An Austrian Analytical Alternative: How Bayesian Analysis Will Reorient Econometric Thought

Austrian economists exist at the edge of their field. Centering their theory on the subjective actions of individuals, Austrians reject the use of econometrics and instead rely on fundamental theories of value to construct their arguments. Their rejection of econometrics leaves them excluded from economic academic journals. I argue by adopting econometric methods, Austrians can engage in econometrics in a fundamentally different way which both highlights the problems of econometrics and improves the methods, while never compromising their recognition of inherent flaws in econometric modeling. I argue that this engagement should occur via the adoption of Bayesian econometric methods, which will allow Austrians access to the problematic world of econometrics while simultaneously incorporating fundamental theoretical structure from their Austrian position. In engaging with econometrics via Bayesian analysis, Austrians will better elucidate the problematic nature of theoretical econometrics while enforcing more critical analysis of both the prior assumptions and succeeding interpretation associated with modeling, offering an approach to econometrics which highlights the flawed conception of econometrics as objective and instead proposing subjective interpretation of econometrics, and disseminating Austrian perspectives through increased publication.

AN AUSTRIAN ANALYTICAL ALTERNATIVE How Bayesian Analysis Will Reorient Econometric Thought By Lauren Waters April 29, 2016 Senior Thesis in Economics Abstract: Austrian economists exist at the edge of their field. Centering their theory on the subjective actions of individuals, Austrians reject the use of econometrics and instead rely on fundamental theories of value to construct their arguments. Their rejection of econometrics leaves them excluded from economic academic journals. I argue by adopting econometric methods, Austrians can engage in econometrics in a fundamentally different way which both highlights the problems of econometrics and improves the methods, while never compromising their recognition of inherent flaws in econometric modeling. I argue that this engagement should occur via the adoption of Bayesian econometric methods, which will allow Austrians access to the problematic world of econometrics while simultaneously incorporating fundamental theoretical structure from their Austrian position. In engaging with econometrics via Bayesian analysis, Austrians will better elucidate the problematic nature of theoretical econometrics while enforcing more critical analysis of both the prior assumptions and succeeding interpretation associated with modeling, offering an approach to econometrics which highlights the flawed conception of econometrics as objective and instead proposing subjective interpretation of econometrics, and disseminating Austrian perspectives through increased publication. Waters 1 TABLE OF CONTENTS INTRODUCTION ................................................................................................................... 2 METHODOLOGY ................................................................................................................... 4 THEORETICAL FRAMEWORK ................................................................................................... 6 REVIEW OF THE LITERATURE ...................................................................................... 10 BAYESIAN INFERENCE: A BREAK FROM FREQUENTIST STATISTICS .......................................10 Bayes Theorem .................................................................................................................11 Differences Between Bayesian Analysis and Frequentist Analysis .................................14 Benefits of Bayesian Analysis ..........................................................................................16 AUSTRIAN CRITIQUES OF ECONOMETRICS ............................................................................17 Problematic Mathematical Assumptions .........................................................................18 Econometric Omission of Economic Goals .......................................................................22 Subjective Econometric Failure .......................................................................................28 FINDINGS ............................................................................................................................. 30 CONCLUSION ...................................................................................................................... 37 BIBLIOGRAPHY .................................................................................................................. 39 Waters 2 INTRODUCTION It's a Saturday morning and you're just getting out of bed. What should you wear? Consider the weather: if it's sunny and warm, you select cooler clothing. Of course if it's chilly and snowing, you'll put on a very different outfit. So, how will you decide? Perhaps you know the distribution of temperatures for this particular day of the year, which predicts it will be 60 degrees and sunny. This is a Frequentist statistical approach. But you're an Austrian economist and reject this statistical approach. There are so many problems! Why should this day be the same as in year's past? What if this particular year is having a cold streak? What if you, as an individual, are always warm? It's time for a new approach; a Bayesian approach. You begin by wearing your pajamas, as this will serve as a baseline. You stick one hand out the door. It feels cold. Walking outside, you're getting wet from melting snowflakes. When you open your eyes, you see the dark storm clouds amassing around you. Each bit of evidence updates your hypothesis, and you determine that pajamas are not the best outfit for the day. You've decided today you need to wear a coat, or maybe get back inside with only your pajamas on… Although this example may seem silly, it well exemplifies the difference between the Frequentist and Bayesian approach to statistics. The Austrian school rejects all statistical analysis on the grounds that statistics cannot accurately model cause and effect, there are problems of abstraction, and a general lack of subjectivity in the statistical sciences. However, I argue that the Bayesian method of statistical analysis which relies on a fundamentally different notion of "updating" a hypothesis using new information, nullifies many of the Austrian critiques, and actually may provide a kind of statistical analysis that should not be rejected by Austrians. The Austrian School of Economics is best known for its reliance on classical economic Waters 3 theory, contributions to mainstream economic thought such as price theory and the subjective theory of value, and uncompromising rejection of econometrics. This rejection of mathematical interpretations contributes to the rejection of Austrian thinkers by other schools in economics. Austrian economists are often excluded from economic journals because of their rejection of modeling, data analysis, and econometrics. I believe the Bayesian approach to econometrics may offer a more philosophically suitable method of econometric analysis. If Bayesian econometrics allowed Austrian economists an acceptable approach to data modeling, Austrian thinking could be more easily published and distributed, and would have a larger impact on the field of economics as a whole. This could be a critical key in distributing Austrian theory to a wider audience, and would also open new fields of study within the Austrian school. In this paper, I will explore the philosophical criticisms of the econometric method from the Austrian perspective. These criticisms contest the validity of a priori econometric thinking, and in particular critique the failure of econometrics to prove causality, in which Austrian economists are particularly interested. Often, mainstream economists do not reject the Austrian critiques of econometrics, instead they simply ignore the problems associated with econometrics and continue to use econometric analysis in development of economic theory. In light of the Austrian criticisms, I will analyze the Bayesian econometric method, in contrast to the traditional Frequentist approach, since Bayesian analysis differs fundamentally from Frequentist analysis, thus offering a philosophically superior approach to data analysis. Although the Austrians offer strong critiques of fundamental assumptions of econometrics, I will endeavor to analyze the relevant philosophical differences between the traditional and Bayesian econometric models, in an attempt to offer an alternative econometric system which better assimilates to Austrian economic thought. In examining the differences between the Frequentist Waters 4 and Bayesian econometric schemes, I will attempt to show that adoption of Bayesian analysis could retract the rejection of econometrics in the Austrian perspective. Thus, in this paper I will attempt to analyze the underlying critiques of econometric theory by Austrian thinkers, examine foundational assumptions of Bayesian theory as a philosophically superior method of data analysis, and use those assumptions to demonstrate the complementary relationship between Bayesian modeling and Austrian theory. METHODOLOGY I will use a two-fold approach in this paper. First, I will lay the groundwork by analyzing the distinctions between traditional statistical analysis and Bayesian analysis. The differences between the two approaches include philosophical differences, mathematical differences (i.e., formulas used, mathematical assumptions, probabilistic differences), and differences specific to econometric study which are not fully appreciated in the larger context of statistics. The basic requisite mathematical principles pertaining to data analysis will be examined first, followed by an analysis of Bayes' theorem. This will provide enough mathematical rigor to guide the discussion of Bayesian and Frequentist differences. Furthermore, I trace the differences in each statistical school and suggest why the Bayesian approach is better suited for analysis, particularly in econometrics. This will conclude my treatment of statistical theory in itself. Analysis of econometric techniques will be followed by an analysis of Austrian critiques of econometrics in general (without limiting ourselves to either Bayesian or Frequentist schools of thought). These Austrian critiques generally take one of three forms. The Austrians either critique statistics in general, due to it's problematic assumptions in the philosophy of statistics. Next, Austrians suspect econometrics does not actually achieve the intended goals of the study of Waters 5 economic theory. Finally, Austrians profoundly critique the inability of statistics to be subjective. The analysis of these critiques will allow us to make connections between Bayesian modeling and potential benefits not found in Frequentist statistics. I will utilize the Mises Institute as a primary resource for my analysis of the Austrian school. The Mises Institute is the premier Austrian economics foundation. The Mises Institute describes itself as promoting the following goals: To promote teaching and research in the Austrian school of economics, and individual freedom, honest history, and international peace, in the tradition of Ludwig von Mises and Murray N. Rothbard. These great thinkers developed praxeology: A deductive science of human action based on premises known with certainty to be true, and this is what we teach and advocate. Our scholarly work is founded in Misesian praxeology, and in self-conscious opposition to the mathematical modeling and hypothesis-testing that has created so much confusion in neoclassical economics.1 This position of the institute offers a foil to the Bayesian approach in that it clearly rejects mathematical modeling at a fundamental level. Thus, by using the institute and its articles to set up the Austrian position, any conclusions drawn through the analysis will be stronger, given their clear dismissal of econometric modeling. In conclusion, I will analyze whether Bayesian modeling techniques alleviate any Austrian concerns with econometrics, suggesting that Bayesian analysis may actually serve as an analytical technique that could be used coherently with Austrian theory. 1. Mises Institute, n.d., "What is the Mises Institute?" Mises Institute: Austrian Economics, Freedom, and Peace, Accessed April 26, 2016, (https://mises.org/about-mises/what-is-the-mises- Institute). Waters 6 THEORETICAL FRAMEWORK The Austrian school of economics has a distinct economic position on many of the issues in the field of economic theory. The Austrian critique of econometrics is fundamentally philosophical, therefore I will analyze the philosophical differences of Bayesian and Frequentist analysis using the theoretical framework of the philosophy of science. In the analysis of these differences, I will also use introductory statistical concepts. Furthermore, I will approach Bayesian analysis and the Austrian critique of econometrics as rooted in different philosophical interpretations of economic theory. There are three primary philosophical debates which will guide the analysis: 1) The debate between subjective and objective reasoning, 2) the debate between deductive and inductive reasoning (which makes use of a priori and a posteriori reasoning), and finally 3) the difference between positive and normative economics. First, the debate between objectivism and subjectivism in the philosophy of science is crucial to analyzing the Austrian perspective. Objectivism "expresses the idea that the claims, methods and results of science are not, or should not be influenced by particular perspectives, value commitments, community bias or personal interests, to name a few relevant factors."2 Generally, econometricians and economists tend to believe their field is objective: given the right theorems and principles, one can deduce anything about their field. The Austrian 2. Julian Reiss and Jan Sprenger, "Scientific Objectivity," The Stanford Encyclopedia of Philosophy, (Edited by Edward N. Zalta, Summer, 2016, Accessed April 26, 2016), http://plato.stanford.edu/archives/sum2016/entries/scientific-objectivity/. Waters 7 school tends to support a more subjective analysis of economics, in which, "because individuals are diverse, we can never get into the mind of each person and observe their private thought processes," and because of this subjective thought process, we can never speak adequately in the objective sense of their reasoning. We can however, "investigate how the objective world affects choices - how, for example, individuals acquire the information that shapes their decisions, … This, again, is much more the proper study of economics."3 This is a subjective approach to economic thought, one that does not deny objective truths, but rather considers them unimportant in the field as a whole. This leads into the debate concerning induction and deduction. Essentially, the distinction between induction and deduction is that "some arguments are such that the (joint) truth of the premises is necessarily sufficient for the truth of the conclusions." In other words, deductive arguments begin with premises such that the validity of any claims that adhere to the premises must be true, whereas inductive validity suggests that the "truth of the premises is very likely (but not necessarily) sufficient for the truth of the conclusion." Induction supposes that based observational evidence, one can make increasingly valid claims about the world. Although those claims are not necessarily sufficient for the truth of the conclusion, by amassing enough evidence, an inductive claim's veracity can become highly probable.4 The Austrians, interestingly enough, argue that the validity of economic claims must come through deduction, even though they view individuals as primarily subjective actors. Because Austrian economic science can discover economic truth, Austrians argue that economics can even be predictive, "not 3. Eamonn, Butler, Austrian Economics: A Primer, Adam Smith Research Trust, 2010, 23. 4. Jc Beall and Greg Restall, "Logical Consequence," The Stanford Encyclopedia of Philosophy, Fall, 2014, Accessed April 26, 2016. http://plato.stanford.edu/archives/fall2014/entries/logical-consequence/. Waters 8 on the basis of observation, theorising and testing, but through a process of deduction."5 By deducing from general principles, human action can be predicted. An example of a general principle would be: humans do not want to starve to death. This could lead to predictive claims of what actions people may take during a famine. At this point it will be helpful to define a priori and a posteriori reasoning, as it relates to the way one can determine truth. A priori knowledge is independent of experience, relying instead on deductive reasoning or tautological statements. In contrast, a posteriori knowledge is dependent on experience or empiricism. These two forms of knowledge will allow us to distinguish between differing methods of truth seeking. Finally, we distinguish between positive and normative economics. In the debate between positive and normative economics, the Austrian critique aligns with the philosopher's critique of economics. For the Austrian, there is a blurred line between what is normative, or what the "facts" are, and what is positive economics, or what economics suggests we should do. For the Austrian, there is little difference between positive and normative economics, as economic theorizing is an inherently subjective human activity. In the field of econometrics, the lack of objectivity results in data collection and analysis that is already skewed in the favor of positive science, as one enters the analysis already expecting a certain result or looking to prove a result, thus collecting data, including variables, or selecting a model differently depending on the desired outcome. That is, the theory and analysis of human activity guides the research and analysis of data. For an Austrian, this is one fundamental critique of normative economics: there really is no such thing. Any analysis done will rely inherently on human theory. The following statistical phrases are key to understanding statistical analysis. First, the term ceteris paribus, in econometric use, refers to the notion of holding other factors equal; 5. Eamonn, Butler, Austrian Economics: A Primer, 27. Waters 9 essentially, the econometric theory occurring is taking place inside a vacuum, with only your variable of interest being assumed to change. Secondly, probability distributions demonstrate the probability of a given outcome for each possible outcome. This traditionally uses a two dimensional curve, with each point on the curve representing the probability (y-axis value) of that event (x-axis value) occurring. These probabilities will add to one, implying a 100% probability that one of the events will occur (this is akin to saying that something must happen, even if that something is nothing). The most famous example of a probability distribution is the normal curve, which suggests that in a normally distributed population, most people will tend to be like most other people. Therefore, the tallest part of the curve is in the middle, suggesting a higher probability of the outcome "being in the middle." Third and finally, the study of econometrics must say something regarding correlation and causation. Any introductory statistics student will tell you that correlation does not imply causation, and this is because correlation, or a relationship between two or more events, does not necessarily mean that one event has impacted the other and caused that event to occur. Finally, the Austrian position relies on three theories: value theory, methodological individualism, and subjectivism. Although it can be unclear how value theory differs from a concept like subjectivism, which also depends on individual values, value theory is very much distinct. Value theory suggests that objects do not inherently have value, nor is that value quantifiable. Rather, objects, actions, and operations have value because individuals attribute value to them. Any of these goods or services rely on a subjective interpretation of value, not one that can be arbitrary assigned. Likewise, the value of a good will differ from person to person, from time to time, and from place to place. This theory suggests that the values attributed to Waters 10 goods and services are constantly changing, inherently differing, and effectively unmeasurable.6 Methodological Individualism is the Austrian belief that because individuals are making subjective decisions, any aggregation of those decisions will be an abstraction from the independent minds of the decision makers. Therefore, any assumptions or interpretations rooted in the belief of collective action is inherently problematic. There are only individual decisions, never collective ones.7 The interpretation of economic theory, based on the two founding principles of value theory and methodological individualism, must necessarily be subjective. Austrians argue that "the ‘facts' of economic science, then, are not statistical aggregates ... Nor even are they individual prices, or investments, or savings plans. These things have no importance except in terms of what they mean to individuals."8 The Austrian approach considers the individual, necessarily personal, attribution of value rather than objectively measurable facts about unimportant factors in the economy like prices, wages, or GDP. REVIEW OF THE LITERATURE BAYESIAN INFERENCE: A BREAK FROM FREQUENTIST STATISTICS Bayesian inference emerged in 20th century but became an even stronger force in the 1980s when computer modeling allowed researches to run huge integrations and create models using algorithms. The Bayesian method of statistical inference can be juxtaposed with traditional statistical analysis. The terms Frequentist and traditional will be used interchangeably and denote 6. Eamonn, Butler, Austrian Economics: A Primer, 24. 7. Eamonn, Butler, Austrian Economics: A Primer, 88. 8. Ibid., 25. Waters 11 the statistical inference method using hypothesis testing and confidence intervals, which are developed using sample data emphasizing the frequency and proportion of the data to build models and make inferences about a larger population of data, based on an assumption of that data's distribution. In contrast, the term Bayesian Statistics refers to an alternative statistical inference in which Bayes' Theorem is utilized to update a probability and hypothesis, based on a sample already known. These samples are updated using new data and a distribution is established based on this data. Here I will evaluate the differences between the two schools of thought, Frequentist and Bayesian, and analyze both the philosophical underpinnings of Bayesian thought and the corresponding advantages in Bayesian analysis over traditional statistics. BAYES THEOREM Understanding the Bayesian approach to inference is best understood in juxtaposition to traditional, Frequentist methods of inference, with which most people are generally acquainted. Traditional conditional probability is denoted by the following formula: (|) = ( ∩ ) () This equation denotes the Frequentists' approach to probabilistic inference. The equation states that a probability of A given B (a statistical way of saying if B occurs, what is the probability of A) is the probability that they happen together relative to the probability that B happens at all.9 This method of analysis is typically taught in statistics and econometrics courses. This approach 9. John K Kruschke, Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and STAN, (2nd Edition. London: Elsevier, 2015), 100. Waters 12 will be critiqued later, in comparison to the Bayesian model. Importantly, this model makes an a priori, pre-sample, probability distribution based argument for its predictive power.10 In contrast, Bayes Theorem (sometimes referred to as Bayes' rule) is as follows: (|) = (|)() () What this equation means, is that the probability of A given B is the probability of B given A occurring, multiplied by the probability that A occurs, relative to the probability that B happens at all. This definition, however, is riddled in Frequentist terms, and it can be more intuitive to rewrite these terms in Bayesian terms that give greater suggestion to their meaning. Rather than referring to the theorem in Frequentist, terms, by simply renaming the equation, we can analyze the equation using Bayesian terminology: P(θ|D) = P(D|θ) P(θ) () Where: (|) is the posterior or the calculated belief, P(D|θ) is the likelihood or the probability that an event will occur, where the likelihood is updated after each "round" of testing, P(θ) is the prior, p(D) is the evidence.11 Here, the posterior is the credibility of values without the data D. The likelihood is the probability that the data could be generated by the model with parameter value . The "evidence" for the model, is the overall probability of the data according to the model, 10. Christopher A. Sims, "Bayesian Methods in Applied Econometrics, or, Why Econometrics Should Always and Everywhere Be Bayesian," (August 6, 2007), 2. 11. John K Kruschke, Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and STAN, 106. Waters 13 determined by averaging across all possible parameter values weighted by the strength of belief in those parameter values.12 Bayesian analysis serves as a useful tool in analysis because even if we assume possibilities a priori, we will be able to examine them using evidence that continues to be collected and updated, thus creating an a posteriori argument instead.13 This is critical in reexamining the Austrian perspective of econometrics, because one of the chief concerns of Austrians is the reliance on a priori theory. However, using this a posteriori argument, one can reduce the number of complaints of Austrians regarding econometrics by at least one. Importantly, the prior distribution, although determined subjectively and in many cases arbitrarily, does not necessarily determine the posterior distribution. That is to say, that simply because the prior distribution is founded either on a basis of equality (for example, we assume that half the population are men and half are women) or on a basis of an estimate (for example, as a physician, I estimate 30% of overweight patients have diabetes). This prior distribution, however, becomes wrapped up in the posterior distribution. As Kruschke puts it, "the posterior distribution then becomes the prior beliefs for subsequent observations."14 This "updating" process allows us to improve our prior beliefs with each repetition of analysis and with greater amounts of data. Bayesian analysis assumes that data are noisy, that is, that there is a significant randomness and variability of any data set in reality. Fortunately, Bayesian analysis embraces this noise. Although the data may not be completely consistent, by virtue of being "real" data, 12. Ibid., 106-107. 13. Ibid., 16. 14. Ibid., 17. Waters 14 the data do remain noisy indicators of the underlying data. As Kruschke says, "we hypothesize a range of possible underlying generators, and from the data we infer their relative credibilities."15 DIFFERENCES BETWEEN BAYESIAN ANALYSIS AND FREQUENTIST ANALYSIS Frequentist and Bayesian models differ in fundamental ways. Frequentist models are based on a priori sampling distributions, Frequentist models are considered "objective" rather than subjective, and Frequentist models are considered deductive rather than inductive. First, as Christopher Sims noted, Frequentist models make a priori, pre-sample, probability distribution based argument for its predictive power.16 Bayesian models do not do this; not in the same way. Although there may be a pre-sample distribution, that prior is updated regularly to improve the predictive power. Rather than establishing an a priori distribution, the Bayesian approach establishes a posteriori arguments, by updating an arbitrary prior assumption to achieve a more accurate posterior distribution. This differs fundamentally with the Frequentist approach. An illustrative example, in traditional statistics the probability distribution is set; that is, if one were to conduct a hypothesis test, they would simply use the appropriate distribution. However, in Bayesian modeling, there is no hypothesis testing, and instead, one simply constructs the appropriate posterior distribution. It is the analogous operation, however, there are very different results. The more controversial issue when it comes to Bayesian and Frequentist analysis is the role of objectivity in the modeling. Frequentists often critique the Bayesian models for being subjective, due to the personal assignment of the prior distribution. Because one cannot know 15. Ibid., 21. 16. Christopher A. Sims, "Bayesian Methods in Applied Econometrics, or, Why Econometrics Should Always and Everywhere Be Bayesian," 2. Waters 15 objectively what the prior distribution actually is, one must make a best guess from existing data. Frequentists argue that there is no such guesswork in their modeling; instead it is empirically set and derived from the laws of mathematics, which annihilate the possibility for subjectivity. However, as Howson and Ubach recognize, total objectivity is unattainable, and that no classical method can be applied without personal judgment and arbitrary assumption. Therefore, this popular critique, if it is to be a critique, could be applied just as easily to the classical econometricians as the Bayesians. This subjectivity, then, would seem an ample opportunity for Austrians to attack, because neither Bayesian nor Frequentists can avoid a certain degree of subjectivity. However, it seems that Austrians do not attack this point, perhaps because their own processes of theorizing are based very strongly on subjectivity. The argument that each individual is making his own subjective decision and the reliance on subjective theories of how the economy works would evidence the avoidance of the topic of subjectivity and objectivity for Austrians, as they would likely be lumped into the scientifically "problematic" (in the eyes of the scientific community) category of subjective theorists. Additionally, Bayesian modeling offers a distinct benefit over Frequentist models due to the intuitive understanding of the results of the model. In traditional Frequentist statistics, the probability distribution is not changed, but rather, one assigns a probability to the sample data given that probability distribution. For example, using a normal curve, you might find that given your sample of male shoe sizes, the probability of getting your specific sample based on the normal curve is 60%, suggesting that your hypothesis is correct. This is inherently confusing; it is much easier to think of supporting a hypothesis, rather than assuming a hypothesis and suggesting a relative amount of support. In the Bayesian model, the probability distribution will physically change as the testing occurs, rather than remaining static as in the Frequentist model. Waters 16 In the Bayesian model, if your sample data is higher than the hypothesized mean of the normal curve, your physical probability distribution will shift to incorporate that new evidence. Given enough evidence, your distribution will look highly accurate. This updating of the distribution itself is much more intuitive than being forced to compare meta-probabilities to probabilities as in the Frequentist approach. BENEFITS OF BAYESIAN ANALYSIS I strongly believe that Bayesian analysis offers a fundamentally more beneficial, intuitive, and demonstrative statistical interpretation of economics. By using inductive subjective theories, Bayesians avoid many of the pitfalls of Frequentist statistics. Furthermore, because the posterior distribution in Bayesian analysis is an actual probability density function, the statistical understanding attributed to Bayesian models is much more clear than in the confidence interval and hypothesis testing Frequentist equivalent. Collin Howson and Peter Urbach state that the problem of induction asks the question: "how can one be certain, in any particular case, that one has selected the correct cause of an event out of the huge, indeed infinite, number of possible causes?"17 In the philosophy of science, two philosophers argued for inductive reasoning. Immanuel Kant argued that everything had a cause, and David Hume that the future will resemble the past.18 Karl Popper attempted to resolve this by noting that "while theories cannot be logically proved by empirical observations, they can be refuted by them," and that deductive consequences can sometimes be verified.19 One 17. Colin Howson and Peter Urbach, Scientific Reasoning: The Bayesian Approach, (La Salle, Illinois: Open Court Publishing Company, 1989), 3. 18. Ibid., 4. 19. Ibid., 5. Waters 17 reason for this long-standing debate regarding inductive knowledge, is that in the history of science and scientific thought, there has been a "strong tendency … to resist complete skepticism" and instead embrace the fact that "absolute certainty cannot be expected, nevertheless, the explanations thought up by scientists, and tested by searching experiments, may secure for themselves an epistemic status somewhere between being certainly right and certainly wrong"20. This is the status of most econometricians today. One of the most fundamental critiques of Bayesian theory is that "Bayesian approaches treat certain subjective factors as relevant to the scientific appraisal theories."21 Essentially, the critique of Bayesian approaches is the incorporation of certain subjective theories into the supposedly "objective" determination of truth that the Bayesian analysis is suggesting. However, Howson and Urbach reject this argument on two grounds. First, the element of subjectivity admitted is minimal, and secondly, the element is exactly right. Although some schools of thought argue for a complete and austere use of objectivity in the sciences, the authors argue that "total objectivity is unattainable and that classical methods, which pose as guardians of that ideal, in fact violate it at every turn."22 AUSTRIAN CRITIQUES OF ECONOMETRICS Austrian Economics refers to an economic school of thought which emphasizes the concept of methodological individualism. Austrians believe that social and market phenomena result from individual decision making. Importantly, Austrians generally reject econometric 20. Ibid. 21. Ibid., 11. 22. Ibid., 11. Waters 18 analysis, given that statistical methods are true a priori, and thus can only generate theories which are true, resulting in an inability to actually test theory. Austrian critiques center around three fundamental problems in the treatment of economics by statistics. These critiques range from a doctrinal avoidance of mathematics to problematic aspects within the field of statistics itself. First, the assumptions required to utilize econometric models are inherently problematic, especially in the field of economics where there is a distinct human factor. This brings us to the second criticism, which is a failure on the part of econometric modeling to adequately capture the human element and subjectivism. Finally, using econometric modeling simply does not advance the goals of economics, which is to explain cause and effect behavior. PROBLEMATIC MATHEMATICAL ASSUMPTIONS First, Austrians recognize many problematic mathematical assumptions. These assumptions are inherent to the field of study of econometrics, for example, econometricians assume unrealistic properties of the world, such as the ceteris paribus condition. Furthermore, because these assumptions are a priori, they fundamentally alter the rest of the econometric analysis, and a change in the assumptions changes the analysis. Finally, mathematics cannot literally quantify something like value, which is a chief concern for Austrian economists. Roger Garrison, an Austrian economist, accepts that use of mathematics can be appropriate; he suggests the proper imperative for economists is not to divulge from mathematics entirely, but rather, "Do not allow the applicability of mathematical and statistical methods to define the scope of economics." Because Garrison does not reject mathematical economics entirely, he elicits two suggestions for using math in economics. First, mathematicians should avoid expressing relationships having any relevance to economics simply with mathematical Waters 19 terms, and secondly, econometricians should be more willing to abandon mathematics in favor of economic descriptive ability. He notes that the problem is not an (Mises Institute n.d.) (Reiss and Sprenger 2016) (Beall and Restall 2014)abstraction away from reality to the field of mathematics, since economics in itself is inherently an abstraction; instead, he argues that the problem is a failure to recognize a distinction between mathematical economics and "mathematical gymnastics." He argues that mathematics assigns properties to economic principles, and proceed to "manipulate mathematical equations without concern about the economic meaningfulness-or the possible meaninglessness-of the resulting relationships."23 Shostak also makes this observation, noting that "To improve an econometric model's capability as a forecasting tool, econometricians often employ various tricks. The predictive capability of each equation in the model is checked against actual data, and the difference between the actual data and the data obtained from the equations, also known as the add factor, is extrapolated forward and incorporated into the models equations." In summary, Shostak claims econometrics has a clear set of problems: "Rather than viewing econometric models as a sophisticated technique that can discover the hidden truth about the economy, we should regard them as clumsy and expensive extrapolative devices, which have nothing in common with reality."24 Furthermore, one of the most problematic practices in econometrics, Garrison notes that It has become standard practice in the profession today to make assumptions-sometimes sometimes bizarre assumptions-in order to render an economic issue mathematically 23. Roger W. Garrison, "Mises and His Methods," In The Meaning of Ludwig von Mises: Contributions is Economics, Sociology, Epistemology, and Political Philosophy, by Jeffrey M. Herbener, (Boston: Kluwer Academic Publishers, 1993), 6. 24. Frank Shostak, "What is Wrong with Econometrics?" Mises Daily, April 17, 2002, Online. Waters 20 tractable.25 Austrians would argue that this reliance on assumptions signifies a corruption of economic thought in the pursuit of mathematical accuracy. Although the reliance on assumption causes philosophical worry, a larger issue in this practice emerges as the acceptance of mathematical assumption actually dilutes and obscures the principle interests of Austrians and economists in general. Garrison notes this occurrence in the study of monetary theory, noting that "the issues of interest to the Austrians-injection effects, monetary distortions of the production process, monetary calculation during periods of inflation-are all swept aside by assumptions that make the remaining issues mathematically tractable." Garrison makes a particularly salient point when he discusses new-classical models constructed in the equilibrium based setting. He argues that the model accurately predicts a ceteris paribus environment, one in which no information flows, capital is homogenous, and all external variables are made equal. This model is powerfully predictive, but, of what? Garrison recognizes that the implications of this model has no real-world significance for actual economies. With all the assumptions added into the model to make it work, it has lost its efficacy to serve as a model in the first place. Thomas Sargent noted that this over simplification has caused the models to have been so abstracted away from the reality of economy, "that it is often difficult to take their predictions in some directions seriously" when the models no longer reveal anything about the actual world.26 This understanding of frequency theory has important implications for econometric study. As Rothbard argues, "if one holds to the objective Mises theory, it is unscientific and illegitimate to apply probability theory to any situations where the events (like the tossing of a 25. Roger W. Garrison, "Mises and His Methods," 7. 26. Ibid., 8. Waters 21 die) are not strictly homogenous, and repeated a large number of times".27 That means that the study of econometrics, currently, relies on that subjective interpretation; the idea that if we have collected data, we can project that data into the future based on the sample that we have already collected. However, it is clear from the reality of data that groups are seldom homogenous, nor are events typically repeatable. For example, if one were to examine the recession of 2008, it is clear that this is not a homogenous event. It affected individuals in different walks of life in very different ways- just consider a new homeowner with a 30-year mortgage compared to a couple who had been in their home for the last 50 years). Nor is it repeatable - we will never have the economic climate of 2008, or the precursors, deregulation, housing inflation, and credit default swaps, again. It's clear that use of the subjective probability theory is problematic, and Austrians, with what little data analysis they do, understand that it's use in the economic setting is illegitimate. Furthermore, there is something especially problematic in the interpretation of models. Models needn't necessarily be rejected outright, but their interpretation is often misconstrued. For example, there is a gap between the real world and the model, particularly because "mainstream economists typically develop highly simplified models of some economic process, and then proceed to criticize the real economy because it does not fit the model."28 This is problematic because that simplified model is actually highly inaccurate for what it is proposing to measure. Gene Callahan admits however, that "as long as one keeps in mind that [the model] is an unrealistic abstraction, isolating just one aspect of the actual market process, it may have its 27. Murray N. Rothbard, "The Correct Theory of Probability," Mises Daily, February 22, 2010, Online. 28. Gene, Callahan "The Myth of the Model," Mises Daily, May 20, 2004, Online. Waters 22 uses."29 This distinction is a critical one. Although models needn't be rejected outright, they should certainly be scrutinized. Although aggregation is typically considered problematic, aggregation in statistics may not eliminate methodological individualism from consideration, as many Austrians would critique. Because individual decisions are often highly subjective and dependent on a multitude of factors, we cannot call them random; however, "we hoped that the decisions of individual actors were sufficiently complicated and unpredictable that it would not be possible to distinguish them from simple randomness." This understanding of statistical randomness is interesting because it allows non-random behavior to become statistically indistinguishable from true randomness. Because this aggregation allows for both non-random and random behavior to coexist, it allows a more nuanced account of modeling that better fits in with the Austrian understanding of individual subjectivism.30 It's important to remember, however, that this analysis of randomness only holds as long as proper understanding of the model being used is retained, which many Austrians believe will consistently fail to be true. However, this interpretation does allow aggregation to coexist with Austrian thought in application to modeling techniques. Acceptance of such an argument brings Austrians one step closer to implementation of Bayesian theories in general. ECONOMETRIC OMISSION OF ECONOMIC GOALS The second critique of econometrics is the incoherence between econometric models and the goals of econometrics. Because Austrians believe the determination of cause and effect is the goal of economics, econometrics is simply the wrong language to talk about this relationship. 29. Ibid. 30. Ibid. Waters 23 The problems with correlation and causation are rampant in econometrics, and this leads to both bad predications and problematic interpretations. Simply put, mathematics is the wrong "language" to use to talk about econometrics. The principal and guiding viewpoint of Austrian Economics, "in Mises's own view is achieved by identifying cause-and-effect relationships between individual actions in the marketplace and the economic phenomena to which they give rise."31 Most critiques of econometrics center on this fact. So what exactly causes Austrians to be so hesitant to use econometrics? Frank Shostak explains the problem via analogy: If the sciences use laboratory experimentation to develop theory and interpret the real world, econometrics would be the analogous experimentation for the field of economics; however, as Shostak recognizes, "there is no equivalent [to the laboratory] in the discipline of economics. The employment of econometrics and econometric model-building is an attempt to produce a laboratory where controlled experiments can be conducted. Part of the problem, is that, according to Mises, "the experience with which the sciences of human action have to deal is always an experience of complex phenomena. No laboratory experiments can be performed with regard to human action. The main characteristic or nature of human beings is that they are rational animals." Because people have the freedom of choice, whereas natural phenomena studied by the sciences come from deterministic laws, people cannot be studied in the same way as the natural sciences. This accents the Austrian position and emphasis on the individual. Individuals make decisions which may be measured in the aggregate but are inherently dependent upon individuals. Furthermore, those individual decisions are reliant upon individual valuations and would require a consistent objective and fixed unit of measurement. As Mises wrote, "There are, in the field of economics, 31. Roger W. Garrison, "Mises and His Methods," 8. Waters 24 no constant relations, and consequently no measurement is possible." Essentially there is no standard measure that can be used to compare the valuation of one individual to another individual, which would be necessary for a truly accurate comparison between individuals. This is one of the principal problems in economics in general, and Shostak recognizes that a truly quantifiable metric is impossible to achieve when it comes to valuation; instead, we can only rank an individuals preferences compared to the individual's personal preferences.32 Shostak critiques the use of probability theory itself in econometrics on the basis of two fundamental problems. The first is an a priori problem, the assumption of a homogenous group when none exists. Because the economic groups being studied are not homogenous, "Each observation is a unique, non-repeatable event caused by a particular individual response."33 This fundamental flaw problematizes the entire study of probability, as the probability distribution is reliant on the assumption that we are working with a homogenous, and therefore non-particular, repeatable event. Essentially, econometrics fails because it is not a good fit for the study of social science. Shostak argues that the perceived benefits of econometric modeling is the production of a good replica of the economy which can enhance the efficiency of government, create a more prosperous economy, assess the validity of economic ideas, and also provide an indication of the future. However, he notes that these are only perceived benefits, and one must rather analyze whether the mathematical method is valid in economics at all for these benefits to be realized.34 32. Ibid. 33. Ibid. 34. Ibid. Waters 25 Forecasting is a particularly problematic study, as often predictions can turn out, frankly, wrong. Robert P. Murphy critically notes that forecasting does not always predict accurately.35 His critique relies on the a priori theorizing of the econometricians. He points to a double standard between game theorists and econometricians; when the game theoretician's model fails, it's because the players did not act according to the model, but when an econometrician's model fails, it can be dismissed simply as an incorrect model, not as incorrect a priori.36 Murphy summarizes the mathematical divide between mainstream and Austrian economists when he says that "most mainstream economists would prefer the precision of a false formal model, versus the generality of a true verbal proposition."37 He is claiming that most economists would prefer a model that formally, but incorrectly, models the behavior of society, rather than elucidating a strong position which may not be as precise, but is more predictive. This is the general critique of econometrics in Austrian examinations. Finally, he somewhat weakens his argument with the following claim: It would be one thing if all of the formal rigor of modeling were followed through to the deepest foundations of economic science. But unfortunately, I believe that in day-to- day practice, the mainstream economist relies on certain assumptions and techniques to address a particular problem, since he knows "how to solve" the question when it is asked in this way.38 I believe this fundamentally weakens his argument against econometrics in general. Instead of disavowing the use of modeling in general, he seems to claim in this conclusion that 35. Robert P. Murphy, "Econometrics: A Strange Process," Mises Daily, July 15, 2002, Online. 36. Ibid. 37. Ibid. 38. Ibid. Waters 26 econometrics may serve as a legitimate form of modeling if only the proper mathematical rigor was met by that model. Although one could claim that his earlier argument rejected the ability of modeling to ever present an accurate description of reality, due to the reliance on a posteriori arguments rather than a priori ones in the modeling process. However, he does note that his attempt here is to "keep hope alive" for econometrics students, although his outlook seems dismal. Alternatively, Roger Garrison fails to reject categorically econometric models on the basis of their reliance on mathematical formulation. Rather, he asks what he claims is a more relevant question, namely, "What sort of language-music, mathematics, or, say, English- allows economists best to communicate their ideas? Which language serves the economist without imposing constraints of its own upon his subject matter?"39 He claims that this question relies on a moral valuation of principles in economics which determine the subject matter with which the economist is concerned. The critical evaluation, then, is "whether or not causality in economics is a worthy concern," which "For Mises causality was the central concern. His methodological individualism has as its goal the establishment of a causal linking of individual actions to observed economic phenomena."40 The critique then, for an Austrian following von Mises' line of questioning, is that "Systems of equations can be suitably employed to describe the consequences of human action, but such mathematical descriptions are inherently blind to notions of intentionality and causality." Further, Garrison notes the importance of the ceteris paribus assumption, that all other variables are held constant, in econometric modeling, which contributes to one of the fundamental problems, in the view of Mises and other Austrians, that 39. Roger W. Garrison, "Mises and His Methods," 2. 40. Ibid. Waters 27 "policy makers and actual consequences that flow from the market process. Systems of equations can be suitably employed to describe the consequences of human action, but such mathematical descriptions are inherently blind to notions of intentionality and causality." In other words, although math can serve as a descriptive tool of what has happened in the market or economy, these models will always be insufficient to imply causation and human intention (this is indicated by the oft repeated phrase in statistics, "correlation does not imply causation"). Garrison continues, recognizing that there are times when modeling is appropriate for use, particularly when "describing an economy in general equilibrium or for describing the evenly rotating economy," which he claims is appropriate because it "derives precisely from the fact that there is no human action in such states."41 Because causation is the primary objective of Austrian studies of econometrics, mathematical modeling, as Garrison suggests initially, simply is not the most indicative language to describe the economic process. This difference is crucial in understanding the difference in philosophical approaches to economics between the mathematical economist and the Austrian. He claims that the mathematician "is content to remain agnostic on the issue of causality … The praxeologist [Austrian], by contrast, seeks to identify the plans and actions of individuals in the marketplace."42 Further, one of Garrison's primary critiques, siding with von Mises, is the notion of means and ends, "where both cause and means are to be understood in terms of the purposes and plans of acting individuals. None of these notions are adequately illuminated by the methods of mathematical economists or econometricians." Essentially, the 'language' of mathematics is too confining for application in Economics as a field. 41. Ibid, 5. 42. Ibid., 3. Waters 28 SUBJECTIVE ECONOMETRIC FAILURE The final critique of econometrics is the failure of econometrics to be properly subjective. Because Austrian theory relies on subjective individualism, econometrics inherently cannot assign values to different human activities. Furthermore, because humans are individual, they are inherently unpredictable, which reinforces the failure of econometrics in understanding human activity. Carl Menger, who initiated the Austrian school of thought, suggests that "economics must start at the level of individuals - an approach known as methodological individualism - and seek to understand how they choose."43 The individualized approach to economics underlies the argument of all Austrian positions. These individualized decisions are what F.A. Hayek (1945) called "knowledge of the particular circumstances of time and place," knowledge that could hardly be codified in textbooks or assembled for the use of central planners, knowledge that can be used, if at all, only by numerous individual "men on the spot." … Subjectivist economists recognize how such factors not only underlie the prices that consumers are prepared to pay for goods but also underlie costs of production.44 These individualized decisions validate the Austrian theory of subjectivism. Austrian economists, in general, tend to prefer subjectivism to objectivism. As Leland Yeager observes, "the broadest subjectivist insight is that economics deals with human choices and actions, not with mechanistically dependable relations. The economy is no machine whose "structure" can be ascertained and manipulated with warranted confidence".45 The Austrian 43. Eamonn, Butler, Austrian Economics: A Primer, 6. 44. Leland B. Yeager, "Why Subjectivism?" The Review of Austrian Economics,(The Mises Institute, 1-10, 2005), 9. 45. Ibid., 5. Waters 29 economist recognizes that an economy is a social activity, and that social activity consists of non-repeatable, individual, independent decisions. Additionally, econometrics consists of no such constants as exist in the sciences; "the way people behave in markets, as in other aspects of life, depends on their experiences and expectations and on what doctrines they have come to believe," suggesting that an objective constant makes little sense in the dynamic market, which is based entirely on subjective, individualized decision making, which takes into account individual tastes and preferences46. Austrians critique policy decisions which try to assign the preferences and values of individuals, instead, Austrians believe that "people can act on their own comparisons of the satisfactions they expect from additional dollars' worth of this and that."47 This is key to the subjectivist approach of Austrian economics, understanding that individuals are free to make their own decisions and will do so; however, in accepting this, the Austrian rejects the ability to predict what any individual may do. Because it's impossible to create "an exhaustive list of all possible outcomes of some decision," and particularly because this cannot be done for all individuals, there is no way to attach a probability to any outcome.48 Yeager offers an interesting interpretation of Austrian subjectivism which suggests an imperfect use of prediction. Although he denies that statistics can foretell the future, he admits that some predictions can be made with warranted confidence. Bayesian Analysis is useful because it demonstrates what assumptions are going into that prediction, so one can subjectively affirm that the confidence attributed to the prediction is, in fact, warranted.49 46. Ibid., 7. 47. Ibid. 48. Ibid., 17. 49. Ibid. Waters 30 FINDINGS I found that although the Austrian critique of econometrics is in many ways valid, I assert that the critique and rigid rejection of econometrics actually harms Austrian analysis. Instead, if Austrians are to incorporate econometric analysis, they must do so in an authentically "Austrian" way. I suggest the Austrians use Bayesian analysis as an alternative to Frequentist statistics to better develop the Austrian understanding of econometrics and further critique and refine the field. Given this framework of Bayesian econometrics, I suggest the Austrians use econometrics as a starting point to explore causation. Correlation does not mean causation, but causation does imply mutual information (although not correlation, as the correlation could still be zero for nonlinear data). Because correlation demonstrates that two variables have a high level of mutual information, it does imply that the two tend to depend on one another. For this reason, even if the correlation does not verify cause and effect, it demonstrates something meaningful about relationships. Therefore, Austrians should explore the correlation, without necessarily drawing conclusions, and Bayesian analysis is the perfect manner for this exploration to occur. In my analysis of Austrian theory, one recurrent critique is the lack of quantifiable analysis. The theories of Austrian economics may be useful, but if they tell us nothing of magnitude, their value ceases to exist. Bryan Caplan, in his critique of Austrian economic theory, suggests that one inherent problem of Austrian theory is this failure to determine magnitude. Essentially, a simple theory about what should or will happen does not tell us anything about the scale of that change. If the goal of economics, as the Austrians suggest, is to determine cause and effect, knowing the size of the effect is paramount. Caplan suggests that "Empirical studies of the imposition of minimum wages [for example] do more than merely illustrate economic theory; Waters 31 they help economists to learn which theoretically relevant factors actually matter... because the analysis of which factors are quantitatively significant" may be missing from Austrian theories, we cannot determine which factors are actually important in terms of economics overall.50 In other words, if there is a small change in an effect, it is not as meaningful as a large change in effect given a certain cause. If Caplan's critique of Austrian reliance on theory is correct, Bayesian econometrics, as a more philosophically appropriate approach, could allow Austrian economists a method of integrating quantitative and not merely qualitative analysis into their work. Because it is fundamentally important in economics to know the magnitude of a change or relationship, this is a hugely important theoretical oversight in the current conception of Austrian thinking. In light of this oversight and by the superiority of Bayesian analysis over Frequentist methods argued here, I suggest adoption of Bayesian methods to remedy this quantification failure in Austrian theory. Caplan goes on to suggest that econometrics, in actuality, contributes relatively little to the field of economics, and as such, it should be regarded with less esteem. However, because econometrics has increased in popularity, it's now almost impossible to do research "in any period lacking convenient "data sets;" it has also enforced an uneasy silence about any topic in economic history (like ideology) that is difficult to quantify."51 Caplan himself argues that "econometrics is not useless, but must become a subordinate tool of the economic historian rather than vice versa."52 Although his paper is a critique on Austrian economic thought, here, it 50. Bryan Caplan, "Why I Am Not An Austrian Economist," 2002, 15. 51. Ibid., 16. 52. Ibid. Waters 32 certainly seems that he advocates for the Austrian distrust of economic modeling. However, his interpretation can guide the use of econometric analysis for Austrians, particularly when using the Bayesian model. Because the Bayesian process of updating a hypothesis relies on a sense of historical continuity (not necessarily an assumption that the past will predict the future, but a recognition that the past can influence the future), which the Frequentist approach misses, Caplan's advice on using econometrics could be readily adopted by Austrian Bayesians. In using Bayesian analysis as a tool to further quantify historical trends, Austrians can better integrate economic theory with analysis. This in turn allows the theory to come before the model, and the Bayesian approach avoids the possibility for great complication in the construction of a model, since it will rely on illuminating a historical activity and theory, rather than illuminating the ability of econometrics to model with high accuracy. Furthermore, Lawrence Nabers argues that "there is no reason why economics should eschew considerations of crucial historical and social problems simply because the method is not satisfying and the results frequently require extensive qualification."53 Because Austrians accept a more historical and individual approach to economics, simply using econometrics does not bar Austrians from continuing to interpret in theoretically Austrian ways. Nabers also recognizes, in the vein of Joseph Schumpeter, that the history of economics has tended to be a positive science. Essentially, economic analysis has, in Schumpeter's words, been a "history of the analytic or scientific aspects of economic thought." There has always been an attempt to quantify and make scientific the field of economics.54 Lending validity to the Austrian conception of the goals of 53. Lawrence Nabers, "The Positive and Genetic Approaches," In The Structure of Economic Science: Essays on Methodology, by Sherman Roy Krupp, (Englewood Cliffs, NJ: Prentice-Hall, 1966), 70. 54. Ibid., 74-75. Waters 33 economic thought, Nabers argues that we must analyze those factors which "are responsible for change and development - namely the way in which policy and values alter in response to historical change- and the historian of economic thought should be concerned with the meaning of economic theory, and the meaning of a theory is found in the use to which it is put."55 Austrians are in a special position for this to occur. Their analysis of econometric findings offers a unique and necessary voice in understanding how individuals can impact econometric results. Even if Austrians reject the modeling process, certainly they can contribute their reasoning. Tobias Basse recognizes two problematic developments in the study of economics. First, econometricians "have begun to concede that there is no true econometric model that can perfectly describe an economy," and secondly, that models cannot even be tested. Given these two facts, we confirm that the econometric model must serve one purpose only, "to quantify an effect, not to establish that it will occur."56 Secondly, models cannot be tested for validity because models are not accurate. The point of the model is an abstraction away from reality; that being said, we can determine the accuracy and usefulness of the model, which is likely to elaborate or quantify theory. In the Austrian school, because individual decisions in the aggregate constitute random behavior, the role of the model could be to demonstrate general trends in the economy that cannot be analyzed when only examining the subjective individual perspectives. This certainly does not invalidate the intrinsically individual subjectiveness, but rather examines it in another way. Basse argues that there is an inherent validity in Austrians studying econometric analysis, even if that analysis is used "to convince mainstream economists from the possible dangers of 55. Ibid., 77. 56. Tobias Basse, "An Austrian Version of the Lucas Critique," The Quarterly Journal of Austrian Economics, 9, 1, 2006), 17. Waters 34 using econometric methods."57 Although, in accordance with von Mises, econometric data can only be understood in terms of economic history, Basse recognizes that "Austrian economists regularly present discussions of historical evidence to illustrate their findings and most Austrians will accept that statistical techniques can be used to understand history."58 He further argues that if Austrians, in following their own model reject empirical analysis and instead turn only to theoretical explanation, "it is not clear why some proponents of the Austrian School of economics seem to think that using empirical tests to analyze historical evidence is not acceptable at all and why they are opposed to empirically check whether their theoretical considerations can explain past events."59 Austrians should be consistent and use Bayesian theory to empirically validate, in the historical sense, all theory. I agree fundamentally with Basse, Austrians should adopt econometric analysis for these reasons, and if econometrics is to be used, it should be Bayesian, as the Bayesian perspective offers distinct advantages over Frequentist models. Finally, Edward Leamer, a Bayesian econometrician, suggests that in order to undo the scientific tainting of the field of economics, we must simply reimagine the way we use econometrics. He argues, much like the Austrians, that "economists have inherited from the physical sciences the myth that scientific inference is objective, and free of personal prejudice. This is utter nonsense. All knowledge is human belief, more accurately human opinion."60 Like Austrians, he understands all decisions and interpretations to be subjective, and economics is 57. Ibid., 22. 58. Ibid. 59. Ibid. 60. Edward E. Leamer, "Let's Take the Con Out of Econometrics," January, 1982, 12. Waters 35 inherently so. There is a myth of objectivity. He offers a method to undo this problematic discourse when he says: If we want to make progress, the first step we must take is to discard the counterproductive goal of objective inference. The dictionary defines an inference as a logical conclusion based on a set of facts. The "facts" used for statistical inference about are first the data, symbolized by x, second a conditional probability density, known as a sampling distribution, (|), and, third, explicitly for Bayesian and implicitly for 'all others,' a marginal or prior probability density function (). Because the sampling distribution and the prior distribution are actually opinions and not facts, a statistical inferences and must forever remain an opinion.61 Leamer is explicitly stating a method by which Austrians could overturn the problematic misrepresentations of data in traditional economics simply by using Bayesian models. The inferences drawn by Austrians using this interpretation will be subjective, it represents an opinion and not fact. However, this subjective opinion can be used to validate theory and infer about individual decision making in a subjective way. This meshes nicely into Austrian theory. Leamer recognizes that most economists reject this line of thinking but notes that the reason for the rejection is a Bayesian "attempt to form a prior distribution from scratch involves an untold number of partly arbitrary decisions.62 The Bayesian will construct the prior model subjectively, stating explicitly those assumptions that are going into the prior distribution. By vocalizing those assumptions, it allows greater conclusions about the model itself to be drawn, as the assumptions are subjective and thus questionable. Austrians are in a particular theoretical position to define priors which would help illuminate the problematic assumptions that other mainstream economists use. Because the theory always exists prior to the model for an Austrian, Basse 61. Ibid., 13-14. 62. Ibid., 17-18. Waters 36 suggests that "Austrian economists, for example, surely never would dare to run a regression without prior thinking about economic theory." He goes on to give a great example, as "econometric research performed by Austrians clearly would also help to show that numerous proponents of active government intervention try to hide their questionable ideas behind batteries of cryptic test statistics."63 This allows for greater discourse and greater econometric honesty. Essentially, "the professional audience consequently and properly withholds belief until an inference is show to be adequately insensitive to the choice of assumptions."64 Austrians will be able to demonstrate their theory is correct by audibly voicing their assumptions. There is special reason to believe that Bayesian Econometrics works particularly well with Austrian theory. Ludwig von Mises brother, Richard von Mises was a mathematician who developed Frequency theory. Although Richard was a positivist, Ludwig and his subsequent Austrian followers accepted Richard's work, and Ludwig incorporated this theory into his work. It could be surprising that the Austrian school would adopt this objective methodology, but it's clear that the acceptance of frequency theory on the part of the Austrians is not due to a philosophical divide between objectivity and subjectivity, but rather, Austrians accept the theory solely on the basis of accuracy. The law of large numbers holds, for example, because it's impossible to suggest that repeating an event a very large number of times will not create a probability distribution that is accurate, since convergence theory can be proven to work this way. However, Austrians recognize Richard von Mises' contribution in noting that the objective way that this should be interpreted is more accurate than the common interpretation. Specifically, Howson and Urbach incorporated Richard's theory into their Bayesian analysis, and found that 63. Tobias Basse, "An Austrian Version of the Lucas Critique," 23. 64. Edward E. Leamer, "Let's Take the Con Out of Econometrics," 29. Waters 37 his "objective" method of analysis worked well with the subjective theory of Bayesian analysis.65 Frequency theory argues that it is meaningless to suggest the probability of any single event's occurrence. For example, by saying that the likelihood of rolling a six on a six-sided die is one-sixth, what one is really saying is that for a large number of throws, a six will appear one-sixth of the time.66 You can never predict the probability of an event occurring simply by estimating the probability a few times; the only way to be certain of a given probability is to toss the die a large number of times. This claim is in contrast to subjective theories of probability that believe that these statistics lie in the individual and thus that probability theory can be applied to the individual case. In other words, if there is a one in six chance of throwing a die and getting a six, a subjective probabilist would argue that there is a one in six chance of rolling an additional six on the next toss. For these reasons, I fully support and suggest a transition to Bayesian econometrics from traditional econometrics, regardless of the school of thought. The modeling is more intuitive, more aware of its assumptions, and more clear in its interpretation. CONCLUSION Austrians, traditionally discredit econometrics as falsely implying cause and effect, imposing false assumptions, failing to quantify or predict events accurately, and being riddled with bad interpretations. Essentially, they believe econometrics is the wrong language for the study of economics. However, my analysis of both Austrian and Bayesian econometrics leads to the conclusion that Austrian analysis, although valid in its critiques of econometrics in many 65. Colin Howson and Peter Urbach, Scientific Reasoning: The Bayesian Approach, 202. 66. Murray N. Rothbard, "The Correct Theory of Probability." Waters 38 respects, is missing a fundamental argument around magnitude. In order to correct this argument, I suggest they incorporate Bayesian econometric methods, as these methods conform better to Austrian philosophical underpinnings. Because Bayesian econometrics offers an approach that is philosophically subjective and more aware of a priori assumptions. In contrast to the Frequentist method of analysis, Bayesian econometrics doesn't hide the assumptions being made, rather, it displays them and puts them on display for questioning. Furthermore, the updating of the prior hypothesis allows for greater evidence to change the likelihood. And this likelihood, in contrast to the uninterpretable Frequentist output, is easily understood and therefore more clear. By it's greater clarity, it reduces the Austrian argument that econometrics is used to hide the facts. These differences also demonstrate the reasons why Bayesian modeling more closely mirrors the philosophical underpinnings of Austrian theory. If Austrians are to become incorporated into the larger economic conversation, they must begin using econometrics; but that use does not mean they must retain traditional techniques. I argue that Austrian adoption of Bayesian econometric modeling will not only allow a conversation between the Austrian and other econometric schools of thought to occur, but will actually allow Austrians to demonstrate superior assumptions and question the problematic nature of others. A recognition of subjectivity is very much in keeping with the Austrian method, and Bayesian econometrics will open a new pathway for that conversation to unfold. Waters 39 BIBLIOGRAPHY Basse, Tobias. 2006. "An Austrian Version of the Lucas Critique." The Quarterly Journal of Austrian Economics 9 (1): 15-26. Beall, Jc, and Greg Restall. 2014. "Logical Consequence." The Stanford Encyclopedia of Philosophy . Fall. Accessed April 26, 2016. http://plato.stanford.edu/archives/fall2014/entries/logical-consequence/. Bismans, Francis, and Christelle Mougeot. 2009. "Austrian Business Cycle Theory: Empirical Evidence." Austrian Econ (Springer Science + Business Media, LLC) (22): 241-257. Butler, Eamonn. 2010. Austrian Economics: A Primer. Adam Smith Research Trust. Callahan, Gene. 2004. "The Myth of the Model." Mises Daily, May 20: Online. Caplan, Bryan. 2002. "Why I Am Not An Austrian Economist." Garrison, Roger W. 1993. "Mises and His Methods." 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