Meeting on 12/2/2021

• turning off "only fire 1 per month" leads to wage rate trending towards the minimum wage while labor value increases
• essentially workers are being paid less than their value
• need to explore this
• other models have contract labor models, which we could potentially do, but it might be easier to just make it probabilistic
• maybe for each person that a firm wants to lay off, the firm succeeds with a constant probability in laying that person off
• that probability would be a field
• want to look at wage rate vs labor value (ratio as a function of layoff probability)
• also want to look at firm profitability as a function of layoff probability
• look at firm turnover/bankruptcy rate as a function of layoff probability
• double check price ratio
• use a loop to do probabilistic layoffs
• investigate discrepancy in price ratios found between main model and price-ratio-experiment model

RE: "How easy it is for firms to lay off workers (we might want to make laying off probabilistic)"

Seems like a good idea. But would it improve the model per se, compared with using a simple arithmetic criterion?

Joseph, what do you mean by "simple arithmetic criterion"?

Experiment 1 Initial Plan¶

Constant Model Parameters¶

setup-structure: two-layer
n-households: 500
n-firms: 30
transactions-per-month: 1
framework-duration: 1
mean-new-agreements-per-month: 2.0
firm-memory-constant: 0.8

Variable Parameters¶

layoff probability

Description¶

The goal of this experiment is to determine to what extent layoff probability affects the relationship between labor value and wage rate. To do this, I will run the experiment for 11 different layoff probabilities starting at 0 and ending at 1, incrementing by 0.1. For each run, I will keep track of the ratio between labor value and wage rate at each tick. At the end of the experiment, I will use data from each run in a jupyter notebook experiment to calculate the correlation between layoff probability and the ratio between labor value and wage rate.

Labor value for a firm will be calculated as tech-parameter * price for primary good firms. Tech-parameter is how many units of a good one laborer can produce, so multiplying that value by price gives the total value the laborer provides for a firm in terms of revenue. For consumer good firms, it will be tech-parameter * (price - unit cost). For the ratio over the entire model, the ratio will be calculated as the average of every individual firm's ratio between labor value and wage rate.

Experiment notes¶

• in order to eliminate uncertainty, I have decided to calculate the actual unit cost for every transaction cycle
• initially I planned to do this by simply summing up the total amount spent on inputs and dividing by the amount sold, but I ran into several issues: 1) not all firms sell goods every cycle, which leads to some divide by zero error 2) if I reset the amount spent at every purchasing cycle, I won't get true unit cost because firms often already have inputs in stock
• what I need is a way of calculating cost independent of the amount sold

Progress Report 1/8/22¶

As of today, I have run the experiment in Netlogo. In order to address the issue with calculating marginal cost, I added a few features to firm procedures to keep a running average unit cost for each input. The data is now in 3 csv files, and the next step will be to process it in a jupyter notebook.

Meeting 1/10/2022¶

Things to try¶

• Running the experiment with a single firm structure/type (we may not get something similar in this case)
• Look at prices of both types of firms
• Hypothesis: once it's too easy for firms to lay workers off, primary good firms are laying off workers because they expect less demand, and so consumer good firms are raising prices
• Look into the differences in how price is adjusted

Progress Report 1/12/2022¶

• The increase in the ratio of labor value to wage does appear to be due to an increase in price, according to the data from a rerun of the experiment
• Consumer good prices increase in the same way that the ratio increases, whereas primary good prices decrease and level out
• A quick sanity check of the model shows that things like price and marginal cost are behaving as expected
• Some quick runs of the experiment just messing with parameters reveals that when the ratio sharply increases, unemployment is also extremely high, and reservation wage consistently decreases
• Firm-memory-constant seems to have an effect on this too; higher values for firm-memory-constant prevent this spiral from occurring

Updated Hypothesis
When firm memory constant < layoff-probability, we get the spiral - unclear why

Progress report 1/14/2022¶

After running an experiment, I have verified there is a correlation between the difference between layoff probability and memory constant, and whether the economy crashes. It isn't exactly when layoff-probability > mem-constant there's a crash, but it's fairly close. Additionally, there appears to be a relationship between the magnitude of that difference and the speed at which the economy crashes. The greater the difference between layoff-probability and memory-constant, the faster the economy crashes. Again, not a perfect correlation, but pretty close. The next step will be to determine why this is happening.

Progress report 1/18/2022¶

My current hypothesis for why there is a relationship between layoff-probability and firm memory constant is as follows: when firm-memory-constant is low, firms place more weight on the immediately preceding production cycle when estimating demand. In the event of one bad month, a firm would likely estimate a second bad month. A high layoff probability would mean the firm can quickly adjust to this new demand estimate, but more unemployed workers means less overall demand and thus even lower demand estimations and more layoffs - a negative feedback loop. A low layoff probability would mean firms may have no choice but to keep some workers through bad times, allowing the economy to recover before a negative feedback loop sets in. I believe this is supported by a key difference in the way demand behaves when the economy crashes vs when it doesn't. When the economy crashes, demand continuously slopes downward, whereas demand remains stable when the economy doesn't crash. It's not clear why the relationship works the way it does (why the numbers are the way they are), a quick experiment playing around with some of the other constants doesn't seem to change the relationship.

Meeting notes 1/19/22¶

General conclusion: it's reasonable that the economy crashes under certain conditions. Our next steps will be to determine why this happens and make sure the explanation makes sense. To do this it makes sense to see whether similar behavior is observed in a single firm structure.

Progress report 1/24/22¶

Experiments for the single firm structure are complete. Unfortunately, I could not get the economy to crash. For the two-layer firm structure, during a crash the liquidity is concentrated among households.

Meeting notes 1/24/22¶

• color scatter plots on the single firm run to see if there's a relationship
• look into the way firms are going bankrupt/out of business
• try decreasing framework-agreement length

Progress Report 2/2/2022¶

• After colorizing the scatterplots from my last experiment in multiple ways, there still doesn't appear to be a relationship between firm-memory-constant, layoff-probability, and either mean-profits, mean-household-liquidity or mean-firm-liquidity
• In a crash condition, firms don't go bankrupt; the model just sort of reaches a stable state of near-total unemployment and very low demand. Firms either have 0 or 1 worker and since most households have low liquidity (save some lucky ones), overall demand from consumers is very low, so firms are able to meet this demand; I still consider it a crash because most people are unemployed
• It appears as though adjusting the length of framework agreements in either direction cannot prevent a crash from happening where there previously was a crash condition; more comprehensive testing will be needed to confirm this
• Again, transactions per month does seem to have an effect on whether or not a crash occurs, but I have yet to conduct thorough testing on this

Progress Report 2/7/2022¶

• Further testing confirms my hypothesis that framework-duration cannot prevent a crash from happening where there was previously a crash condition. This occurs even at edge cases (on the border between starting conditions that lead to a crash and conditions that allow a stable economy). The duration doesn't even have a consistent effect on how long it takes for a crash to happen.
• Currently working on trying to induce a crash in the single-layer structure
• It seems as though for a single firm structure, there isn't a crash state equilibrium, even if the economy starts in a crashed state unemployment very quickly goes down to normal levels (albeit slightly higher than if the economy started in a normal condition). It's worth pointing out that this is assuming new firms entering the economy to replace bankrupt ones startup as if there weren't a crashed economy (which I think makes sense, you wouldn't open a business under any circumstances if you didn't have the liquidity to do so)
• the only way to sort of induce a crashed state in the single firm setup is to adjust the number of transactions per month (which doesn't really make sense to me)
• the same doesn't seem to be true of the two-layer firm structure, if anything increasing the number of transactions per month actually delays or prevents a crash from happening (at the expense of some increased volatility)
• started playing with number of households and firms, got some interesting results, sometimes able to avoid a total crash (although it's not what I'd call good)

Meeting notes 2/7/2022¶

• Look into transactions per month
• Try an extreme crash (one household with all of the liquidity) for single firm structure
• Look into the difference between crash-start in two-firm and single-fir (why does one recover and the other doesn't)

Progress report 2/12/2022¶

• First thing I did today was modify the setup-crash procedure to setup an extreme crash, where all of the liquidity is concentrated in one household at the start of the model
• at first it seemed like I found a crash equilibrium, because I ran the model and unemployment started at 100% and then dropped to about 85% and stayed there, but when I changed to the old setup-crash procedure and ran it again, I got the same result
• I discovered that when I reduced firm-memory-constant below 1, the model recovered from the crash in both cases (although liquidity was still very unequally distributed which is perhaps not ideal)
• the same phenomenon does not translate over to the two firm structure, it cannot recover from a crash
• Currently working on figuring out why the single firm structure always recovers and the two firm structure never does (unsure of a method)

Progress Report 2/13/2022¶

• Currently looking into why the single firm structure is able to recover from a crash setup
• At the start of a crash setup, demand vastly exceeds the max production of firms
• With that in mind, and looking at the graphs of output vs demand, my best guess as to why this economy always recovers is because the discrepancy between supply and demand at the beginning of the model leads firms to sharply increase price at first, but eventually they demand many more workers and unemployment levels return to "normal"
• This is evidenced by a few things: demand decreases until it meets output potential and then both increase to non crash levels, and demand-for-labor starts very low but increases over time and plateaus around the same time the supply and demand reach an equilibrium
• Upon immediate inspection of the two-firm structure, the first thing I notice is that demand for consumer goods starts very high still, but the supply of consumer goods does not rise to meet it; consumer good prices increase and stay high, so firms are attempting to compensate and earn a profit, but for some reason they are not demanding more labor
• As of now, I don't know why they aren't demanding more labor

Progress report 2/14/2022¶

• Ok, so for some reason, in the single firm structure, after a crash setup, as time goes on, the amount that firms want to produce goes up (as you'd expect), but it doesn't for consumer good firms in the two-firm structure; if anything, it goes down slightly
• I learned this by printing out "expected-future-sales + ideal-buffer" in the "adjust-output-and-price" function
• At the start of a crashed run for the two firm structure, pretty much every firm goes bankrupt, my guess is they spend a lot on inputs so they can't afford to pay workers; this isn't a problem with the single firm structure setup
• Short answer: I have absolutely no idea why the two firm structure keeps crashing

Meeting Notes 2/14/2022¶

• Somehow consumer good prices are skyrocketing in the two-layer structure but the primary good prices are actually falling, this is a problem
• So it might be that primary good firms are unable to produce more because they're not earning enough and so there's not enough input for consumer good firms so they're increasing prices until they reach an equilibrium
• Look into why that's happening
• Maybe give one firm extra cash and follow that firm

Progress report 2/24/2022¶

• In examining the code to try and figure out why primary good firms were lowering price, there was one line that gave me pause, and it was essentially that a firm was not to increase its price unless that price was lower than the average price of all other firms with that type, which doesn't necessarily make sense to me, especially in a shortage
• Ultimately, however, this line did not prove to make much of a difference in the crash setup; removing it allowed primary good firms to raise price a little at first, but then it went back down while consumer good prices continued to skyrocket
• I then noticed that primary good firm inventories almost never dropped to 0 - they always had goods leftover after production cycles, which was strange to me given that consumer good firms were consistently running out and inventories were droppping to 0
• The inventory information explains why primary good firms have lower prices - they don't need to raise them because they for some reason have goods leftover
• It could be the case that since primary good firms don't make a lot of money, they are unable to increase production, so consumer good firms eventually do not demand as much from them, but this still doesn't make a lot of sense; if primary good firms needed to increase production and didn't have enough money to do so, why couldn't they just increase price?
• I also graphed "liquidity limiter" for all firms - essentially the % of ideal production a firm is able to produce given its liquidity and estimated production costs; there was not a huge difference between the crashed state and non crashed state

Meeting notes 3/28¶

• We've resolved the issue of dividends and how it relates to why the multi-firm structure is incapable of recovering from a crash
• Next steps: re-run big crash experiment with single and multi-layer firm structures, see what happens
• If crashes occur in both, great, otherwise there's an issue we need to look into

Progress report 4/4/2022¶

• I reran the crash experiments
• We have all of the data necessary to replicate any individual run
• Both firm structures are capable of crashing, but the crashes in the single firm structure are much more random
• In either case, crashes are very infrequent
• Under the old dividend payment structure, the two-layer model still crashes a fair amount, with some correlation between layoff probability and firm memory constant

Meeting notes 4/4/2022¶

• Generally speaking, this issue is closed
• Last steps would just be to clean up the code and merge it with the main branch
• Write some tests (I write for Will, Will writes for me)
• Once testing has been resolved, we can run some experiments
• Write a final summary note

Meeting notes 4/11¶

• document the code you wrote with comments describing what it's supposed to do
• when testing land-procedures, read comment and write test based on what the code is supposed to do

Summary¶

This issue started as a way of looking at the relationship between labor value and wage rate. In researching this issue, we discovered that the economy crashed under certain conditions, and that crashes were inconsistent across firm structures. After many tests, we discovered the issue mainly lay in the procedure firms followed when determining how much to distribute in dividends. Essentially, firms were only taking into account labor costs when deciding how much money to save, not other input costs as well. Once this issue was addressed, the bug was fixed and the model behaved more consistently.