We have two estimators for b : b 0 and b 1. Under the null hypothesisboth of these estimators are consistentbut b 1 is efficient has the smallest asymptotic varianceat least in the class of estimators containing b 0.
Under the alternative hypothesisb 0 is consistent, whereas b 1 isn't. Then the Wu—Hausman statistic is: . If we reject the null hypothesis, it means that b 1 is inconsistent. This test can be used to check for the endogeneity of a variable by comparing instrumental variable IV estimates to ordinary least squares OLS estimates. It can also be used to check the validity of extra instruments by comparing IV estimates using a full set of instruments Z to IV estimates that use a proper subset of Z.
Note that in order for the test to work in the latter case, we must be certain of the validity of the subset of Z and that subset must have enough instruments to identify the parameters of the equation.
Hausman also showed that the covariance between an efficient estimator and the difference of an efficient and inefficient estimator is zero. Assuming joint normality of the estimators. Using the commonly used result, showed by Hausman, that the covariance of an efficient estimator with its difference from an inefficient estimator is zero yields.
The Hausman test can be used to differentiate between fixed effects model and random effects model in panel analysis. In this case, Random effects RE is preferred under the null hypothesis due to higher efficiency, while under the alternative Fixed effects FE is at least as consistent and thus preferred.
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Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version.Today we are going to study a group of variables that I personally dislike: endogenous one. When you have an endogenous regressor, your OLS estimates become inconsistent and it may happen thanks to measurement error or omitted variable biases. That is why we need to find another variable, called an instrument, that is exogenous and it is correlated with the outcome variable only through its effect on the endogenous regressor.
Are you ready to play with them? We will need to use a special database named card. This dataset contains information on a sample of working men aged between 24 and 34 who were part of the wave of the US National Longitudinal Survey of Young Men and it is usually studied to replicate the estimates of the earnings equations.
It includes a measure of the log of hourly wages in lwagea measure of years of education educyears of labour market experience experthe square of years of labor market experience expersq and other useful variables we can look at through the describe command:. We want to investigate returns to schooling that means how much your earnings can increase if you spend more years of your life to study and form yourself at school.
If we want to study the sign of this relation, the perfect starting point is a scatter plot. The relationship is positive!
The answer is likely to be NO, because of other confounding variables such as ability that affect both education and earnings. The idea is that, being all else equal, individuals are less likely to choose college education if they live far away from a suitable college. Assuming that the presence of a nearby college is uncorrelated with ability controlling for family background factorscollege proximity is a potential instrumental variable for schooling.
Does it seem reasonable to you? As we can observe, one of the regional dummies was dropped due to multicollinearity because we inserted the intercept. If you missed this point, you can review the theory here. The coefficient of education is positive and significant meaning that one-year more of schooling implies an increase of 7. Remember that this is a log-lin model that we studied hereso its coefficients should be interpreted with caution. This method allows you to introduce instrumental variables in your regression model and is named like that because it is a two-step procedure.
In the first step, we are going to regress the endogenous variable on all its possible instruments. Here we want to check that the instruments have explanatory power so that they are both valid and informative :. As we can see, both nearc2 and nearc4 are predictive of education, individuals who lived near to a college were significantly more likely to choose additional education.
How can we state if they are good instruments? The problem with instrumental variables is that we cannot choose weak instruments for our explanatory variables because it could lead to worse estimates than OLS, already biased. Weak identification arises when the excluded instruments are correlated with endogenous regressors, but only weakly.
Estimators can perform poorly when instruments are weak and different estimators are more robust to weak instruments than others are. Testparmwhich we introduced with panels, is a post estimation test that works like an F-test on joint significance of coefficients. From the first-stage regression, we can estimate residuals:. Now we can use OLS to estimate the second stage regression including the estimated residual of the first-stage to the education variable like this:. Ivregress can fit a regression via 2SLS but also via GMM generalized method of moments, we will address this topic in another postso if we want to use 2SLS we have to specify it.
It can directly shows the estimates of both the second and the first stage by imposing the first option. Useful Tip: You can have more than one instrument for a single endogenous variable as in this example. In this case, the strongest instrument you can obtain is the linear combination of the instruments. If we assume a priori that OLS methods lead to upward-biased estimates of the true causal effect of schooling then, larger IV estimates are puzzling.
In this case, the estimates can be interpreted by saying that individuals who lived near to a college were significantly more likely to choose additional education and have better salaries. You must install this package on Stata if you want to use it. I recommend you to check it out because it provides a more powerful alternative to Ivregress. Indeed, it also provides tests of over-identifying restrictions and implements various test for under-identification or for weak instruments.Quick links.
Hausman test For econometric discussions not necessarily related to EViews. After running 2sls with random effect, I did hausman test to see whether random effect is appropriate for each equation. However, based on the result, it shows that it's proper to use fixed effect in equation 1, while random effect in equation 2.
Is it normal to have different effect in one model? THanks for reply! Also, I attached 2 pictures showing the result of Hausman test. Please see the words in red box.
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Could you explain what do they mean? You do not have the required permissions to view the files attached to this post. The first result indicates that the Hausman test is obtaining an invalid variance, probably because of small sample issues. It's hard to say, but my first guess is that your samples are so small that the estimators don't have enough data to determine much of anything. The asymptotics of the Hausman test require T to go to infinity. As to the differences, I'm afraid that I don't understand what you are comparing Jump to.
Who is online Users browsing this forum: No registered users and 6 guests.Linear regression is a standard tool for analyzing the relationship between two or more variables. The main contribution is the use of settler mortality rates as a source of exogenous variation in institutional differences. Such variation is needed to determine whether it is institutions that give rise to greater economic growth, rather than the other way around. For an introductory text covering these topics, see, for example, [Woo15].
The plot shows a fairly strong positive relationship between protection against expropriation and log GDP per capita. Specifically, if higher protection against expropriation is a measure of institutional quality, then better institutions appear to be positively correlated with better economic outcomes higher GDP per capita.
Given the plot, choosing a linear model to describe this relationship seems like a reasonable assumption. Visually, this linear model involves choosing a straight line that best fits the data, as in the following plot Figure 2 in [AJR01]. As the name implies, an OLS model is solved by finding the parameters that minimize the sum of squared residualsi.
We will use pandas dataframes with statsmodelshowever standard arrays can also be used as arguments. We need to use. Note that an observation was mistakenly dropped from the results in the original paper see the note located in maketable2. We can use this equation to predict the level of log GDP per capita for a value of the index of expropriation protection. For example, for a country with an index value of 7. An easier and more accurate way to obtain this result is to use. So far we have only accounted for institutions affecting economic performance - almost certainly there are numerous other factors affecting GDP that are not included in our model.
As [AJR01] discuss, the OLS models likely suffer from endogeneity issues, resulting in biased and inconsistent model estimates. To deal with endogeneity, we can use two-stage least squares 2SLS regressionwhich is an extension of OLS regression. The new set of regressors is called an instrumentwhich aims to remove endogeneity in our proxy of institutional differences. The main contribution of [AJR01] is the use of settler mortality rates to instrument for institutional differences.
They hypothesize that higher mortality rates of colonizers led to the establishment of institutions that were more extractive in nature less protection against expropriationand these institutions still persist today. The second condition may not be satisfied if settler mortality rates in the 17th to 19th centuries have a direct effect on current GDP in addition to their indirect effect through institutions.
For example, settler mortality rates may be related to the current disease environment in a country, which could affect current economic performance. As we appear to have a valid instrument, we can use 2SLS regression to obtain consistent and unbiased parameter estimates.
The instrument is the set of all exogenous variables in our model and not just the variable we have replaced. The data we need to estimate this equation is located in maketable4. The second-stage regression results give us an unbiased and consistent estimate of the effect of institutions on economic outcomes. We can correctly estimate a 2SLS regression in one step using the linearmodels package, an extension of statsmodels.
Note that when using IV2SLSthe exogenous and instrument variables are split up in the function arguments whereas before the instrument included exogenous variables. Given that we now have consistent and unbiased estimates, we can infer from the model we have estimated that institutional differences stemming from institutions set up during colonization can help to explain differences in income levels across countries today.
If you are familiar with R, you may want to use the formula interface to statsmodelsor consider using r2py to call R from within Python. In the lecture, we think the original model suffers from endogeneity bias due to the likely effect income has on institutional development. Although endogeneity is often best identified by thinking about the data and model, we can formally test for endogeneity using the Hausman test.
It is also possible to use np. You can download a copy here. In the paper, the authors emphasize the importance of institutions in economic development.Next the data — dependent, endogenous and controls — are summarized. The controls are grouped into a list to simplify model building.
And finally the simple correlation between the endogenous variable and the instruments. THe correlation of firmsz is especially low, which might lead to the weak instruments problem if used exclusively. The OLS estimates indicate that insurance through an employer or union leads to an increase in out-of-pocket drug expenditure. The just identified two-stage LS estimator uses as many instruments as endogenous variables. In this example there is one of each, using the SSI ratio as the instrument.
The with the instrument, the effect of insurance through employer or union has a strong negative effect on drug expenditure.
Using clustered requires also passing the clustering variable s. By default, 2-step efficient GMM is used assuming the weighting matrix is correctly specified.
The weighting matrix in the GMM objective function can be altered when creating the model. This example uses clustered weight by age. The covariance estimator should usually match the weighting matrix, and so clustering is also used here. The continuously updating GMM estimator simultaneously optimizes the moment conditions and the weighting matrix.
It can be more efficient in the second order sense than standard 2-step GMM, although it can also be fragile. Here the optional input display is used to produce the output of the non-linear optimizer used to estimate the parameters. Usually a dictionary or OrderedDict is used to hold results since the keys are used as model names. The advantage of an OrderedDict is that it will preserve the order of the models in the presentation.
With the expectation of the OLS estimate, the parameter estimates are fairly consistent. Standard errors vary slightly although the conclusions reached are not sensitive to the choice of covariance estimator either. T-stats are reported in parentheses. The test statistic can be directly replicated using the squared t-stat in a 2-stage approach where the first stage regresses the endogenous variable on the controls and instrument and the second stage regresses the dependent variable on the controls, the endogenous regressor and the residuals.
If the regressor was in fact exogenous, the residuals should not be correlated with the dependent variable. Here there is little difference. When there is more than one instrument the model is overidentifiedthe J test can be used in GMM models to test whether the model is overidentified — in other words, whether the instruments are actually exogenous assuming they are relevant. In the case with 2 instruments there is no evidence that against the null.
When all instruments are included the story changes, and some of the additional instrument lowincome or firmsz appear to be endogenous. It can be useful to run the just identified regressions to see how the IV estimate varies by instrument.
The OLS model is included for comparrison. The coefficient using firmsz is also very different, but this is probably due to the low correlation between firmsz and the endogenous regressor so that this is a weak instrument. First stage diagnostics are available to assess whether the instruments appear to be credible for the endogenous regressor. The Partial F-statistic is the F-statistic for all instruments once controls have been partialed out. In the case of a single instrument, it is just the squared t-stat.
LIML can have better finite sample properties if the model is not strongly identified. The parameters are identical. Navigation index modules next previous linearmodels 4.Login or Register Log in with. Forums FAQ. Search in titles only. Posts Latest Activity. Page of 1. Filtered by:. Rashesh Shrestha. I have a question regarding interpretation of coefficients in a model with endogenous dummy variable.
I have an instrument Z, which is continuous. I run a 2sls model using Stata's "ivregress" command. Is such an interpretation unique to the case of endogenous dummy regressors? In the attached example, "formal2" is the endogenous dummy, and "worker" is the continuous instrument. The OLS coefficient is 0. How should I interpret the two coefficients?
Please let me know your thoughts! Thank you. Rashesh Attached Files logfile. Tags: None. Mark Schaffer. Rashesh: 1 " This is actually how the Durbin-Wu-Hausman test of endogeneity works it's a vector of contrasts test, and here the length of the vector is 1. If the two estimates of b are similar, then you can interpret this as evidence that both the OLS and IV estimates are consistent; if they're different, you can interpet this as evidence that OLS is inconsistent since the usual null is that IV is consistent either way.
See e. This is wrong, or maybe there's something missing from the claim. For example, if you multiply your instrument by 10, you'll find the IV estimate of b is unchanged, which of course contradicts the claim. Maybe you can provide the reference or double-check?
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. I know that we can do a BP test for the cross-equation correlation of errors, but what should the null and alternative hypotheses of a Hausman test be? I do not really see how this is to work. Now, 3SLS is "merely" a system estimator that may be more efficient than estimating the coefficients of each equation by 2SLS if the error terms of the equations are indeed correlated.
Both use the same moment conditions, though, and hence are in- consistent in the same situations. Indeed, it is called 3SLS because it uses preliminary consistent 2SLS estimates to get residuals to estimate the covariance matrix of the errors.
One exception one could think about is looking at the coefficients of one equation only. If we get the moment conditions of another equation wrong, that misspecification may "pollute" the entire system of equations when using 3SLS, whereas doing single-equation 2SLS would not be affected.
EDIT: the systemfit package provides an implementation of the test I am referring to in the last paragraph. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 5 years, 5 months ago. Active 4 years, 8 months ago. Viewed 1k times. Active Oldest Votes. Christoph Hanck Christoph Hanck Sign up or log in Sign up using Google.
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