As long as we can hear you. Now.

>>So thank you, Professor Cameron, for that kind introduction and

thank you to all of you for coming. It is quite an honor to have been

invited to this conference, and it is an honor to be here. So my name is Cynthia Lin Lawell, I am

an associate professor in the Agricultural and Resource Economics Department. The lead author on this

paper is Karen Tomey. She was formerly a PhD student

in the Agricultural and Resource Economics Department

at UC Davis and then subsequently a post-doctoral scholar. She is currently a research

agricultural economist at the USDA Economic Research Service. Unfortunately she could not be here,

so here I am and hopefully I can do justice to her work. So the title of our paper is

investment in corn ethanol plants in the midwestern United States. And when I received the invitation from

Professor Cameron, he indicated that, a good title for

this conference would also include. The methodology. So, actually [chuckles] so

the title, I guess the title of my talk is the investment corn-ethanol

plants is the Mid-Western United States. A structural kind of metric

model of the dynamic ink And so, for this particular conference in

difference into professionals camera, and this conference I have this in this title

by also talk about a little bit more about the mythology and then I would

generally in talk of this shortly. So first I’ll start talking about ethanol. So ethanol has attracted

considerable policy attention from policy makers worldwide. And one reason is that it’s a,

potentially, environmentally friendly

alternative to imported oil. And another reason policy makers worldwide

have been interested in ethanol is that, potentially, it’s a way to boost

farm profits in rural livelihoods. In terms of the ethanol

industry in the United States, the United States is the largest producer

of ethanol in the world and in fact, has passed Brazil in ethanol

production back in 2005. And most plants In the United States use corn as

a feed stock for producing ethanol. So most of these ethanol plants are

located in the Midwestern United States. In the United States

there’s a lot of promotion of industry through government policy. Here’s some examples of policies

that have been implemented. To promote the ACNO industry in

United States at the federal level we have the Renewable Fuel Standard. The Renewable Fuel Standard was

implemented in 2005 setting up although a 7.5 million gallons of

renewable fuels by the year 2012. And so this Was called the RFS1 for

renewable fuel standard one. The renewable fuel standard was extended

in 2008 setting of 15 billion gallons of 16 billion gallons of by 2022 and this new expanded RFS which is

now what’s emplaced today is There also have been policies that

support ethanol at the state level, and these include a ban on MTBE. So the clean air act has

mandated that we blend oxygenates into gasoline, and one of these

choices was MTBE and another was ethanol. However due to concerns about

environmental and health issues related to MTB, MTB was banned by

states at different times. So from an empirical standpoint what was

nice about this ban was the ban came into effect at different times for

each state. Another policy, state level policy, that

supports ethanol as a producer tax credit, and, again, from a standpoint, one thing

that’s nice in terms of identification is not all the states in the sample

have producer tax credits, and those that do were in place for plants

that opened in different And so what we do in this paper is that we focus on

investment decisions of ethanol-producing firms in the Midwestern United States

during the time period 1996 to 2008. Here is a snapshot of our dataset in two years, the first year of our

dataset, which is in the top panel, and the last year of our dataset,

which is in the bottom panel. What we’ve shown here

is the number of plants by county in the ten midwestern

states we’ve analyzed. And basically, the bluer the square,

the more plants are in that county, and the most plants that we see in any county during the time

period of our data set is three. So what we did this paper, is we analyzed

how economic factors, government policy, and strategic interactions affect

decisions about whether and when to invest in

building new ethnoplants. So as we saw in those two snapshots

in the data there have been entry and the building of ethnoplants in Different counties in the midwestern United States

over the time period of our data set. And then what we do is that we

use the estimated structural parameters to simulate the effects

of various counterfactual policy scenarios on

investment in ethanol plants. And so, the method we use is a structural

econometric model of a dynamic gain. And what we do is that we use

the parameter estimates of our model to simulate counter factual policy scenarios. So, the structural econometric model

we use is a dynamic model, and so, you might ask, why do we use a dynamic

model to model the ethanol and plant investment decision Well, you can think of

decisions to invest in building an ethanol plant as decisions that are investment

decisions made under uncertainty. These ethanol plants,

when you invest in them, they are at least partially irreversible,

so when you start building this ethanol plant,

it’s very hard to reverse that decision. So one characteristics of this

decision-making is that we’re making irreversible investments. Another characteristic of

the decision-making is that there’s uncertainty over the future rewards

from making that investment so there’s uncertainty about the rewards

from having [INAUDIBLE] including potential future revenue,

costs, things like that. And so potential policy environment. So there’s a lot of uncertainty. Moreover, there’s leeway over the timing

of when you can do the investment. So you can decide whether and when you make that investment, you don’t

necessarily have to make that investment decision at a particular time period. You might Want to wait. And because of all of these three

characteristics, the irreversibility, the uncertainty and the leeway over the

timing, there’s a potential option value to waiting that is characteristic of

decisions of investment under uncertainty. And decisions with this type of

characteristic are best modeled with a dynamic model. [INAUDIBLE] Another feature of

our model is that we’re not only using a dynamic model, but

it’s a model of dynamic gain. So in this case, potential investors

are not only making dynamic decisions, but the decisions that also potentially

strategic, in a gain theoretic sense. And there are several, sources of

strategic interactions there are several reasons why the decisions of one potential

investor in an Ethno Plant might depend on decisions that might be

need by other investors. One source is a competition affect. So these plants might compete in

local feedstock input markets. So if you have an ethanol plant

you need to purchase feedstocks, in this case corn,

in order to produce your ethanol. And it’s possible that

an ethanol plant might compete on the local feedstock input

market with other nearby plants. And therefore whether or not other people are investing

nearby might affect your decision. Another type of competition is that we

might be competing in the output market. We might be competing in the local

fuel ethno output market with other local plants. The reason why there might be this local

competition particularly in the both the input and

output markets in the case of ethnol It’s due to the high transportation costs

in both the feedstock and ethanol markets. And because of these high

transportation costs, some of these markets can

be somewhat localized. And so, there might be some

local competition, so whether or not you want to build a plant in a

particular county may depend on whether or not there are other plants in that county. And also depend on whether or not you think other people will Eventually

invest in building plans in that county. Another source of strategic

interaction which goes in the opposite directions is agglomeration effect. So, the competition effect,

all else equal, probably makes you less likely to

locate your plant near others. And less like to build a plant if

others will be building a plant. The agglomeration effects suggest that

there might be reasons why you might wanna locate near other plants due

to positive spill-overs. And one might be the transportation

marketing infrastructure. So I had mention that transportation

is very important in this market, and a lot of, for example, ethanol, needs to be transported

by tank trucks, and often by rail. And so if you have other plants nearby, maybe they have already We started

building some improstration terms of transportation and maybe also in marketing

that we might be able to benefits from so might be beneficial to locate near other

plants another source of the glamorization that you’ll might benefits from

is a having educated board first particularly one specialized working with

this eco plants that might beneficial to have might be able to benefit with that

If you’re locating near other plants. So there’s these two sources

of strategic interactions, a negative competition effect and

a positive agglomeration effect. For those reasons it’s possible that

a potential investor in an ethanol plant might condition their decisions on what

they They think others might be doing. So potential investors might base

their investment decision on other investors gravity. So there’s some advantages to using

a structural econometric model to model the decision making of

potential investors. One advantage is that we explicitly

model the dynamic investment decision, and In particular we’re incorporating

the continuation value to waiting, which explicitly captures how expectations

about the future affect current decisions. So when they’re making their decisions,

they’re thinking about the future. And with a structural model we’re

explicitly modeling how that takes This place. Another advantage of the structural model

is that, we’re estimating structural parameters of the underlying dynamic

with direct economic interpretations. So the parameters we estimate

are parameters are useful in terms of economic theory. And so that’s a nice thing to have. Parameters that have direct interpretation

in terms of economic theory. And these parameters includes the effect

of each state variable in the expected payoff from investment. So these are parameters. In payoffs that you get from investments,

so those are objects that we care about. We also have parameters measuring

the net effective strategic interaction. So that’s another set of

parameters we care about. And in contrast, if parameters from

reduced farm models are not structural models are confounded

by continuation values. So they don’t have a direct

Economic interpretation unlike the parameters that we estimate. Another advantage of a structural

[INAUDIBLE] model is that we better estimate the strategic

interaction between potential entrance. So we’re explicitly modeling how

expectations are formed about what other potential competitors will be doing. And so we’re incorporating

that Explicitly in our model. Another advantage is that, because we’re

estimating parameters through structural interpretation and economic parameters,

we can use these to calculate welfare. And so,

that’s something that would nice to do. And also, we can use the parameter

estimates to simulate the effects of counterfactual scenarios on decisions

about investment and welfare. So, those are all advantages of

having the structural model. Catholic welfare and also seeing like the facts of

counterfactual scenarios and policies. Okay so our model is that our modeling

decisions made by potential investors or potential entrance in the ethanol

industry we index them by i. These investors are making dynamic and

strategic decisions of whether to invest in an ethanol plant in

a particular county k in year t. And in each year t, all investment

decisions are made simultaneously, and our i for decision maker i and

county kat time t is a for investment by potential investor i,

county k, and year t. And investment decisions may

depend on a variety of variables. First they might depend on publicly

observable county level state variables. And we call the steady state variable

omega k t k for the county t for the time per year and there are three

sort of categories of such variables. N K T will be our variables

measuring the strategic interaction, G K T is our government policy and

X K T are our economic factors. So our decisions may depend on strategic

interaction, government policy and economic factors. In addition, our investment decisions

may also depend on private information. So these private observed shocks,

epsilon IKT. Which may capture, for example,

private shocks to our cost of building an. So let me parse out each

of those three variables. Strategic interaction,

government policy, economic factors. The strategic interaction is going

to be our dummy for whether or not another investor has built

an ethnoplant in county k by time t. So whether or not there’s a ready,

a plant in that particular county. And this measures the net effect of

competition and agglomeration effects. That’s measuring whether or not we have

someone there already, in accounting. And so the potential entrance may

condition their investment decisions, not only on the current number of

ethanol plants that are already there. when they’re making their decision but

also on expectations about future number of ethanol which includes

the expectations about what they think. People who are currently not in

the county might doing the whether or nothing might be building this are In terms of government policy a second set of

state variables, the government policies we include are the ones I talked

about before the MTBE ban which is a ban on another type of oxygenate

that you can use in blending gasoline. Which means that ethanol Becomes

sort of one of the only choices for running in gasoline, which is a sort

of a policy that’s towards ethanol. We also included government policy for

tax credits, and the two stages of the renewable

fuel standard, RFS1 and RFS2. In terms of economic factors we include

some factors that affect the revenue from building an ethanol plant. And this includes ethanol price which is

your price of the output, gasoline, price. And so. If can view ethanol as a substitute for gasoline then gasoline both might have a

positive, having a higher gasoline price. Higher price for your substitute might

possibly affect Your revenue in your past. However, if you viewed ethanol as an or

an additive or a complement to gasoline,

then if gasoline prices are higher, potentially that might

have a negative effect. So that’s a part of empirical

question that we could see, that we can answer when

we Estimate our model. Another factor that affects revenue

is our proximity to cattle. Why is that so? So this is going to proxy for

sales of distiller’s grains. Distiller’s dry grains or solid drills is

a co-product of corn ethanol production. So when you’re producing ethanol as a

co-product, you also end up producing some of the Distillers grain, and you can

sell that co-product for animal feed. And so cattle, among other animals, may be

able to consume some of these co-products, and that’s a sort of

a source of revenue too. Another set of economic variables we

include are factors that include cost The effect cost include, including

the availability of corn which is your feed stuff, so

transportation is cost as I mention so how available corn is near

by will effect your cost. Corn price will effect

your cost as soil price, another potential thing the ETE

printing or the effect of you cost Natural gas price, which is a major

energy source for milling corn. It might affect your cost,

likewise electricity price. And also, whether or

not there’s a biodiesel plant nearby, because that might The biodiesel plant

may compete indirectly in the feed stock market since much of the Midwest

can be planted to soil form. So biodiesel plants,

biodiesel by large uses soy. And so, as a farmer considering

what to do with the land, often times they can plant either corn or

soy. And so, having a biodiesel plant nearby

may effect these farmer decisions and therefore affect What’s going

on in the feed stock market and my input prices if I wanna

use corn as feed stock? Okay, and so, we have our function

of payoff from investments. So if I decide to invest, I get a payoff, which you can think

of as a present discounted value, an entire stream of payoffs,

after I’ve made my, decided to invest. And so here that payoff is

a function of strategic interactions economic factors

is also a function of that type of information you can

actually separate them. So we have a deterministic action

Which is deterministic function of the publicly observed state

variables and then the [INAUDIBLE]. And so here we’re going to use our

notation omega kt to indicate our set of publicly observed

state variables so you can write this notational

more as the following. And here our our private information

we’re going to assume is distributed identically, independently with an

exponential distribution associated with parameter sigma. and so the parameters you want to estimate are

parameters in this deterministic component of the per period or deterministic

component of the pay off from investment. And the parameter sigma in the

distribution of the primary information, and so our econometric estimation

will take place in two steps. In the first step we’ll estimate

continuation values, and predicted investment probabilities, and the second step we use generalized

methods and moments, or GMI to match the predicted probability

to the active probability In the data. And so, the valley function, so what I had written out previously was

a path you get if you decided to invest. Well the valley function is going to tell

you what the present discounted value and stream of expected payoffs is for

a potential entrant. Well that’s going to be

the maximum of two things. It’s going to either equal the payoff from

investment which is what we showed before. So if I decide to invest,

I get the payoff from investment. If I decide not to invest, instead of

getting the payoff from investment, I get beta which is a discount factor

times The continuation value, and the continuation value is what I

get if I decide to continue and wait, and not invest now but

potentially invest in the future. So the continuation value is the expected

value of my value function which is the same value function here. Except now it’s evaluated at next

peer state variables and shocks but I do not yet know what next period

statements and shocks are so I take the expectation of what they

might be conditional on what I do know which is today’s state variable and

the fact that I did not invest. Invest today. So I either decide to invest today, which incase I get the payoff from

making that investment or I wait. And if I wait I get continuation value, which is basically the option

of investing tomorrow. And then tomorrow I’m faced with

the same problem, do I invest or do I wait until the next year. And so, basically which ever is

higher will yield a decision, so decide an investment a particular

year if my payoff that year is higher than anything I

can get from waiting, which incorporates my expectations of

what I’ll get in the future if I have that preserved option of investing in

the future instead of And so that’s the continuation value in the investment

probability so my probability investing we can write up the probability investing

conditional just a private excuse me. Just a public information and it’s using

our exponential distribution assumption we have this particular expression. And so the idea from the behind

the Estimation techniques of falling, First we obtain a non perimetric estimator

of the continuation value in the first step, We plug it into our expression for

the investment probability and then now we have estimate for

the investment probability predicted by the model and

we choose perimeters that best matched The predicted probabilities predicted

by the model with the actual data. So that’s the idea behind how

we’re estimating the parameters. And just a little bit about

the nonparametric estimator for the continuation values. So this is based off of

dynamic programming, and we’ve vectorized everything. And so this is This BC will represent

our a sort of vectorized notation for the continuation value. And it turns out with an exponential

distribution assumption, we have a nice closed form expression. And M is a transition matrix and

we have the continuation value here. And we have the investment probability for

which we use empirical probability To estimate so the transition density will

use empirical probabilities to estimate. The predictive probabilities will use

empirical probabilities to estimate and we see the continuation value

appears on both sides and the way we obtain a non parametric

estimator for the continuation value. Is that we solve for a fixed point. And then that will give our estimator for

the continuation value, which we plug into our expression for

the investment probability, in which we then choose parameters

to best match with the data. So that’s,

sort of in a nutshell what’s going on. And so, a little bit about the results

from the structural model First we find that the payoffs of ethanol investment are

positively affected by number of things. So they’re positively affected by

the corn production intensity. Of that particular county which

is the corn anchorage in that county divided by the total

area of the county. Which is the measure of available

corn is in that local area. It’s also effected by whether or

not we have banned MTBE. So, if we have banned MTBE then the potential revenues

from ethanol are higher. And so

they are more likely to invest there. Also the second stage, the current RFS2,

positively affects investment decision. And also private information shops. Positively affect investment decisions. And so,

we use the prime estimates to simulate several counterfactual

policy Policy scenarios. So we simulate a situation where we have all the policies that are currently

in place, except we take out one. So one simulation is we

take out the RFS of one but leave all of the other policies in place. Another counterfactual scenario

that we simulate is that we have all the policies we have currently

in place but we just take one and this time we only take out

The RFS 2 the expanded version. Another policy is the only one policy we

take out is the tax credit, another one is we have all the policies and we just take

out the MTBE band and then we have sort of the scenario where we take out all the

policies, so there’s no policies in place. And so, here, I have the results of simulating over using the information

from the full time period of our data set. And so, I’m presenting for

each of the simulations, the number of entrants we end up

having in that particular simulation, the total welfare, and then the welfare,

mean welfare per entrant. And the base case is if we’re

just simulating the actual scenario with all the policies and case. And it turns out, I don’t present it here, but the simulations on the model actually

replicate the actual data very well. So but we’re gonna compare with the base

and then you have the different Scenarios where we take out one

of each of these policies and the scenario where we take

out all the other policies. And we normalize the welfare so that the mean welfare per entrant of

the no policies scenarios go to one. So all these welfare values

are normalized against that. So first I would present, so the stars here present the significant

level of a two sample T test. Between each of these scenarios and

a base. So I’m comparing these counter facts or scenarios with the actual situation

where we have all the policies in place. And so how do we interpret this? What this is saying is that

if you have stars scenario. These numbers are significantly

different from the case where we have all the policies. And so here we can see that

the number of entrants and welfare, are significantly lower

when there is no RFS two. So if you take out RFS two

these numbers are lower, moreover they’re significantly

lower indicated by the star. So without that second expanded

RFS two we have fewer entrants. Industry and also welfare is lower. We can also do a two-sample t-test

now comparing each scenario, instead of a base,

we’re comparing against no policy. How does this,

having all the policies except for that one policy we have now In that

scenario compare with having no policy and here first we can see all the situations

which includes at least one policy or as have significantly higher

number of entrance and welfare compare to the situation with

no policy and so that’s take away here Here we also present results from the pre

RFS period so it turns out that all the states in our sample ended up being an

MTBE by the time the first RFS took place. Which means we can identify

the MTBE In the post RFS period, because there’s no situations were we have

an RFS and a state without the MTBE band. So in order to look at this MTBE band we

have to limit to a sub period of our data. And so again, now we’re comparing

the Each scenario against the base where we have all the policy and

then we can see that the number of entrance in the welfare are significantly

lower when there is no MTBE band. So if we take out that band and now we

have fewer and in lower welfare and now if we compare all of these scenarios having

no policy We can see that having no MTB has similar affects on welfare and to the

a lesser of steps that is not significant. The number of entrance excuse

me since this is significant. The lesser the number of entrance

Comparing this with no policy, you don’t have a significant

difference in welfare and you only have sort of

a somewhat significant in and the numbers are actually not that

much different in terms of entrance. And so here, if you just take MTB E-band, it’s very similar as taking

out all of your Policies, so on conclusion first we can say that

the intensity of corn production. Government policies and

private information jobs have all significant effects on

ethanol payoffs and decisions. And other policies analyze MTB event and RFS2 blood to the most of

the investment during this time period. And in terms of possible implications. One implication is that maybe why are

these posses working and not the others? One possible reason the MTBE ban was

effective in inducing investment and building ethanol plants is

that increased the demand for ethanol as an oxygenate in place of MTBE. And similarly, one possible

reason the RFS2 was effective in inducing investment in building

ethanol is that increased demand for ethanol by mandating an expansion

ethanol consumption. And so the similarity here is

that our results should suggest that policies that increase the demand for

ethanol have the potential for inducing investment in

building Ethanol plants. So that’s one policy implication. Maybe increase demand for ethanol. A second policy implication

is that both the MTBE ban and the renewable fuel

standard can function as implicit blending [INAUDIBLE] [INAUDIBLE]

However, according to economic theory. When we have unpriced emissions

as a sole market failure. It turns out that what achieves the first

best would be something like a carbon tax or a cap and trade program. And in contrast, a mandate, implicit or

not, is unable to replicate the first. And so another former PhD student of mine,

Gabriel Lade, who is now Assistant Professor,

Iowa State. In his research, he finds that

if you have to have a mandate, a mandate is not going

to give you first best. If you combine it with a cost containment

mechanism, such as a credit window price. Then you can actually increase

the efficiency of that policy. And so Passwal implication is that

in our result we find MTB band and renewable fuel standard seem to work to

induce investment in building ethanol plants but if we wanna make it more

efficient one thing to do is maybe combine with a cost containment mechanism or

better yet use a market based instrument. And then the third structural

have many advantages and maybe particularly useful for analyzing

designing policy and you can use them all scenarios on decisions So

thank you very much. We have [APPLAUSE] Ok,

we can take a couple questions. Any questions? Maybe I can ask one. So is there data available just on to what extent ethanol is being used? Oxygenate to substitute for MTB.>>Yeah, that’s a great question. It’s tricky to, I guess,

separate out why we’re using ethanol.>>Okay.

>>So, right now, most, a lot of the ethanol we use

is blended with gasoline.>>Yeah.

>>So if you think about when you go to the gas station,

whether or not we know it, some of>>Of the gasoline we have is blended with ethanol and up to E10. And most of our cars can handle that. And so it’s hard to tell whether or not when that happens and

it does satisfy the oxygenate requirement. But it also, for a variety of reasons,

they might be doing it. So it’s hard to separate out Exactly

the reasoning for that blending and so for that reason it’s that I did x

amount of gallons because of the oxygenate requirement but I think

it’s a really interesting question and it might be something

that’s worth tackling here.>>So it’s not really a stack question but

the on ethanol is actually. Doesn’t save all that much

energy necessarily right but if it has this other purpose of we

don’t have to do it with MTBE and that’s actually something

a positive aspect.>>That’s right.>>Yes?

>>In the game you’re restricting your competition to just within counting other

firms, I’m wondering how sensitive your. Results are to integral access in

county level restraint to maybe moving a neighboring county

is affected in competition.>>Yeah please Ben. So that’s an excellent question. So we actually before we did

the structural model we did some exploratory analysis using despot models,

in part just as he said we actually did the delineation of the boundary of what

a particular game or market is at. Is very important. And there are various you know, or

factors you want to consider when making that decision,

including how the data is also delineated. That for better or

worse might affect your decision making. But when we didn’t reduce our model, what

we did do is we also you know, reduce for a model we allowed for what we called

spatial lags of neighbor’s decisions. So we had That neighboring decisions

from neighboring county as well, we found out that actually

wasn’t as important. There was a lot of decay as you

might expect as you go further away from the county. From a computational perspective

when you do these structural models, the more potential neighbors you have, the

more computationally expensive it becomes, the more difficult it is to estimate And

based on our results from our reduced firm model that suggested

that beyond a county level, this last [INAUDIBLE] neighbors coming from

bordering countries were as important. Based on those results, we decided a good trade off with

a limit of market to a county level. But it is an excellent consideration

that I’m bad at English, so pardon me.>>Okay, thank you, once again.>>[APPLAUSE]

>>Okay, that’s good. You’re good.

All right, thank you.>>I guess I should say that

>>Last two presenters are regular students, prestige students. Last two we had someone from

environmental science enforcing I hope each year we have room for one or

two prestige students to present as well. Okay, that’s it.>>Okay, thank you [Kahn?],

thank you very much for inviting me and again this is a great honor

>>To be a part of this, so my name is I’m a candidate

in the economics department and today I will present my job migrant

paper named drowning the labor market, impacts of immigrants and natives and for

this presentation I’ve stripped down all the economics and I’ve mostly

concentrated on the methodological part. So there will be a lot of things

that I will be skipping but I’ll pay most attention

to the methodology. So there is such question I’m interested in is what’s the impact of immigrants

on native’s wages and employment. This is a very important question. So immigration

>>In modern days society that

plays a crucial role. So, for instance in the United States one

of six workers is foreign born currently immigrations of major part

of political campaigns, and the major part of

the president campaign. Of Donald Trump’s campaign

It’s also an important part of the policymaker’s agendas worldwide. And it’s also everywhere

in the media nowadays. So here I have a picture

from the Economist, an issue of the Economist from

this summer, where they’re saying, now immigration actually

declines the political spectrum, where we have people of the left

>>Who say, we welcome immigrants, and we like them. And then here, we have people here on the

right side who are afraid of immigrants. So understandably,

coming impacts of immigrants is critical. And I wanna emphasize that besides

economic, they have also cultural and other social impacts. But here, we’ll be focusing only on

the impact of On the baby market outcome. All right, so here is a basic scatter plot

if we have a, so for each labor market. I’ll define labor market in a little bit,

but on the Y axis we have natives wages, and on the X axis we have immigrants and

this is their changes. For about 1,400 they were

marketing the United States. And we see the basic

correlation is negative. However a big problem in

estimating this impractical is what we call that

the immigration is indulgent. So by indulgent means where

immigrants located is usually not. Not random. So they would choose to go to cities

that are actually doing well, they pay higher wages. So in the data it could be difficult

to find the negative correlation. Even if, in fact, there is one. So usually we have instruments and we can

hope to correct from this [INAUDIBLE] and estimates get a little bit

more negative once we do that. A second problem of this

literature is that researchers report a whole array of estimates, okay. So here we have a computer histograms of these impacts of

immigrants on Native’s wages. So beta is the stimulus [INAUDIBLE] Was the percent change in Native’s

wages when immigrants. This share increase by

one percentage point. So this is by different approaches, and

the approaches doesn’t really matter, just the different ways to estimate this

in fact.So here we say that, here we see that regardless of the approach we

really have estimates all over the place. And actually moreover, recent years, using the same data set oftentimes

they reach an opposite conclusion.>>So this a lot of examples in

the literature assuming the focusing on the same case study is in the exactly

the same you can get opposite results. Here is the same just by United States or the rest of the world

>>We see that a lot of the estimates cost around zero, but

actually, the variance is really high. And no matter what

country we condition on.>>So, what is.>>Yeah.

>>What would be a big number? What would 0.1 mean? So 0.1 means we increase the share of

immigrants by one percentage point, so, let’s say, from 10 to 11. Natives’ wages will decrease by what? 0.1%.

So really these are small numbers, but actually I’ve solved in

the bottom corner at 1.5. So, there’s some for example right there. See, this paper is saying okay, we don’t actually need new ones because we

already have almost [INAUDIBLE] the ones. What we need is some

sort of reconciliation. We need to think what is

the feasible range that is of this impact that could actually be So

I take a step back and identify this interactive immigrants

of under much weaker assumptions. So I apply a bounds which rely on milder instrumental variable and assumptions which I can claim

[INAUDIBLE] in this part. [INAUDIBLE] So you realize the assumption

[INAUDIBLE] homogeneity and [INAUDIBLE] conditions that

are embedded in classic linear models. So if we have a linear model and

even with [INAUDIBLE] two stage square. Estimation will rely on a linear equations

and rely on the being homogenous for across all units or

across only in the markets in this case. So we can imagine that some

market maybe easy maybe more maybe better just To observe immigrants

in terms of the industry composition for example, so they may have a smaller

magnitude or even positive impacts. And some labor markets may be very,

very hurt from immigrants. They may experience

a larger negative impact. And I also would like,

The exaggeration of the instrument, which I’ll talk about in

just a couple of slides. So a couple of the contributions that I

can highlight from this presentation is that I narrowed the battlefield or the field of disagreement among

researchers in the literature about what is actually the true value of

this parameter that we’re interested in. And they provide the first non-parametric

estimate So this is the first paper to consider relaxing these

assumptions in the literature. So now we get into the empirical part. This slide just lays out the notation. So we have a variable d,

which is our treatment variable. So you can think of share of immigrants. D has to be discreet. D has to take a, find a number of values. So we have, let’s say we have a group

of cities or labor markets that receive the least number of immigrants and

then some that’ll get more. And then we have again the last group

who gets the most Share of immigrants, or growth of immigrants. Then we have outcomes, potential outcomes. So here you can think of this as

a native’s wages in a given labor market. So, two things are important here. First is that this variable

has to be bounded. It needs a bounded support. So there is a lowest possible value and

there’s the highest possible value. Second, we’re in this

potential outcome framework. So for each labor market you can imagine outcome under each

different treatment level. Okay so for instance San Jose let’s say

let’s take the city of San Jose has a large immigrant so you can imagine what

would’ve happened if San Jose didn’t have any immigrant or had a little bit and

so on under all possible treatments. We have an instrumental variable which so the dominant instrument in the literature

is the so called shift share.>>But for this presentation,

you can think of it as just the lag. So just the sheer evidence may be 30 or

40 years ago, whatever date is available. And we have some covariance

which I will not condition on. The notation just to simplify it. So most of the results go through,

conditional on some control variable. So now we can go back to the potential

outcomes and as I said for each labor market only one is observed but there are also unobserved

counter factual outcomes. So then we can compose each treatment

level we will compose the mean potential outcomes into parts that we observed,

so these are potential outcomes. That are actually observed in the data for

each city, and the probabilities are easy

to estimate as well. But then in red are potential outcomes

which happen in a different world, something that we don’t know

what would have happened. So for instance,

this is the average potential outcome. So here this would be What would have

happened to San Jose if they didn’t have any movements, for instance, so

the whole empirical strategy would rely on substituting this with something

we could observe in the data. So, as usual when interested

in between let’s say for now I need to different treatment values

for instance this could be The cities that got the most immigrants and the cities

that got the least just for instance, then average treatment effect is just a

difference in two main potential outcomes. So now we can think about

bounding these average treatment effects in the following sense. So we can think of, What is the smallest that this ever

should have an effect to this. So this will give us the lower value. You cannot go more,

you cannot go smaller than that. Well this is smallest when

this term here is smallest and when this is largest, okay? So this is exactly what I have right here. So when we have the lower value

of the first potential outcome The first treatment level and

the upper bound and the mean potential outcome

under the second treatment and very similarly we can think what

is the largest that this could be? Well this one is largest,

one of the first terms is largest and when the second term is largest. So this give us an upper bound

of the actual treatment in fact whichever it means right here. So could you just clarify it’s the upper

bound of a what, on what distribution.>>It’s in the upper bound on

the average [INAUDIBLE] Method. Of the difference between

these two potential So what’s the larger in [INAUDIBLE] and

what’s the smallest? All right, why don’t you continue?>>Okay. Let’s talk about it later So now in the next few slides, I will

introduce assumptions which are weaker than the usual assumptions of the linear

models that we often estimate, so they will not point and identify a single

value for beta for our treatment effect. But they will give a set

of values called bounds that are consistent with

these weak assumptions. This a weak number metric assumption. So first we begin with this

no assumption bounds without making more [INAUDIBLE] restrictions. So here we say that we don’t

know what this term is. But we know that it cannot be longer than

[INAUDIBLE] Or it cannot be higher than. So we just substitute this here

with y min and y max right here. So in the boundary boundaries

we substituted y min and in the upper boundary

we substituted y max. So this gives us a so

called null assumption or imperial bounds on the mean potential outcomes and

therefore on the average treatment effect. Where does y min and y max come from?>>Well [INAUDIBLE]. Yes so

you have to assume a bounding support. So if your bounding probability, that’s even an assumption because

it’s already between zero and one. I will show you how I round this later. So I wanna talk a little bit about this

graph because it will be useful in the next two slides. So here, this, so

the dashed line here is the lower bounds, the solid line is the upper bound,

and it’s exactly the representation of the equation that I have up above, and

here it says for each treatment level d, we have three types of units,

there are three types of labor markets. We have labor markets that

are attractive Fewer immigrants. With labor markets that have attracted

exactly the same number of immigrants, so which are easy because we

can observe the outcomes. And we have labor out markets that

have attracted more immigrants. So, what this graph says is for

the first and the third group there are unobserved

potential outcomes under [INAUDIBLE] unobserved So we know that it’s

going below the line here and if you don’t get higher why not,

it’s just the same thing in the figure. So now I’ll introduce

the first assumption, it’s called monotone treatment attraction,

so in the literature, if you’re seeing on this paper,

it’s called monotone treatment selection. Here I changed the wording. Just a little. So speaking,

this assumption is interpreted in this context as better cities

attract more immigrants. And formally speaking,

if you have two treatment levels, then given that a labor market has

chosen the higher treatment, so given that it has attracted more

immigrants Then its mean potential outcomes would be at least as

large under all treatment levels. So in a sense better cities will

attract more immigrants and here’s how identification works,

here I have it in pictures and here I have exactly the same

thing in equation form. So, this is just the same picture

from the previous slide, and this vacation goes as follows. So, for each treatment of the D. There are 3,000 labor markets. The ones that are attracted fewer,

the great ones that are attracted exactly the same, which are the good ones

because we reserve those, and ones that have attracted more So

under the monitoring treatment assumption, it says what

are the first groups. So the first group,

they are attracted viewers, in a sense so were in the sense of a lower wages. Were they to increase the treatment, were they to get more immigrants The

outcomes cannot be higher than the one of the group that is currently

getting that treatment level. And similarly for the third group so

the third group is a group of so were they to get fewer immigrants their outcome

could not be lower than the second group. So this is the intuition of the. Identification result. And here is exactly the same thing. So then, once you weight it by

the probability of being in each state. Then you get the balance

on the potential outcomes. And then on the treatment effect. So here, the next assumption is

called [INAUDIBLE] response. And it’s assumption on

the treatment of that sign. So here I assume that immigrants

depress native’s wages. So I didn’t mention this earlier but

in the paper I placed more focus on the lower bound, I’m more interested in

the lower bound for a couple of reasons. So assuming this, we’ll even give it

an even more negative lower bound, so it’s that this is a mild assumption if

we’re interested in the lower bound. So the identification

follows a similar reasoning. So the next slide, I’ll talk

about instrumental variables, and then we go on to the data and the results. So in this slide, I wanna introduce two distinct

instrumental variable assumptions. So the first one is the one that we’re all

used to, it’s the exclusion restriction of That we routinely make in applied work. So I think here’s a good time,

well yeah I mentioned the instrument you can think of the instrument

as the lack of the immigrant. So the first assumption says

that no matter what level of. Of your instrument you

have then the current the mean potential outcomes are exogenous,

they are all equal. So the interpretation

in this context is that the location of past immigrants

is exogenous in this sense. And of course this is the strong

assumption if you have a linear model you add in for every treatment effect or

you can also add in by local average treatment effect

in a slightly different setting. So the way that identification works

is actually pretty straightforward so then we estimate the lower of

the no assumption lower bound. And the no assumption upper bound,

so we estimate exactly these bounds. On each point of the support of our

instrument, and then for a lower bound. So because it’s exogenous, for

a lower bound we can take the largest lower bound of the conditional bound. And for the upper bound we can take the smallest

Upward bound of the condition advance. So you can imagine without any assumption, the bounds are negative infinity and

positive infinity, right? So our goal is to shrink the two bounds so that we hopefully get some more,

some informative The results. Then they show that actually this in a certain context this assumption

could be difficult to justify. So we can relax this assumption

by substituting this equality sign with an inequality. So, this results in the monotone

instrumental variable assumption, and this assumption Allows for

a relationship between your instrument and the mean potential outcome. So it says that if [INAUDIBLE]

attracted more, [INAUDIBLE] marketing attracted more immigrants back in the day,

then they currently are also doing better. So this is important. Because, researchers have argued against the usual instrument of variable in the

literature, which says, if some city is, had what we called the demand

charts back in the day, they were doing really well, then these

demand charts could be auto [INAUDIBLE], and they can still attract

more immigrants today. So in that case if you understand

the IV of your model then you have this correlation between your

instrument and your error term. So you’re getting inconsistent estimates. So then at the [INAUDIBLE] Under

the model [INAUDIBLE] Variable, slightly similar it’s definitely simpler

than I think [INAUDIBLE] Formula makes it look like, yeah. So again, you do this at each

point of the support of Z, and then, however,

only one part of the support is. And then you have to condition out, you have to weight by

the probability of being each Each. At each point. So now very quickly I’ll talk

about the data that I use and then I’ll show you the results. The resulting under each

of these assumptions. So I use United States census data. And as the labor market,

I define in the mainstream. Specification and defined a city or

a commuting zone by education group. So for instance again in San Jose, the low skilled people in San Jose,

they compete in one labor market. They compete for the same jobs. And again same skilled people in same

city compete for different jobs. It’s a different labor market. So as my variables, I take difference. So these bounds are constructed for

cross section of data. So I cannot use the panel

structure of the senses. So I think differences in [INAUDIBLE]

specification between 2010 and 19 90 so for each level of market I take the

difference in the log wages of natives and here’s this, so I bound the support

of this variable by the first and the 99th percentile. Colin I think it what you

were talking earlier, so this is what empirically

people do in the literature. Unless you have probabilities which

are bounded by definition for treatment variable use difference in the foreign point as

a percentage of the initial population. And I discretize this into five groups

with equal number observation so if you’re in the first 20th percentiles

then you you’re assigned And they go 2, 1, and so on and so forth. And I focus an average effect,

comparing the labor markets that received the most immigrants with the other three

groups, with the other four groups. And I have an instrument,

which you can think of. So these are my main results So this is already in the units of beta, and

the scale goes from negative 0.8 to 0.8. Here we begin with the null assumption

.So each line corresponds to the bounds obtained under the respective assumption. And this orange points are confidence. So you can imagine how each of

these points are estimates right, so they come with some

kind of variability. And it’s reflected in

the conflict interval. So we’ll start with a values go

roughly between -0.4 and 0.4 And we see that As we add more assumptions,

so the more colonies from the variable assumption is a weaker assumption

than the instrumental variable one. So the inbounds they cannot be narrower. Okay?

So we see if only we use the instrumental variable assumption, again we’re in

this setting Then the resulting bound is about half of the width of

the no assumption bound. Then we have the monotone

treatment response assumption, which was the assumption

of the treatment effect. So this restricts the treatment

effect to be negative. And we still don’t get very much

traction on the lower bound. Monotone treatment attraction

was the assumption that says. Better cities attract more immigrants. So really mild assumption, and we the upper bound quite a bit,

and the lower bound not so much. If we combine this assumption with

instrumental variable assumption, okay? Then we get a narrow informative Results. And here we have the point

estimates from the linear model. So you have only linear model. Then you get, you’re sort of in

the middle of the no assumption bound. And I want to lastly I want to

put these in perspective, so if you think, if we again plot

what the literature estimates or this is all estimates on the United States

then here this is my null assumption or my imperial bound we see that under very

mild assumption without relying on any instrument variable, about a. Only about a fourth of the estimates are

in the literature actually consistent with these. So this is a very I think

surprising finding. Even if you have minimal

assumption structure, you get an informative,

in this sense, result. And as my preferred balance

that have the [INAUDIBLE] and IV estimates would actually define the

narrow amount of feasible values for beta. And here is the similar thing just when we condition most of the [INAUDIBLE]

we get similar results. And I’ll end with other questions. We’re already a little bit fast.>>[APPLAUSE]

>>Any questions?>>Couple questions.>>Yes.

>>I was wondering if you could empirically test some of your assumptions, like the monotone treatment of attraction,

and monotone treatment of response. Let’s say you Empirically?>>Yes, so that’s a really good question. Unfortunately, you cannot. So these are assumptional

potential outcomes. It’ll so you cannot test them,

but if you combine these two assumptions And

they have the same signs so you see here the sign is positive, here the sign is

negative so in this case it doesn’t work. But if you combine them and they have

the same sign then you can test them. So then they lead to the hypothesis

that depending on the sign the outcomes are either increasing or

decreasing in the treatment level. So if you combine it then you can test.>>That would be in a different

application to yours?>>Yeah in a different so

not in my way yeah.>>In your application they’re not?>>Yeah.

>>It’s not reasonable to assume the

>>Right.>>science?

>>Exactly so I didn’t show this but I can motivate this assumption

from economic theory and economic theory happens to be

>>Compatible in this side of the assumption. That’s a really good question.>>So two questions. One is, when you look at your

favorite bounds at the end.>>Yeah.

>>And you look at the most negative number,

is it big enough to be a positive? [INAUDIBLE]

>>So is it by having a mild

effect on native wages or is it substantial enough

that Donald Trump is, right?>>So

I need to prepare more on this question. I would imagine the answer is subjective.>>Yeah I need to think more about it.>>Okay and the other one is it seems that

this procedure to me the more you dice it, so the more labor markets you have and

the more treatment levels you have it seems to

me that you might get broader bound.>>Right?

Is it to incorrect, and what is it really important to make sure you define

your labor markets correctly because it does seem your results will change

according to you you define the landmark. So, again first question I don’t

see your intuition Can you.>>That’s fine no no it’s

fine just say that yeah. That’s fine yeah.>>In the paper I have quite

a few Robertson’s checks and in fact I’m not sure if I

have it here I don’t think. So my first Robertson’s

check I just look at labor markets just on geographic

limit without having these. Groups, and

they don’t seem very different.>>Thank you.

>>I don’t see too sure. And the second question?>>It was related, it’s fine.>>Okay.

>>Thank you.>>Okay.

>>Thank you very much.>>Thank you.>>[APPLAUSE] Okay, well our last speaker is Jeran Choy, and he’s also from Economics. And take it away.>>Okay, I’m Jeran, and

I’m the last speaker of the conference. Thank you for remaining seated until now. And the title is measuring

intergenerational income elasticity using rit IV method for

two sample IV regression. And this is a joint work with

Jiang Yu of University of Toronto and Shu Shen of UC Davis. So, before we talk about the two

simple linear adding model. Let’s first talk about

the [INAUDIBLE] If you are interested in the impacts

of education on the race. The typical assumption is

[INAUDIBLE] secretly shot. That’s not affecting their

education [INAUDIBLE] So this is a correlation between w and

u is equal to 0. Under a little more assumptions,

the OLS estimator is consistent. However, in many cases. Like an unobservable ability that’s

simultaneously affecting education and. Then the x estimator is the inconsistent. In this situation, we use instruments

such as mother’s education level, and father’s education level. That’s related to the W, but

not related to the individual stability. And in this situation, we used ID

estimator Defined this beta hat i v is equal to z prime double

inverse z prime y and on the assumptions this i v estimator is

consistent the impact of educational. However in many cases we observe

the independent variable y. And w in two separate samples,

while the instrument z in both samples. There are many empirical examples,

in such a situation and Krueger propose computing the z

prime w inverse from one sample, and the z prime y from the second sample. And more fully, we define that I had two

sample ideas to where subscript ID 0 is the first sample, and subscript ID

2 you know is the second sample. And using the second sample’s

moment to use this to input this. And to the first sample, moment to Inpute this then under certain assumptions

this two sample ID estimator is consistent for

the coefficient of the repressor. So let’s take. Say for example, so 20, 15, They study and they estimate this trigger

in the generational income elasticity between father’s and children

of both sexes in the United States. And let’s take a table, look at the table. So in the first sample They

only observe white one, which is early because there was son. And that observed

the father’s earnings level, while they observed

instruments in the sample. While in the second sample,

they can now observe son’s income, but they can observe the father’s income Data. And also they can observe

instruments of z. And they use, in this two-sample

structure, they use two-sample, two [INAUDIBLE] estimator,

which is an expansion of two-sample IV, to a case where there are more than

instrument z, than instrument w. Which is defined as this. Where beta hate two sample

two square is as follows and this is first using the second

example regress w 2 and z 2 and they impute unobserved fathers in

count w one hat which is now observed. And using this double one hat,

then they also regress y on the w one hat. Then they can get too simple too [INAUDIBLE]

Estimate. However, the problem of their

paper is they’re too central, too [INAUDIBLE] Estimator suffers

from weak instrument problem. More precisely to be the problem is

[INAUDIBLE] to our weekly collaborative in [INAUDIBLE] sweepers in the [INAUDIBLE]

to the first stage of the question. The problems of this slick and [INAUDIBLE]

problem on standard one simple idea progression framework as well as

[INAUDIBLE] Such as this estimator this bias in small samples and

this bias is towards and their inference methods are incorrect

such as test of significance have incorrect size and

confidence intervals are wrong, yes?>>So when you say small samples here. Yeah.

>>How small are you talking about?>>[INAUDIBLE]

>>So, you know just 50 observations. It could be 1,000 observations and

you’d still have this problem? Yeah.>>Yeah. So, your problem is just the essence on a

theory Just it needs really really really large sample in order to go through okay.>>Yes and in one sample standard case instrument roles instrument method

such as Anderson Ruby test and Kleinberger’s test and test and developed

and we can use that inference method. Now, how can we do any difference in

this procedure in the two simple idea lessons with three differences,

such as the [INAUDIBLE] most case. And it would be [INAUDIBLE] literature

in found that there are no such methods exist in the [INAUDIBLE] different. What should you do? Should make [INAUDIBLE] procedure, right? So let’s review the problems, the two

sample the two standard risk estimator on the we do Monty Carlo simulations and

generated beta hat two sample two stage risk scale estimators

and our left-hand side and righthand side. So where k indicates

the number of instruments. A lambda over k measures

the strength of instrument. When the lambda over k is equal to one,

in this picture, we say weak ID case. And lambda over k is 16. We say a strong instrument case. As you can see in the left panel

This blue line is the distribution of two sample two series peers and

this red line is the normal distribution. As you can see, this distribution of the type two series your s varies

far away from normal distribution. And the case is quite similar

to normal distribution. So this two sample two stage list

curve estimator is poorly approximated by a normal distribution there

by invalidating the conventional inference method that are based on sorry

based on the number of approximation. Right this is the first problem.>>So just to be clear on that first one. The actual estimator just

an enormously more variability than what our usual theory says it is.>>Yes.

>>Thank you.>>So this is the first problem of two stages on the this case. And the second problem is two sample,

two stages can be And we’d use as one less with

the general risk because we first gave [INAUDIBLE] we

come to the [INAUDIBLE] and we generated regressive, and first it

says we then we have measurement areas. If the first test has a measurement error,

and we suffer from this two

state Two [INAUDIBLE] bias. The bias goes toward zero and is larger

where the first case is [INAUDIBLE] so following the calculation of [INAUDIBLE]

paper we can approximate this bias

of [INAUDIBLE] as follows. As you can see it depends on data and this term is the first h f the strength

of the instrument plus one. And let’s analyze this and the bias is let’s first think about extreme case where

f is zero, it’s extremely instrument. Then this is one so

the bias is equal to minus peter. Which means the type, too simple

which shows the bias is towards you. And the second is is lower

than we get higher bias. Which I already mentioned. And the third is if beta is zero,

then the bias is zero, which means the bias gets larger

when beta is away from zero. There are three points. So, for both those reasons, for a normal

approximation could not kick in, and the [INAUDIBLE] bias problem We do not

recommend the two simple two-stage estimator when involving the instrument. So this is the coverage of 95% interval of two simple two-stage

estimation So we expect. If the inference method is correct,

we expect the number is 0.95. And this lambda over k is the weakest. One is weak and

4 is medium and 16 is strong. And k is the number of instrument,

1, 5, 10. And in the data generating process of

beta equals negative 2 and 0 and 2. And as I said when beta is away

from zero we expect larger bias. So this is far from 95% and

if beta is zero, we do not have the bias but

the normal approximation does not kick in. So especially in this when

instruments number is one and the big instrument is 0.99 is far

away from 95 So how should we do? So we have to make

a testing procedure that is robust under two sample

linear ideal model. So what we do is we stand which

instruments goes methods from standard one sample to two sample linear either model

And we do what they call a simulation. We have good size property. And also, we found that [INAUDIBLE]. And we propose two test statistics. One is the two sample. And the other is two sample [INAUDIBLE]. And in general, two sample has better

[INAUDIBLE] than a two sample [INAUDIBLE]. And lastly, we apply our methods

to one empirical seminar study by that adapts the two sample ID

framework on the weak ID and they, what they did is to estimate,

is to recall and we apply our method and

compare it with their method. Okay, this is the direction of the top. So let’s first briefly talk

about the test statistics. So this is as follows. Consider a two sample id regression

model with [INAUDIBLE] w and multiple instrumental variable z. So if we can observe y w z in one sample,

we don’t need the sample two. Right but we can now observe

this w 1 in sample 1 that’s why in sample 2, w 2 equations. And we are interested in testing

the two sided null hypothesis where null is beta is beta naught and the alternative is beta is not equal to

beta naught and we also want to construct. Say, 95 confidence interval. And the problem is existing method

such as AR and CLR are not directly applicable of this case because

we have more and more equations. So this is our proposed two testing

methods Which is the forms of the AR and CLR test statistics defined

in Andrew’s 2006 paper. Where recall t1 is a test statistic,

which is defined as q s hat. And the second is t2,

which is the two step CLR test statistic. And this test is kinda

transformation of and and omega hat where omega

hat s kinda transform linear IV model of error

covariance matrix. So this our new proposed Methods, there’s a complete cook book to sample

IV [INAUDIBLE] framework even under the instrument case, and the our purpose

to my associates are consistent, and control signs [INAUDIBLE] partially even

under the identification And we can also construct confidence by inverting

the decision groups of the proposed tests. So let’s check whether it really is so we do Monty Carlo simulations and

this is the basic data generating process from data set

one where our sample size is 1,000. Y and w, so this is sample one. And this is sample two,

where we have 200 observations. And instrument z follows

normal distribution where k is the number of instrument. And interesting thing is here rho,

rho measures of this y1 and w1. But we said this could be one point

0.1 throughout the simulation with all our geniorisity because the [INAUDIBLE]

one and two are independent. So, saving more than one

is without [INAUDIBLE] and we can see there that the [INAUDIBLE]

are generating processes. They can number of instruments one and

two and ten So one instrument, two instruments, and ten instruments. And lambda over k, I said this measures the strength

of instrument one week 16 strong. And also this lambda over k is one to pi. And also note that this lambda

over k is approximately, F is approximately equal to

this concentration plus one. So concentration parameter is 1,

which is is 2. And concentration parameter is 16, is 17. For all simulation we used

5% significance letter, and you report the proportion of rejections

under a total of 5,000 rejections. So first let’s take a look at the size

comparison Size is the probability of falsely rejecting null hypothesis

when the null is true. Okay so we expect all the this x axis is beta under the null beta and

this is a proportion of rejection. So we. We expect it to be 0.05. So, and as you can see, ARSCLR has,

no matter how the number of instrument, k. How the number of instrument and

how the strength of the instrument, ARSCLR is 0.05, which a control size. While the two separate two

[INAUDIBLE] Fails to size, right? As you can see here. And when the problem is

more aggravated with it. Especially when the lambda over K is

equal to one [INAUDIBLE] The problem is more aggravated. And also we have more

instrument the problem. Is worse, okay? So in this sense,

our proposed methods control size well. Even under re-identification. Let’s go, next thing is the power. Power compressing under no hypersis

is better, is equal to zero. And power is defined the probability

of correctly rejecting When is true okay so that’s power and so what’s the proposal power comparison

because we want to compare a r and r so from here when null hypothesis

is true we expect 0.05. However, when beta is not equal to

zero we expect a higher number and that means a higher power. And throughout, in general,

we found the seal, our purpose two sample sealer has better

power performance than the two sample AR. So this is a power compressor. And this is a coverage of

95 confidence interval. So first, this is as I already

showed you are very poor. And this is our propose AR and

our propose CR. And as you can see,

no matter how the number of instrument, how the strength of instrument,

the call reach of this cost is around .95. So in this sense our propose

are really And now let’s apply. Let’s apply [INAUDIBLE] two

methods to one empirical study which is [INAUDIBLE] 2015 by [INAUDIBLE]. Where they estimate historical into

generational [INAUDIBLE] between fathers and children of both

sexes in the United States. This is the basics of the paper. Where y1 is the son’s income,

local son’s income. And in example one we cannot,

so father’s income. So this is now observed. And z1 is the instrument,

where they use a full set, the first name which conveys social

economy status Since we can observer w1, we need the second sample,

which is w2 at the farthest [INAUDIBLE]. And the instrument. There, [INAUDIBLE] strategy, is using first student’s first name,

which convey socio-economic status, as instrument to create [INAUDIBLE]

links across generations. And how they do is exactly two separate,

two stage [INAUDIBLE]. First, they regress [INAUDIBLE]

on a full set of [INAUDIBLE]. And they create [INAUDIBLE]

which is predicted [INAUDIBLE]. And then they again

[INAUDIBLE] on y1 [INAUDIBLE]. This is exactly two sample,

two [INAUDIBLE] estimator. And what they find is they find

the father, son-in-law, and experience, two increases, one in 1870 and

another big jump in 1900. So this is their main figure. And the problem we pose it is they use two sample two estimation for

in case of reforestation. The problems I already showed to you and

emphasized and what we do is a plan are two simple CLR method and

replicating their result and compare it. So let’s proceed what their result is, so first let’s focus on the blue

line which is the father son-in-law intergenerational elasticity

[INAUDIBLE] So before I explain this. What’s the meaning of

intergenerational income elasticity? Let’s think about 0. 0 means father’s income and

son’s income are not correlated. Which means the society is mobile. Let’s think about number one. Father’s income is very highly

correlated with son’s income. Which mean the society is kind of unequal. Is immobile. So what they asking is that

let’s first look at the. IT’s around 0.4, right? And there’s a two big jump,

one in here and one in here. That’s what they find. And next, let’s look at the first stage. This is what we do. We calculated their F statistics. First stage F as you can see is

around 23 which is very, very low F. And from this figure what we find is that

there is one big jump in here, right? One big jump from 2.2 to like 3. And the first beginning I emphasized

when f is lower, kind of this we expect, the two sample two by towards zero right? That’s what I first introduced when f is

lower the bias is lower and towards zero. This kinda around zero and what do you expect our result,

our CLR confidence interval? Any suggestions? [LAUGH] No suggestion there,

let’s look at the next slide. So this is 90% confidence interval for

their result. There is jumping here. And this is what we replicate

the result with our purpose to sample, see a lower method. 90% constancy interval. And we see unlike their result, what we

is there is a big jump from 870 to 900. And there’s a big drop in statistics. We trace the society’s becoming

more immobile and then mobile. That’s what we interpret the results. And last is the same one,

the intergenerational statistic. And the first is two sample

90% confidence interval and this is our two sample CLR

90% confidence interval and this is a sample size and what you see. In general our 90% confidence

interval is wider and higher And this is,

what we guess is that the bias is 0. Right, it is low. So that’s why we guessed their 90%

confidence interval is lower than ours. Okay, so

I think this Is the end of the program. Thank you for listening and any questions? Okay. [APPLAUSE]>>So

you focused mainly, it’s a great topic, so you focused mainly on the indoctrunous

independent variable, lets say you also had some other control variables. Are there any restrictions than what you

need if you have these two data sets. Do you need to be able to absorb all the involved data sets you know

>>Yes>>Or one what happens on your first date and a related

>>The question is that I guess if you’re observing

variables in multiple datasets.>>Mm-hm.>>Like say your instrument or

any of the regressors.>>Mm-hm.>>Are there requirements about. Do they have to be exactly

the same value if you happen to observe something that’s

a common observation? Or what happens if something’s

imperfectly measured. So I guess two [INAUDIBLE].>>Good questions.

So first.>>In two samples,

we have to have same axis. And the second question,

we impose some assumptions. Let’s say expected value of z1 prime z1 is

equal to expected value of z2 prime z2. Some kind of these

reasonable assumptions And we get this result. So, [INAUDIBLE]

is only one IBS estimated. Those go through.>>I need to ask Shu Shen for help. [LAUGH]

>>[LAUGH]>>I’m not sure if it made sense. I’ve never heard of

two-sample [INAUDIBLE].>>No, yeah, no, me neither. So, the thing that [INAUDIBLE]

does is to try to use a kind of [INAUDIBLE]

To take out this bias. Originally, yeah. To take out the many item bias, right? So but then in this too simple case. There’s no [INAUDIBLE] Bias because

the first [CROSSTALK] [INAUDIBLE]>>So, the bias and stuff comes from another Grace that’s a [INAUDIBLE]

still so you

>>[INAUDIBLE]>>Any more questions?>>So your result is kind of showing that the previous research has

overestimated the mobility. Right?

>>Right.>>But that doesn’t, like at some point

you said something about equality.>>Right.>>But that’s completely different right, like it could be,

you could have very mobile society.>>Right.

>>And very unequal at same, all the possible combinations

of inequality and mobility.>>Right right. I should be more careful,

mobile versus immobile. Yeah. Right.>>Okay, well thank you very much.>>[APPLAUSE]

>>That’s it for this year. Okay, so next year hopefully we’ll have the same thing, and

we’ll spread the word, and tell more people what a great conference it is.

Okay.