Instrumental Variable Help

[Falco Wolf]

Hi,

I'm having trouble with a new instrumental variable. So I'm trying to find some causality, between how people think what their prices are and what they are. To get this causality I need some variables, and I've been directed to create some IV's, and have done many. So I believe that one of the driving factors are mortgage rates.

I tried this one below.
reghdfe SVoverLiquidTW log_fam_income age sex educ mstatus emp_status fam_members (misper_final = l2.misper_final), absorb(ZIP510 year) vce(cluster msa2 year)

And was told I was wrong, and that I should use an IV that is ela*libor. That is, the elasticity of prices(x)the interest rate of the market.

Does this mean my IV will have to look like: reghdfe SVoverLiquidTW log_fam_income age sex educ mstatus emp_status fam_members (ela*intrate), absorb(ZIP510 year) vce(cluster msa2 year)? Or have I just done an interaction variable?

I'm putting some of the code below but I believe it wont be very useful since i'm missing many values for the first 100 observations.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(SVoverLiquidTW log_fam_income age) byte(sex educ) float(int_rate elasticity10)
.  9.950609 48 1 0     . .
.  9.950609 48 1 0     . .
.  9.392662 57 1 0     . .
.  9.950609 48 1 0     . .
.  9.392662 57 1 0     . .
.  9.950609 48 1 0     . .
.  9.950609 48 1 0     . .
. 10.005592 49 1 0     . .
. 10.005592 49 1 0     . .
. 10.005592 49 1 0     . .
.  9.511111 58 1 0     . .
. 10.005592 49 1 0     . .
.  9.511111 58 1 0     . .
. 10.005592 49 1 0     . .
.  10.08581 50 1 0     . .
.  10.08581 50 1 0     . .
.   9.62905 59 1 0     . .
.  10.08581 50 1 0     . .
.  10.08581 50 1 0     . .
.   9.62905 59 1 0     . .
.  10.08581 50 1 0     . .
.  10.05406 50 1 0     . .
.  10.05406 50 1 0     . .
.  9.756436 60 1 0     . .
.  10.05406 50 1 0     . .
.  10.05406 50 1 0     . .
.  9.756436 60 1 0     . .
.  10.05406 50 1 0     . .
.  10.10234 52 1 0  7.38 .
.  10.10234 52 1 0  7.38 .
.  9.765604 60 1 0  7.38 .
.  10.10234 52 1 0  7.38 .
.  9.765604 60 1 0  7.38 .
.  10.10234 52 1 0  7.38 .
.  10.10234 52 1 0  7.38 .
.   8.88461 63 2 0  8.04 .
.  10.03012 53 1 0  8.04 .
.  10.03012 53 1 0  8.04 .
.  10.03012 53 1 0  8.04 .
.  10.03012 53 1 0  8.04 .
.   8.88461 63 2 0  8.04 .
.  10.03012 53 1 0  8.04 .
.  9.298168 64 2 0  9.19 .
. 10.210972 54 1 0  9.19 .
. 10.210972 54 1 0  9.19 .
.  9.298168 64 2 0  9.19 .
.   9.11603 24 1 0  9.19 .
.   9.11603 24 1 0  9.19 .
. 10.210972 54 1 0  9.19 .
.  9.480368 25 1 1  9.04 .
.  9.595603 26 1 1  9.04 .
.  10.37349 54 1 0  9.04 .
.  9.595603 26 1 1  9.04 .
.  10.37349 54 1 0  9.04 .
.  10.37349 54 1 0  9.04 .
.  9.480368 25 1 1  9.04 .
.  9.828603 27 1 1  8.86 .
. 10.388995 56 1 0  8.86 .
. 10.388995 56 1 0  8.86 .
.  9.585346 26 1 1  8.86 .
. 10.388995 56 1 0  8.86 .
.  9.585346 26 1 1  8.86 .
.  9.828603 27 1 1  8.86 .
.   9.62245 27 1 1  8.84 .
. 10.545341 57 1 0  8.84 .
. 10.545341 57 1 0  8.84 .
.  9.974319 28 1 1  8.84 .
. 10.545341 57 1 0  8.84 .
.   9.62245 27 1 1  8.84 .
.  9.974319 28 1 1  8.84 .
. 10.496815 57 1 0  9.63 .
.  9.384294 28 1 1  9.63 .
. 10.496815 57 1 0  9.63 .
.  10.25136 29 1 1  9.63 .
.  10.25136 29 1 1  9.63 .
. 10.496815 57 1 0  9.63 .
.  9.384294 28 1 1  9.63 .
. 10.499573 29 1 1 11.19 .
. 10.499573 29 1 1 11.19 .
.  9.480368 23 1 1 11.19 .
.  9.267477 30 1 1 11.19 .
.  9.480368 23 1 1 11.19 .
.  9.480368 23 1 1 11.19 .
.  9.267477 30 1 1 11.19 .
. 10.545341 30 1 1 13.77 .
. 10.663966 31 1 1 13.77 .
. 10.663966 31 1 1 13.77 .
.  9.517825 24 1 1 13.77 .
.  9.517825 24 1 1 13.77 .
. 10.545341 30 1 1 13.77 .
.  9.517825 24 1 1 13.77 .
. 9.2591305 25 1 1 16.63 .
. 9.2591305 25 1 1 16.63 .
. 9.2591305 25 1 1 16.63 .
. 10.738568 31 1 1 16.63 .
. 10.738568 31 1 1 16.63 .
.   10.4601 31 1 1 16.63 .
.   10.4601 31 1 1 16.63 .
. 10.897054 33 1 1 16.08 .
.  9.350102 26 1 1 16.08 .
end

[Sven-Kristjan Bormann]

I don't see how your second specification defines an Instrumental-Variable (IV) estimation.
As usual with IVs, the choice has to depend on your background knowledge. If you believe that your chosen IV is not correlated with outcome, but correlated with the endogenous variable, then it might be at least a weak IV.
I can only guess what your variable names mean, therefore it is a bit tricky to give you good advice without further information about the variables and exactly you want to do. The data alone is not useful in this data, because your question is not about the data but about the variable selection.
There is also something wrong with your example data because your dependent variable "SVoverLiquidTW" is missing and some other variables from your estimation commands are not included in the example data.

So I'm trying to find some causality, between how people think what their prices are and what they are.

I don't understand what you want to say. Maybe some words are missing.

[Falco Wolf]

You are right, I explained myself horribly. I am not an expert using IV's.

What I am trying to find out is why the population "believes their home prices are otherwise than the market price indicates". So above market or below market. I was told I have to use an IV because I should try to find some causality within' some of the variables I have,
and specifically using variable eintrate (eintrate = elasticity * interest rates)

Now my question would be, how would I specify this as my IV in the regression? So I am saying that my variable eintrate is the IV that explains most of the misperception.
So my regression would have to look as below? (In Bold) or is there another way of specifiing the regresion?

reghdfe SVTW TWHV fam_income age sex educ mstatus emp_status fam_members (eintrate = misper?), absorb(zipcode year) vce(cluster zipcode year)


fam_income is family income
age is the age of an individual
sex is male female
mstatus is married or not
emp_status is working or not
fam_members is how many people living in a hh
SV = total assets in stocks the HH has
TW = the proportion of their assets being their own house
SVTW = stock value over the wealth HH has
TWHV = Total wealth over the Houshold (real) value.

[Sven-Kristjan Bormann]

So I am saying that my variable eintrate is the IV that explains most of the misperception.

As far as I understand the -reghdfe- command, then you need to specify the regression exactly the other way around.
Change

reghdfe SVTW TWHV fam_income age sex educ mstatus emp_status fam_members (eintrate = misper?), absorb(zipcode year) vce(cluster zipcode year)

to

reghdfe SVTW TWHV fam_income age sex educ mstatus emp_status fam_members (misper=eintrate ), absorb(zipcode year) vce(cluster zipcode year)

The other issue is that I don't understand how misperception and the elasticity * interest rates are related to each other. Do household's observe the elasticity of interest rates (or times interest rates?) and then get a misperception about their stock value?
But why is the elasticity not related to the stock value? Not to mention, that the concept of elasticity is outside of economics a not so well known concept. Therefore, I question it a bit that a household would actually know and care about the elasticity to form their perception of their home prices.

The next issue is the endogeneity between stock value and misperception: I can understand the stock value might lead to some misperception of the household's wealth but I don't see a way how the misperception influences the stock value unless the misperception leads to actions which then, in turn, influence the stock value. But without having information about the potential mediating factors, your estimation will be biased because of omitting important variables.
If my understanding is correct, then your dependent variable should be the misperception and not the stock value and there is no need to use Instrumental Variables because there is no reverse causality from the misperception to the stock value.

Of course, you are the expert regarding your data and theory but from the outside, the whole estimation does not seem to stand on solid ground.

[David Benson]

Falco, I'm not sure this is going to help (not with the IV specification anyway), but my impression from personal experience is that people tend to have "sticky" perceptions of what their house is worth based on its value at the highest point. Suppose the boom time for real estate was 2002-2006 and then the market crashed. If someone's house was worth $500K in the boom, they may know that it has adjusted down, but won't adjust enough. (They may think it is still worth $450K even though similar houses are selling for $400K or $375K). (There is a psychological literature on "anchoring"). (You could also look at the endowment effect).

1) I also find that people use sites like Zillow as a proxy for what their house is worth (and pick the high end)

2) You might be able to find a difference in states where sales prices of homes are public record vs states they are not. (If it's not public record, the anchoring effect or the effect of Zillow should be more pronounced). Michigan, where I used to live, is a public record state, so you can see what houses around you sold for. For example, see here and here
Utah, where I now live, is not.

Hope that helps!

[Falco Wolf]

Thanks Sven and David.

I'll give it some more thought and come back later with some updates.