“Risk Sharing and Transaction Costs; Evidence of Kenya’s Mobile Money Revolution”
by Suri and Jack
How does risk sharing work?
Earlier in the course:
Each member of village (somewhere in Africa) offered a choice: $5 now, or flip a coin: heads=$25, tails= nothing.
Notice: this repeated game is a supermartingale! (fancy math term for “profit on average”)
Notice: the “risky” option has higher expected gains.
apparently most of the villagers chose the $5 option; ok so they have a concave income utility function and are risk averse.
Even if each villager is risk averse, there’s definitely a way to profit while avoiding risk: pooling their resources!
How does this work? Benevolent social planner tells everyone to take the risky option and split the winnings at the end.
Math:
Suppose: N villagers
Optimal Contract defines Arrow-Debreu Security that everyone gets an equal cut in the end
If everyone took safe option, total winnings =5N
If everyone takes risky option: total winnings = 25*Binomial(0.5,N)=X random variable
Chebyshev’s inequality:
We can very easily put upper bound on probability we end up worse off than had we all just taken the safe option instead
Moral of the story: with increasing N village size, law of large numbers kicks in, which cushions “risk shocks” to any particular member of village, the essence of “risk sharing.”
Potential explanations for why people in developing countries do not implement “risk sharing” mechanisms:
A. lack of training:
Apparently many people in developing countries have not received training in probability theory. That’s ok, the grad students Ben TA’ed in EE505 “probability for engineers” also did not receive training in probability theory, and yet all we grad students are covered by UW insurance, so that’s not the problem.
B. Moral Hazard/Adverse Selection:
This is apparently a big deal especially in developing countries, as we’ve learned in this course.
(e.g. somebody doesn’t pay up when the time comes with the Arrow Debreu Security and it’s difficult to enforce, or a slacker decides to sign on for free riding.)
C. Physical/practical transportation limitations of actually literally getting wealth or money from one place to another
This is exactly what this paper addresses.
Risk sharing model no transaction costs:
3 players all with the same income-consumption utility function
Aggregate income normalized to 1
Mathematical model boils down to:
i=1,2,3 players
s= [1, 2, 3 … S] states of the world
Expected utility is always the same, we just want to minimize risk to make everyone happy; analogous to BLUE estimation from statistics
Intuition: optimal contract just shoves every outcome from anywhere on the triangle directly right at the center
Risk sharing model WITH transaction costs:
We define cost k each time wealth moves from one person to another. (e.g. somebody physically has to take a bus to deliver.)
3 cases:
A. 2 transactions, we share resources equally:
B. 1 transaction, highest gives to lowest income:
C. no transactions, everyone keeps their stuff they originally had:
Risk sharing model WITH transaction costs:
Here’s what the optimal income sharing plan looks like:
Intuition similar to previous: push towards the center when far away, paying k for each bus trip worth it. When near the center, don’t bother. When there’s a very clearly distinguished first, second, and third place, first place gives to third place.
Random related side note #1:
This is very analogous to the theory of optimal transport
Wasserstein distance metric/ earth mover’s distance quantifies the amount of resources it takes to reallocate “stuff” and is very useful in probability theory for proving convergence in distribution using Stein’s method
However notice here that each transfer is a fixed cost rather than a penalty proportional to amount of stuff times the amount of distance that stuff was moved
Random related side note #2:
Terrance last week: “Ben are you going to talk about thermodynamics or something?”
Supposedly the phase regions change shape with increasing k cost of transport in the third dimension, but they maintain the same general outline
Indeed directly from the previously proposed model:
Main pertinent physical/practical limitations of cash transfers in Kenya:
A. bus fare expensive
B. bus ride is a long and timely voyage
C. bus does not exist
D. people get robbed on the way
E. destination is simply too far away (other side of the country)
(so if we’re going to have to get someone to deliver the moneys by bus, each transaction delivery costs k.)
B and E are particularly pertinent in Kenya since families are dispersed far apart, like our galaxies
So to get around this, we must use technology!
Solution: digital cash!
In economically developed countries, we have credit cards, bitcoin, NFT’s, and Husky Dollars on UW ID cards, which practically EVERYONE uses.
In Kenya, they have “M-PESA” which everyone uses: send money via SMS
In China, homeless people beg for money by asking donors to scan their wechat qr code on their phone, backing up Professor Riley’s original claim that China is no longer a developing country
Rest of the paper: statistical analysis of real-world collected data from Kenya over time: putting this theory to practice.
Research question: does mobile money in Kenya help people share risk?
TL;DR
Experimental design/analysis methodology:
2 groups: Mobile money users versus non-mobile money users
Compare their incomes during a “shock” versus normal income.
Clearly there are many other variables to consider in the linear model as well as adjusting for confounding for average causal treatment effect, but that’s the big picture idea.
Here’s the data
key take home points from the very very long 20+ page statistical analysis
Experiment: 2282 households surveyed in 2008 and then they followed up in 2010.
During this time:
M-PESA users jumped from 43 to 70 percent
Cell phone users jumped from 69 to 76 percent
Indeed M-PESA percentage < cell phone percentage
Clearly the significant increase of M-PESA users comes from the increase in M-PESA infrastructure:
Hopefully we get some Huawei infrastructure too in the United States
key take home points from the very very long 20+ page statistical analysis
Results:
If M-PESA user: on average, when they suffer a negative “shock” in income, consumption stays the same/unaffected
If not: when they suffer a negative “shock” in income, consumption decreases about 7% on average.
We care about “poor” group in development economics
key take home points from the very very long 20+ page statistical analysis
Statistical/econometric theory: lots of hypothesis testing and making sure there’s no conflicting other factors in our measurements to really make sure we’re measuring the direct causal effect of “M-PESA usage” on “cushioning income shocks on dynamic consumption over time.”
Long story short here: it seems pretty apparent that the advent of M-PESA does significantly have a big effect on consumption during an income recession shock.
Is it a causal effect? I mean in layman terms, what else could have caused it? Why else would M-PESA users have constant consumption whereas non-M-PESA users didn’t?
Intuitively: if my income fluctuates a lot, I have to cater my consumption to be commensurate to the instantaneous level of income, unless I’m good at saving, which we already saw was not the case in poverty and developing countries. If my income is more or less constant, I can have more or less constant spending.
So anyways, on with the consequences and perspective of this…
Insightful consequences of this study:
Supposedly in Macro ECON502 last quarter which Ben dropped since engineers can’t cram all of undergraduate macro, all they do is try to “ease the shocks” from real business cycles to make growth smooth or whatnot.
In the controls systems department of electrical engineering, we spend all our time designing stable autonomous dynamical systems to avoid perturbations from these shocks.
In this paper, the advent of M-PESA allows people to stabilize their consumption over time.
I suppose engineering and economics aren’t so different after all!
In terms of the consequences to directly relevant to development economics:
Insightful consequences of this study:
Supposedly people in Kenya are on average willing to fork up 3-4 percent of their income to ease the burden of shocks of low income and have more constantly smooth income, which of course will smooth out their consumption.
Mathematical insight: I suppose in solving the dynamical Euler equation we apply a electrical engineering low pass convolution filter to the utility consumption function over time.
Supposedly this is the essence of CFRM at UW: people are willing to pay for managing and mitigating risk involved with their pay.
Perhaps a way out of poverty and helping development and economic growth: mitigating risk definitely contributes to this.
Mitigating risk has direct contribution to social global welfare and has inherent economic value, just like how bitcoin’s inherent value is in the fact it facilitates transactions not backed by any government.
So indeed, helping facilitate risk-sharing is indeed very useful.
Insightful consequences of this study:
M-PESA’s direct contribution to the facilitation of risk sharing:
Removes transaction costs
Expands the network! People can collaborate with people from distant lands
This is helpful and further reduces risk: law of large numbers kicks in with bigger N in the village. (This is exactly how pooled insurance agencies work.)
Also because M-PESA from the government, they can have organized insurance systems among strangers, not just among family members and friends.
This is very similar to Ben’s research with UW Marketing Professor Shulman involving Block-Chain Cryptographically secure smart contracts for crowdfunding purposes:
Ben was originally planning to go to Tsinghua University’s communications engineering PhD program but ended up at UW Electrical Engineering instead, so it is worth mentioning: the advent of new technologies and communication networks has important consequences not only in the engineering world, but also in the business economics and development economics fields as well.
Open-ended discussion:
What other ways could mobile money be used in Kenya other than risk sharing? Alibamazon?
If you can’t think of anything; more evidence that M-PESA has a direct causal effect on income consumption smoothing and risk-sharing!
Do you think that mobile money could help facilitate a financial sector in developing countries?
Do you think it’s easy for rural villagers to latch onto this foreign novel concept of mobile money?
Ben saw a lot of cell phones in rural Senegal in 2010, but mobile money is a bit of a jump