Sunday, July 30, 2017

Dani Rodrik and pluralism


Photo source: Wikimedia Commons, Andrej Barabasz (Chepry)
Photo license: CC BY-SA 3.0

About a month ago, I read the book Economics Rules by Dani Rodrik. I believe that the central message of the book is that economists should embrace a large tool kit of economic models. He also emphasizes the importance of being able to select the right model depending on the specific economic situation. Rodrik also has some interesting things to say about mathematical economics and critics of the economics profession.

This post is some of my favorite quotes from the book. I received permission in an email from Rodrik to create this post.

Support for pluralism


"Rather than a single, specific model, economics encompasses a collection of models. The discipline advances by expanding its library of models and by improving the mapping between these models and the real world. The diversity of models in economics is the necessary counterpart to the flexibility of the social world." (page 5)

"In part because economists take the natural sciences as their example, they have a tendency to misuse their models. They are prone to mistake a model for the model, relevant and applicable under all circumstances." (page 5)

"Knowledge accumulates in economics not vertically, with better models replacing worse ones, but horizontally with newer models explaining aspects of social outcomes that were unaddressed earlier." (page 67)

"In the end, it was clear that no single theory could fully explain the story of the U.S. inequality since the 1970's. Nor was there a good way of parsing the relative contributions of different theories. Certain theories (models) gave us a better understanding of the channels through which trade, technology and other factors may have operated. The failure of other theories allowed us to rule out mechanisms that appeared equally plausible at the outset. There was no closure, but there was plenty of learning along the way." (page 143)

"Today it is almost a mantra for development economists, finance experts, and international agencies that no single set of policies is appropriate for all countries that domestic reforms must be tailored to specific circumstances." (page 167)

How to choose the right model


"[A model's] conclusions are true only to the extent that their critical assumptions approximate reality. When they don't, we need to rely on models with different assumptions." (page 18)

"As Stanford economist Paul Pfleiderer explains we always need to apply a 'realism filter' to critical assumptions before a model can be treated as useful." (page 26)

"Economic models are cases that come with explicit user's guides (teaching notes on how to apply them). That's because they are transparent about their critical assumptions and behavioral mechanisms." (page 73)

"Freshly minted PhD's come out of graduate school with a large inventory of models but virtually no formal training (no course work, no assignments, no problem sets) in how to choose among them." (page 84)

"Eventually, we developed a decision tree that helped us navigate across potential models... We would start at the top of the tree by asking whether the constraints on investment were mainly on the supply side or on the demand side... At each node of the decision tree, we tried to develop informal empirical tests to help us select among models that would send us down different paths." (page 89)

Support for simple models


"In truth, simple models of the type that economists construct are absolutely essential to understanding the workings of society. Their simplicity, formalism, and neglect of many facets of the real world are precisely what make them valuable." (page 11)

"What are economic models? The easiest way to understand them is as simplifications designed to show how specific mechanisms work by isolating them from other, confounding effects." (page 12)

Support for mathematical economics


"Math ensured that the elements of a model (the assumptions, behavioral mechanism and main results) are clearly stated and are transparent. Once a model is stated in mathematical form, what it says or does is obvious to all who can read it." (page 31)

"[Math] ensures the internal consistency of a model (simply put, that the conclusions follow from the assumptions). (page 32)

"Verbal arguments that seem intuitive often collapse or are revealed to be incomplete under closer mathematical scrutiny. The reason is that 'verbal models' can ignore nonobvious but potentially significant interactions." (page 34)

Critique of mathematical economics


"Math plays a purely instrumental role in economic models. In principle, models do not require math, and it is not the math that makes the models useful or scientific." (page 33)

"Too many economists fall in love with the math and forget its instrumental nature. Excessive formalization (math for it's own sake) is rampant in the discipline." (page 35)

"The profession's stars and most heavily cited economists are those who have shed light on important public problems... not its mathematical wizards." (page 37)

"Efforts to construct large-scale economic models have been singularly unproductive to date. To put it even more strongly, I cannot think of an important economic insight that has come out of such models." (page 39)

Analysis of the 2008 financial crisis


"That economists were mostly blind-sided by the crisis is undeniable. Many interpreted this as evidence of a fundamental breakdown in economics... But what makes this episode particularly curious is that there were, in fact, plenty of models to help explain what had been going on under the economy's hood. Bubbles (steady increases in asset prices divorced from their underlying value) are not a new phenomenon." (page 154)

"Models of self-fulfilling panic (a coordination failure in which individually rational withdrawals of credit lines produce collective irrationality in the form of a systemic drying up of liquidity) were well know to every student of economics." (page 155)

"A key pattern in the run up to the crisis was excessive risk taking by managers of financial institutions. Their compensation depended on it, but their behavior was not consistent with the interests of the banks' shareholders. This divergence between the interests of managers and shareholders is a centerpiece of principal-agent models." (page 155)

"In sum, economists became overconfident in their preferred models of the moment: markets are efficient, financial innovation improves the risk-return trade-off, self-regulation works best, and government intervention is ineffective and harmful. They forgot about the other models." (page 159)

What are the critics saying?


"I felt that many of the criticisms coming from outside the field missed the point. There was too much misinformation about what economists really do." (page xiii)

"Many of the complaints are well known: economics is simplistic and insular; it makes universal claims that ignore the role of culture, history and other background conditions; it reifies the market; it is full of implicit value judgments; and besides, it fails to explain and predict the developments in the economy. Each of these criticisms derives in large part from a a failure to recognize that economics is, in fact a collection of diverse models that do not have a particular ideological bent..." (page 6)

"One of the most frequent complaints about economics labels it a club that shuns outsiders. This exclusiveness makes the discipline insular, according to the critics, can be closed to new and alternative perspectives on economics. Economics should become more inclusive, they argue, more pluralistic and more welcoming of unorthodox approaches." (page 196)

"Pluralism with respect to conclusions is one thing; pluralism with respect to methods something else. No academic discipline is permissive of approaches that diverge too much from prevailing practices, and economics is unforgiving of those who violate the way work in the discipline is done. An aspiring economist has to formulate clear models and apply appropriate statistical techniques." (page 199)

"For some, these constraints represent a kind of methodological straitjacket that crowds out new thinking But it is easy to exaggerate the rigidity of the rules within which the profession operates." (page 200)

Friday, June 30, 2017

Chess metaphor for macroeconomics

Photo license: CC BY-SA 3.0

I think of macroeconomics as being like a chess game. Similar to chess, the world economy is made of many different economic actors with different abilities and placements. The world economy has a structure that is continually evolving. Instead of relying on a particular macroeconomic theory, I think it's more effective to pragmatically analyze the structure of economic actors in an economy to determine the best course of action. In chess, players must also pragmatically analyze the structure of the pieces to make decisions.

Here is what each chess piece represents in the economy:

  • Pawns: non-wealthy individuals
  • Queen: billionaires
  • Rooks, bishops and knights: companies
  • King: planet earth
  • Opponent's pieces: goods and services

Pawns represents non-wealthy individuals because pawns have the least mobility and are the weakest pieces on the board. If a pawn is able to reach the other side of the board, they acquire the abilities of a queen. This represents when a non-wealthy individual through hard work and luck is able to become a billionaire.

The queen represents billionaires because the queen has the greatest mobility and power in the game. Billionaires are the most powerful actors in the economy.

Rooks, bishops and knights represent companies because they have a lot of power but not as much as the queen. Companies are extremely diverse, therefore it's fitting that they can be either a rook, bishop or knight.

The king represents planet earth because if the king dies, the game is over. If planet earth becomes so polluted that it's uninhabitable, it's game over for society. A defensive strategy to protect the king is symbolic of regulations to protect the environment.

The opponent's pieces represent goods and services because the goal of economics is to produce goods and services. The goal of chess is to conquer the opponent's pieces.

When playing chess, it's important that all of your pieces work together. It's important that your pieces back each other up. Unsupported pawns stand no chance of surviving. Pawns need the help of more powerful pieces to make a greater contribution. Bottom line, your pieces must act like a team. Imagine playing a game of chess without moving your queen; you will lose. This is the similar to not taxing billionaires to pay for things that will improve society.

Here's a quote from Adam Smith referring to chess,
...in the great chess-board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might choose to impress upon it. If those two principles coincide and act in the same direction, the game of human society will go on easily and harmoniously, and is very likely to be happy and successful. If they are opposite or different, the game will go on miserably, and the society must be at all times in the highest degree of disorder. (The Theory of Moral Sentiments, 1759)
I have one last thing I want to say about metaphors. Metaphors are not supposed to be perfect equivalencies. I'm aware this metaphor has flaws if you expect chess to be a perfect representation of an economy. All metaphors break down at a certain point with enough scrutiny. This post is merely a list of connections that I think make sense.

License: CC BY-SA 4.0

Saturday, June 17, 2017

What is economics?


Photo source: Wikimedia Commons, AndrewHorne

What is economics? Here is my definition:
Economics is the study of the production, distribution and consumption of goods and services.
In other words, economics is the study of the economy.

This post is a collection definitions for 'economics' from famous economists. I have divided the definitions into four categories: scarcity, wealth, decision-making and open-ended. This post was inspired by Roger Backhouse and Steven Medema's paper 'On the Definition of Economics'.

For each definition, I have provided a short analysis. There are 17 definitions below.

Wealth based definitions


Adam Smith (1723-1790)
"[Economics is] the nature and causes of the wealth of nations." (The Wealth of Nations, 1776)
  • I think Smith's definition in agreement with the definition I stated above. 'Wealth' is a good substitute word for 'goods and services'. 'Nature and causes' is a good substitute for the word 'study'.

Jean-Baptiste Say (1767-1832)
"[Political economy is] the science of production, distribution and consumption of wealth." (A Treatise on Political Economy, 1803)
  • This definition is basically the same as the one I provided above. 'Wealth' isn't as descriptive as 'goods and services' but means the same thing. My only problem with this definition is that the word 'wealth' could be misinterpreted for 'abundance', therefore I prefer the phrase 'goods and services'.

John Stuart Mill (1806-1873)
"[Political economy] is the science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth in so far as those phenomena are not modified by the pursuit of any other object." (On the definition of Political Economy, 1867)
  • Although this definition is confusing, I agree that economics revolves around the 'wealth'. That's really all this definition is saying.

Thomas Adams (1873-1933), Richard Ely (1854-1943), Max Lorenz (1876-1959) and Allyn Young (1876-1929)
"[Economics is] the wealth-getting and wealth-using activities of man." (Outlines of Economics 4th edition, 1926)
  • I agree that economics has to do with  'wealth-getting' (production) and 'wealth-using' (consumption) but I think this definition would be better if it mentioned 'wealth-distribution'.

Scarcity based definitions


Lionel Robbins (1898-1984)
"[Economics is] the science which studies human behavior as a relationship between ends and scarce means which have alternative uses." (Essay on the Nature and Significance of Economic Science, 1932)
  • This is currently the most influential and popular definition of economics. I'm generally against 'scarce' definitions of economics because I don't think 'scarce' is an accurate mindset for a world with unlimited opportunity.

George Stigler (1911-1991)
"[Economics is] the study of the principles governing the allocation of scarce resources among competing ends when the objective of the allocation is to maximize the attainment of the ends." (The Theory of Competitive Price, 1942)
  • Once again, I don't think economics should be about 'scarce resources'.

Milton Friedman (1912-2006)
"[Economics is] the science of how a particular society solves its economic problems... an economic problem exists whenever scarce means are used to satisfy alternative ends." (Price Theory: A Provisional Text, 1962)
  • I don't think economics should revolve around 'problems'.

Paul Samuelson (1915-2009)
"Economics is the study of how people and society end up choosing with or without the use of money to employ scarce productive resources that could have alternative uses, to produce various commodities and distribute them for consumption, now or in the future, among various persons and groups in society. It analyzes the costs and benefits of improving patterns of resource allocation." (Economics 10th edition, 1976)
  • I agree with this definition except that I would replace the word 'scarce' for 'limited'. But even the word 'limited' is kinda wrong. There are some economic resources I would describe as 'abundant'. Maybe it would be best to just remove the word 'scarce'.

Gary Becker (1930-2014)
"[Economics is] the study of allocation of scarce means to satisfy competing ends." (Economic Theory, 1971)
  • I think this definition is too focused on the 'distribution' and 'consumption' part of economics with not enough emphasis of 'production'.

Robin Bade and Michael Parkin
"[Economics is the] social science that studies the choices that individual, business, government and entire societies make as they cope with scarcity." (Foundations of Microeconomics, 2002)
  • This definition revolves around scarcity. It's as if society is given a pie that must be divided up with no potential to create more pie. This definition doesn't talk about the 'production' part of economics.

Decision-making based definitions


Carl Menger (1840-1921)
"[Economics] is related to the practical activities of economizing men." (Principles of Economics, 1871)
  • What does it mean to economize? According to Google, "to spend less; to reduce one's expenses". Although this definition kinda works, I think its too broad and doesn't properly define the boundaries of what economics is.

Alfred Marshall (1842-1924)
"Political economy or economics is a study of mankind in the ordinary business of life. It examines that part of individual and social action which is most closely connected with the attainment and with the use of the material requisites of wellbeing... thus it is on the one side a study of wealth and on the other, and more important side, a part of the study of man." (Principles of Political Economy, 1890)
  • For the most part I agree with this definition. I agree that 'ordinary business of life' revolves around economics. I like how this definition focuses on what is 'most closely connected with the attainment and use of the material requisites of wellbeing'.

Summer Slichter (1892-1959)
"The subject matter of economics is industry; the process by which men get a living... economics studies industry, not as a technological process, but as a complex of human practices and relationships." (Modern Economic Society, 1931)
  • This definition is very similar to Marshall's definition. I agree that economics is all about 'industry' (goods and services) and the 'process by which men get a living' (production, consumption).

James M. Buchanan (1919-2013)
"[Economics is] the study of the whole system of exchange relationships."
  • This definition has too much emphasis on the 'distribution' part of economics while ignoring 'production' and 'consumption'.

David Colander (1947-now)
"Economics is the study of how human beings coordinate their wants and desires, given the decision-making mechanisms, social customs and political realities of the society." (Microeconomics 6th edition, 2006)
  • Although I think this definition is valid for economics, I think its better suited for sociology.

Greg Mankiw (1958-now)
"Economics is the study of how society manages its resources." (Principles of Economics 2nd edition, 2001)
  • This is a broad definition but I think it works. Ultimately, this definition has to do with the production, distribution and consumption of 'resources'.

James Gwartney, David MacPherson, Russell Sobel and Richard Stroup
"Economics is the study of human behavior with a particular focus on human decision-making." (Microeconomics: Private and Public Choice 11th edtion, 2006)
  • This definition seems better suited for psychology.

Open-ended


Jacob Viner (1892-1970)
"Economics is what economists do." (Quoted by Kenneth Boulding in Economic Analysis, 1941)
  • This definition is completely inadequate. What's the point of definitions and words in the first place? Without words and concepts we are lost children in the woods.

Sunday, June 4, 2017

EconTalk: six part series on econometrics

Photo license: CC BY 2.0

In March 2016, Noah Smith had a blog post titled, Russ Roberts and the new empirical world. In the post, Smith mentions six episodes from Russ Roberts' podcast EconTalk about econometrics. I enjoyed listening to this series because it's informative to hear verbal explanations about econometric concepts.

This post is a collection of quotes from the six episodes.

Ed Leamer on the State of Econometrics (May 10, 2010)

"Economists don't observe feathers in a vacuum. They observe feathers when the wind is blowing, when humidity varies, eagle feathers, duck feathers. Tons of things that will affect the result."

"All we have, especially in macro is opinions and their either persuasive and well thought out or not."

Joshua Angrist on Econometrics and Causation (December 22, 2014)

"Regression is just a way to control for things, to try and hold characteristics of groups that you're trying to compare fixed."

"Each of these is an attempt to generate some kind of apples to apples comparison out of observational data."

Noah Smith on Whether Economics is a Science (December 28, 2015)

"The most important difference with natural experiments is you can't replicate them or repeat because each natural experiment happens only once."

"If you're going to believe the results of an experiment you always have to make a leap of faith that all the reasonable stuff has been controlled for, right? That the experimenter has good controls and that's an assumption and a leap of faith you have to make in every science experiment."

Adam Ozimek on the Power of Econometrics and Data (February 8, 2016)

"I think the research comes out and looks at slightly different angles and adjusts for slightly different mechanisms and we know so much more about the minimum wage than we did 10 years ago... If you look at the literature closely it doesn't look like a draw where two sides just lob evidence back and forth. It looks like progress to me."

"The stimulus act isn't something like the minimum wage. It's not a discrete policy where you turn the fiscal level up and it goes from 0 to a 1 to a 2 to a 3. The stimulus act was like a dozen different things and so to say that research hasn't told us whether the stimulus act was good or not or increased jobs, well I mean you could write a 100 page paper on just what was in it... but I do think that within the stimulus package there are things we can learn and have learned."

James Heckman on Facts, Evidence and the State of Econometrics (January 25, 2016)

"I think there's been a huge shift away from understanding behavior and moving towards statistical artifacts that are hard to interpret as responses to economic questions. So I think the credibility revolution has been somewhat overstated and not properly appreciated as having really turned focus away from serious economic analysis towards something I think is purely statistical."

"Calibrated models are models looking at some stylized facts that are putting together different pieces of data that are not mutually consistent. I mean literally you take estimates of this area, and estimates from that area and you assemble something that's like a Frankenstein..."

David Autor on Trade, China and U.S. Labor Markets (March 14, 2016)

"It's not that I think our estimates are cooked or even that sensitive. It's that they might miss other important margins. And I'm happy to concede that point. I mean, we've tried. It's not that we've sort of agreed to just sort of punt on that question. There's probably a lot of ways to look for those missing margins. We really haven't found them."

Monday, May 29, 2017

Macroeconomic experiments

In an earlier post I provided a list of 10 economic statements from famous economists. For this post I attempted to create a list of macroeconomic events that can be used to analyze each statement. I'm aware there are many confounding variables impacting these events, but I believe this list is a good starting point for compiling potentially useful macroeconomic experiments.

1. John Maynard Keynes (1883-1946):
"The right remedy for the trade cycle is not to be found in abolishing booms and thus keeping us permanently in a semi-slump; but in abolishing slumps [with fiscal and monetary policy] and thus keeping us permanently in a quasi-boom." (The General Theory of Employment, Interest and Money, 1936)

Key variable: GDP growth

Fiscal policy
  • United States' New Deal (1933-1938)
  • United States in World War II (1939-1949)
  • United States' American Recovery and Reinvestment Act (2009)
  • Greece austerity (2010-now)
Monetary policy
  • Federal Reserve quantitative easing (2008-2014)
  • Bank of Japan quantitative easing (2001-now)

2. Adam Smith (1723-1790):
"By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention." (The Wealth of Nations, 1776)

Key variable: GDP growth
  • Union of Soviet Socialist Republics communism (1922-1991)
  • United States free trade (1776-now)

3. Milton Friedman (1912-2006):
"I am in favor of cutting taxes under any circumstances and for any excuse, for any reason, whenever it's possible... because I believe the big problem is not taxes, the big problem is spending. I believe our government is too large and intrusive, that we do not get our money's worth..." (Quoted in Conservatives Betrayed, 2006)

Key variable: GDP growth
  • United States tax policy (1932-1988)
  • Sweden tax policy (1939-1988)

4. Joseph Schumpeter (1883-1950):
"The innovation is hazardous, impossible for most producers. But if someone establishes a business having regard to this source of supply, and everything goes well, then he can produce a unit of product more cheaply, while at first the existing prices substantially continue to exist." (The Theory of Economic Development, 1934)

Key variable: comparison of new versus replaced businesses
  • Walmart (1962-now)
  • Microsoft (1975-now)
  • Amazon (1994-now)

5. David Ricardo (1772-1823):
"Under a system of perfectly free commerce, each country naturally devotes its capital and labour to such employments as are most beneficial to each." (Principles of Political Economy and Taxation, 1817)

Key variable: GDP growth
  • World Trade Organization and China (2001-now)
  • Smoot-Hawley Tariff Act (1930)
  • North American Free Trade Agreement (1994-now)

6. Friedrich Hayek (1899-1992):
"The misconception that costs determined prices prevented economists for a long time from recognizing that it was prices which operated as the indispensable signals telling producers what costs it was worth expending on the production of the various commodities and services, and not the other way around." (Coping with Ignorance, 1978)

Key variable: price of goods and services
  • It's hard to think of what specific event can help test this statement. Maybe a good example could be the event that the popularity of an artist takes off and the price of their paintings greatly exceeds the cost of production.

7. John Kenneth Galbraith (1908-2006):
"In recent times no problem has been more puzzling to thoughtful people than why, in a troubled world, we make such poor use of our affluence." (The Affluent Society, 1958)
  • I can't really think of any experiments to use for this statement.

8. Robert Owen (1771-1858):
"The advantage of pure, and the disadvantage of impure air are experienced each time we breathe, and all who understand the causes of disease know that an impure Atmosphere is most unfavourable to the enjoyment of health, and an efficient cause to shorten human existence within the natural life of man. It is therefore most desirable that decisive measures should be devised and generally adopted to ensure to all a pure atmosphere, in which to live during their lives." (The Book of the New Moral World, 1836)


Key variable: quality of life indicators
  • United States quality of life
  • Sweden quality of life

9. Robert Thomas Malthus (1766-1834):
"The employment of the poor in roads and public works, and a tendency among landlords and persons of property to build, to improve and beautify their grounds, and to employ workmen and menial servants, are the means most within our power and most directly calculated to remedy the evils arising from that disturbance in the balance of produce and consumption." (An Essay on the Principle of Population 2nd Edition, 1836)


Key variable: unemployment
  • Europe's Marshall Plan (1948-1951)
  • United States' New Deal (1933-1938)

10. Karl Marx (1818-1883):
"The worker's existence is thus brought under the same condition as the existence of every other commodity. The worker has become a commodity, and it is a bit of luck for him if he can find a buyer... " (Paris Manuscripts , 1844)

Key variable: unemployment
  • Industrialization (1800-1900)
  • Computerization (1900-now)

Saturday, May 20, 2017

Tjalling Koopmans: pioneer of optimization models


Photo source: Wikimedia Commons, Eric Koch, CC0 1.0

Tjalling Koopmans (1910-1985) was an influential economist best known for optimization models and applying linear programming to general equilibrium models. He was also director of the Cowles Commission (1948-1955) and is 1975 co-recipient of the Nobel Prize in Economics. The Concise Encyclopedia of Economics said,
"Koopmans showed the conditions required for economy-wide efficiency in allocating resources. He like Kantorovich, used his activity analysis techniques to derive efficient criteria for allocating between the present and the future."
Economist Thomas Sargent said,
"Koopmans complained that macroeconomic models weren't satisfactory because they didn't handle randomness." (Conversations with Economists by Arjo Klamer)
The rest of this post is some quotes from Koopmans.

Philosophy of economics


"One is led to conclude that economics as a scientific discipline is still somewhat hanging in the air." (Three Essays, 1957)

"We looked upon economic theory as a sequence of conceptual models that seek to express in simplified form different aspects of an always more complicated reality." (Three Essays, 1957)

Pierre-Simon Laplace and probability theory


Photo source: Wikimedia Commons, Sophie Feytaud

Pierre-Simon Laplace (1749-1827) was an influential mathematician and scientist best known for his contributions to probability theory and celestial mechanics. Mathematician Morris Kline said,
"Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature." (Mathematical Through from Ancient to Modern Times, 1972)
Journalist Kathryn Schulz said,
"Pierre Simon Laplace refined the distribution of errors, illustrated by the now-familiar bell curve... Laplace used the bell curve to determine the precise orbit of the planets... By using the normal distribution to graph... individually imperfect data points, Laplace was able to generate a far more precise picture of the galaxy... aggregate enough flawed data, and you get a glimpse of the truth." (Being Wrong: Adventures in the Margin of Error, 2011)
The rest of this post is some quotes from Laplace.

Probability


"The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible..." (Philosophical Essay on Probabilities, 1812)

"The most important questions of life... are indeed for the most part only problems of probability." (Philosophical Essay on Probabilities, 1812)

Expansion of knowledge


"All these efforts in the search for truth tend to lead it [the human mind] back continually to the vast intelligence... but from which it will always remain infinitely removed." (Philosophical Essay on Probabilities, 1812)

"Imaginary causes have gradually receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes." (Philosophical Essay on Probabilities, 1812)