Our co-author Michael is a math major at Princeton, and those who have contributed to this article through comments and informal conversations include professors and graduate students in economics, mathematics, and political science. Every election, he just says that the Republican candidate has a 50% chance of winning, and the Democratic candidate has a 50% chance of winning. About ESOBE: ESOBE stands for European Seminar on Bayesian Econometrics. 21 0 obj Two people may start with different prior beliefs and may take a long time to converge to what the truth is, but in Bayesian theory, they will eventually agree on the distribution of uncertainty, unless the two people put zero probability on the other person's model. He played college football at Texas. Brilliant minds by these ârevisionist statisticians.â. The issue is that the forecasters, through their complex probability models, have made this game easier for themselves. 3 Sims (2002) and Pagan (2003) have recently discussed and criticised the models traditionally used at central banks. ); and maybe Iâll assign a 52% probability for a percentage between 25% and 35%, and such and so onâ¦, So, the Bayesian method allows you to start making predictions even with very small datasets! So you will eventually get hit by a car if you cross the road for enough times, but that âenough timesâ may mean 2000 years which is entirely unrealistic to expect. 1 See Marvin Goodfriend and Robert G. King (1997), ... Bayesian estimation methodology provides a natural framework for testing which frictions But we think thereâs an even more philosophical and deeper argument to be made here, which is that Nate Silver cannot really be right or wrong when thereâs no strict standard to judge him. Frequentists would say: I don't know what that percentage is, but I know that value is fixed, meaning that it is a number that is not random. Those against Silver, however, would argue that Silverâs forecast was misleading, and expecting the public to understand the nuances of probability is unrealistic. Bayesian approaches might become more practical and prevalent. Then, letâs say convergence of beliefs will definitely happen, it may simply take forever that people lose their patience. 14284 August 2008 ... Frank Schorfheide and Chris Sims for comments. Together with Thomas Sargent, he won the Nobel Memorial Prize in Economic Sciences in 2011. 3036 Nanovic Hall Email me University of Notre Dame (574) 631-6309 (voice) Notre Dame, IN 46556 (574) 631-4783 (fax) He was right then, and he is again right today saying that Trump has a 10% likelihood of winning. We're not sure, but most likely not. I say it doesnât accurately represent Trump because heâs more or less a dramatic âregime changeâ that really broke most prediction/polling models back in 2016. There are principled, practical procedures for doing this. << /S /GoTo /D (section.2) >> Bayesian estimation with Dynare Michel Juillard October 10, 2008 Exercice feedback Use Dynare version 4.0.1, yesterday’s snapshot introduced a bug in forecasting Only ./matlabshould be added to Matlab path. The difference is just 5% of the vote â how can you drastically reduce his winnings odds to 10%?! Bayesians would say: sure we may never be able to ask every Americanâs opinion of Trump, but given our polling of people around us, we may be able to assign a probability distribution to that unknown percentage weâre interested in. 24 0 obj (What it is) endobj In fact, many pollsters openly admit to using unconventional samples or weights because they have some qualitative belief that they think it will better match the true outcome. Do we assume there is a set of facts (some policyâs impact like President Trumpâs tax cut or the scientific truths behind climate change) that are fixed but we don't know and therefore random, or do we treat them as non-random? The result is that the public receives much more and noisier information, while their understanding of the elections has not been improved. But instead, he gives a probability like 16% (which few people understand the true meaning and calculation behind it). Markus K. Brunnermeier & Darius Palia & Karthik A. Sastry & Christopher A. Sims, 2019. Program committee: Mark Jensen (Chair), Federal Reserve Bank of Atlanta Hedibert Lopes, Insper Herman van Dijk, Erasmus University Rotterdam Sylvia Frühwirth-Schnatter, Wirtschaftsuniversität Wien. What Nate Silver does is a fundamentally beautiful statistical process. endobj The fundamental objections to Bayesian methods are twofold: on one hand, Bayesian methods are presented as an automatic inference engine, and this This was confirmed in thesis work carried out at the University of Minnesota by Robert Litterman under Sims’ direction (see Litterman, 1979, 1986a, 1986b). 0! The question for those making models becomes how strong of a predictor they are regarding the actual election outcome. Silver is only looking at the voter sentiments as they are and then making predictions based on these data, rather than incorporating possibilities like a coup. The questions we seek to answer here are: Can we even judge whether a forecaster is right or wrong? The problem, though, is that in state races, the data is not as accurate as it is nationally, and many pollsters often have neglected to actually weight their polls. Clinton support was overstated. Journal of Economic Dynamics and Control 12 (1988) 463-474. Kristin Scheyer Administrative Contact European Seminar on Bayesian Econometrics matrictint Scale factor for a matrix t distribution, like the posterior from a VAR. English: Christopher Albert "Chris" Sims (born October 21, 1942) is an econometrician and macroeconomist. Another way to estimate X is to go beyond polling, and perhaps use historical election data with some Bayesian inference method. For any pollster or election forecaster to model these events would mean incurring serious risks to their reputations. What about the recent record Covid-19 cases in many regions of the country? Gary Koop: lecture notes and Matlab codes for Bayesian inference in VARs, time-varying parameters VARs and time-varying parameters FAVARs. 36 0 obj All in all, it is much easier to look at a poll number and see if itâs a âgood guessâ. endobj This semester, Tiger, Jack, and Tom have been taking Princeton’s 1st-year PhD econometrics sequence with Prof. Chris Sims, who won the Nobel Prize in Economics in 2011 for his work in macroeconomics – more specifically, his pathbreaking application of Bayesian inference to evaluate economic policies. For the past few months, Trump has been consistently polling at below 45%, and Silver has now assigned him a 10% probability of winning at the moment. Are the forecasts a chaotic or controlled system? endobj As your Bayesian inference gets more complicated, the bias in the inference data is much harder to rigorously detect than bias for polling data. Chris Sims at Princeton has written extensively on this point over the last 15+ years: basically a flat / non-informative prior does not make sense if you expect that there are dynanics because you need to deal with the fact that the ML model addresses the conditional … Itâs very likely that national averages will be quite accurate, but polls that have less accurate weighing (or none at all) should be viewed with more skepticism. Furthermore, elections clearly arenât a well-posed mathematical system. mode_check : when mode check is set, Dynare plots the minus of the posterior density for values around the computed mode for each estimated parameter in turn. Does the recent appointment of Justice Amy Coney Barrett change the courtâs decision of any contested election? What plagued many polls was probably an issue of weighting. You cannot expect the American public to react to a 16% likelihood as âoh Trump actually has pretty good odds!â. Two, polling can be and has been wrong, but itâs usually due to weighting. In the later part of this article, prior simply means the belief you used to have before being exposed to any new data; posterior simply means the updated belief after seeing new facts and data. native Bayesian methods. (Frontiers: ``Weak Assumptions'') Simms also played for the Denver Broncos and the Tennessee Titans. This is happening again in this election cycle. Should forecasters incorporate âBlack Swanâ events into their models? << /S /GoTo /D (section.1) >> (IV,GMM) In other words, people have really, really strong (and often inconsistent) priors, and their updating procedure is dependent on their prior beliefs. But again, the forecasters have cleverly transformed their predictions from binary outcomes into continuous random variables. Media in category "Christopher A. Sims" Keywords: mixture of normal distributions, consistency, Bayesian conditional density estimation, heteroscedasticity and non-linearity robust inference. There are currently many more algorithms available (and they are likely to grow). X2! << /S /GoTo /D (subsection.1.3) >> It would be a much more transparent and stricter benchmark to judge them on binary outcomes (whether the winner of the election is the winner you predicted), but theyâve created a âheads I win, tails you loseâ situation. (You may skip this technical segment if you just want to read why Nate Silver is worse than Crackhead Jimâ¦). /Filter /FlateDecode 28 0 obj The alternative, then, seems to be to only use data we have since 2016, which may simply not be enough data for us to come up with anything meaningful either! Chris Sims, Princeton University . endobj After de-scribing the solvers, we turn to Bayesian estimation using a state-space and ﬁlter approach, and posterior simulation using a Markov Chain Monte Carlo algorithm. ), which can cause a less-probabilistic election outcome to occur. After all, the likelihood of oneâs prediction of actually coming into fruition in some way on election night is only 15% or so. X1! So what can we conclude for this year? You don't need to believe there's a fixed truth; you just need to be willing to update your beliefs, and update them especially strongly when something unexpected happens. I just love this piece by Chris Sims: "Bayesian Methods in Applied Econometrics, or, Why Econometrics Should Always and Everywhere Be Bayesian", from 2007. He is currently the John F. Sherrerd ’52 University Professor of Economics at Princeton University. 445{450 Objections to Bayesian statistics Andrew Gelman Abstract. âI think you will be surprised at how far away 45% is from 50%,â an older economics graduate student extremely knowledgable in econometrics and statistics explained to us. So, were the polls wrong in 2016? Silverâs final prediction on the 2016 election night was around 30% likelihood of Trump winning, and before then he fluctuated around 16% likelihood of Trump winning. The random variable people really care about, letâs call it X, is who is going to win the election, which is largely dependent on how many people vote for each candidate at some future date. We may tally up how many elections a forecaster was right on, since this gives some notion of verifiability for the forecaster. Many pollsâ samples often skew democratic, independent, or republican. Consider the example of Crackhead Jim. Do we have enough data to predict someone like Trump? The variance for this prediction is way too high, and itâs hard to say. If someone, even if you think theyâre really smart, gives you a prediction based on a black-box Bayesian inference method (or any machine learning algorithm that you donât know), my personal hypothesis is that the underlying distribution of X is way too complicated for any prior information you assume to not induce too much bias error. In other words, theoretically, as long as they give some serious consideration to the other side's argument, they will eventually agree with each other. endobj For example, if one believes that climate change isnât due to human factors, then the effect of new information on this personâs posterior may heavily depend on whether it agrees with the existing prior â a fact of CO2 emissions will influence the person very little, while some fact about the âunpredictability of weatherâ may deeply reinforce this personâs conviction that climate change is not due to human actions. 29 0 obj So hereâs the dilemma proposed by Michael: You can either use all the previous election results data, which have less variance in your prediction, but your prediction may very likely be skewed because they donât accurately represent Trump. endobj The counter-argument would be: well, we already have experienced four more years of Trump, which means four more years of careful analysis and repeated polling of voter sentiments. For the most part, we should see polls as the latter; polls, when properly executed, are a measure of the preference of voters at a certain time. Matthew Will the announcement of 7.4% record-level GDP growth one week before the election sway voters? You may wonder about all these âsimulationsâ on 538 and why Silverâs predictions change every now and then â itâs because Silver keeps testing his beliefs against new data and updating his predictions. Trump ultimately won that district by over 10%. Assuming that the remaining 55% are with Biden, then you are asking over 7.5 million Biden/undecided supporters to suddenly change their mind on elections day. He was drafted by the Tampa Bay Buccaneers in the third round of the 2003 NFL Draft. << /S /GoTo /D (subsection.1.2) >> And it can show evidence for your effect, evidence against your effect or it can say you don't have enough evidence to decide. (Bayesian Inference is a Way of Thinking, Not a Basket of ``Methods'') Do we have enough data to make predictions for someone like Trump? << /S /GoTo /D (section.3) >> Itâs true that most state polls had Hillary leading going into election day, though her lead had narrowed considerably after the âOctober surpriseâ from Mr. Comey. endobj endobj xڅWM��&��W��Z@B��$���*��֩=l��el+# �@3�OC#Y{�����~��a��rAh\$Q3����fA�=��˂�8��?�/�~���~[P��^�V. But as you ask more people (hopefully now some people on the Right), youâll realize that your âpriorâ belief (probability distribution) was wrong, and you can update your âposteriorâ belief based on the conservatives youâve just talked to. Political scientists have utilized this type of effect to explain poll-result disparities before: in 1982, Democratic candidate Tom Bradley, a Black man, ran for governor of California; despite leading in the polls, he lost narrowly to the white Republican, George Deukmejian. << /S /GoTo /D [38 0 R /Fit ] >> The only way for us to measure the consistency of our data is for the election to happen. This is something we cannot predict for sure, so a Bayesian would put some probability distribution for this number, and we might look at previous elections to come up with that probability distribution. This minimum is then used as a trial point for a new function evaluation. An intuitive way to get an estimate on X is to estimate how many people are voting for each candidate right now. But if you seriously reason through the probability, Silver is correct: in a two-person game where whoever gets above 50% wins, it is entirely reasonable to assign less than a 20% chance of winning to the candidate who has consistently polled at 45% or below for months. First version: November 25, 2008, current version: February 5, 2012. yWe thank John Geweke, Chris Sims, Bo Honore, participants of the microeconometrics seminar at Maximization of the likelihood É We will use a software by Chris Sims: csminwel É It is a minimization routine, so we will minimize the negative likelihood. Nate Silver is a Bayesian, and his forecasting isnât just popular amongst the public, but also highly regarded by many seasoned econometricians weâve talked to. Keywords: U.S. monetary policy, Interest rate rules, DSGE models, Bayesian model comparison JEL Classi cation: E43, E58, C11 IWe thank Alejandro Justiniano, Robert King, Thomas Lubik, Ed Nelson, Giorgio Primiceri, Ricardo Reis, Keith Sill, Chris Sims, and several seminar and conference participants for their comments. The side supporting Silver believes that Nate Silver wasn't wrong in 2016. For instance, maybe the first 50 people you talked to are all liberal college kids, so you might arrive at a belief that nobody supports Trump. Bayesian Estimation Aim of week four Prior distribution(s) Prior choice and speciﬁcation Consequences There are two big takeaways: one, itâs very possible for undecided voters to skew heavily towards either Trump or Biden (remember from before that unlikely outcomes still can happen! But one hypothesis is that Trump is simply so different from all other political candidates that we used to know. %PDF-1.4 Sure, the math checks off in many models for String Theory, but thereâs no fundamental way to say whether itâs a good theory because we still cannot run experiments on it to prove itâs in line with reality. Because of their lack of knowledge in statistics, the supporters of Silver would say, they could not grasp the true meaning of Silverâs forecast. Program Committee: Mark Jensen, Federal Reserve Bank of Atlanta. Polls are weighted using demographic data on education, race, marital status, and political affiliation. << /S /GoTo /D (subsection.3.1) >> The question now is: if you think a regime changing event like a contested election or Trump pulling off a coup could happen, should you take it into consideration in your probability model? In addition to the solid content, there are some great take-away snippets, such as: "Bayesian inference is hard in the sense that thinking is hard." Thus we can explicitly exploit the factor structure of the data and the law of motion of the extracted factors. When Tiger first told his parents that heâs writing a long article on the theories and applications of elections forecasting, they said: ânobody cares about your math; just tell us who the winner will be.â This is what millions of voters truly want â clarity, simplicity, and accuracy. Make sure to read the fine print on state polls to understand their methodology, lest you make the same mistake of 2016! endobj These are things that I will pass with a grain of salt unless theyâre telling me exactly their method of inference. mgnldnsty Computes a VAR estimate and the integrated posterior, with a proper prior Likewise, any verification of oneâs election prediction would involve having some reasonably good simulation of American voters, and we repeatedly run the simulation to see if Trump or Biden would win. As long as your polls are unbiased and we can assume people wonât change their vote too much until the election (probably an easier assumption than unbiased), and you polled enough people, basic probability theory gives a good guarantee that basic polling will give a good estimate. The usual caveat applies. Hedibert Lopes, Insper. 9 0 obj Bayesian statistics allows you to model check while building your model. Let us first set the scene. Sims and Zha [1998] review Bayesian methods for multivariate models and their advantages: our paper is in that tradition. North-Holland BAYESIAN SKEPTICISM ON UNIT ROOT ECONOMETRICS* Christopher A. SIMS University of Minnesota, Minneapolis, MN 55455, USA Received January 1988 This paper examines several grounds for doubting the value of much of the special attention recently devoted to unit root econometrics. The punchline is: IF THEREâS NO WAY THAT I CAN TELL YOUâRE WRONG, I WILL NEVER SAY THAT YOUâRE RIGHT! We would sincerely appreciate any feedback and hope this is only the start to many exciting conversations to come. Keywords: Forecasting, Bayesian methods, Marginal Likelihood, Hier archical model-ing, impulse responses ... robilis, Frank Schorfheide, Chris Sims, Raf Woutersand participants in several conferences and seminars for comments and suggestions. is a univariate, non-Bayesian and non-autoregressive special case of the model 1I am deeply indebted to Niel Shephard, who found a mistake-now fixed-in Theorem 2 in an early version of this paper, as well as to Chris Sims. Questions? We also thank Qingquan Fan, Jinfeng Luo, and Haotian Jia for excellent research assistance. Well, yes and no. Probability theory says that any event with a nonzero probability will eventually happen if you keep doing it. This isn’t necessarily the case in machine learning. Should forecasters incorporate the likelihood of a coup / contested elections in their models? As mentioned above, frequentists wouldnât assign probability distribution on unknown values. 4 See Leeper and Zha (2002) for a discussion of modest policy interventions in the context of Bayesian VARs. 37 0 obj Say weâre interested in the percentage of people who will vote for Trump vs. Biden on Election Day. For DSGE models, the library can solve models using Harald Uhlig's method of undetermined coefficients and Chris Sims' canonical decomposition; When you do a Bayesian t-test instead of a frequentist one, the result you get is not a p-value but a number called a Bayes factor. 5 0 obj The way you solve a problem using Bayesian inference is, you construct some joint probability distribution for your knowns and unknowns â and then use the laws of probability to make statements about the unknowns given the knowns. Christopher David Simms (born August 29, 1980) is a former American football quarterback who played in the National Football League (NFL). (1984). The document con- We also thank the NSF and the Sloan Foundation for generous research support. Ulrich K. Müller. You then go ask more people; and based on how right/wrong you are, you keep updating your belief and continue down this processâ¦. This sounds absurd to most people at first sight. As long as you can ask everyone (and everyone answers truthfully), youâll get that number. Sims (1980a) speculated that some sort of Bayesian approach might work better. 5% sounds small, but in reality it will be a dramatic shift. Obviously the polls were off last election, perhaps bias here is to blame, but thatâs tough to say. Sylvia Frühwirth-Schnatter, Wirtschaftsuniversität Wien. 17 0 obj Why the disparity between state and national polls? For instance, I would assign almost zero probability that only less than 10% of people actually want to vote for Trump (highly improbable! This is why physicists refuse to definitely conclude whether String Theory is right or wrong. When we talk about statistical inference â the process that draws conclusions from sample data â two popular frameworks are the frequentist and Bayesian methods. This practice is common among some pollsters, which are often denoted with (D) or (R) on polling aggregators like RealClearPolitics, in order to make support seem higher for a preferred candidate. Bayesian Analysis (2008) 3, Number 3, pp. Well, we first need to ask ourselves a question: what does it mean for a poll to be accurate? Some would suggest that people responding to polls didnât want to admit that they opposed Bradley, lest they seem like they opposed him due to his race, thus causing his support to seem inflated in polling. Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix.

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