Zi Yang Kang
@ziyangkang.bsky.social
Economist + assistant professor at the University of Toronto
20/ Finally, perhaps the most important thing: Mitch is also a wonderful human being and colleague.
Hire him and find out for yourself! ☺️
Mitch's JMP: www.mitchellwatt.com/files/toppin....
Our other paper: www.mitchellwatt.com/files/OIKR.pdf.
Hire him and find out for yourself! ☺️
Mitch's JMP: www.mitchellwatt.com/files/toppin....
Our other paper: www.mitchellwatt.com/files/OIKR.pdf.
www.mitchellwatt.com
December 3, 2024 at 6:16 PM
20/ Finally, perhaps the most important thing: Mitch is also a wonderful human being and colleague.
Hire him and find out for yourself! ☺️
Mitch's JMP: www.mitchellwatt.com/files/toppin....
Our other paper: www.mitchellwatt.com/files/OIKR.pdf.
Hire him and find out for yourself! ☺️
Mitch's JMP: www.mitchellwatt.com/files/toppin....
Our other paper: www.mitchellwatt.com/files/OIKR.pdf.
19/ Outside of these two papers, Mitch has a ton of other work, including:
- a paper (R&R at ReStud) with Paul Milgrom
- an empirical(!) paper with @johnjhorton.bsky.social and @shoshievass.bsky.social
- his own papers
Check out his long CV here: www.mitchellwatt.com/files/Mitche....
- a paper (R&R at ReStud) with Paul Milgrom
- an empirical(!) paper with @johnjhorton.bsky.social and @shoshievass.bsky.social
- his own papers
Check out his long CV here: www.mitchellwatt.com/files/Mitche....
www.mitchellwatt.com
December 3, 2024 at 6:16 PM
19/ Outside of these two papers, Mitch has a ton of other work, including:
- a paper (R&R at ReStud) with Paul Milgrom
- an empirical(!) paper with @johnjhorton.bsky.social and @shoshievass.bsky.social
- his own papers
Check out his long CV here: www.mitchellwatt.com/files/Mitche....
- a paper (R&R at ReStud) with Paul Milgrom
- an empirical(!) paper with @johnjhorton.bsky.social and @shoshievass.bsky.social
- his own papers
Check out his long CV here: www.mitchellwatt.com/files/Mitche....
18/ By solving these, we also derive other results in the papers, including:
- comparative statics with respect to redistributive weights
- results on how valuable *preventing* topping up is to the social planner
- extensions with budget constraints and equilibrium effects
- comparative statics with respect to redistributive weights
- results on how valuable *preventing* topping up is to the social planner
- extensions with budget constraints and equilibrium effects
December 3, 2024 at 6:16 PM
18/ By solving these, we also derive other results in the papers, including:
- comparative statics with respect to redistributive weights
- results on how valuable *preventing* topping up is to the social planner
- extensions with budget constraints and equilibrium effects
- comparative statics with respect to redistributive weights
- results on how valuable *preventing* topping up is to the social planner
- extensions with budget constraints and equilibrium effects
17/ Summarizing these technical difficulties for my fellow nerds:
Mitch's JMP 👉 topping up allowed 👉 social planner's problem = convex program with FOSD constraints.
Our other paper 👉 topping up not allowed 👉 social planner's problem = convex program with SOSD constraints.
Mitch's JMP 👉 topping up allowed 👉 social planner's problem = convex program with FOSD constraints.
Our other paper 👉 topping up not allowed 👉 social planner's problem = convex program with SOSD constraints.
December 3, 2024 at 6:16 PM
17/ Summarizing these technical difficulties for my fellow nerds:
Mitch's JMP 👉 topping up allowed 👉 social planner's problem = convex program with FOSD constraints.
Our other paper 👉 topping up not allowed 👉 social planner's problem = convex program with SOSD constraints.
Mitch's JMP 👉 topping up allowed 👉 social planner's problem = convex program with FOSD constraints.
Our other paper 👉 topping up not allowed 👉 social planner's problem = convex program with SOSD constraints.
16/ The analysis is tricky because the outside option of each consumer depends on his demand type.
We overcome this by guessing Lagrangian multipliers and verifying that they are optimal.
It took us many guesses and sleepless nights, but now we can write them out:
We overcome this by guessing Lagrangian multipliers and verifying that they are optimal.
It took us many guesses and sleepless nights, but now we can write them out:
December 3, 2024 at 6:16 PM
16/ The analysis is tricky because the outside option of each consumer depends on his demand type.
We overcome this by guessing Lagrangian multipliers and verifying that they are optimal.
It took us many guesses and sleepless nights, but now we can write them out:
We overcome this by guessing Lagrangian multipliers and verifying that they are optimal.
It took us many guesses and sleepless nights, but now we can write them out:
15/ Also, this result concerns the social planner's *marginal* incentives to intervene, but it doesn't tell us what the *global* optimum is.
To do that, we develop mechanism design tools.
To do that, we develop mechanism design tools.
December 3, 2024 at 6:16 PM
15/ Also, this result concerns the social planner's *marginal* incentives to intervene, but it doesn't tell us what the *global* optimum is.
To do that, we develop mechanism design tools.
To do that, we develop mechanism design tools.
14/ Of course, this assumes that you want to redistribute to consumers with the lowest demand.
There are cases (think disability care) where you might want to redistribute to consumers with the highest demand.
Our result covers these cases too.
There are cases (think disability care) where you might want to redistribute to consumers with the highest demand.
Our result covers these cases too.
December 3, 2024 at 6:16 PM
14/ Of course, this assumes that you want to redistribute to consumers with the lowest demand.
There are cases (think disability care) where you might want to redistribute to consumers with the highest demand.
Our result covers these cases too.
There are cases (think disability care) where you might want to redistribute to consumers with the highest demand.
Our result covers these cases too.
13/ So, on the margin, the cash transfer effect dominates. This means that a sufficient statistic for when it's optimal to intervene is the *average* social value of a dollar to consumers.
Intervention is optimal if + only if this exceeds the shadow cost of that dollar!
Intervention is optimal if + only if this exceeds the shadow cost of that dollar!
December 3, 2024 at 6:16 PM
13/ So, on the margin, the cash transfer effect dominates. This means that a sufficient statistic for when it's optimal to intervene is the *average* social value of a dollar to consumers.
Intervention is optimal if + only if this exceeds the shadow cost of that dollar!
Intervention is optimal if + only if this exceeds the shadow cost of that dollar!
12/ We use a first-order approach to bound these effects (quantity distortion vs cash transfer).
We show that an ε quantity of a free public option leads to:
- an O(ε^1.5) 👆 in consumer utility from quantity distortion
- an O(ε) 👆 in consumer utility from cash transfer
We show that an ε quantity of a free public option leads to:
- an O(ε^1.5) 👆 in consumer utility from quantity distortion
- an O(ε) 👆 in consumer utility from cash transfer
December 3, 2024 at 6:16 PM
12/ We use a first-order approach to bound these effects (quantity distortion vs cash transfer).
We show that an ε quantity of a free public option leads to:
- an O(ε^1.5) 👆 in consumer utility from quantity distortion
- an O(ε) 👆 in consumer utility from cash transfer
We show that an ε quantity of a free public option leads to:
- an O(ε^1.5) 👆 in consumer utility from quantity distortion
- an O(ε) 👆 in consumer utility from cash transfer
11/ Since you want to redistribute to low-demand consumers, this is the best targeting that you could hope for.
With linear subsidies, there would have been 👆 quantity distortion for *all* consumers.
With linear subsidies, there would have been 👆 quantity distortion for *all* consumers.
December 3, 2024 at 6:16 PM
11/ Since you want to redistribute to low-demand consumers, this is the best targeting that you could hope for.
With linear subsidies, there would have been 👆 quantity distortion for *all* consumers.
With linear subsidies, there would have been 👆 quantity distortion for *all* consumers.
10/ Why? When topping up is allowed (Mitch's JMP), having a tiny quantity of a free public option results in:
(1) 👆 quantity distortion for low-demand consumers
(2) 🚫 quantity distortion for high-demand consumers
(3) 💵 cash transfer (= price of public option) to all consumers
(1) 👆 quantity distortion for low-demand consumers
(2) 🚫 quantity distortion for high-demand consumers
(3) 💵 cash transfer (= price of public option) to all consumers
December 3, 2024 at 6:16 PM
10/ Why? When topping up is allowed (Mitch's JMP), having a tiny quantity of a free public option results in:
(1) 👆 quantity distortion for low-demand consumers
(2) 🚫 quantity distortion for high-demand consumers
(3) 💵 cash transfer (= price of public option) to all consumers
(1) 👆 quantity distortion for low-demand consumers
(2) 🚫 quantity distortion for high-demand consumers
(3) 💵 cash transfer (= price of public option) to all consumers
9/ So when is it optimal to intervene with nonlinear subsidies?
When you're trying to redistribute to consumers with lower demand: if + only if it’s optimal to intervene with a *free public option*.
Note that we would've gotten the wrong answer by focusing on linear subsidies!
When you're trying to redistribute to consumers with lower demand: if + only if it’s optimal to intervene with a *free public option*.
Note that we would've gotten the wrong answer by focusing on linear subsidies!
December 3, 2024 at 6:16 PM
9/ So when is it optimal to intervene with nonlinear subsidies?
When you're trying to redistribute to consumers with lower demand: if + only if it’s optimal to intervene with a *free public option*.
Note that we would've gotten the wrong answer by focusing on linear subsidies!
When you're trying to redistribute to consumers with lower demand: if + only if it’s optimal to intervene with a *free public option*.
Note that we would've gotten the wrong answer by focusing on linear subsidies!
8/ It turns out that whether consumers have the ability to top up or not drastically affects the analysis.
So, Mitch's JMP 👉 topping up is allowed.
Our other paper 👉 topping up is not allowed.
So, Mitch's JMP 👉 topping up is allowed.
Our other paper 👉 topping up is not allowed.
December 3, 2024 at 6:16 PM
8/ It turns out that whether consumers have the ability to top up or not drastically affects the analysis.
So, Mitch's JMP 👉 topping up is allowed.
Our other paper 👉 topping up is not allowed.
So, Mitch's JMP 👉 topping up is allowed.
Our other paper 👉 topping up is not allowed.
7/ And why do we have two papers rather than one? Because housing is different from health care!
You cannot top up your public housing unit by renting more space privately.
But you can top up your public health care with visits to private doctors/clinics.
You cannot top up your public housing unit by renting more space privately.
But you can top up your public health care with visits to private doctors/clinics.
December 3, 2024 at 6:16 PM
7/ And why do we have two papers rather than one? Because housing is different from health care!
You cannot top up your public housing unit by renting more space privately.
But you can top up your public health care with visits to private doctors/clinics.
You cannot top up your public housing unit by renting more space privately.
But you can top up your public health care with visits to private doctors/clinics.
6/ So what makes our take on them new?
(A) Motivated by instruments we see (e.g., free public option), we allow for *nonlinear* subsidies.
(B) Unlike much (most!) of mechanism design, outside options are *not* zero (everyone can always consume their laissez-faire allocations).
(A) Motivated by instruments we see (e.g., free public option), we allow for *nonlinear* subsidies.
(B) Unlike much (most!) of mechanism design, outside options are *not* zero (everyone can always consume their laissez-faire allocations).
December 3, 2024 at 6:16 PM
6/ So what makes our take on them new?
(A) Motivated by instruments we see (e.g., free public option), we allow for *nonlinear* subsidies.
(B) Unlike much (most!) of mechanism design, outside options are *not* zero (everyone can always consume their laissez-faire allocations).
(A) Motivated by instruments we see (e.g., free public option), we allow for *nonlinear* subsidies.
(B) Unlike much (most!) of mechanism design, outside options are *not* zero (everyone can always consume their laissez-faire allocations).
5/ Of course, we are far from the first to ask these questions.
There are many excellent papers (e.g., in public finance) that have examined them!
There are many excellent papers (e.g., in public finance) that have examined them!
December 3, 2024 at 6:16 PM
5/ Of course, we are far from the first to ask these questions.
There are many excellent papers (e.g., in public finance) that have examined them!
There are many excellent papers (e.g., in public finance) that have examined them!
4/ In each of these two papers, we answer these questions by:
(1) Developing "sufficient statistics" that give necessary + sufficient conditions to intervene.
(2) Building new mechanism design tools to figure out optimal interventions, which we can cutely summarize like this.
(1) Developing "sufficient statistics" that give necessary + sufficient conditions to intervene.
(2) Building new mechanism design tools to figure out optimal interventions, which we can cutely summarize like this.
December 3, 2024 at 6:16 PM
4/ In each of these two papers, we answer these questions by:
(1) Developing "sufficient statistics" that give necessary + sufficient conditions to intervene.
(2) Building new mechanism design tools to figure out optimal interventions, which we can cutely summarize like this.
(1) Developing "sufficient statistics" that give necessary + sufficient conditions to intervene.
(2) Building new mechanism design tools to figure out optimal interventions, which we can cutely summarize like this.
3/ But is this optimal? Specifically:
(1) *When* should governments intervene with these instruments?
(2) *How* should governments optimally design these instruments?
(1) *When* should governments intervene with these instruments?
(2) *How* should governments optimally design these instruments?
December 3, 2024 at 6:16 PM
3/ But is this optimal? Specifically:
(1) *When* should governments intervene with these instruments?
(2) *How* should governments optimally design these instruments?
(1) *When* should governments intervene with these instruments?
(2) *How* should governments optimally design these instruments?
2/ Here's the gist: Governments often redistribute by intervening in markets such as housing and health care.
Common instruments for interventions include a baseline "public option" (think public housing/healthcare) and subsidy programs (like private subsidies).
Common instruments for interventions include a baseline "public option" (think public housing/healthcare) and subsidy programs (like private subsidies).
December 3, 2024 at 6:16 PM
2/ Here's the gist: Governments often redistribute by intervening in markets such as housing and health care.
Common instruments for interventions include a baseline "public option" (think public housing/healthcare) and subsidy programs (like private subsidies).
Common instruments for interventions include a baseline "public option" (think public housing/healthcare) and subsidy programs (like private subsidies).
I think the bigger point is just that there are other reasons for intervention in markets than for the sake of economic efficiency (equity being an example here).
December 2, 2024 at 5:17 PM
I think the bigger point is just that there are other reasons for intervention in markets than for the sake of economic efficiency (equity being an example here).