Statistical Methodology in the Social Sciences 2016: Session 3

Statistical Methodology in the Social Sciences 2016: Session 3


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.

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