The fact that Gary S. Becker is perennial manifests itself in various ways. One of them is that he still receives his copy of the Journal of Economic Perspectives from the American Economic Association.

## UChicago chronicle #4

The map of my kingdom and my passport to that. First day at the Kenneth C. Griffin Department of Economics at the University of Chicago. A lifetime dream coming true. My room overlooks the Rockefeller Memorial Chapel.

## UChicago chronicle #3

I arrived in Durham the same day two weeks ago. My plan was to spend a fortnight at Duke University‘s David M. Rubenstein Rare Book & Manuscript Library, where the Lucas papers, all his correspondence, drafts, notes and other unpublished materials are archived. It was supposed to be an overture to my program in Chicago. I started working on my personal collection of the Lucas papers six years ago, in 2016, during my first visit to the library. Even if I then paid some attention to this stuff, my collection remained seriously incomplete. I was superficial, admittedly. So the time had come to make amends. I am happy to say that in the past two weeks I could do what I wanted: now all the 11 boxes of correspondence are fully processed. The real part of the work is still ahead of me, of course: to go over the collection, piece by piece, and to piece them together into a coherent picture. Not at once. First I need to dig deep in the material of the first few years: from the beginning up to the late 1960s. As you may remember, I am currently working on a paper discussing his turn from firm micro to endogenous growth theory and then to the theory of large-scale fluctuations and business-cycle theory eventually. These letters will help us to better understand the process.

Although it was anything but my intention, this trip turned out to be more adventurous than I had ever wanted. Everything started at my arrival. When planning, I wrote an email to the entire Duke community in seach of a room in a furnished flat located within walking distance to the university. In less than half an hour a librarian reached out to me, and said she planned to be away in the second half of July and was hoping to find someone willing to feed her cat – a red giant Maine Coone – in return for a discount on the rent. As I am a cat person, I really am (two kittens are waiting for me to come home) I was her man (not literally, of course). So I agreed to feed the cat. It was the plan. When we were approaching mid-July hence my arrival, I asked her about my options for travelling between the airport and the flat, and she kindly offered me a ride, even if my flight was scheduled to land very late in the evening. It was a mistake – not the landing, but accepting the drive. We fixed up the meeting at the conveyor belt, to find together to her car. And here came the first surprise. We needed to find her car literally. She forgot the area where she dropped it. Areas in the multi-storey parking lot are indicated with the number of level, and the combination of a letter and a number, say, G2. Sometims to letters like EE. She insisted that she had left the car in Sector GG of Level 2, but on Level 2 there was no such a sector. This was something she couldn’t believe, so she set out for a couple of times in the hope of findig the GG sector that she didn’t in the previous rounds. She thus gave a whole new content to the age-old claim that insanity is when you always do the same, always in the hope of a new outcome. I was just standing there, after 27 hours of travelling, with bags weighing around 40 kgs in sum. Physically destroyed and utterly exhausted – with all this happening in the middle of the night. I tried to follow her in a distance for fear she might have lost me as well, but I wasn’t that quick. Roaming the structure, the search process started at 11:30PM with a simple method: she kept pushing the button on the key fob so as to catch the sound of the car when opening and closing the doors, over and over again. A little fly in this ointment was the fact that the car is a VW, which is quite intelligent, so when the car (which was around all along) realized that someone kept pushing the button, it thought this someone was a theft, so it simply blocked itself. When we found the car at 1:30AM, we were just standing and staring, unable to get in. Needless to say that she was unaware of the slot built in the handle by which, using the key, she could have physically opened the door and, once in, started the engine. Nope, instead we settled down in the terminal to wait for the Sun rise and for the first shuttle to arrive in the morning.

Here came the second surprise. In this light chat once she just mentioned as a minor and wholly insignificant fact that the cat has diabetes, so he is supposed to be fed every 12 hours, and to be given an insulin shot right after meal. Moreover, the cat is so individualistic and has such a mature personality (her words!) that he picked his feeding times himself. And these feeding times happen to be 2AM and 2PM. Yes. Exactly. So, she really expected me to get up in the middle of the night and leave my reserved desk in the library in the middle of the day just to hop on the ‘bike’ she gave me to ride back home to feed the cat. I am a gentleman and usually I don’t pay attention to things that I don’t expect to affect me – and I knew, I really did, that there was and there is no way I wake up for a cat in the middle of the night. So I was just smiling and nodding politely. How interesting, I said. She hastened to add, to my reliefe, that I wouldn’t need to set the alarm clock. Nope, the cat would wake me up by himself. Superb! I was happy to hear it: even if the cat made an attempt, I would gently relocate him from my bed to the floor by a nicely planned and accurately executed movement of my legs.

After she left for the bike ride, the fun part actually started. The cat really woke me up. He turned out to be a nasty piece of work, pushing me for food from 1AM. Every night. It was terrible. I felt torn apart. If I had listened to my heart, I would have fed him in the end, but my night would have been over – which I could not afford, given my (occasionally demanding) morning runs and my work at the library. But if I hadn’t, the cat would have kept making noises and tried to find a way to chase dreams away. Plus, my landlady, to my surprise, also kept pushing me with mails to ask how “THE 2AM FEEDING” was. So I gave it up. I moved, leaving the cat not to his fate, but to the goodwill of the downstairs neighbor (who is really pretty anyways). She was so enthusiastic to help my landlady to explain to me what it takes to feed a cat in the middle of the night that it was much better to leave the whole stage to her. My new location is a dream: quite, cozy and friendly. Leni is a great host and friend. And I am so lucky to have found it. As it is situated far in the east from downtown Durham, I can roam such parts of the town I had never visited before.

On Monday I am leaving for Chicago, and the real part of my program starts finally.

## Lucas’s early engagement in endogenous growth theory

This paper describes Lucas’s involvement in endogenous growth theory research of the 1960s. It is argued that the literature of the time suggested various strategies for the endogenization of Solow’s technical progress one of which was a call for a choice-theoretical approach to the explanation of the technological investment of the firm. In answer to this challenge, Lucas elaborated a series of models in the mid-1960s that elucidate investment decisions as optimizing responses under the assumption of a common penalty for rapid change in physical capital and technology. Particular attention is paid to Lucas’s presentation at Hirofumi Uzawa’s 1966 growth theory seminar held at the University of Chicago. References to the Lucas archives underpin the claims.

The full text of the paper can be found here. I have started a discussion for comments which you can join here. Any comments are warmly welcome.

## Robert E. Lucas on Monetary Neutrality: A 50th Anniversary

Back in 1972, Robert E. Lucas (Nobel ’95) published a paper called “Expectations and the neutrality of money,” in the* Journal of Economic Theory* (4:2, 103–124). The paper was already standard on macroeconomics reading lists when I started graduate school in 1982, and I suspect it’s still there. For the 50th anniversary, the *Journal of Economic Methodology *(22:1, 2022) has published a six-paper symposium on Lucas’s work and the 1972 paper in particular.

Reading the heavily mathematical 1972 paper isn’t easy, and summarizing it isn’t easy, either. But at some substantial risk of oversimplifying, it addresses a big question. Why does policy by a central bank like the Federal Reserve affect the real economy? In the long-run, there is a widely-held belief (backed by a solid if not indisputable array of evidence) that in the long-run, money is a “veil” over real economic activity: that is, money facilitates economic transactions, but at over time it is preferences and technologies, working through forces of supply and demand, that determine real economic outcomes. To put it another way, changes in money will alter the overall price level over long-term time horizons, but it is “neutral” to real economic outcomes.

Timothy Taylor, managing editor of the *Journal of Economic Perspectives*, devoted a comprehensive blog post to Lucas’ neutrality paper apropos of the anniversary special issue of the Journal of Economic Methodology. Defenitely a must.

## UChicago chronicle #2

Route 66 also starts in Chicago. Of course.

## UChicago Chronicle #1

“Hi Peter, how are you. Congratulations, your Visiting Scholar appointment has been approved. The next step is for the signed J-1 form to go to our Office of International Affairs (OIA). That will be done sometime today. They will be in touch with you soon after.“

Thanks to the generous financial support of the Rosztoczy Foundation and my home institution, Budapest Business School, I spend the next academic year as an appointed visiting scholar at the Kenneth C. Griffin Department of Economics at the University of Chicago. It gonna be exciting, it gonna be thrilling. It gonna be uplifting, it gonna be tough. But anyway, it gonna be perhaps the most memorable time of my life. I have a research project to complete at the Department, but there is a thing which is more important to me now. To learn. Once you can reach the gods of our profession, try to learn from them as much as possible.

## Historical methods in economic methodology

My presentation entitledHistorical Methods in Economic Methodologyas an episode in the Philosophy, politics and economics seminar series run by the Center for the Study of Economic Liberty, Arizona State University,starts in an hour. Let’s meet there! |

Friday, April 1, 20222–3:30 p.m. AZ MST via Zoom Meeting |

## Spectral analysis of second-order processes

A weak ago, or so, I promised to devote some space to the spectral analysis of processes governed by second-order difference equation. The idea of spectral analysis is the fact that the variance of a process can be decomposed into the oscillations of processes with various frequencies. The spectrum of any process governed by a general ARMA structure can be plotted in a figure, and the eye should be kept on whether there is a peak at a frequency other than zero. The portion of the variance of a series ocurring between any two frequencies is given by the area under the spectrum between those two frequencies. In other words, if there is a peak in the spectrum at a given frequency, that frequency dominates the variance. From this, it is easy to calculate the cycle in a series by comparing its dominant frequency to the full cycle of of the cosine function *2π*. For instance, if the peak is at *ω = π/3*, the cycle is *2π/(π/3) = 6* periods, which equals to one and a half year if we work with quarterly data. Meaningful business cycles have the length of about 3 years (12 periods).

Spectrum of second-order processes of the type y_{t} = t_{1}*y_{t-1} + t_{2}*y_{t-2} + e_{t} shows typical pattern effectively summarized in the figure below:

**Tom Sargent’s summary of the patterns in the spectrum of second-order processes**.

This is the same triangle as we have already seen when analyzing the cases of damped and explosive oscillations. Of course, this figure also comes from Tom Sargent’s 1975 draft textbook entitled ‘Notes on macroeconomic theory’ and reappears in his ‘Macroeconomic theory’. Now we will focus only on the clear areas where there is peak of through in spectrum. It is easy to realize that the process y_{t} = y_{t-1} – 0.95*y_{t-2} + e_{t} falls into the category of peak in spectrum. Accordingly, we find this:

The peak is around *ω = π/3*, so the length of the cycle in the generated series is some 6 periods. Similarly, the process y_{t} = -0.5*y_{t-1} – 0.5*y_{t-2} + e_{t} also falls into this class, but has a very nice spectrum:

The peak is about *ω = 2π/3*, the cycle is thus shorter (approximately 3 periods, less than a year given the quarterly horizon). By contrast, the process y_{t} = 0.5*y_{t-1} + 0.45*y_{t-2} + e_{t} is a through-type equation. Accordingly:

The peak is at *ω =* 0, which defines a cycle of infinite length – not a meaningful case in terms of business-cycle analysis.

## A naive business cycle theory

This is the title of the chapter in Tom Sargent’s 1975 draft textbook ‘Notes on macroeconomic theory‘. A large part of these notes reappears in his later ‘Macroeconomic theory’ (Elsevier / Academic Press, 1987). In the aforementioned section Sargent addresses the problem of how to represent real-life business cycles with simple difference equations, or in other words, how to set up difference equations whose dynamics bear close resemblance to economic time series. The theory is based on the familiar figure:

**Different dynamics of a second-order difference equation y**

_{t}= t1*y_{t-1}+ t2*y_{t-2}+ b*x_{t}.As Sargent argues, business cycles are characterized by repeated patterns in the series – this is the sense in which cycles are cycles. If one wants to describe her cycles with clearly defined lengths, she needs complex roots, so the area under the line t_{1}^{2} + 4t_{2} = 0 is relevant. Under complex roots, a second-order difference equation can be described as a cosine function of time, so as *t* is increasing, the dependent variable shows cycles of a given length. I wanted to have a deeper understanding of the connection between parameters t_{1} and t_{2} of the difference equations and cyclical behavior. Where roots are complex, between the fields ‘explosive oscillations’ and ‘damped oscillations’, there is the line where t_{2} = -1. This is the region where oscillations have constant amplitude. Let’s focus on this line.

We know that t_{2} = -1, from which it follows that the growth parameter *r* = 1 (constant amplitude). However, t_{1} is not yet set. Using this piece of information we have the *y _{t} – t1*y_{t-1} + 1*y_{t-2} = b*x_{t}*, where

*y*is the deterministic part, and

_{t}= t1*y_{t-1}+ t2*y_{t-2}

*b*x*is the stochastic component with

_{t}*x*taken as a white-noise term. The

_{t}*φ*argument of the complex root is given by cos

*φ*= t

_{1}/2. The length of the cycle is measured by comparing

*φ*to the whole cycle of the cosine function, which is

*2π*. Let’s set the cycle length arbitrarily to 50 periods; in this case

*2π/φ*= 50. It means that

*φ*= 7.2°, or 0.04

*π*(measured in radians), from which it follows that t

_{1}= 1.984229. The general solution of a second-order difference equation is

y_{t} = A*r^{t} * cos (*φ*t + ω),

where *A*r ^{t}* is the amplitude of oscillation in period

*t*, while

*r*is the growth parameter, and

*ω*is the phase. As we know

*by having set the length of the cycle to an arbitrary value,*

*φ**A*and

*ω*are the only unknown parameters. It is no big deal: they can be found by solving the equation for the first two values of the series.

Now the deterministic part is *y _{t} = 1.984229*y_{t-1} – y_{t-2}*. This equation produces a cycle with a length of 50 periods; this is the time the series needs for walking along a full cycle from the start to the end. In this example y(1)=1461.7 and y(2)=1484.6 (arbitrarily set values). In 100 periods the series undergoes two full cycles:

Whit some calculations it is easy to get to the general solution to the deterministic part of the equation. Expressing the angles in radians, the equation is

x(t)=1487.287462**cos(0.04π***t-0.099156638π*)

If we plot these two equations in the same figure, they are in complete line:

We have done a great job: a deterministic difference eqation is represented with a cosine function that appropriately expresses the cycles. More interestingly, we can add stochastic noises to the difference equation, so the cosine function will describe the center of oscillations. I have run two simulations. In the first case, b = 20:

And in the second case, b = 50.

The blue line contains the stochastic noises, while the orange line, standing for the clear cyclical representation, describes the dynamics of the deterministic part. Both oscillate with the same cycle with the length of 50 periods.