2}}\right)}\ln \left({\frac {Y_{ik}}{Y_{il}}}\right)-\sum \limits _{i}{\left({\frac {S_{ik}+S_{il}}{2}}\right)}\ln \left({\frac {X_{ik}}{X_{il}}}\right)$
where $k$ and $l$ are adjacent time periods, the $Y$'s are output indices, and the $X$'s are input indices, the $R$'s are output revenue shares, the $S$'s are input cost shares and the $i$'s denote the individual inputs or outputs. It has been shown that this equation is an exact index number to a homogeneous translog production or transformation function.

#### Panel Data

This definition of TFP lacks particular desirable properties if a time-series-cross sectional comparison is to be made. Since many transportation data sets form a panel (combination cross-section & time series) an alternative procedure is proposed. It is constructed in such a way as to make all bilateral comparisons both firm and time invariant. This form of TFP has been the term the "multilateral TFP index" and has been used extensively in both transportation and other industry studies to compare the performance of firms over time and against competitors. Robert Windle dealing with international comparisons of TFP used the following:

#### Comparing TFP

$\ln \left({\frac {TFP_{K}}{TFP_{L}}}\right)=\sum \limits _{i}{\left({\frac {R_{ik}+{\overline {R_{i}}}}{2}}\right)}\ln \left({\frac {Y_{ik}}{\overline {Y_{i}}}}\right)-\sum \limits _{i}{\left({\frac {R_{il}+{\overline {R_{i}}}}{2}}\right)}\ln \left({\frac {Y_{il}}{\overline {Y_{i}}}}\right)-\sum \limits _{i}{\left({\frac {S_{ik}+{\overline {S_{i}}}}{2}}\right)}\ln \left({\frac {X_{ik}}{\overline {X_{i}}}}\right)-\sum \limits _{i}{\left({\frac {S_{il}+{\overline {S_{i}}}}{2}}\right)}\ln \left({\frac {X_{il}}{\overline {X_{i}}}}\right)$
An important additional issue in TFP analysis is attribution of TFP. One approach has been to decompose TFP into scale effect, pricing effect and pure technological change. These are important because scale effect is due to market opportunities or managerial decisions. Pricing is also a market or managerial decision while the pure technological change effect is exogenous to the firm. Another way of attributing TFP is to take the calculated TFP index and regress it on a set of variables which describe the characteristics of the firm. An example of this procedure is contained in Gillen, Oum and Tretheway.

## References

* ↑ Aschauer, D.A. (1988) "Is Public Expenditure Productive?" Federal Reserve Bank of Chicago.
* ↑ Boarnet, M.G. (1998) "Spillovers and the Locational Effects of Public Infrastructure" Journal of Regional Science 38(3) 381-400.
* ↑ Nadiri, M.I. and Mamuneas, T.P. (1996) Contribution of Highway Capital to Industry and National Productivity Growth Federal Highway Administration. Office of Policy Development.