Notes on time: economics, discounting, innovation, etc.

I’m fascinated with time, the history of wrist watches, how the clock made the modern world, how our modern months and days got their names, the concept of time keeping, the psychology of time, time’s importance in economics, discounting, and so on.

These are my collected notes on time. 

Time, discounting, and time preferences

A common theme in the behavioral economic literature is that individuals make irrational decisions. One of the most well known of these tendencies is called hyperbolic discounting. 

Hyperbolic discounting seems like a fancy term, but it merely means that a person will prefer smaller, more immediate rewards rather than larger rewards in the future. As the theory goes, people should discount in a linear fashion but instead they have a tradeoff function that looks like a hyperbola curve. Sometimes this notion is called present bias. Within the tech and privacy space, this phenomenon is typically called “benefit immediacy.”

What’s interesting is that humans aren’t the only ones who do this. Lots of other animals exhibit time preferences that are approximately hyperbolic. Mazur (1987) was among the first to find this tendency in other animals in an experiment with pigeons but the tendency has since been replicated elsewhere. 

So why is it that the animal kingdom broadly violates these “rules” of rationality? Why is it that humans do it as well? It’s because the models of rationality aren’t carefully considering how the likelihood of an event happening is actually experienced. This likelihood, also known as the hazard rate, is typically understood to be known by the person. But that’s not right because the real world is uncertain.   

P. D. Sozou’s paper titled “On hyperbolic discounting and uncertain hazard rates” (1998) was incredibly refreshing when I read it because it all just clicked. The abstract explains the intuition, which is honestly very simple:  

If the risk manifests itself at a known, constant hazard rate, a risk-neutral recipient should discount the reward according to an exponential time-preference function. Experimental subjects, however, exhibit short-term time preferences that differ from the exponential in a manner consistent with a hazard rate that falls with increasing delay. It is shown here that this phenomenon can be explained by uncertainty in the underlying hazard. 

In other words, when the hazard rate changes, risk preferences change. While this research is still in its infancy, it is exceptionally promising in helping to explain a bunch of supposed anomalies.

For example Enke, Graeber, and Oprea (2023) note that 

We provide experimental evidence that core intertemporal choice anomalies – including extreme short-run impatience, structural estimates of present bias, hyperbolicity and transitivity violations – are driven by complexity rather than time or risk preferences. First, all anomalies also arise in structurally similar atemporal decision problems involving valuation of iteratively discounted (but immediately paid) rewards. These computational errors are strongly predictive of intertemporal decisions. Second, intertemporal choice anomalies are highly correlated with indices of complexity responses including cognitive uncertainty and choice inconsistency. We show that model misspecification resulting from ignoring behavioral responses to complexity severely inflates structural estimates of present bias.

Epper and Fehr-Duda explain in “Risk in Time: The Intertwined Nature of Risk Taking and Time Discounting” that, 

Standard economic models view risk taking and time discounting as two independent dimensions of decision making. However, mounting experimental evidence demonstrates striking parallels in patterns of risk taking and time discounting behavior and systematic interaction effects, which suggests that there may be common underlying forces driving these interactions. Here, we show that the inherent uncertainty associated with future prospects together with individuals’ proneness to probability weighting generates a unifying framework for explaining a large number of puzzling behavioral findings: delay-dependent risk tolerance, aversion to sequential resolution of uncertainty, preferences for the timing of the resolution of uncertainty, the differential discounting of risky and certain outcomes, hyperbolic discounting, subadditive discounting, and the order dependence of prospect valuation. Furthermore, all these phenomena can be accommodated by the same set of preference parameter values and plausible levels of inherent uncertainty.

And in “Cognitive Uncertainty in Intertemporal Choice,” Enke and Graeber find that, 

By experimentally measuring and manipulating cognitive uncertainty, we document three economic implications of this idea. First, cognitive uncertainty explains various core empirical regularities, such as why people often appear very impatient, why per-period impatience is smaller over long than over short horizons, why discounting is often hyperbolic even when the present is not involved, and why choices frequently violate transitivity. Second, impatience is context-dependent: discounting is substantially more hyperbolic when the decision environment is more complex. Third, cognitive uncertainty matters for choice architecture: people who are nervous about making mistakes are twice as likely to follow expert advice to be more patient. 

Time value of innovation

I have written on the topic of time and innovation before in “Today’s one dollar delay is worth \$39 billion in the future, some comments on Cowen’s Stubborn Attachments.” Here is the setup:

Chapter 4 of Tyler Cowen’s Stubborn Attachments has long stuck with me, but it has always left me wanting for more. The chapter is all about the moral distance of time, which is brought into sharp focus through the lens of the discount rate.

Discount rates come from finance as a means of estimating the current value of a future project, what’s known in the biz as a net present value (NPV) calculation. The logic is simple, but powerful. Given that a company can put cash into the market or their own internal projects for a return, the discount rate becomes the opportunity cost of investing in the project rather than in capital markets. Discount rates allow for values to be compared across time.  

In turn, net present values are highly sensitive to discount rates. The value that is placed on a project at some point in the future but in today’s dollars, depends on how we understand the future. A high discount rate translates into a lower present value for the sum of the future cash flows. Lower discount rates flip the logic such that projects are valued much more in the future. 

As I explained, 

One dollar today at a 5 percent discount rate is worth \$131.5 in a hundred years’ time and \$39 billion in five hundred years into the future. 

Next let’s tweak the assumptions ever so slightly and think about not getting paid a dollar this year. Since costs are merely negative benefits, that one-dollar delay today comes to a loss of $131.5 in a hundred years time and \$39 billion in five hundred years. 

Today’s one-dollar delay is worth \$39 billion in the future.

The world is full of one-dollar delays. Life-saving drugs have to go through lengthy approval processes here in the States, even if they are allowed in the EU. Until late last year, drones couldn’t be flown past the line of sight of their operator, limiting the scope of operation. The one-dollar delay is also encapsulated in that adage, “The best time to plant a tree was 20 years ago. The second best time is now.” 

Innovation and startup culture is built on the one-dollar delay. To me, that’s what is exciting about tech and innovation, and what isn’t understood about Silicon Valley and startup cultures. In explaining “Why the Canadian Tech Scene Doesn’t Work,” Alex Danco made this exact point:

Startups are a bet that the future will be radically different from the present, and they are valuable on the way up because they are, effectively, a call option on that future coming true. Their founders set out to discover that future; their value is indefinite, not definite. One day they might become giant, cash-gushing businesses; but not anywhere near your current horizon. Your only goal right now is grow, explore, and earn the right to keep growing and exploring.

There is a time value to innovation, which I explained here:

Economists Kenneth Arrow and Anthony Fisher formalized the idea in a 1974 paper that showed risk-neutral societies should favor precaution since it allows for more flexibility in the decision space in the future. But there is one significant caveat to this line of logic that was critically added by Avinash Dixit and Robert Pindyck in 1994: Being risk-neutral in the decision space can come at the expense of potential returns, since not making a decision has a cost, after all. The same logic applies to innovation. There is a clear time value to innovation that often isn’t properly accounted for with treatments of the precautionary principle. There is an opportunity cost embedded in the precautionary principle.  

Other interesting papers and research:

  • Individuals who heavily discount future time investments are more likely to become entrepreneurs.
  • There are benefits to being future focused. Experimental work has shown that it promotes generosity. 
  • “Long Term Bias” by Michal Barzuza and Eric L. Talley; Abstract: “An emerging consensus in certain legal, business, and scholarly communities maintains that corporate managers are pressured unduly into chasing shortterm gains at the expense of superior long-term prospects. The forces inducing managerial myopia are easy to spot, typically embodied by activist hedge funds and Wall Street gadflies with outsized appetites for next quarter’s earnings. Warnings about the dangers of “short termism” have become so well established, in fact, that they are now driving changes to mainstream practice, as courts, regulators and practitioners fashion legal and transactional constraints designed to insulate firms and managers from the influence of investor short-termism. This Article draws on academic research and a series of case studies to advance the thesis that the emergent folk wisdom about short-termism is incomplete. A growing literature in behavioral finance and psychology now provides sound reasons to conclude that corporate managers often fall prey to long-term bias—excessive optimism about their own long-term projects. We illustrate several plausible instantiations of such biases using case studies from three prominent companies where managers have arguably succumbed to a form of “long-termism” in their own corporate stewardship. Unchecked, long-termism can impose substantial costs on investors that are every bit as damaging as short-termism. Moreover, we argue that long-term managerial bias sheds considerable light on the paradox of why short-termism evidently persists among supposedly sophisticated financial market participants: Shareholder activism—even if unambiguously myopic—can provide a symbiotic counter-ballast against managerial long-termism. Without a more definitive understanding of the interaction between short- and long-term biases, then, policymakers should be cautious about embracing reforms that focus solely on half of the problem.”

Economics and time

The table below charts a high and low estimate of average hours worked using data provided by the Economic History Association. Admittedly, data from the early 20th century does pose problems, but the trend is clear. Keynes wrote the essay in 1928 and U.S. estimates from next year suggested that workers were putting in 48 to 51 hours weekly. In 1988 that had dropped to around 39 hours per week. Currently, the BLS estimates that the average weekly hours worked is 34.7.

Back out the data into the 1800s and the trend comes into sharp focus.

Again, data from the 1800s has its issues, which are detailed here, but the economics profession has generally agreed upon this sharp decline.

Other interesting papers and research:

  • “Cheap Thrills: the Price of Leisure and the Global Decline in Work Hours” Kopytov, Roussanov & Taschereau-Dumouchel (2021). Abstract: “Recreation prices and hours worked have both fallen over the last century. We construct a macroeconomic model with general preferences that allows for trending recreation prices, wages, and work hours along a balanced-growth path. Estimating the model using aggregate data from OECD countries, we find that the fall in recreation prices can explain a large fraction of the decline in hours. We also use our model to show that the diverging prices of the recreation bundles consumed by different demographic groups can account for much of the increase in leisure inequality observed in the United States over the last decades.”
  • “The Rising Value of Time and the Origin of Urban Gentrification” Su (2022). Abstract: “In recent decades, gentrification has transformed American central city neighborhoods. I estimate a spatial equilibrium model to show that the rising value of high-skilled workers' time contributes to the gentrification of American central cities. I show that the increasing value of time raises the cost of commuting and exogenously increases the demand for central locations by high-skilled workers. While change in the value of time has a modest direct effect on gentrification of central cities, the effect is substantially magnified by endogenous amenity change driven by the changes in local skill mix.” [AEJ]
  • “Why Do Americans Work so Much More than Europeans?” Prescott (2004). Abstract: “Americans now work 50 percent more than do the Germans, French, and Italians. This was not the case in the early 1970s when the Western Europeans worked more than Americans. In this paper, I examine the role of taxes in accounting for the differences in labor supply across time and across countries, in particular, the effect of the marginal tax rate on labor income. The population of countries considered is that of the G-7 countries, which are the major advanced industrial countries. The surprising finding is that this marginal tax rate accounts for the predominance of the differences at points in time and the large change in relative labor supply over time with the exception of the Italian labor supply in the early 1970s. This finding has important implications for policy, in particular for making social security programs solvent.”
  • “Examining inequality in the time cost of waiting” Holt & Vinopal (2023). Abstract: “Time spent waiting for services represents unproductive time lost while fulfilling needs. We use time diary data from the nationally representative American Time Use Survey to estimate the difference between high- and low-income people in time spent waiting for basic services. Relative to high-income people, low-income people are one percentage point more likely to wait on an average day, are three percentage points more likely to wait when using services, spend an additional minute waiting for services on a typical day and spend 12 more minutes waiting when waiting occurs. The unconditional gap in waiting time suggests low-income people spend at least six more hours per year waiting for services than high-income people. The income gap in waiting time cannot be explained by differences in family obligations, demographics, education, work time or travel time. Further, high-income Black people experience the same higher average wait times as low-income people regardless of race.”
  • “Time Discounting and Wealth Inequality” Epper, Fehr, Fehr-Duda, Kreiner, Lassen, Leth-Petersen, & Rasmussen (2020). Abstract: “The distribution of wealth in society is very unequal and has important economic and political consequences. According to standard life-cycle savings theory, differences in time discounting behavior across individuals can play an important role for their position in the wealth distribution. Empirical testing of this hypothesis has been difficult because of serious data limitations. We overcome these limitations by linking an experimental measure of time discounting for a large sample of middle-aged individuals to Danish high-quality administrative data with information about their real-life wealth over the life-cycle as well as a large number of background characteristics. The results show that individuals with relatively low time discounting are persistently positioned higher in the wealth distribution. The relationship is of the same magnitude as the association between years of education and the position in the wealth distribution, and it robustly persists after controlling for a large number of theoretically motivated confounders such as education, risk aversion, school grades, income, credit constraints, initial wealth, and parental wealth. These findings support the view that individual differences in time discounting affect individuals’ positions in the wealth distribution through the savings channel.”

Is time is speeding up?

  • “The definite probability that the allotment of time to decision-making is undergoing systematic compression remains a neglected consideration, even among those paying explicit and exceptional attention to the increasing rapidity of change.” — Nick Land (link) 
  • Record labels’ study shows performances of Bach are almost 30 percent faster than they were 50 years ago. [Rolling Stone]
  • According to Underwood et al. (2018), the average span of time covered in typical passages has decreased significantly since the 1700s, shrinking from a day to roughly an hour, which represents a 24-fold reduction. Authors now place greater emphasis on individual experiences rather than broader events.

Hard philosophy and time

A former colleague of mine studied the philosophy of time. Here are some of his suggested readings for the hard philosophy of time:

Rhetoric and communication of time

Linguists will notice right away the importance of these categories, often described as deixis. Deixis are those words that provide context about a person’s position in relation to her world, the people, and objects in it. Personal deixis locates some other entity in relation to the speaker, like he, she, and it. Spatial deixis locates the context of the speech within space. The typical example of spatial deixis includes this, that, or there. Lastly, temporal deixis localises some utterance within time, for example, whenever we use the term now or then or afterward. Clearly, these terms help to provide context to what we say. If you want to do a deeper dive on the topic, check out Indiana University’s Professor Mike Gasser’s review. Since language is embodied, the categories of deixis provide grounding to our communication.

Walter Benjamin’s messianic time v homogenous time dichotomy:

  • Homogeneous empty time is quantitative; messianic time is qualitative. Homogeneous empty time is a continuous flow; messianic time is fully immediate. Homogeneous empty time is experienced as anaesthetising, desensitising and meaningless. Messianic time is experienced as emotionally intense, like a drug high. It is filled or fulfilled. Homogeneous empty time is continuous; messianic time is ruptural. Homogeneous empty time is meaningless (empty); messianic time is the time of a ‘specific recognisability’ - it means something specific to those who experience it.