The Problem With The Pure Time Preference Theory Of Interest

06 Dec 2023

Pure time preference theory has a fatal flaw. The flaw is that it argues people always commit to decisions in the present with perfect knowledge about the future.

Homo oeconomicus agents not only have to be perfectly rational, they also need premonition, otherwise optimality is not guaranteed. Homo oeconomicus clearly is a super human agent, one that would have to be created artificially, through genetic engineering or through cybernetic prostheses or simulated as an artificial intelligence.

What if we relax the constraint and let homo oeconomicus make decisions with imperfect information? Given perfect information I and an incomplete subset of that information \(D_0\) which is available at the time \(t_0\). Then if a decision spanning \([t_1, t_2]\) is made at \(t_0\), the additional information \(D_t\) may arrive at any point between \(t_1 \leq t \leq t_2\). This means that a rational agent that commits to the decision dictated by \(D_0\) for the whole period \([t_1, t_2]\), may end up performing worse than a rational agent that commits to a shorter period of time such as \([t_1, (t_1+t_2)/2]\).

Now, you may object to this argument and say that a rational agent will simply adjust his own time preference to account for uncertainty, but then the time preference theory becomes completely meaningless at that point, because the core argument behind time preference theory is that tradeoffs between points in time are purely the result of patience or impatience. If time preference includes an uncertainty adjustment, what else does it contain? Possibly everything.

There is a difference between wanting the ability to decide between two options, which can include the ability to choose at any time in-between two points in time and a cold hard tradeoff between two points in time. These things look very similar, but they aren’t!

Pure time preference theory is ridiculous

Let us assume that you have to make decisions for the time periods \(t_0\), \(t_1\), \(t_2\), \(t_3\), \(t_4\). You now have the option of consuming during the time period \(t_0\) or to save and consume at a later time period. As your goal is the maximization of utility, you proudly proclaim: “Wow, so all I have to do is optimize the objective function \(\sum_{i=0}^{4} u(t_i, c_i)\) where \(u\) is the utility function taking in the time period and my consumption spending at that time point. Every time period I can decide whether to consume all my income as \(c_i\), or save money as \(s_i\) and make it available in a future period. Easy!”. As you can see, there is a problem here. You might argue that this is an easy optimization problem, because it doesn’t necessarily have to be NP-hard. You can optimize \(t_0\) first, then \(t_1\), and so on, because all you have to do is decide how much money to keep left over in \(t_0\), then \(t_1\), then \(t_2\). Except, for you to know how much money to keep left over in \(t_0\), you would need to know how much utility you derive from that money in the future. This makes the present dependent on the future. Essentially what you are doing is the following: The moment you are born and you are faced with having to make the first decision of your life, you have also made the last decision of your life, that is, you have created the perfect and ultimate life plan that you will live out for the rest of your life. Beyond that moment, beyond that point in time, you are no longer making any decisions anymore. Instead, you are just living out the perfect decisions you made as an infant on your first day on this planet. This is the perfect breeding ground for the just world fallacy. People aren’t poor by circumstances, they made the voluntary decision to become and stay poor. Being poor and being ridiculed for being poor is part of their perfect and ultimate life plan. If your decisions make others poorer, then it is because they agreed to it. If you have been bullied in school, it’s because you chose your bully on day one. Economists love complaining about central planning when others do it. When they do it? It’s rational! The obvious problem with pure time preference theory is that people change their minds. They don’t make a single big decision and then live with it. To be fair, neoclassical economists consider pure time preference, which is actually commonly espoused by Austrian economists, to be a special case. What this means is that it can and does happen, but it is not the rule and it should not be relied upon.

The biggest fallacy that Austrian economists commit to though, is to assume that time preference and therefore the market interest rate must always be positive, that is, people always value present consumption over future consumption and require compensation or bribes for future consumption. When we look at the most essential form of consumption, such as food and water, we do not observice this whatsoever. The average western household does not have a scarcity of food and water, they have an overabundance. Worse, the household routinely throws a lot of the food away, because there is too much of it. This situation doesn’t exist in economists models, because either the household is modeled to be perfectly liquid, that is, food is always produced without leftovers or alternatively, all food is consumed because of the infinite wants and finite resources assumption. The latter assumption simply denies the existence of underutilized resources and also downplays the harm of overutilizing resources. It doesn’t have to be said, really, but every time someone throws out food, they don’t consume it and they even have to pay for the privilege of garbage disposal! Does it mean they are infinitely patient? No, it obviously does not. The reason why we throw out food is that it goes bad over time. It is because the present abundance turns into future scarcity. In the first place, it doesn’t even make sense that patience should be rewarded as an axiom. Whether patience or impatience is a good thing depends on the context, but especially Austrian economists think that saving money is morally good behavior that should always be rewarded, which is kind of ironic, because it means they have to criticise more general markets where future abundance can be lower than present abundance. That is the special case I have been talking about. For pure time preference to make sense, you need a permanently growing economy with both economic growth and population growth to keep the demographics young. In an aging economy, it is kind of ridiculous to expect monetary savings to be rewarded, because even if you have money, if there are no working age people, you can’t buy anything, because nobody is selling anything.

The loanable funds model

Neoclassicals not only consider the patience and impatience of people, but also the relative abundance or scarcity of capital over time. What this means is that interest rate depends on the supply and demand for loanable funds. The loanable funds model is essentially an extension of the idea that the real supply of savings vs demand for investment determine the interest rate. This is a more general concept than pure time preference theory as it takes into account that there can be an oversupply of capital in the present and a shortage of capital in the future. Don’t believe me? Just take a look at the demographics. Once all the young people have disappeared, why would you expect the pyramid scheme to go on? If we take one step further and also include money balances, those very money balances that are created by private banks, then the interest rate is determined not only by real factors, but also monetary factors. There is nothing particularly wrong with such a theory, in fact, it even allows for hoarding of money, ahem delayed decision making, to affect the interest rate. What is unfortunate however, is the fact that banks in the real world are a tiny bit more creative than the economists applauding the loanable funds model. As this post is still about time preference and not about banks in the real world, I am willing to let the neoclassicals get away with the loanable funds model for now.

Can the efficient market hypothesis help us out?

The efficient market hypothesis is only loosely related to time preference theory. It does not state that agents have perfect information, however, what it states is a relaxation of the same idea. Instead of making decisions with perfect information, the agent makes decisions based on all available public information. This means that given an information distortion that happens to affect everyone equally, everyone will make an equally bad decision and thus it is expected that people cannot beat the market on average.

So, what if the time preference oriented agent followed this idea? Since new information arrives at every time period, new decisions can be made using that new information. What this means is that in \(t_0\), the agent may save money so that e.g. a bond matures in \(t_4\), where it derives the most utility. However, for the sake of the argument, once new information arrives in \(t_1\), it becomes obvious that period \(t_2\) will result in the highest utility. What this means is that a continuous time preference agent, one that makes decisions every period based on existing information, will routinely make suboptimal decisions, because his time horizon is too far into the future and he therefore commits himself to very long duration bonds. This means that once new information arrives, he does not have enough flexibility or room to make new decisions as his savings are locked up in the bond and he would have to sell the bond at a discount. However, if the agent anticipates that a bond duration of 4 is optimal in the moment but perhaps not in a future moment, couldn’t he just buy two bonds with a duration of 2 each? He could, and in the real world this is done all the time. However, this is not time preference theory. It is something very different. It’s called liquidity preference. Meanwhile Austrian economists argue that the problem is actually that the central bank is secretly setting the interest rate too low, as if the end of the central bank could somehow magically make information about the future available in the present.

Delayed decision making

In fact, once new information arrives, agents want to make new decisions, but they not only need the decision itself, but also the ability to execute that decision. Thus, there will have to be an allocation of money that is neither consumption nor saving. Performing the purchase of a consumption or investment good requires preparation. Performing that preparation is an act in itself and one can prepare oneself, even if it is unknown which decision is ultimately made. In fact, you could say that this allocation of money is purely transactional in nature. We anticipate future transactions and therefore we keep some money always ready, just in case new information arrives. In case our car breaks down and we need to repair it, in case our credit card gets declined and we have to pay offline with cash. We will hold money, not because we planned on doing things with it, rather, the opposite is the case. We keep it, because we have planned nothing in particular. To call this “saving” would be dishonest. This money is not available in the capital markets. Nobody, except the holder, directly benefits from holding money. Meanwhile with saving, there are always two parties. Either the investor and the investment, the lender and the borrower or sometimes we just keep a stock of goods for future consumption directly. Just as the holder of money is able to not have made his decisions yet, there are people on the other side, awaiting that person to make his decision. The breakdown of a car is difficult to predict of course and therefore you might say that these people are waiting for a very good reason. After all, the mechanic should only fix the car, once he knows that it is broken. If the information about the reason for the breakdown cannot be known ahead of time, then it only makes sense to wait until it happens. In other words, money, especially money in the form of cash and liquid bank accounts with no spending restrictions, allows us to delay our decision making. This delayed decision making is not possible in a barter model. After a barter based trade, both parties do not owe one another. The balances net to zero. There is an equilibrium. It is impossible to perform delayed decision making with barter by definition. Delayed decision making has been excluded from the model and that is a conscious decision by neoclassicals. The introduction of money gives rise to the ability to delay decision making, which is an absolutely necessary aspect of real world economics and one of the biggest reasons why people use money in the first place. In fact, delayed decision making describes a disequilibrium situation and therefore it is unsustainable in the long run, but that doesn’t make it any less real and it doesn’t make it any less impactful on our lives and it certainly doesn’t make people stop doing it. Even if there is a tendency toward jumping from equilibrium to equilibrium, this doesn’t mean that the equilibria are connected continously.

An out of place analogy might be to use the phase transition of water from ice to water and back from water to ice. The equilibrium situation modeled by barter is represented by ice, which in theory can be formed in any shape, yet moving to a different equilibrium and therefore a new shape, requires the ice to become liquid. It has to leave the equilibrium state temporarily, then it is put in a different form and finally frozen again to become a solid. Money therefore represents this liquid state in the economy. It gives us the necessary degrees of freedom that allow the formation of a more complex economy. Neoclassical economists insist that the liquid state is unnecessary and that we could in theory rearrange the ice in its solid state atom by atom and therefore we can get any shape we want. We get continous transitions from equilibrium to equilibrium and no nastiness could ever befall us, for we have the most beautiful and elegant economic model! This is the neoclassical fallacy regarding money. For a neoclassical economist, solids ARE liquids. They are the same thing to them…

Let’s do something silly and say compound interest is a myth

One of the weirder aspects of pure time preference theory is that it assumes that the interest rate is positive forever. First of all, as mentioned, the economy must grow at this interest rate otherwise the interest income must come at the expense of another person. In fact, if the latter case occurs, you will get an economy where the most patient agent owns everything and everyone else owns nothing and supposedly everyone agrees to it. I don’t know about you, but I would probably rebel. In fact, this is one of the problems with Thomas’ Piketty’s book where he mentions the concept of \(r > g\), where the return exceeds the growth rate. I do believe Mr. Piketty has a very good reason to argue in favor of this theory, but the problem is that he must explain why it is the case. Marx simply claims that the productivity of capital is absolute and offers power over workers. The problem is that capital can be manufactured by socialists until its return matches the growth rate. So the explanation cannot lie in a simple lack of capital. The explanation must be a little bit more complicated. It must argue that the capital is never manufactured because of some other preventative factor. The requirement is that there is indeed a rent seeker somewhere and he owns products that cannot be produced or at least whose production is strongly limited. The most obvious candidate is properly zoned land and permitted buildings. Local politicians can restrict the availability of land and existing homeowners can block new construction.

The problem with compound interest is that it is exponential. If time preference is a constant positive exponential discounting factor, like most economists and investors claim, then it would never end. In fact, this theory now forces us to argue in favor of infinite growth. It is kind of ridiculous. However, let’s first illustrate a simpler concept. Simple interest. Simple interest is interest that is spent on consumption and is not reinvested. What is elusive about simple interest is that it seemingly doesn’t exist. If I can invest with 3% interest and consume the interest income, why can’t I invest the interest income at get compound interest? It doesn’t work that way for a simple reason: Simple interest is not compound interest. It is difficult to understand this. In fact, simple interest could look like compound interest for decades, heck, for an entire human lifetime or even multiple human generations and yet simple interest will never be compound interest. The essential difference is that simple interest can only exist with a finite duration and yet compound interest is inherently durationless. What do I mean by that? A bond with a fixed interest rate only pays you that interest rate over the duration of the bond. It does not pay interest after the bond has matured. You have to find another bond and that is exactly the problem. There is absolutely no guarantee that you will find such a bond. You can only reinvest the proceeds of the bonds, if a willing borrower steps up and issues the next bond. Therefore, you can literally have exponentially compounding interest that doesn’t compound. How is 3% compounding for 10 years any different than 34% simple interest over 10 years? The problem is that there is no difference! Compound interest simply doesn’t exist! Any attempt to create compound interest, such as a pure time preference theory of interest, is bound to fail. You might say that the interest payments on your checking or liquid savings account are durationless, but you are forgetting that the interest rate can change at any date. It isn’t fixed. You can map any non-exponential function to an exponential function. \(e^{ln(x)}\) is just \(x\).

Liquidity preference theory

An obvious complaint about liquidity preference theory is that it is purely monetary, but a purely monetary phenomenon requires money that isn’t neutral. This is a tough pill to swallow. It means that money does have a special effect on the economy. It also means that the mere distribution of money has an immense impact on the real world even if the quantity is the same. Neoclassicals assume that money plays no role in the economy and that monetary and real terms are equivalent if you adjust them for inflation. Liquidity preference theory implies that money casts a giant shadow on our economy and influences every aspect of it. Without an explanation of what makes money so special that people are obsessed over it, it is somewhat esoteric, especially in the face of economists who believe that money is neutral and therefore irrelevant. After all, we aren’t talking about money as in shiny metals. Money is closer to something one could call “organizational capital”. It is an information exchange network. Just like physical capital reduces the amount of physical labor required, organizational capital reduces the amount of organizational labor required. Thus, any commodity must also contain an “objective” element called liquidity premium, which makes it rational for all economic agents to possess liquidity preference, as opposed to time preference, which is purely subjective and a mere input to take into account during optimization.

So what exactly is the difference between time preference and liquidity preference?

If you would like to have a explanation of the difference, then you are in luck! When economists talk about low interest rates and therefore low time preference, what they are talking about is that lenders are becoming more patient and more future oriented. For the Austrian economist, this interest rate is essentially a reward for patience. Patient agents can arbitrage the interest rate difference between the minimum interest rate they expect and the maximum interest rate others are willing to burden themselves with. The patient get rewarded for their supposedly good moral behavior. Yet liquidity preference tells us the exact opposite story. Instead of interest being a reward for good moral behavior, the interest rate represents not patience or impatience, but rather punctuality and tardiness, or better yet “decisiveness and indecisiveness”. Why did I say the opposite? Think about it! For the sake of the argument, you are standing in a queue at fast food restaurant such as subway. There is this guy in front of you, taking up the waiters time, because he constantly keeps changing his opinion on what he should order. Time preference theory would imply that we should reward this person for his patience. Meanwhile liquidity preference theory would imply that we should punish this person for his indecisive and tardy behavior. In short, time preference theory can be used to justify inaction and laziness as good and moral behavior that benefits the economy! And that is why I call it “delayed decision making” rather than lumping it in with “consumption” or “saving”. Time preference theory simply pretends that there is no such thing as delayed decision making! People always make decisions and commit themselves to them!

Generational anomalies of time preference theory

Instead of assuming that a person makes a decision that has an impact only on his life, what if we had an example where an old person makes a decision that has an impact on a young person? After all, the young are dependent on the old until they grow up. This breaks down the concept of voluntary transactions and preferences always being reflected in the market. The problems of climate change and aging demographics are intergenerational problems that span individuals. It is no longer appropriate to talk about economic agents as being independent. They exist in the context of a society created by their predecessors. Elderly people are reaching the end of their life and therefore their time preference or impatience should be quite high. If these people are in power, they would make decisions that exacerbate climate change or prevent mitigations to climate change in the short term and make the problem worse. The argument that we should respect climate change worsening policies because of their high time preference is ridiculous. As climate change is a persistent problem in time scales of less than a thousand years, today’s young will be impacted when they become the “old generation”. They will be the ones with the high time preference. In fact, every generation will one day become the “old generation”, which means that age dependent time preferences are actually irrelevant on a societal scale. If old people decide that society should end with them, should the young respect that decision? Of course not. I am so tired of the “just world” fallacy, where people pretend that all outcomes are the result of people making consensual decisions. Reality tells us otherwise. Children inherit the mistakes of their parents.

Of course, in the case of a neoclassical solver that merely concerns itself with GDP maximization, we can simply try to solve for that. We have two agents that live in two different time spans. The first agent makes a decision that impacts a later agent. If the agent does not possess premonition to know about future agents, he is bound to make suboptimal decisions, because he makes these decisions in the absence of the agents. If the agent has premonition, then he might have to sacrifice himself for the benefit of the future generation. As premonition does not exist in the real world, the second agent is at the complete mercy of the first agent. What we have here, is a time based power disparity, depending on who gets to make the first move. Something that most neoclassicals wouldn’t admit, as they want to pretend that power struggles do not exist.

Conclusion

The pure time preference theory of interest is unsatisfactory. It requires premonition to make sense as time preference is inherently a trade off between the utility of a future event and a present event. Pure time preference theory is illogical in the presence of a non growing market that cannot satisfy it. Pure time preference theory alternatively implies that there is a lower bound to the durability of any asset so that only positive returns can exist. (i.e. food cannot spoil). I seriously hope nobody gets tricked by this nonsense. The only reason to believe in time preference theory is to validate one’s just world fallacy as it gives us seemingly simple answers and argues that consent is underlying every inter-temporal economic transaction as all inter-temporal decisions are fully informed.