With the publication of Public Representations, I’ve finally realized that I am no longer an active researcher. I’ve begun looking back over my work and evaluating it. There are numerous perspectives from which to evaluate your research. Was it imaginative conceptually? Was it well-executed methodologically? Was it impactful in academe or in the wider world? If it was the last project in a body of research, should I have stopped at that point or gone farther?

As the title of this post suggests, my focus is on an article that represented the culmination of a line of research that I now realize I could have taken farther. The article is in transportation economics and is quite technical. For the benefit of most readers, I will summarize my ideas without any algebra. For more technically inclined readers, the article was published in 1984 in The Canadian Journal of Economics, entitled “The economic effects of non-optimal pricing and investment policies for substitutable transport facilities” (16:1, pp. 80-98). It is available online through university libraries. If you can’t access it, I will email you a pdf.

The Line of Research

My doctoral dissertation was about the economics of airport planning and used Toronto as a case study. I discussed it in a recent blog post because of its relevance to the Ford Government’s proposal to expand Billy Bishop Airport. Economic science has a clear criterion to guide decisions to manage and invest in publicly owned transportation infrastructure. The objective is to maximize economic welfare, which is defined as the net present value of the difference between what people are willing to pay for the use of transportation infrastructure (roads, subways, airports) and the operating and capital cost of providing it over time. This is a microeconomic measure of social well-being for one sector of the economy, the counterpart of gross domestic product per capita, which is a macroeconomic measure of wellbeing for the entire economy.

Because transportation infrastructure becomes congested as it approaches capacity, marginal cost pricing (which takes into account the delays users impose on each other) requires the adoption of congestion tolls. The social opportunity cost of capital, a weighted average of the cost of capital to the public and private sectors, determines the discount rate used to calculate net present value (that is, the weight used to translate money in the future into money today). Therefore, the optimal policy combines congestion pricing with the use of a discount rate equal to the social opportunity cost of capital.

The paper looks at the impact of a wide variety of suboptimal pricing and investment policies for two cases: an airport and an urban transportation corridor containing both a subway and an expressway. I demonstrate that, for a considerable range, suboptimal policies do not generate large losses relative to the economic optimum. Empirically, this means that the economic welfare measure is equal to hundreds of billions of dollars, whereas the economic loss from suboptimal policies is equal to tens of millions of dollars, generally no more than one percent of the former. The implication of this finding is that, from an economist’s point of view, there are a wide range of transportation policy options that, while not optimal, are acceptable.

What is particularly innovative about this paper is how I present my findings. I develop a three-dimensional graphic display, where the net present value of economic welfare is on the vertical axis, the government’s pricing policy is on one horizontal axis, and the discount rate used for investment decisions is on the other horizontal axis. Taking advantage of mainframe computing technology that had become available in the early 1980s, I calculate economic welfare for several hundred pricing-investment options that then form a grid, or surface. The program was so demanding of computer capacity that it had to be run overnight when the machine was not being used for other purposes.

Here is the grid that I present in the paper, seen from two perspectives. This grid is for the airport case. The higher a point is on the vertical axis, the greater the economic welfare. On one horizontal axis, the landing fee goes from 0 to $5000 and on the other horizontal axis the social opportunity cost of capital, or interest rate used to discount future costs and benefits, goes from 0 to 50 percent.

The economic welfare surface encompasses a plateau around the optimum, say for landing fees between $1000 and $2000 and interest rates between 5 and 15 percent). It is only when there are large policy distortions relative to the optimum (landing fees of 0 or $5000 or interest rates near zero or 50 percent) that a point on the surface is far below the plateau.

The referees for the first journal to which I submitted the paper rejected it because they thought I was downplaying the significance of the economic loss due to deviating from economic optimality. The second journal accepted it. In that version, I added a provocative conclusion, namely the assertion that many economists were attaching so much importance to optimality that their mental map of the economic welfare surface is distorted to look like the Matterhorn, a mountain peak that falls off sharply on all sides. The actual welfare surface that I demonstrate in the diagram above (and others like it) looks more like the flatter peaks in older mountain ranges, such as the Laurentians or Adirondacks. In other words, my computer modelling demonstrates that their mental modelling is unrealistic.

Changing Directions

I published this paper in 1984, and then I stopped this line of research. Why?

In the 1984-85 academic year I took my first research leave. For part of that year, I went on a grand tour of Asia, encompassing Hong Kong, Thailand, Nepal, Singapore, Malaysia, China, and Japan. I became interested in Asian economic development, then a hot topic in the academic world. A few months later, I made a second trip to Japan, to do research for a paper on Japanese public management and its lessons for western public sector managers. In the early 1980s, I was pursuing interests in both transportation economics and public policy. Transportation economics began to seem narrow and technical, and my disagreement with the reviewers for the first journal suggested that this line of research would involve ongoing, stressful doctrinal conflict.

Though I had boundless energy – so it seemed – to pursue a variety of topics, after the Asian tour I shifted my interests away from transportation economics to public policy.

Observing Pricing Experiments

The technological advances that made my transportation modelling possible were also making it possible to take road pricing from an idea in the academic literature to a practice on streets and highways. I published a paper about a technologically successful but politically unpopular attempt to implement road pricing in downtown Hong Kong in the mid-Eighties. I did the research for it by interviewing public servants and representatives of citizens’ groups during a visit to Hong Kong. I had the opportunity to serve on the board of the Crown corporation implementing electronic pricing on Ontario’s Highway 407 ETR (Electronic Toll Road) and I co-authored a book about its construction, tolling, and privatization.

The Geometry of Optimality

With the help of a recent AI-assisted search, I began to realize that my 1984 paper bore a family resemblance to other scholars’ papers, starting in the mid-Eighties, that dealt with topics such as flat maxima, near-optimality, satisficing, and robust policy. They were making the same point as me, namely that there exists a wide range of policy options that, although not optimal, are acceptable. After sampling some of these literatures, I think my paper is still unique in its use of three-dimensional computer-generated geometry. If I had continued that line of research, I would have explored the geometry of the welfare surfaces in more detail. This might have involved using less complicated empirical models to generate the welfare surfaces. I could then have focused more attention on the factors generating the shape of the welfare surfaces. Also, simpler models would have required less computing power. Perhaps I could have developed demand and cost models and decision criteria that would have generated welfare surfaces that looked like the Matterhorn. Then I could have evaluated the different models in terms of their resemblance to the real world.

Exploring the geography of economic optimality was the intellectual road I didn’t travel. It might have carried me to a prominent place among academic economists. Rereading the paper, I see a measure of beauty in the algebra I worked out and the geometry my computer program produced, and I am satisfied.