# robustness test in econometrics

If you really want to do an analysis super-correctly, you shouldn't be doing one of those fill-in lists above for every robustness check you run - you should be trying to do a fill-in list for every assumption your analysis makes. F test. I have a family. Robustness is a different concept. 7 Π= + − 0 0 1 01 0 10 ˆ 1 2 1 δ k m δ δ. Indeed, if not conducted properly, robustness checks can be completely uninformative or entirely misleading. B [estimate too high/estimate too low/standard errors too small/etc...], that the variance of the error term is constant and unrelated to the predictors (homoskedasticity), among groups with higher incomes, income will be more variable, since there will be some very high earners. If the coefficients are plausible and robust, this is commonly interpreted as evidence of structural validity. The same problem applies in the opposite direction with robustness tests. Robustness of the regression coecient is taken as evidence of structural validity. The purpose of these tools is to be able to use data to answer questions. Just try to be as sure as you reasonably can be, and exercise common sense! 3 Despite being very common practice in economics this isn't really the best way to pick control variables or test for the stability of a coefficient. By continuing you agree to the use of cookies. Filling in the list includes filling in C, even if your answer for C is just "because A is not true in lots of analyses," although you can hopefully do better than that.2 As a bonus, once you've filled in the list you've basically already written a paragraph of your paper. Don't be fooled by the fancy stuff - getting to know your data and context well is the best way of figuring out what assumptions are likely to be true. speci–cation testing principles articulated in Hausman™s (1978) landmark work apply directly. That sort of thinking will apply no matter what robustness test you're thinking about. No! There are lots of robustness tests out there to apply to any given analysis. # Estimate unrestricted model model_unres <- lm(sav ~ inc + size + educ + age, data = … After all, if you are doing a fixed effects analysis, for example, and you did the fixed effects tests you learned about in class, and you passed, then your analysis is good, right? robustness test econometrics 10 November, 2020 Leave a Comment Written by 355 0 obj > endobj Robustness tests were originally introduced to avoid problems in interlaboratory studies and to identify the potentially responsible factors . "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers Archive 1832, Iowa State University, Department of Economics. This paper investigates the local robustness properties of a general class of multidimensional tests based on M-estimators.These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. This conveniently corresponds to a mnemonic: Ask what each (A)ssumption is, how (B)ad it would be if it were wrong, and whether that assumption is likely to be (C)orrect or not for you. How broad such a robustness analysis will be is a matter of choice. Sometimes, even if your assumption is wrong, the test you're using won't be able to pick up the problem and will tell you you're fine, just by chance. These kinds of robustness tests can include lots of things, from simply looking at a graph of your data to see if your functional form assumption looks reasonable, to checking if your treatment and control groups appear to have been changing in similar ways in the "before" period of a difference-in-difference (i.e. Copyright © 2020 Elsevier B.V. or its licensors or contributors. robustness test econometrics 10 November, 2020 Leave a Comment Written by . Because a robustness test is anything that lets you evaluate the importance of one of your assumptions for your analysis. Copyright © 2013 Elsevier B.V. All rights reserved. Robust regression might be a good strategy since it is a compromise between excluding these points entirely from the analysis and including all the data points and treating all them equally in OLS regression. One of the reasons I warn against that approach to robustness tests so much is that I think it promotes a false amount of confidence in results. Any analysis that checks an assumption can be a robustness test, it doesn't have to have a big red "robustness test" sticker on it. Many of the things that exist under the banner of "robustness test" are specialized hypothesis tests that only exist to be robustness tests, like White, Hausman, Breusch-Pagan, overidentification, etc. On the other hand, a test with fewer assumptions is more robust. ‘Introduction to Econometrics with R’ is an interactive companion to the well-received textbook ‘Introduction to Econometrics’ by James H. Stock and Mark W. Watson (2015). ANSI and IEEE have defined robustness as the degree to which a system or component can function correctly in the presence of invalid inputs or stressful environmental conditions. The more assumptions a test makes, the less robust it is, because all these assumptions must be met for the test to be valid. Testing the robustness of the results of a model or system in the presence of uncertainty. In this test, the … What do these tests do, why are we running them, and how should we use them? Weighted least squares (WLS) 2. This page is pretty heavy on not just doing robustness tests because they're there. For example, one may assume that a linear regression model has normal errors, so the question may be how sensitivity is the Ordinary Least Squares (OLS) estimator to the assumption of normality. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. We are grateful to the participants at the International Symposium on Econometrics of Specification Tests in 30 Years at Xiamen University and the seminars at many universities where this paper was presented. A common exercise in empirical studies is a “robustness check”, where the researcher examines how certain “core” regression coefficient estimates behave when the regression specification is modified by adding or removing regressors. So the real question isn't really whether the assumptions are literally true (they aren't), but rather whether the assumptions are close enough to true that we can work with them. In fact, they promise something pretty spectacular: if you have the appropriate data and the tool is used correctly, you can uncover hidden truths about the … Robustness Tests for Quantitative Research The uncertainty researchers face in specifying their estimation models threa- tens the validity of their inferences. In field areas where there are high levels of agreement on appropriate methods and measurement, robustness testing need not be very broad. Without any assumptions, we can't even predict with confidence that the sun will rise in the East tomorrow, much less determine how quantitative easing affected investment. H1: The assumption made in the analysis is false. Because the problem is with the hypothesis, the problem is not addressed with robustness checks. For example, it's generally a good idea in an instrumental variables analysis to test whether your instrument strongly predicts your endogenous variable, even if you have no reason to believe that it won't. In areas where correctness) of test cases in a test process. We can minimize this problem by sticking to testing assumptions you think might actually be dubious in your analysis, or assumptions that, if they fail, would be really bad for the analysis. Let's fill in our list. This paper investigates the local robustness properties of a general class of multidimensional tests based on M-estimators.These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. The book also discusses You can test for heteroskedasticity, serial correlation, linearity, multicollinearity, any number of additional controls, different specifications for your model, and so on and so on. "Robustness checks and robustness tests in applied economics." So if parental income does increase your income, it will also likely increase the variance of your income in ways my control variables won't account for, and so be correlated with the variance of the error term, use heteroskedasticity-robust standard errors, that my variables are unrelated to the error term (no omitted variable bias), the coefficient on regime change might be biased up or down, depending on which variables are omitted, regime change often follows heightened levels of violence, and violence affects economic growth, so violence will be related to GDP growth and will be in the error term if not controlled for, the coefficient on regime change is very different with the new control. In your econometrics class you learn all sorts of analytic tools: ordinary least squares, fixed effects, autoregressive processes, and many more. A common exercise in empirical studies is a “robustness check”, where the researcher examines how certain “core” regression coefficient estimates behave when the regression specification is modified by adding or removing regressors. If the coe¢ cients are plausible and robust, this is commonly interpreted as evidence of structural validity. So we are running a regression of GDP growth on several lags of GDP growth, and a variable indicating a regime change in that country that year. No! We discuss how critical and non-critical core variables can be properly specified and how non-core variables for the comparison regression can be chosen to ensure that robustness checks are indeed structurally informative. Heck, sometimes you might even do them before doing your analysis. Why bother with this list? Is this the only way to consider it in an econometric sense? That's the thing you do when running fixed effects. P Z =Z(ZZ)−1Z′ is a n-by-n symmetric matrix and idempotent (i.e., P Z′P Z =P Z).We use Xˆ as instruments for X … Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters.One motivation is to produce statistical methods that are not unduly affected by outliers. Does free trade reduce or increase inequality? Pilot-Testing: The process of administering some measurement protocol to a small preliminary sample of subjects as means of assessing how well they measure works. Robust M-Tests - Volume 7 Issue 1 - Franco Peracchi. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers Archive 1832, Iowa State University, Department of Economics. Robustness test for Synthetic Control Method I am working on a basic Synthetic Control Method (SCM) analysis for establishing the causal effect of a change in bankruptcy legislation (treatment) on the level of entrepreneurship (the outcome variable) in a certain country (the treated unit). etc.. But the real world is messy, and in social science everything is related to everything else. A common exercise in empirical studies is a “robustness check”, where the researcher examines how certain “core” regression coefficient estimates behave when the regression specification is modified by adding or removing regressors. We also thank the editor and two anonymous referees for their helpful comments. Robustness testing analyzes the uncertainty of models and tests whether estimated effects of interest are sensitive to changes in model specifications. Narrow robustness reports just a handful of alternative specifications, while wide robustness concedes uncertainty among many details of the model. Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. In that case, our analysis would be wrong. Of course, for some of those assumptions you won't find good reasons to be concerned about them and so won't end up doing a robustness test. Sure, you may have observed that the sun has risen in the East every day for several billion days in a row. The researcher carefully scrutinized the regression coefficient estimates when the … Thinking about robustness tests in this way - as ways of evaluating our assumptions - gives us a clear way of thinking about using them. Second, let's look at the common practice of running a model, then running it again with some additional controls to see if our coefficient of interest changes.3 Why do we do that? Robustness checks involve reporting alternative specifications that test the same hypothesis. Thinking about robustness tests in that light will help your whole analysis. And that might leave you in a pickle - do you stick with the original analysis because your failed test was probably just random chance, or do you adjust your analysis because of the failed test, possibly ending up with the wrong analysis? No! ‘Introduction to Econometrics with R’ is an interactive companion to the well-received textbook ‘Introduction to Econometrics’ by James H. Stock and Mark W. Watson (2015). Abstract A common exercise in empirical studies is a "robustness check," where the researcher examines how certain "core" regression coe¢ cient estimates behave when the regression speci–cation is modi–ed by adding or removing regressors. Figure 4 displays the results of a robustness test, with the top temperature (TS-Data) occasionally falling below the minimum limit (TVL-Lim).The bottom temperature (BS-Data) from the plant data can be higher or lower than its reference temperature (BS-Ref). But you should think carefully about the A, B, C in the fill-in list for each assumption. Beginners with little background in statistics and econometrics often have a hard time understanding the benefits of having programming skills for learning and applying Econometrics. as fuzz testing [30, 31]. Why not? We didn't run a White test just-because we could. Robustness tests are all about assumptions. Often, robustness tests test hypotheses of the format: But if you want to predict that it will also rise in the East tomorrow, you must assume that nothing will prevent it from occurring - perhaps today is the day that it turns out Superman exists and he decides to reverse the Earth's rotation so the sun rises in the West. Most empirical papers use a single econometric method to demonstrate a relationship between two variables. Thus, y 2 in X should be expressed as a linear projection, and other independent variables in X should be expressed by itself. The uncertainty about the baseline models estimated effect size shrinks if the robustness test What is the best method to measure robustness? Robustness tests are always specialized tests. If the coefficients are plausible and robust, this is commonly interpreted as evidence of structural validity. Narrow robustness reports just a handful of alternative specifications, while wide robustness concedes uncertainty among many details of … The reason has to do with multiple hypothesis testing, especially when discussing robustness tests that take the form of statistical significance tests. Let's put this list to the test with two common robustness tests to see how we might fill them in. But that's something for another time... 4 Technically this is true for the same hypothesis tested in multiple samples, not for multiple different hypotheses in the same sample, etc., etc.. C'mon, statisticians, it's illustrative and I did say "roughly," let me off the hook, I beg you. 643711). https://doi.org/10.1016/j.jeconom.2013.08.016. Often they assume that two variables are completely unrelated. Second is the robustness test: is the estimate different from the results of other plausible models? So we have to make assumptions. The following example adds two new regressors on education and age to the above model and calculates the corresponding (non-robust) F test using the anova function. A new procedure for Matlab, testrob, embodies these methods. This tells us what "robustness test" actually means - we're checking if our results are robust to the possibility that one of our assumptions might not be true. In regression analyses of observational data the  true model  remains unknown and researchers face a choice between plausible alternative speci Roughly, if you have 20 null hypotheses that are true, and you run statistical significance tests on all of them at the 95% level, then you will on average reject one of those true nulls just by chance.4 We commonly think of this problem in terms of looking for results - if you are disappointed with an insignificant result in your analysis and so keep changing your model until you find a significant effect, then that significant effect is likely just an illusion, and not really significant. ‘Introduction to Econometrics with R’ is an interactive companion to the well-received textbook ‘Introduction to Econometrics’ by James H. Stock and Mark W. Watson (2015). However, robustness generally comes at the cost of power, because either less information from the input is used, or more parameters need to be estimated. You might find this page handy if you are in an econometrics class, or if you are working on a term paper or capstone project that uses econometrics. Given that these conditions of a study are met, the models can be verified to be true through the use of mathematical proofs. "To determine whether one has estimated effects of interest, β; or only predictive coefficients, β ^ one can check or test robustness by dropping or adding covariates." We previously developed Ballista , a well-known robustness This page won't teach you how to run any specific test. Second, the list will encourage you to think hard about your actual setting - econometrics is all about picking appropriate assumptions and analyses for the setting and question you're working with. Robustness Tests: What, Why, and How. Checking of robustness is one of a common procedure in econometrics. Does a robustness check First, it will make sure that you actually understand what a given robustness test means. We provide a straightforward new Hausman (1978) type test of robustness for the critical core coefficients, additional diagnostics that can help explain why robustness test rejection occurs, and a new estimator, the Feasible Optimally combined GLS (FOGLeSs) estimator, that makes relatively efficient use of the robustness check regressions. Let's imagine that we're interested in the effect of regime change on economic growth in a country. A few reasons! Or do you at least remember that there was such a list (good luck on that midterm)? Here, we study when and how one can infer structural validity from coefficient robustness and plausibility. What was the impact of quantitative easing on investment? Cite 1 Recommendation Lu gratefully acknowledges partial research support from Hong Kong RGC (Grant No. Focusing on each dimension of model uncertainty in separate chapters, the authors provide a systematic overview of existing tests and develop many new ones. In most cases there are actually multiple different tests you can run for any given assumption. logic of robustness testing, provides an operational de nition of robustness that can be applied in all quantitative research and introduces readers to diverse types of robustness tests. In statistics, the term robust or robustness refers to the strength of a statistical model, tests, and procedures according to the specific conditions of the statistical analysis a study hopes to achieve. Because your analysis depends on all the assumptions that go into your analysis, not just the ones you have neat and quick tests for. Does the minimum wage harm employment? If my analysis passes the robustness tests I do, then it's correct. In the post on hypothesis testing the F test is presented as a method to test the joint significance of multiple regressors. These are things like the White test, the Hausman test, the overidentification test, the Breusch-Pagan test, or just running your model again with an additional control variable. Why not? I would like to conduct some robustness checks in Stata (by using the method of Lu and White (2013) - Lu, Xun, and Halbert White. The White test is one way (of many) of testing for the presence of heteroskedasticity in your regression. Abstract A common practice for detecting misspecication is to perform a \robustness test", where the researcher examines how a regression coecient of interest behaves when variables are added to the regression. This book presents recent research on robustness in econometrics. If the D you come up with can't be run with your data, or if you can't think of a D, then you have no way of checking that assumption - that might be fine, but in that case you'll definitely want to discuss your A, B, and C in the paper so the reader is aware of the potential problem. Beginners with little background in statistics and econometrics often have a hard time understanding the benefits of having programming skills for learning and applying Econometrics. If the coefficients are plausible and robust, this is commonly interpreted as evidence of structural validity. Every time you do a robustness test, you should be able to fill in the letters in the following list: If you can't fill in that list, don't run the test! But this is not a good way to think about robustness tests! 355 0 obj > endobj Robustness tests were originally introduced to avoid problems in interlaboratory studies and to identify the potentially responsible factors . If you just run a whole bunch of robustness tests for no good reason, some of them will fail just by random chance, even if your analysis is totally fine! But then, what if, to our shock and horror, those assumptions aren't true? Inefficient coefficient estimates Biased standard errors Unreliable hypothesis tests: Geary or runs test Accordingly, we give a straightforward robustness test that turns informal robustness checks into true Hausman (1978)-type structural speci–cation tests. We didn't just add an additional control just-because we had a variable on hand we could add. Here, we study when and how one can infer structural validity from coe¢ cient robustness … Journal of Econometrics 178 (2014): 194-206). Or, even if you do the right test, you probably won't write about the findings properly in your paper. Type I error, in other words. In fact, they promise something pretty spectacular: if you have the appropriate data and the tool is used correctly, you can uncover hidden truths about the world. We added it because, in the context of the regime change analysis, that additional variable might reasonably cause omitted variable bias. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Robustness checks and robustness tests in applied economics. Also, sometimes, there's not a good E to fix the problem if you fail the robustness test. Robust data processing techniques – i.e., techniques that yield results minimally affected by outliers – and their applications to real-life economic and financial situations are the main focus of this book. The idea of robust regression is to weigh the observations differently based on how well behaved these observations are. Notice that in both of these examples, we had to think about the robustness tests in context. After all, they're usually idealized assumptions that cleanly describe statistical relationships or distributions, or economic theory. However, robustness generally comes at the cost of power, because either less information from the input is used, or more parameters need to be estimated. We ran it because, in the context of the income analysis, homoskedasticity was unlikely to hold. Heteroskedasticity is when the variance of the error term is related to one of the predictors in the model. When considering how robust an estimator is to the presence of outliers, it is useful to test what happens when an extreme outlier is added to the dataset, and to test what happens when an extreme outlier replaces one of the existing datapoints, and then to consider the … Keep in mind, sometimes filling in this list might be pretty scary! Robustness testing has also been used to describe the process of verifying the robustness (i.e. Suppose we –nd that the critical core coe¢ cients are not robust. So that's what robustness tests are for. We are worried whether our assumptions are true, and we've devised a test that is capable of checking either (1) whether that assumption is true, or (2) whether our results would change if the assumption WASN'T true.1. It's impossible to avoid assumptions, even if those assumptions are pretty obviously true. Beginners with little background in statistics and econometrics often have a hard time understanding the benefits of having programming skills for learning and applying Econometrics. These are often presented as things you will want to do alongside your main analysis to check whether the results are "robust.". But do keep in mind that passing a test about assumption A is some evidence that A is likely to be true, but it doesn't ever really confirm that A is true. Running fixed effects? It's easy to feel like robustness tests are a thing you just do. The purpose of these tools is to be able to use data to answer questions. The more assumptions a test makes, the less robust it is, because all these assumptions must be met for the test to be valid. In both settings, robust decision making requires the economic agent or the econometrician to explicitly allow for the risk of misspecification. What does a model being robust mean to you? We use cookies to help provide and enhance our service and tailor content and ads. Do a Hausman. The final result will not do, it is very interesting to see whether initial results comply with the later ones as robustness testing intensifies through the paper/study. There's not much you can do about that. Do you remember the list of assumptions you had to learn every time your class went into a new method, like the Gauss-Markov assumptions for ordinary least squares? Third, it will help you understand what robustness tests actually are - they're not just a list of post-regression Stata or R commands you hammer out, they're ways of checking assumptions. 2 In some cases you might want to run a robustness test even if you have no reason to believe A might be wrong. That's because the whole analysis falls apart if you're wrong, and even if your analysis is planned out perfectly, in some samples your instrument just doesn't work that well. Let's say that we are interested in the effect of your parents' income on your own income, so we regress your own income on your parents' income when you were 18, and some controls. So you can never really be sure. That's because every empirical analysis that you could ever possibly run depends on assumptions in order to make sense of its results. Breusch-Pagan test White test: 1. We've already gone over the robustness test of adding additional controls to your model to see what changes - that's not a specialized robustness test. 1 If you want to get formal about it, assumptions made in statistics or econometrics are very rarely strictly true. Test-retest method: A method of testing robustness in which the similarity of results in assessed after administering a measure to the sample at two different times. Robustness testing is a variant of black-box testing that evaluates system robustness, or “the degree to which a system or component can function correctly in the presence of invalid inputs or stressful environmental conditions” . Robust regression is an alternative to least squares regression when data is contaminated with outliers or influential observations and it can also be used for the purpose of detecting influential observations. H0: The assumption made in the analysis is true. But it will tell you what the tests are for, and how you should think about them when you're using them. At the same time, you also learn about a bevy of tests and additional analyses that you can run, called "robustness tests." As we show, there are numerous pitfalls, as commonly implemented robustness checks give neither necessary nor sufficient evidence for structural validity. It can lead to running tests that aren't necessary, or not running ones that are. You just found a significant coefficient by random chance, even though the true effect is likely zero. If the coefficients are plausible and robust, this is commonly interpreted as evidence of structural validity. On the other hand, a test with fewer assumptions is more robust. As a robustness test and in order to deal with potential issues of endogeneity bias, we also employ a panel-VAR model to examine the relationship between bank management preferences and various banking sector characteristics. These assumptions are pretty important. Since you have tests at your fingertips you can run for these, seems like you should run them all, right? Regardless, we have to make the list! So is it? No more running a test and then thinking "okay... it's significant... what now?" Robust standard errors: Autocorrelation: An identifiable relationship (positive or negative) exists between the values of the error in one period and the values of the error in another period. parallel trends). A common exercise in empirical studies is a “robustness check”, where the researcher examines how certain “core” regression coefficient estimates behave when the regression specification is modified by adding or removing regressors. In your econometrics class you learn all sorts of analytic tools: ordinary least squares, fixed effects, autoregressive processes, and many more. The aim of the conference, “Robustness in Economics and Econometrics,” is to bring together researchers engaged in these two modeling approaches. Test-retest method: A method of testing robustness in which the similarity of results in assessed after administering a measure to the sample at two different times. A good rule of thumb for econometrics in general: don't do anything unless you have a reason for it. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. It normally refers to the sensitivity of an estimator with respect to the violation of certain assumptions of the model, especially in finite samples. First, let's look at the White test. Why not? Increased understanding of the relationships between input and output variables in a system or model. It's tempting, then, to think that this is what a robustness test is. Sometimes, the only available E is "don't run the analysis and pick a different project." I will also address several common misconceptions regarding robustness tests. Pilot-Testing: The process of administering some measurement protocol to a small preliminary sample of subjects as means of assessing how well they measure works. There's another reason, too - sometimes the test is just weak! But what does that mean? A video segment from the Coursera MOOC on introductory computer programming with MATLAB by Vanderbilt. Robust M-Tests - Volume 7 Issue 1 - Franco Peracchi. 19 The main advantage of this methodology is that all variables enter as endogenous within a system of equations, which enables us to reveal the underlying causality among … But this is generally limited to assumptions that are both super duper important to your analysis (B is really bad), and might fail just by bad luck.