 Viena instrumentia on tärkeää senarjoa, jossa instrumenta-verboilla on vain viikkoa korraalitettavaa ja endo-ojinus-explanatio-verboilla. Mitä se ei ole? Viena instrumenta-verboilla on tämä korraalitettava, joka on X ja Z. Jos X ja Z ei ole korraalitettavaa, niin instrumenta-verboilla kannattaa olla todella ympäristössä, ja se kannattaa olla ympäristössä. Toi ymmärtää, miten se on tapahtunut, niin katsotaan ympäristössä alueella ympäristössä. Olet tuntua, että mietitään, että se on tämä korraalitettavaa, joka on Z ja Y, ympäristössä on X ja Z. Y on järjestelmä, jotta sinä olet k seat sena, että se on se, mitä ympäristöe on ympäristössä Everybodye. Y-um esa on z X korraalitettavaa. Tätä tulee ympäristössä. ja siellä death is rare, so you can solve the data. So why would there be a problem if this correlation is very small? It's a problem because then the sampling variation of that correlation, whatever is our estimate, will be relatively large compared to the population value. And when this magnitude of this correlation is small but its variance is high, we can see that when we divide the first correlation in the second one, we will get a widely different result. ja me voimme käyttää todella yksityistä. Yksityistä, joka on yksityistä, on, että me voimme sanoa jotain X ja Y-tuntia, jos usein Z, ja jos Z ei ole kohdalla kohdalla X, niin ei voi ottaa niin paljon informaattia kohdalla X, Y-tuntia. Jos instrumentti on viikon, tämä on yksi trein eri problemi. Problemi ovat yksityistä ja yksityistä, ja myös kompromis- ja statistiikasta testaamista. Bias on tärkeä instrumentissa, sample size ja kuvaa instrumentissa. Mikä on tärkeä sample size ja kuvaa instrumentissa? Se on tärkeää, jos ajattelimme 2-staitseja ja 1-staitseja regresson analysointia. Me tiedämme, että r-square-regresson analysointia on tärkeää. Jos ymmärrän sample size ja ymmärrän nr. predictorissa, r-square-regresson analysointia on tärkeää. Kun r-square-regresson analysointia on tärkeää, olemme todella ymmärrän modelissa, niin ymmärrän valojen r-square-regresson analysointia on tärkeää. Instrumenta- ja varavillaan estimatioita on tärkeää, kuin ovarilaisestimatioita. Jos on tärkeää instrumentissa ja sample size on tärkeää, niin on tärkeää, koska on tärkeää r-square-regresson analysointia. Tämä suurin r-square-regresson analysointia on tärkeää. There are tests or diagnostics for detecting weak instruments. Let's take a look at how Stata handles this problem. This is fairly representative of how we would analyze the weak instrument case. So this is from Stata's user manual. I've run the example here. I've omitted the actual regression results. And then I do a post-estimation diagnostics for the first day's regression analysis. Stata provides us r-squares, f-tests, and then this table here that we will take a look at in a moment. So what do these r-squares tell us? So the first two sets are, let's take a look at the model first. So the model has one dependent variable rent, and then we have percent urban, which is the one exogenous variable. So we know that we have two predictors. That predictor here is endogenous, and present urban is exogenous. And then this endogenous predictor is instrument with family income and three dummy variables that indicate different regions. So we have four excluded instruments. The instruments are excluded because they are not used as predictors of rent. So the first day's regression analysis, in the first day's regression analysis, we regress the endogenous variable on the instruments that are excluded and the explanatory variable, the exogenous explanatory variables. So this first day's regression analysis has five predictors, three dummies, family income and percent urban. The first two statistics are normal r-square statistics from that regression analysis. So if you just regress the endogenous variable on present urban, family income and three region dummies, you will get those r-squares. But those are not very relevant, because we are using present urban in the model, so it doesn't really add any new information for dealing with endogenous. So what we need to know is how much more information these excluded instruments or the instrument of variables add to the model, and that's what the partial r-square tells us. So this partial r-square tells us what is the r-square of the instruments after we have partialed out the effect of a percentage urban from instruments and the dependent variable. So it tells how much these instruments explain the endogenous explanatory variable uniquely when we control for this exogenous variable. And that is the key quantity. This needs to be high enough so that we can conclude that the instruments are not weak. And then there's a test. And this test here is an F-test for this partial r-square being zero. And we can see it has four degrees of freedom. That's the number of variables. So we have four excluded instruments and 44 is the sample size. The F-test is highly significant. But in this case, the statistical significance is insufficient. So statistical significance basically tells us that it's implausible that these instruments are all exactly uncorrelated with the endogenous explanatory variable. The weak instruments problem starts to occur at low correlations that are still quite far from the zero correlation. So there are some rules of thumb and some research on how much this F-statistic should be for there to be a problem. So this p-value is not informative here. The p-value tests like weak instruments in an absolute sense that the instruments are completely useless. They are pretty useless when they are weak even before with the recent zero correlation. One of the most commonly cited articles in this context is a paper by Stokan Jogo here. And they present this kind of calculations. There are the article contains lots of reference tables that they calculated for the F-statistic here. So they calculate what is the expected bias of Tuesday's least squares here as a function of the F-statistic. And how we apply this table is that we choose what is our acceptable level of bias. If we think that 5% bias is acceptable, then we conclude that our cutoff is 16.85. And this F-statistic here is less than that cutoff than the instruments are too weak for our purpose. And if we are okay with 10% bias, which is pretty large, then this F-statistic would be okay. So it depends on how much bias we are willing to tolerate. And these reference values are calculated by state for your model, for your sample size, and for the number of variables that you have in your analysis. Then this is a significant test. We will get false positives. So there are normally false positive rate. This is 5% when a test is valid. But if instruments are weak, then these tests with Tuesday's least squares and limited information maximum likelihood, they will tend to reject the null hypothesis more often than they should. And then we take a look at, okay, so what kind of a false positive rate are we happy with? If we are okay with 10% false positive rate for a test that says that the false positive rate is 5%, then we should say that, okay, if F-statistic is more than 24.58, then we know that the false positive rate will not exclude 10%. So basically the weak instruments issue here is that you need to decide how much bias and how much false positives you are willing to accept. And then you choose your cutoff for the F-statistic based on their acceptable level of bias and false positives. You compare the F-statistic. If it's larger, then you're okay. If it's smaller, then you have a problem. There are quite a few other tests available. This stock and yoga heuristic is the most commonly used. This article from Journal of Operations Management lists some of the other tests. And if you have some issues with the stock and yoga test, for example, if you have lots of heteroskedasticity in your data, then you should be looking at these other tests. But the idea in these tests is basically the same. You look at whether the instruments as a set are sufficiently strongly correlated with the endogenous explanatory variable.