Monthly Archives: March 2016

On Public Infrastructure Investment

There are two popular narratives about our infrastructure in the United States. The first is that our infrastructure is crumbling. The second is that our infrastructure spending is allocated based on its political value rather than its economic value. Maybe you believe one of these stories. Maybe you believe both. Maybe you believe neither. Regardless, these narratives are indicative of two important questions. How can we efficiently manage our public infrastructure? And how can we ensure that infrastructure investment isn’t used as a political tool? I have a new paper that proposes an answer to both questions. My proposal is to create a rule of law for public infrastructure based on option values. This rule of law would ensure that infrastructure is maintained efficiently and also that politicians would not be able to use infrastructure spending as a political tool.

The standard way to evaluate public infrastructure projects is to figure out the benefits of the infrastructure over its entire lifespan and then compute the present value of those benefits. Then you do the same thing with the costs. When you subtract the present value of the costs from the present value of the benefits you get something call a net present value. Infrastructure investments are evaluated using a positive net present value criterion. In other words, as long as the present discounted value of the benefits exceeds the present discounted value of the costs the project is desirable.

In theory the net present value approach seems like a good idea. Of course we would want the benefits to outweigh the costs. This approach, however, is much different than how a private firm would value their assets. A firm that owns a factory knows that the factory can eventually become outdated. To the firm the value of the factory is the sum of two components. The first component is the value of the factory to the firm if the firm never shuts down the factory or builds a new one. The second component is the value of the option to build a new factory or add to the current factory’s capacity in the future.

The same general concept is true of public infrastructure investment. The value of any existing infrastructure is the value of the infrastructure over its entire lifetime plus the option value of replacing that infrastructure in the future. This option value is associated with a tradeoff. Since infrastructure depreciates over time, the value from existing infrastructure is declining. This means that as time goes by, the opportunity cost of replacing the infrastructure declines and therefore the option value of replacing the infrastructure rises. However, the longer the government waits to replace the infrastructure, the longer society has to wait to receive the benefit of replacement. This reduces the option value. My proposal suggests that the government should choose the value of the current infrastructure that optimally balances this tradeoff. What this ultimately implies is that the government should wait until the value of the current infrastructure is some fraction of the net present value of the proposed replacement project.

The reason that this option approach is preferable to the net present value approach is as follows. First, even though a current project has a positive net present value, this does not necessarily imply that now is the optimal time to undertake the project. Replacing infrastructure entails an opportunity cost associated with the foregone benefit that society would have received from the existing infrastructure. In other words, society might get greater value from the project if the government chooses to wait a little longer before replacing what is currently there. Second, my approach provides a precise moment at which it is optimal to replace the infrastructure. In contrast, the net present value approach says nothing about optimality; it’s simply a cost-benefit analysis. Given the possibility that society could get an even larger benefit in the future, the option approach should be strictly preferred. Third, the option approach provides an explicit way for the government to maintain an infrastructure fund. In my paper I provide a simple formula for computing the amount of money that needs to be in the fund. This formula is simple; it only needs to take into account the cost of each project and the relative distance that project is from its replacement threshold. This sort of fund is important because it would also allow the government to continue funding infrastructure projects at the optimal time even during a recession when infrastructure budgets, especially at the local level, are often cut.

The final and most significant benefit of my approach, however, is that it would provide the means for establishing a rule of law for public infrastructure projects. This rule of law should appeal to people across the ideological spectrum. I say that for the following reasons. First, if the government adopted this option value approach as a rule of law, this would require that the government fund any and all infrastructure projects that had reached their replacement thresholds. This would ensure that the infrastructure in the United States was maintained efficiently. Second, because the only projects that would receive funding would be those that had reached the replacement threshold, politicians would not be able to use infrastructure spending as a tool for reelection or repayment to supporters. As a result, the option approach would provide the means for a rule of law for infrastructure investment that is both transparent and efficient.

Establishing such a rule of law would be difficult. The same politicians that benefit from allocating infrastructure investment for political reasons would be the same ones who would have to vote on the legislation to enact this new rule. Nonetheless, there is evidence that politicians vote in favor of infrastructure projects that benefit their constituents, but vote against aggregate investment. If the group of politicians that benefit most from this state of affairs is small, then the legislation might be easier to pass. In addition, there is nothing to stop departments of transportation at both the state and federal level from calculating option value and making the data available to the public. This greater transparency, while not a rule of law, would at least be a step in the direction of a more efficient management of our public infrastructure.

The Importance of Safe Assets

A theme you often hear among bloggers, but a bit less so in seminars, is the idea that the supply of and demand for safe assets matter. David Beckworth is one such blogger who talks about this, but critics often find it hard to think about the macroeconomy in these terms since the role of money has been marginalized within the New Keynesian wing of macroeconomics. I say this because David’s intuitive explanation of safe asset equilibrium seems to be a cross between New Keynesian intuition and Old Monetarist intuition. He is trying to communicate his message to what is essentially the mainstream of the discipline, but by emphasizing something that isn’t generally in their models.

Along these lines, I was happy to stumble upon this paper by Caballero, Farhi, and Gourinchas. In my view this paper is quite similar to David’s views regarding safe assets and monetary policy and so I thought it might be interesting to outline the basic model in the paper and talk about the mechanisms for monetary policy.

The model is a modified version of an IS-LM model. The one modification to the model is a supply and demand condition for safe assets. Formally, the model consists of the following three equations:

$y - \bar{y} = -\delta (r - \bar{r}) - \delta_s (r^s - \bar{r}^s)$
$r^s = \max[\hat{r}^s + \phi(y - \bar{y}), 0]$
$s = \psi_y y + \psi_s r^s - \psi_{\Delta} (r - r^s)$

where $y$ is output, $r$ is the risky interest rate, $r^s$ is the rate on safe assets, $\hat{r}^s$ is the target interest rate, $s$ is the supply of safe assets, $\bar{y}$ is the natural rate of output, $\bar{r}$ is the natural risky interest rate, and $\bar{r}^s$ is the natural safe interest rate, and the greek letters are parameters. Inflation is assumed to be zero such that there is no difference between real and nominal interest rates.

This framework is a familiar IS-LM framework with the first equation is an IS equation, the second equation is a Taylor Rule subject to a zero lower bound, and the third equation determines the safe asset equilibrium.

The best interpretation of the safe asset equilibrium, as they describe it in the paper, is in terms of the flow of safe assets. According to this view, the flow demand for safe assets is a function of output, the rate of return on safe assets, and the risk premium ($r - r^s$). Thus the supply of safe assets, in this interpretation, is the net increase in the supply of safe assets.

Given that setup, let’s see what the model can tell us.

The first assumption that they make is that the supply of safe assets is unresponsive to the risk premium. In other words, in terms of the model, $\psi_{\Delta} = 0$. Given that many safe assets are exogenously supplied, this seems like a reasonable assumption.

Now, let’s think about the determination of the natural rate of interest. If the central bank sets the interest rate on safe assets equal to the natural rate, then output will be equal to potential (essentially by definition). It then follows from the IS equation that the risky interest rate is also equal to the natural risky interest rate. But how does one determine the natural interest rate?

Consider the equilibrium condition for safe assets. The interest rate on safe assets is the rate that exists when output is equal to potential. From the safe asset equilibrium condition it follows that

$\bar{r}^s = {{s - \psi_y \bar{y}}\over{\psi_s}}$

The central bank then needs to set $r^s = \hat{r}^s = \bar{r}^s$.

However, suppose that the net increase in the supply of safe assets is not high enough to keep up with the demand for new safe assets. In particular, suppose that the net increase in the supply of safe assets is so low that

$s < \psi_y \bar{y}$

In this scenario, the natural interest rate would be negative. However, from the Taylor rule, the market rate of interest is subject to a zero lower bound. As a result, the central bank cannot set the interest rate low enough to clear the market for safe assets. So what happens? Well, the central bank sets the safe interest rate as low as it can go $r^s = 0$. Which implies that output is pinned down by the net increase in the supply of safe assets:

$y = {{s}\over{\psi_y}}$

It then follows that $r > \bar{r}$. In other words, the risky interest rate is “too high” and the risk premium rises. But since the risky rate of interest is higher than the natural risky rate, the IS equation implies that output must fall in order to reduce the demand for safe assets and restore equilibrium.

The policy implication is that to escape this scenario, one needs to increase the supply of safe assets. By increasing the supply of safe assets, this increases output toward potential and thereby reduces the risk premium.

As the authors note, early attempts at quantitative easing in the United States did exactly what the model would prescribe because they swapped the risky assets in the market for safe assets. Fiscal stimulus can also help, but not through any sort of production done by the public sector, but because it increases the supply of safe assets (Treasuries).