Coda: “Please Count My Time in Hours not in Millimeters”

Coda: “Please Count My Time in Hours not in Millimeters”

 

Macroeconomics suffers from dimension aberration, or misaligning the dimensions of terms in the equation. This rudimentary negligence often leads to reverse causation, an unforgivable sin if in a science. Naturally or providentially, macroeconomics is more like a parable, far from “empirical.”

             In classical economics, “the market” is not anything other than a metaphor to discover a conceptual price that might have “cleared the market” over a certain accounting period. In the diagram, “the equilibrium price,” as often called, on the ordinate (p for price) is ex post and “equilibrium” is in terms of quantity on the abscissa (q for “quantity traded”). Actual prices are all different, but nevertheless the subjunctive price works as “the baton of the invisible hand” in the medium to long run.

             Trade is based on strength of the medium’s purchasing force between the demanding and supplying hands. There is no time dimension involved in individual exchanges. Notwithstanding, the market is supposed to exist for the community; thus, time (T for time in dimension denotation) enters the equation in the negative for the job of “financial accounting” of the community. In short, accounting is everywhere per period per space (T^-1∙L^-2, L for length in space dimension). The only reason why the two boundary conditions may not be explicated in economic textbooks is that they are implicitly taken for granted.

             Demanders and suppliers from the community are intelligent enough to adapt to “the price” in the market but at the earliest in the following period of accounting. Such rational behavior of households helps allocate communal resources to best uses across industries (L^-2) in the medium to long run (T¹). 

             Ironically, somehow, the accounting period  of the market, say, a week (T¹) for grocery shopping, is everywhere longer than the name “short run” (T⁰) of macroeconomics. In other words, nearly all the aggregates of macroeconomics are supposedly as at a moment or in an undefined period (T⁰ in both cases).

             Back to basics, the time is the critical “variable” in our life primarily because “We are all dead in the long run.” Life is presupposed to lapse with the time up to the very moment into the otherworld. As such, careful planning over the time line is indispensable while we are here on Earth. More specifically, each of us shall mind the time duration in every step onward, (if not across different choices or scenarios). Put it differently, in our practical life “when” or “how long” of the performance is usually more important than “what.”

             A magnum opus of a great master with the time dimension out of question would belong to other worlds, if not no work at all (“0” for nil). For instance, a sheet of music by Virtuoso without tempo noted would just mean noises (“0” as stands for theoretical irrelevancy), if not graffiti (“0” for being outlandish to music).

             Somehow we have “stability macroeconomics” which was virtually envisioned at Cambridge less than a century ago. The two most critical “variables” therein are the preferred liquidity (this “L” for liquidity, or M^d) and the “money supply” (this “M” for the monetary balance, i.e. M^s), both defined as at a moment. So conceived and instantaneously born (T⁰, for time irrelevancy) is the IS-LM model, usually featured in a confined plane (T⁰∙L^-2).

             In the model, per tempus gets marginalized to in momento while money (M) is spending time with GDP (Y). Put differently, Cambridge concerns are not over a certain period (T^-1) but as of a point in time (T⁰). Ergo, “ex post” equals “ex ante.”

             Dependent on the path, macroeconomists regard time as flying on the spatial line (L¹ as it really is) rather than lapsing along the time line (T¹ as it virtually is). In addition, macroeconomic “demand” comes to mean a “wish” of the household while “supply” a wish of the central bank.

             Further on, the market is the “pretty much standard” microcosm of the economy. The market when in recession is convicted for “failure,” or the invisible hand is found “in paralysis.” No quarrel, trade equals production even if the former is based on “money,” while the latter on “production factors.” The logic extended on the force of inertia, finance can more or less liberally be alloyed with economy.   

             At a moment, which is certain (t₁) to some but uncertain (t_?) to others, of the year when “liquidity preference” (L) joins forces with “money supply” (M), AD (for aggregate demand) gets arms crossed with AS (aggregate supply). As a result, stability or growth can be achieved with no reverence to Time. In the first place, GDP (Y) is defined as a score (L¹) on the abscissa of a diagram on a plane (L^-2). Where on Earth is a place for Time?

             Every trader in the market is no slave of anyone else, but many a macroeconomist is not liberated from a Scribbler or two. No wonder, the market is always in “equilibrium” at the price (p) while the economy is everywhere “recessionary” with no regard to the price level (P).

 

At this spot on, we take a walk through history from free-market economics to Cambridge-bound macroeconomics:

1)     Adam Smith notices that consumption is the end of production; where there is consumption there is production (and vice versa because time is limited on both sides). In between, the market is the best resources allocator not only across consumable products on the demand side but also across the producers on the supply side.

              In the market, the strength of the purchasing force greatly matters. The presumed price in a certain scale makes company with the presumed quantity in another scale. An effective tool to “business success” is the score of demanders and suppliers on the two predefined scales. The two parties of trade are equipped respectively with the purchasing force and the product, viz. a good or a service. In other words, we when in “the market” need the metric of various kinds and degrees on one hand and the wherewithal on the other hand. 

              Smith finds “division of labor” across sections of the factory as a way of economizing on the production process. His disciples come up with ‘the law of diminishing returns” across the size of production at the factory of a certain good as opposed to a service.

              He may and his disciples do assume “the accounting period” in the market so as to determine and name the price and the quantity traded. The period depends on the nature of the product and the size of community: for instance, a week for widgets and a month for gadgets in the community of an ideal size.

2)     David Ricardo identifies “comparative advantage” as the key to specialization between two products between two communities. He showcases that international trade is critical to efficient allocation of resources. Again, time enters the “2x2” framework for the purpose of naming “quantities traded.”

3)     Thomas Malthus is worried about the over-time mismatch between consumption and production. The Malthusian concern is not about individual products but about the relative speed of growth in AD vs. AS, as it were.

              Speed is by definition the length or the quantity over the running time. Time primarily and “endogenously” enters the macroeconomic equation: that is, g^d= Δ(log AD)/ Δt vis-à-vis g^s= Δ(log AS)/ Δt, where “g” is the percentage growth rate.

4)     J.S. Mill warns against speculative justification as opposed to theoretical abstraction.

5)     W.S. Jevons helps popularize the concept of “marginal.” Alas, “No genius is completely prodigious” (indebted to Eugene Fama). Jevons is confused while confusing others that the term “marginal” may mean “nicely differentiable.”        

              He is right in naming Δx but wrong in substantiating dx in its place. The two are very different. For instance, the marginal unit of the US currency is a dollar in full rather than a nickel or a dime. To be honest, most of us wouldn’t care about an (unlucky) penny, not to mention an “indefinitely small fraction” thereof. Nearly all of us dream of wealth in billions, while definitely none imagines the wealth of billionths.

              In addition, Jevons introduces the value dimension (U for value of utility) in economics on top of the dimensions (T, L³ and M) in some other walks of science. After all, economics is the science on the value of utilities. Regretfully, he is not particularly clear about the negative time dimension (T^-1 as opposed to T¹).

              Best of all, he clarifies that the marginal utility in a particular accounting period of a certain product declines. More than clearly, “marginality” is applicable to a choice out of many alternatives; for instance, the fifth unit of apple at the margin of consideration versus all the other forgone opportunities of comparable utility.

6)     On the same page referring to Sir Giffen, Alfred Marshall illustrates how the “product” and the “demand” are to be defined. He in effect warns against erroneously proposing a “Giffen good” (1920, p. 132 and footnote).

7)     Irving Fisher is prescient: he suggests that money be useless until it is spent. He on the other hand names as the “real interest rate” the nominal interest rate save the inflation rate. The rates are usually quoted in the percentage per annum (% PA). 

              Probably, macroeconomists apply the concept of “real rate” (T^-1) in the wrong way, that is, in terms of “real quantities” (T⁰). Worse, the end of economic discourse is never production of real quantities but consumption of utilities as “revealed in the market.” If in economics, it’s the value!

8)     J.M. Keynes frequently refers to Thomas Malthus in association with economic doldrums, while effectively sweeping the time dimension under the rug of “short run.” Consequentially, the time dimension has become irrelevant.

              Specifically in Chapter 13 (1936), he says M (for liquidity preference) but means a change thereof (ΔM), without naming the run of time (Δt). There surely is aberration in time dimension between M vs ΔM/ Δt. As opposed to mathematical variations, at any rate, all variations in the real economy do take place over time.

             On the way, Keynes regards “marginal propensity to consume” as applicable to a macrocosm. By definition, a macrocosm is in itself a “marginal” unit for the purpose of thinking, analyzing, proposing and theorizing. There in the (macro)-economy is no such things as MPC (for marginal propensity to consume) other than APC (for average propensity to consume).

              There in the fiscal year is only one ratio of AVC= C/ Y, while all spending, fiscal or private, is equal before the law of GAAP. Furthermore, each and every spending enters the books particularly of national income accounting once and for all, with no “multiplication” of any kind.                            

9)     J.R. Hicks pulls the “Cambridge Quantity equation” M= k∙I (I for “Total Income,” 1937) in the domain of macroeconomics. Other disciples including Ben Bernanke uphold “for the sake of convenience” that the central bank be the “controller of money supply.”

              What if endogenous “liquidity preference” is not met by the exogenous central bank, or M^d≠ M^s? An expedient answer: The nominal GDP (“I” of Hicks) is to adjust itself in momento, primarily because none of us is legally allowed to vary or bury M^s for the purpose of suiting oneself.      

10)  Disciples including household names develop a “model of markets,” that is, IS-LM, to illustrate “the monetary transition mechanism” probably out of good intentions.  

              Nicely done but for: “Honey, I put the Horse before the Cart.” The Master (p.168) means that the interest rate (r) from outside determines the size of “preferred liquidity.” Notwithstanding, faithful disciples interpret that the interest be determined by the “preferred liquidity” (T⁰) endogenously in “the money market.”

              All in all, macroeconomists de facto declare, “We are independent from economics!” In economics jargon, the quantity traded is a “flow” while the quantity preferred a “stock.” With “financial markets” on hold, “a stock market” or “a stock variable” is an oxymoron (at least to the ears of “intellectually dishonest” people).

11)  On the wayside, Ronald Coase realizes that “transaction costs” hinder and hamper efficient allocation of resources all across the nation.

              The hands, visible or invisible, that “fail” the economy in the short run and “the nation” (borrowed from Daron Acemoglu and James Robinson) in the long run might well be “transaction costs”: such as information deficiency disorder, “fear,” “lost confidence” or centrifugal trust. Overleaf, the market is by conception immune from acute paralysis and chronic defects.

12)  Joseph Schumpeter claims that creative destruction be the locomotive of economic progress, or positive growth over the time (+g in % per annum).

13)  F.A. Hayek asserts that the free-market economy of millions with the rule of law firmly established will save us from the Road to Serfdom.

14)  Paul Samuelson falls prey to his own success of evangelizing “fallacy of composition” (1948~2010) and “uselessness of preferred liquidity” (e.g. 2010 with William Nordhaus). He in real promotes the ideas of “backward bending” Giffen good, “marginal propensity to consume,” “paradox of thrift,” “liquidity trap,” “insufficient aggregate demand,” the price level (P) as “baton,” and so forth.

15)  Alvin Hansen and Larry Summers among others predict that people may steadfastly produce what they won’t consume so as to turn the stagnation “secular.” Otherwise, people might be suspected to be “intellectually dishonest” (from Paul Krugman post Milton Friedman, NYRB 2007).

16)  Milton Friedman keeps shouting Free to Choose, but not exactly in the wilderness.

17)  Robert Solow applies “cross-sectional” law of diminishing returns to “longitudinal” growth. He is liberal in trading “fast and slow” (from Daniel Kahneman) of growth for “high or low” of the production cost. The economy certainly gets higher and higher to some extent, but may stall at a certain distance (L¹).

              Like others in the community, he regards all the economy as walking in tandem with each market or even with each factory. Probably, the invisible hand has long been “paralyzed” so as not to be able to allocate resources across industries (L^-2).

 

In effect, the accounting period is almost totally disgraced in macroeconomics. On the contrary, mathematics is amazingly respected as legitimate device of scientific reasoning.

             In the mathematical sunshine, nothing (dx in infinitesimal) can surely be “nicely integrated” into anything intended (Xⁿ, X in a wished scale raised to the “demanded” power of n). While time is stopped (T⁰) or flown across (T⁰∙L^-1), GDP as welfare index cannot only be stabilized in the short run, but may also grow or shrink millions of times in the long run.

             At some point in the run, all of us are presupposed to transit from Here (L³) to Eternity (T⁰). In “harmonic series” with GDP (Y), in the meantime, a hyper-high price level (P) would be gracefully “differentiated” into “rest” (L⁰) and stay “in peace” (T⁰).

 

At the intermission, history has observed in some other walks of life:  

i)      Ever since the Big Bang, there have been Time (T), Space (L³), and Masses (M), subject to multilateral interactions based on forces of various kinds.

ii)    In a certain run post the Bang, there was Adam created and endowed with a defined life and a confined physical capacity. So was Eve. Since before the time of homo sapience began, consumption and production has been and shall be periodic until post mortem.

        Time, timing, and accounting have become more than critical. Time is the providential currency while accounting is for the sake of human economy. Presumably saying, Adam and Eve, now defunct, counted productivity, efficiency or economy with the valuable work per tempus (M∙U∙T^-1), never the value-free walks per spatium (M∙L^-1).

        Ab initio, time was absolutely scarce but space was positively unlimited.

iii)   Descendants of Adam and Eve create communities. Communal names and rules are made ex ante. Names are addressed and rules are observed during the day. Performance is measured and declared ex post at the end of the day.

        Descendants of descendants devise and utilize various instruments of convenience, positive or negative, depending on intentions, good or bad. One caveat: “The road to the hell is paved with good intentions.”

iv)    Centuries BCE in China, Confucius Say “Masters Get the Names Correct” (正名, zhèngmíng). Or, they will mislead people.

        The stock, the price and the rate are all ex post and shalt not be named as endogenous “variable.” “Time” by definition lapses over the “run” of one kind but it never flies across the “run” of the other kind.

       As a matter of real fact, a metaphor or a handy tool, gone too far, can confuse earnest students or other listeners many times over up to conversion. Umm, “Excessiveness is no better than shortness” (過猶不及, guòyóubùjí).

v)     About two century after Confucius, Mencius preaches communal division of labor across jobs on the basis of comparative advantage (the episode of 許子, huzi). Incidentally, the expected convert (huzi) did not listen at the time of first sermon.

       He adds that secular hunger or thirsty ruins the taste (飢渴害之, jīkěhàizhī). He hints the possibility of a different map of indifference curves across the income level (L^-1) or over the income change (T^-1).   

vi)    In centuries into Common Era, many households tried alchemy in preference of gold, all in vain partly because there was no sovereign supplier of gold. Then on, alchemy is not chemistry. Amalgam is not chemical, either.  

vii)  Circa a millennium and a half AD, a mathematician named Luca Pacioli from Venice systemizes financial accounting which covers a specific time period.

        Over the defined period, all the inflows from the right-hand side shall be identical to all the outflows to the left. At each and every moment, anyone’s credit is someone else’s debit. The former per tempus is to economy what the latter in momento is to money, banking and finance.

        Economy is everywhere, while trade is only in marketplaces. In Principles, nevertheless, the market, financial “markets,” and the whole economy are everywhere in “equilibrium” in the meaning of accounting identity of real quantities in monetary, banking, financial and “nominal” terms. Somehow, his way of Accounting is Generally Accepted by now.

        To be precise off the books, our wish always and everywhere outweighs the wherewithal. Blessedly, nevertheless, trade in the market is consistently and continuously in equilibrium: what is bought is everywhere the same as what is sold but for in magic, fraud or a fairy tale.

viii)           Isaac Newton discovers that gravity gets a work done such as dropping an apple. He also shows that without an “outside shock” what is stuck stays invariable. Once exogenous will remain exogenous, as well.  

       His disciples create and mobilize all different dimensions out of the natural T, L³ and M in efforts to account for physical efficiency.

       Come to think of it, how to measure anything without defining-cum- confining the boundary? Either in appreciating the economy or in depreciating the currency, we for the purpose of setting the boundary need among others the time dimension in the negative (T^-1). It’s “per accounting period”!

ix)   In classical physics, a “force” moves the mass (M) to a distance (L) before doing something, for better or for worse. On the other hand, a “power” runs for certain duration of time (T) before getting the job done, generally for better. By naming, the force is bilateral while the power unilateral.

       We might get the name of “purchasing power” corrected to purchasing force: the gravity of money is of no use (U⁰) until it moves the product (M) or the asset (M) to the demanding hand. The product gives the energy (M∙U in economics; M∙L²∙T^-2 in physics) for the present period while the asset begets the creative power (M∙U∙T^-1) in the future periods.

       The gravity denoted as “g” in physics is everywhere 9.807m/s²; the purchasing force of the aureus is always one (1) aureus. The attractive force of money” is surely “constant,” or analogously horizontal, in “the money market” of “trading money for liquidity.” Aha, the marginal gravity of aureus is always the unity (1) while the “differentiated” gravity disappears (0) into the thin air.  

x)     In modern finance, the time (T) is recognized to have its own value. The shorter the “run” from the starting “line,” the pricier the time by, say, 2% per annum. In other words, the time dimension is even more relevant to us “in the short run” yet ante mortem than otherwise. Probably, the “time value of money” helps determine the average propensity to consume, namely, APC= C/ Y.

xi)   Finally, services take the lion’s share of modern economy. Thereto is often applied the principle of “network effect,” which is the polar opposite of the “law of diminishing returns” sometimes governing production of goods.

 

On the demand side in reality, there are consumption of products and investment in assets; there on the supply side is production by creative powers. Under GAAP all the way from Luca Paciloi, the two sides are equal no matter when and where. “Equilibrium” of any other kind is metaphorical, surreal, virtual or eternal.

             The gap between the short run (_T) and the long run (T) is a matter of degree, while the chasm between time (T) and distance (L) is a matter of kind. The mule as mixture of different species, for instance, is never reproductive; stability or growth of its population depends on chances (“0” in science). The simple truth: The mule is neither a horse nor a donkey. What is macroeconomics all the way from Cambridge like?

 

In fine, we do have an alternative where to run in the short or long:

             As Irving Fisher and Paul Samuelson attest, we hoard money for the purpose of doing away with it. In this regard, Willian Baumol (1952) from Princeton offers a clue how much money for us to prefer. On his shoulders, we derive the simplistic equation g+ π= 2m, where “g” for the real growth rate in % PA of the monetary GDP, “π” for the inflation (ditto) of the currency unit and “m” for the growth of the monetary balance.

             Apparently, growth (g) and inflation (π) are in tradeoff. More specifically, we shall have inflation when GDP fails to grow twice as fast as “money is eased.”

            According to the old paradigm of quantity equation P∙Y= M∙V, “quantitative easing” of money affects the economy through a double channel: the very quantity of money (M) and the velocity (V) of spending it. To paraphrase, we get rid of money as swiftly as tailored to the two causes: one, the incremental money (+ΔM) is convenient in purchasing our wants yet to be fulfilled; the other, with the monetary income (P∙Y) given, the money of no use but inconvenience is as much dis-preferred (+ΔV).

             “Keep it simple, please.”