Consumers in Macroeconomics: Part I

This is the first in a series of posts where I explore the basic macro model which is taught in graduate macro courses. A bit of reflection to put things in perspective.

Prologue

I decided to do a shorter post because it gives me space to break the thought process into smaller, albeit continuing pieces and makes theory accessible (hopefully enjoyable). All my previous posts are long because they aim completion of thoughts. But they can be tight for a casual reader. I want to be inviting rather than dissuading.

I start with this spirit. I remember that I looked forward to my first macro class in my grad school during my doctoral studies. I was excited and scared about the classes at the same time. I always wanted to be a macro economist, partly because of the excellent theory which was taught at Jawaharlal Nehru University, India.^[1] The subject was also taught with so much passion that I knew, if I had the chance to be an economist, I would be a macroeconomist. I remember reading Tobin, Patinkin, Malinvaud etc. for my macro classes even though I do not remember a lot of what I read. So, I was excited.

In USA for my doctoral degree, I was in a new country and had a new routine. My family wondered how many years I might study further. I think they were starting to worry. I enjoyed the process, so I was not bothered by the time spent learning if I had enough to finance my basic lifestyle. But it is what I call “an experience” or what people usually call “responsibility”, retrospectively obviously. I neither had the maturity nor the insight to call it that when I was living it.  

In between all of that, I went into this macro class where the general introduction which was given to me was that graduate macro is going to be tough. The professor went on to say that it usually is the most challenging methodologically and you must handle a lot of math which makes qualifying macro courses a bit more difficult. I remember feeling grim about macro.

As the semester went by, we ended up doing a lot of what was called “fancy math” but was really deterministic dynamic programming. I don’t think you need to know what that is, but it isn’t fancy! I think the general direction given to problems reflected a lack of organization. I also think if one does not enjoy these things, that shows up while teaching and that might have happened.^[2] Importantly, it was un-inspiring. I think the most important thing which a first-year macro course must do is to inspire students to look at problems which macroeconomics can do. It should also guide students towards methods but place them in context of the problem.^[3]

Often departments are limited by their staff, but the best of the departments should keep their first sequences of all subjects inspirational to the larger problems in economics. And that comes with perspective. Through these posts, I want to lead my younger self towards a macroeconomics I envisage. I hope it finds its way into graduate programs and inspires graduate students to pursue macroeconomics. I will dispense with the math, direct you to sources which have them but tell you the underlying story.

If you are lucky, you are at least taught the optimization properly – in case you aren’t, have a look at these excellent notes by Pascal Michaillat on his website and substack. If you are taught by someone who combines these technical advances with a bit of perspective, then that’s even better. Ideally, the economics should drive our search for methods and models with the idea that the techniques are there to facilitate and structure the argument.

The Modern Approach to Macro

Most models in macroeconomics after the late 1970s start with the behavior of individual consumers and then add them up to understand aggregate consumption, and from there total output or the Gross Domestic Product. The reason for this shift in 1970s is a critique extended by Robert Lucas Jr. who argued that models which start with an ad-hoc expression for aggregate consumption might fit the data well but is of little use to a policy maker.^[4] This is because they cannot predict reactions by consumers to policy because the model is not equipped to do so. This is called the Lucas critique.

His suggestion was to build models with a consumer (or producer) as the decision maker, so that one could observe how policy changes alter their decision, explicitly. This can then be added across consumers to give us the aggregate consumption function. This would be more appropriate than the ad-hoc version of the model where you write down the relationship you observe in data without examining reasons for the underlying relationship. ^[5]

As a result, economists responded to Lucas and incorporated micro-foundations to macroeconomic models. This changed a lot of how macro was taught. Those who came into the discipline asking questions which were at an aggregate level were disciplined to learn micro carefully, intently. It was also because micro as a discipline had developed more rigorous tools which were amenable to theorization and mathematization. This also led towards a larger agenda to integrate economics from the ground up. At the core of this integration was a consumer.^[6]

Representative Consumer

The consumer in most macro models is representative of the entire population. The intention is to understand a simplified economy where everyone behaves the same way, has the exact same preference over commodities and time. What this means is that whatever our consumer does can be added up to represent a stylized economy. In essence, we reduce the problem into something which has fewer dimensions. Hence these models are called representative consumer models.^[7]

Is this the correct approach? Well, the answer is, it depends. If we want to understand how much of the current inflation is affected by demand for home ownership or new renters, then treating all consumers as equal does not make sense. This question looks at a special consumer – the homeowner or the renter – and tries to link their behavior to a broader macroeconomic phenomenon. By treating all homogenous consumers as homeowners, we might mis-calculate the importance of housing market. In this situation, either we need heterogenous consumers – those who participate in housing versus those who don’t, or we need a model which only describes housing market and is silent on the interaction of this market with other markets in the economy. ^[8]  

In certain situations, referring to a representative consumer may not pose significant issues. For instance: if you are interested to know how German government spending affects Spanish inflation, then you can think of representative consumers and focus on the linkage between the two economies and their goods market through trade. Choosing to use non-representative consumers is only worthwhile when your narrative revolves around this heterogeneity in consumer preferences. The bottom-line is that your story should determine modelling choices.

Time: Continuous or Discrete

We will come back to what this representative consumer does soon but let’s talk about the model environment. These are mathematical details which necessarily do not have significant economic implications. They are often mathematical conveniences.

The first modelling choice is a measure of time. Why is time so important? The economic intuition behind this is the possibility of consumer decisions being connected over time. What we consume today might dictate what we consume tomorrow. So, time might be important even for a consumer’s underlying decision.

So, how do we measure time? Time can be any unit of measure and for the model, it does not really matter. It can be the length of the day, a week, a fortnight, a quarter, a year etc. This decision is driven by the kind of data that we possess for the consumer’s actions rather than any theoretical choice.

Time can be also thought as continuous or discrete, which again does not matter for the model.^[9] The only difference that it makes is the kind of mathematics which can be applied to the model. It turns out that the properties of discrete numbers^[10] are different from properties of continuous numbers. Most of the fancy math that you come across in terms of derivatives and integrals are largely over continuum – developed by Newton and Leibniz in late 17^th century. In most macroeconomic models, we consider time to be discrete and other variables to be continuous. Thus, we consume a continuous amount of goods at a discrete point in time. This lets us map discrete data to the model and makes the math easier to understand.^[11]

Infinite vs. Finite Lives

After we are decided on time, we should think of end points of the time interval. Physicists take this very seriously, and so do economists.

Should we think of our representative consumer as living infinite lives or should we think of consumer’s life as a countably finite reality? We all live finite lives – and that’s probably the biggest motivation which forces us towards our achievements – legacy within this short duration of time.

The choice of infinite and finite lives depends on whether you think life’s finiteness changes the problem in ways which cannot be captured if we think of our lives as infinite. There are a lot of models which examine the implications of age dependent decisions – life cycle and overlapping generation models.^[12]

Their main message is that we can think of our consumption decisions over our finite lifetime as an age dependent variable. When we work, we save a lot so that we can consume when we are still old. The question here is whether these decisions which are seemingly age dependent, determine significant movement in macro-economic variables or not?

Certainly, the answer is in magnitude, but it is safe to conclude that age is not the only factor which is important in modern macro models. Hence, there is a preponderance of infinitely lived macro models, partly also because they are easier to treat mathematically – largely borrowing the methods applied to physical variables.

Now that we have made our first choice, we talk about our consumer’s economic choice and the underlying trade-off in the next post.

Aside

In my wish list is a post on the Indian economy in the recent times. What stops me from writing that post has something to do with how I think. I think from the point of view of theory. In the small world of theory, it’s easy to limit yourself and talk about things with certainty. When I look at the data, this thought disappears and I am back to grad school. But I am working on it.

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^[1] To be fair, I do not remember much theory from those times. The parts that I do remember are from Prabhat’s lectures on money, on Guha’s lectures on growth and these one off lectures by Amit Bhaduri.

^[2] I enjoy it so much that I am writing an obscure blog post which not a lot of people are going to read. I am okay with it for now.  

^[3] Recently, MIT removed the requirement of learning macro from its first-year courses because they thought it was not important and not a lot of people use it anyway. I have read Jón Steinsson and Pascal Michaillat talk about the need to reorient these courses and a lot of good ideas are out there. There is a need to reorient teaching first year macro. There is serious dearth of macro teachers in the universe.

^[4] Lucas Jr, R. E. (1976, January). Econometric policy evaluation: A critique. In Carnegie-Rochester conference series on public policy (Vol. 1, pp. 19-46). North-Holland. https://web.sgh.waw.pl/~atoroj/makroekonomia_zaawansowana/lucas76.pdf

^[5] I have a simple reservation against taking Lucas’s critique seriously. What if we are in a world where the aggregate behavior so represented by data fits a version of the model with heterogenous consumers because a lot of decisions counteract each other when aggregated. This means that the aggregate behavior with micro foundations looks very similar to the one without micro foundations – i.e. the aggregate implications of the data are identical. The critique does not matter if one is only worried about aggregate macroeconomic variables. This critique should not be taken seriously, unless I write a paper on this!

^[6] Depending on which book you read, you are bound to start with either consumer behavior or producer behavior in micro. The standard approach is to start with consumer.

^[7] Don’t tell me you want to know about HANK and you don’t believe in representative consumer yet.

^[8] Piazzesi, M., & Schneider, M. (2016). Housing and macroeconomics. Handbook of macroeconomics, 2, 1547-1640. https://doi.org/10.1016/bs.hesmac.2016.06.003. Additionally, if you think about housing, it might be best to think about partial equilibrium models which only focus on the housing market, especially since there is so much data about housing.

^[9] The only difference is computational i.e., the time spent by the computer in solving these models. Rendahl, P. (2022). Continuous vs. discrete time: Some computational insights. Journal of Economic Dynamics and Control, 144, 104522. https://doi.org/10.1016/j.jedc.2022.104522

^[10] Discrete mathematics is a branch of mathematics that deals with discrete structures, which are typically represented by integers, sets, graphs, and other discrete objects. The following are some of the main tools used in discrete mathematics: (a) Logic: Discrete mathematics is built on the foundation of mathematical logic, which provides a formal language for describing and reasoning about mathematical objects and structures. (b) Set Theory: Set theory provides a framework for defining and manipulating sets, which are fundamental to many areas of discrete mathematics, including combinatorics, graph theory, and number theory. (c) Combinatorics: Combinatorics is the study of counting and arranging objects, and it is a key tool in discrete mathematics. It includes topics such as permutations, combinations, and generating functions. (d) Graph Theory: Graph theory is the study of graphs, which are mathematical structures that represent pairwise relationships between objects. Graphs are used to model many real-world phenomena, such as computer networks, social networks, and transportation systems. (e) Number Theory: Number theory is the study of the properties of integers, including prime numbers, divisibility, and modular arithmetic. It has important applications in cryptography and computer science. (f) Algorithms: Algorithms are a central tool in computer science and discrete mathematics. They are used to solve problems efficiently and to analyze the complexity of algorithms and data structures. These are just a few of the main tools used in discrete mathematics. Other important areas of study in discrete mathematics include combinatorial optimization, coding theory, and game theory.

^[11] I think it is more of a convention than an ease of understanding – or an accidental choice. Most early papers were written in discrete time, but there has been a recent push towards using continuous time methods since they help us solve more complicated problems faster.

^[12] Gourinchas, P. O., & Parker, J. A. (2002). Consumption over the life cycle. Econometrica, 70(1), 47-89. https://doi.org/10.1111/1468-0262.00269.