Bernoulli and Poisson are in a bar …

Bernoulli asks, “how long have we been here?” Poisson replies, “I have no idea.”

Bad joke aside, memoryless behavior is a key component of a toy model of car rentals I made a while ago. I recently noticed that I was a bit lazy in my choice of RANDOM functions, so I’ve produced an update.

The difference is in the use of Poisson and Binomial distribution functions. In the original, I used the Poisson distribution everywhere to represent arrival processes. That’s reasonable in the limit, where a large number of candidate arrivals are realized with a small probability, such that the expected arrivals occur at some finite rate.

Think of a lemonade stand on a busy street – there’s a very large population of potential lemonade buyers, but only a small fraction actually stop for a drink. Normally, we don’t want to model the street and the traffic generation process, so it’s reasonable to assume independent arrivals from a large pool at some rate that we can measure, using the Poisson distribution. This is similar to using a cloud in SD to indicate a source or sink that we aren’t modeling. Continue reading “Bernoulli and Poisson are in a bar …”

ICE Roadkill

Several countries have now announced eventual bans of internal combustion engines. It’s nice that such a thing can now be contemplated, but this strikes me as a fundamentally flawed approach.

Banning a whole technology class outright is inefficient. When push comes to shove, that inefficiency is likely to lead to an implementation that’s complex and laden with exceptions. Bans and standards are better than nothing, but that regulatory complexity gives opponents something real to whine about. Then the loonies come out. At any plausible corporate cost of capital, a ban in 2040 has near-zero economic weight today.

Rather than banning gas and diesel vehicles at some abstract date in the far future, we should be pricing their externalities now. Air and water pollution, noise, resource extraction, the opportunity cost of space for roads and parking, and a dozen other free rides are good candidates. And, electric vehicles should not be immune to the same charges where applicable.

Once the basic price signal points the transportation market in the right direction, we can see what happens, and tinker around the edges with standards that address particular misperceptions and market failures.

A conversation about infrastructure

A conversation about infrastructure, with Carter Williams of iSelect and me:

The $3 Trillion Problem: Solving America’s Infrastructure Crisis

I can’t believe I forgot to mention one of the most obvious System Dynamics insights about infrastructure:

There are two ways to fill a leaky bucket – increase the inflow, or plug the outflows. There’s always lots of enthusiasm for increasing the inflow by building new stuff. But there’s little sense in adding to the infrastructure stock if you can’t maintain what you have. So, plug the leaks first, and get into a proactive maintenance mode. Then you can have fun building new things – if you can afford it.

A Titanic feedback reversal

Ever get in a hotel shower and turn the faucet the wrong way, getting scalded or frozen as a result? It doesn’t help when the faucet is unmarked or backwards. If a new account is correct, that’s what happened to the Titanic.

(Reuters) – The Titanic hit an iceberg in 1912 because of a basic steering error, and only sank as fast as it did because an official persuaded the captain to continue sailing, an author said in an interview published on Wednesday.

“They could easily have avoided the iceberg if it wasn’t for the blunder,” Patten told the Daily Telegraph.

“Instead of steering Titanic safely round to the left of the iceberg, once it had been spotted dead ahead, the steersman, Robert Hitchins, had panicked and turned it the wrong way.”

Patten, who made the revelations to coincide with the publication of her new novel “Good as Gold” into which her account of events are woven, said that the conversion from sail ships to steam meant there were two different steering systems.

Crucially, one system meant turning the wheel one way and the other in completely the opposite direction.

Once the mistake had been made, Patten added, “they only had four minutes to change course and by the time (first officer William) Murdoch spotted Hitchins’ mistake and then tried to rectify it, it was too late.”

It sounds like the steering layout violates most of Norman’s design principles (summarized here):

  1. Use both knowledge in the world and knowledge in the head.
  2. Simplify the structure of tasks.
  3. Make things visible: bridge the Gulfs of Execution and Evaluation.
  4. Get the mappings right.
  5. Exploit the power of constraints, both natural and artificial.
  6. Design for error.
  7. When all else fails, standardize.

Notice that these are really all about providing appropriate feedback, mental models, and robustness.

(This is a repost from Sep. 22, 2010, for the 100 year anniversary).

Fuel economy makeover

The EPA is working on new fuel economy window stickers for cars (you can vote on alternatives). I like this one:

New Fuel Econ Sticker
hoisted from the comments at jalopnik

There are some things to like about the possible new version. For example, it indicates fuel economy on an absolute scale, so that there’s no implicit allocation of pollution rights to bigger vehicles (unlike Energy Star and the CAFE standard):

New Fuel Econ ScaleSince the new stickers will indicate fueling costs, emissions taxes on fuels will be a nice complementary policy, as they’ll be more evident on the dealer lot.

When rebates go bad


There’s a long-standing argument over the extent to which rebound effects eat up the gains of energy-conserving technologies, and whether energy conservation programs are efficient. I don’t generally side with the hardline economists who argue that conservation programs fail a cost benefit test, because I think there really are some $20 bills scattered about, waiting to be harvested by an intelligent mix of information and incentives. At the same time, some rebate and credit programs look pretty fishy to me.

On the plus side, I just bought a new refrigerator, using Montana’s $100 stimulus credit. There’s no rebound, because I have to hand over the old one for recycling. There is some rebound potential in general, because I could have used the $100 to upgrade to a larger model. Energy Star segments the market, so a big side-by-side fridge can pass while consuming more energy than a little top-freezer. That’s just stupid. Fortunately, most people have space constraints, so the short run price elasticity of fridge size is low.

On the minus side, consider tax credits for hybrid vehicles. For a super-efficient Prius or Insight, I can sort of see the point. But a $2600 credit for a Toyota Highlander getting 26mpg? What a joke! Mercifully that foolishness has been phased out. But there’s plenty more where that came from.

Consider this Bad Boy:


The Zero-Emission Agricultural Utility Terrain Vehicle (Agricultural UTV) Rebate Program will credit $1950 in the hope of fostering greener farms. But this firm knows who it’s really marketing to:


Is there really good control over the use of the $, or is public funding just mechanizing outdoor activities where people ought to use the original low-emissions vehicle, their feet? When will I get a rebate for my horse?

The real Kerry-Lieberman APA stands up, with two big surprises

The official discussion draft of the Kerry-Lieberman American Power Act is out. My heart sank when I saw the page count – 987. I won’t be able to review this in any detail soon. Based on a quick look, I see two potentially huge items: the “hard price collar” has a soft ceiling, and transport fuels are in the market, despite claims to the contrary.

Hard is soft

First, the summary states that there’s a “hard price collar which binds carbon prices and creates a predictable system for carbon prices to rise at a fixed rate over inflation.” That’s not quite right. There is indeed a floor, set by an auction reserve price in Section 790. However, I can’t find a ceiling as such. Instead, Section 726 establishes a “Cost Containment Reserve” that is somewhat like the Waxman-Markey strategic reserve, without the roach motel moving average price (offsets check in, but they don’t check out). Instead, reserve allowances are available at the escalating ceiling price ($25 + 5%/yr). There’s a much larger initial reserve (4 gigatons) and I think a more generous topping off (1.5% of allowances each year initially; 5% after 2030). However, there appears to be no mechanism to provide allowances beyond the set-aside. That means that the economy-wide target is in fact binding. If demand eats up the reserve allowance buffer, prices will have to rise above the ceiling in order to clear the market. So, the market actually faces a hard target, with the reserve/ceiling mechanism merely creating a temporary respite from price spikes. The price ceiling is soft if allowance demand at the ceiling price is sufficient to exhaust the buffer. The mental model behind this design must be that estimated future emission prices are about right, so that one need only protect against short term volatility. However, if those estimates are systematically wrong, and the marginal cost of mitigation persistently exceeds the ceiling, the reserve provides no protection against price escalation.

Transport is in the market

The short transport summary asserts:

Since a robust domestic refining industry is critical to our national security, we needed to make a change. We took fuel providers out of the market. Instead of every refinery participating in the market for allowances, we made sure the price of carbon was constant across the industry. That means all fuel providers see the same price of carbon in a given quarter. The system is simple. First, the EPA and EIA Administrators look to historic product sales to estimate how many allowances will be necessary to cover emissions for the quarter, and they set that number of allowances aside at the market price. Then refineries and fuel providers sell fuel, competing as they have always done to offer the best product at the best price. Finally, at the end of the quarter, the refiners and fuel providers purchase the allowances that have been set aside for them. If there are too many or too few allowances set aside, that difference is made up by adjusting the projection for the following quarter. These allowances cannot be banked or traded, and can only be used for compliance purposes.

In fact, transport is in the market, just via a different mechanism. Instead of buying allowances realtime, with banking and borrowing, refiners are price takers and get allowances via a set-aside mechanism. Since there’s nothing about the mechanism that creates allowances, the market still has to clear. The mechanism simply introduces a one quarter delay into the market clearing process. I don’t see how this additional complication is any better for refiners. Introducing the delay into the negative feedback loops that clear the market could be destabilizing. This is so enticing, I’ll have to simulate it.

My analysis is a bit hasty here, so I could be wrong, but if I’m right these two issues have huge implications for the performance of the bill.


Like spreadsheets, open-loop models are popular but flawed tools. An open loop model is essentially a scenario-specification tool. It translates user input into outcomes, without any intervening dynamics. These are common in public discourse. An example turned up in the very first link when I googled “regional growth forecast”:

The growth forecast is completed in two stages. During the first stage SANDAG staff produces a forecast for the entire San Diego region, called the regionwide forecast. This regionwide forecast does not include any land use constraints, but simply projects growth based on existing demographic and economic trends such as fertility rates, mortality rates, domestic migration, international migration, and economic prosperity.

In other words, there’s unidirectional causality from inputs  to outputs, ignoring the possible effects of the outputs (like prosperity) on the inputs (like migration). Sometimes such scenarios are useful as a starting point for thinking about a problem. However, with no estimate of the likelihood of realization of such a scenario, no understanding of the feedback that would determine the outcome, and no guidance about policy levers that could be used to shape the future, such forecasts won’t get you very far (but they might get you pretty deep – in trouble).

The key question for any policy, is “how do you get there from here?” Models can help answer such questions. In California, one key part of the low-carbon fuel standard (LCFS) analysis was VISION-CA. I wondered what was in it, so I took it apart to see. The short answer is that it’s an open-loop model that demonstrates a physically-feasible path to compliance, but leaves the user wondering what combination of vehicle and fuel prices and other incentives would actually get consumers and producers to take that path.

First, it’s laudable that the model is publicly available for critique, and includes macros that permit replication of key results. That puts it ahead of most analyses right away. Unfortunately, it’s a spreadsheet, which makes it tough to know what’s going on inside.

I translated some of the model core to Vensim for clarity. Here’s the structure:


Bringing the structure into the light reveals that it’s basically a causal tree – from vehicle sales, fuel efficiency, fuel shares, and fuel intensity to emissions. There is one pair of minor feedback loops, concerning the aging of the fleet and vehicle losses. So, this is a vehicle accounting tool that can tell you the consequences of a particular pattern of new vehicle and fuel sales. That’s already a lot of useful information. In particular, it enforces some reality on scenarios, because it imposes the fleet turnover constraint, which imposes a delay in implementation from the time it takes for the vehicle capital stock to adjust. No overnight miracles allowed.

What it doesn’t tell you is whether a particular measure, like an LCFS, can achieve the desired fleet and fuel trajectory with plausible prices and other conditions. It also can’t help you to decide whether an LCFS, emissions tax, or performance mandate is the better policy. That’s because there’s no consumer choice linking vehicle and fuel cost and performance, consumer knowledge, supplier portfolios, and technology to fuel and vehicle sales. Since equilibrium analysis suggests that there could be problems for the LCFS, and disequilibrium generally makes things harder rather than easier, those omissions are problematic.

Continue reading “Fuzzy VISION”

LCFS in Equilibrium II

My last post introduced some observations from simulation of an equilibrium fuel portfolio standard model:

  • knife-edge behavior of market volume of alternative fuels as you approach compliance limits (discussed last year): as the required portfolio performance approaches the performance of the best component options, demand for those approaches 100% of volume rapidly.
  • differences in the competitive landscape for technology providers, when compared to alternatives like a carbon tax.
  • differences in behavior under uncertainty.
  • perverse behavior when the elasticity of substitution among fuels is low

Here are some of the details. First, the model:


Notice that this is not a normal SD model – there are loops but no stocks. That’s because this is a system of simultaneous equations solved in equilibrium. The Vensim FIND ZERO function is used to find a vector of prices (one for each fuel, plus the shadow price of emissions intensity) that matches supply and demand, subject to the intensity constraint.

Continue reading “LCFS in Equilibrium II”