Inflation Predictions

Revolution

Never make a politician grant you a favor (Doo-doo-doo-doo)
They will always want to control you forever, eh! (Forever, forever)
So if a fire make it burn (make it burn, make it burn)
And if a blood make ya run (make ya run, run, run)
Rasta de 'pon top, can't you see? (Doo-doo-doo-doo)
So you can't predict the flop eh-eh! (Doo-doo-doo-doo)

What can you predict?

NPR’s Planet Money recently aired an episode titled Predictions: Inflation.  These predictions might have been easier if it was recognized that the Consumer Price Index is a combination of long term inflation, which is related to the US  money supply, (the medium of exchange between buyers and suppliers), and short term inflation, which is related to changes in the demand (buyer) and supply curves. If the proposed equations of long term inflation is removed, the changes in inflation (as measured by the Consumer Price Index) show a much different picture.

Viewed in this manner, changes in price appear much more stable than would otherwise be expected.  Taking a deep breath when viewing year to year changes in prices would appear to be warranted.  Most of what is called inflation may be long term inflation caused by the money supply, not by changes in the supply and demand curves. Making predictions about the short term changes in CPI could  be a lot easier if we realize that there is also a long term component.

Blame

 

The Name Game

Billy, Billy, bo-gil-ly, bo-na-na
Fanna, fo-fil-ly,
Fee fi mo-mil-ly, Billy!

The Name game is harmless fun.  Can we say the same about the Blame game?

When  you try to assess blame you are looking only at the past.  You look at a harmful act that has already occurred and try to assign responsibility for that harm.  But if those harmful actions were random, or you can not determine the cause of the harm, it may be tempting to assign blame to an individual.  But assigning blame to individuals who are not responsible for that action can’t prevent those harmful actions from occurring again.  If an investigation does correctly assess blame, and that blame is criminal, penalties can be  imposed to prevent that action from occurring again or make the individual who is responsible mitigate that harm.  Either the individuals who are responsible can be prevented from undertaking take that harmful action again, or those who might have considered such an action are deterred from that harmful action because the costs of that action outweigh the benefits.

But if those individuals are not responsible, punishing those individuals serves no purpose. It does nothing to  prevent the action from happening again.  The purpose of an investigation should be to prevent that action from occurring again.  If you assign blame incorrectly and punish the wrong individuals, those resources can not go into actually identifying the correct cause and possibly preventing such an action from ever occurring again.  Blaming the right person only has a benefit if it deters the harm attributable to that person in the future.  Blaming the wrong person can not deter harm in the future. Doing the right thing in response to a tragedy may be commendable, however doing the wrong thing is worse than doing nothing at all. Finding out correctly who, or what, is responsible is productive.  Simply assigning blame, particularly if that blame is assigned incorrectly, is not.

Money

 

Money (That's What I Want)

The best things in life are free
But you can keep them for the birds and bees
Now give me money, (That's what I want)
That's what I want
(That's what I want)

But what is money?

I have blogged about this before, but it is  important enough to do it again.  Money is the medium of exchange in trades.  We rely on our sovereign to vouch for that medium.  We can agree that precious metals are a medium of exchange in each trade because they have value and they can be exchanged for other goods.  The problem is that the weight of those precious metals is not easily determined (who carries a scale around with them?) and who can be sure that that precious metal is what it is claimed to be (iron pyrite anyone?).  The solution was that coins were minted by the sovereign who attested that the coin was indeed what you expected, and was a weight of which you could be certain.

It is no accident that, in the United Kingdom the unit of money is the Pound Sterling (silver).  The US Dollar is named after the Spanish Dollar, a coin of sterling silver.  It was common to break this coin into eight pieces (pieces of eight) and to use these bits as a medium of exchange ( a shave and a haircut, two bits,  2/8th of a dollar, one quarter).  The accepted precious metal became to be gold as governments shifted away from silver ( “You shall not crucify mankind upon a cross of gold"- William Jennings Bryan).

The key to precious metals as a medium of exchange is that  they are limited and not easily created.  Alchemists spent much in resources in trying to turn lead into gold.  The search for precious metals, especially gold, drove much of the frenzy in exploring the Americas.  The forced removal of Native Americans from their ancestral lands followed the gold rush in the Carolinas in 1799 ( the Trail of Tears) and the Gold Rush in the Black Hills of the Dakotas in 1874 ( the infamous Custer expedition).  Ironically the relocation to what was long called Indian Territory, and is now called Oklahoma,  was followed by the discovery of oil there. (Black Gold.  The moral arc of the universe is long but it bends towards justice, indeed! ) The use of precious metals as currency can still be seen in today’s crypto currency.  Bitcoins have the value that they do because like gold, they are rare and there is a limited number (21 million) that can be created. The creation of new Bitcoins is called “mining:”

Precious metals are heavy, hard to weigh, hard to protect, etc.  As a result, governments’ printed paper currency that was backed by precious metals.  This led to the “discovery” that currency had value merely because the Nation said that it had value.  ( the Native Americans that had long used wampum must have FOTFLTAO when the Great White Fathers “discovered” this.) The United States went off the Gold Standard in the 1930s, but gold was still used as a medium of international trade until the Bretton Woods Conference, in 1944, where the US Dollar at a fixed price of gold, became the international trading currency.  This was maintained until the Nixon Shock, in 1971, when the US Dollar in international trade was no longer backed by gold.

This led to a predictable response by the international holders of those US dollars.  The international holders of those dollars used their dollars to bid up the price of physical goods.  The result was the spike in inflation of the 1970s.  The Federal Reserve banks, founded in 1914, were charged with maintaining a stable economy in the United States.  That they did this admirably is seen in the fact that the Consumer Price Index, CPI,  between 1913 and 1944, was virtually flat, despite economic cycles, the Great Depression and two World Wars during this period.   

Since that time the Consumer Price index has not been flat.  11-year-old me mourned when my beloved comic books increased in price from 10 cents to 12 cents in 1962.  My first year at Brown University in 1969 was less than $4000 for room board and turion.  I graduated with a grand total of $1,600 in student loans.  When my son was ready to go two days a week for a few hours a day to nursery school in 1987, it cost more for his tuition than my first year of college!

It would be tempting to say that inflation has been simple and continuous, but that is not well correlated  with the observed Consumer Price Index.  It would be tempting to say that inflation is compound and continuous, but that also does not correlate well with observations.  What does correlate well is a simple linear equation with two discontinuities which happened in 1944, the year of Bretton Woods, and 1971, the year of the Nixon Shock.  It is suggested that these years are not an accident.

Before Bretton Woods, the US Dollar was used primarily for domestic trade. The Federal Reserve did an admirable job of seeing that the supply of money was consistent with the economy.  After Bretton Woods, despite John Maynard Keynes' suggestion that the Bancor be used for international trade, the United States Dollar backed by gold was the currency used in international trade, with results that were predictable (at least to economist Robert Triffin).  Eventually international trade grew to such an extent, that the Nixon Shock of 1971 occurred, with predictable results.

The CPI has increased steadily since that time.  It would appear that the growth in international trade has not been accounted for by the Federal Reserve, and since the US Dollar is still a major international trading currency, the Federal Reserve apparently grew the US money consistent with the growth in the US economy, but did not grow the US currency consistent with the growth in international trading. Today’s current persistent inflation is the result.

Kamila Valieva

 

Children Will Listen

Guide them along the way,
Children will glisten
Children will look to you for which way to turn
To learn what to be
Careful before you say, listen to me.
Children will listen.

Blaming the victim does not punish a crime.  Punishing the crime punishes the crime.

Is there a Russian team at the Winter Olympics or are there athletes at the Winter Olympics that happen to be Russian?  Based on the Parade of Nations, the playing of the National Anthem of the Gold Medal Winner, the display of the National flags for the Gold, Silver and Bronze medals on the podium, and the display of National flags on the uniforms of the athletes, etc., it would appear that Nations are at the Winter Olympics.  At least one Nation appears to have violated the rules of the Olympics and in doing so has placed its athletes in jeopardy.   If the International Olympic Committee cared about those athletes, it would not allow them to be placed in jeopardy.

It seems merciful not to penalize athletes for violations of their country.  But allowing those athletes to compete under these circumstances is not mercy for those athletes, it is being complicit in jeopardizing their well being.  Placing the onus on other athletes, who violated no rules and yet finish behind those athletes who have been found to violate Olympic rules, is unfair to those other athletes.  If the Olympics seeks to promote good sportsmanship, how is disputing the awarding of medals to those who finished above you ever promoting good sportsmanship?

Was the athlete involved in the  violation of Olympic rules a minor?  Absolutely, but that does not change the truth that the rules were violated.  Could a minor have violated those rules? Not according to the law.  Should the adults who violated those rules be punished? Absolutely.  But if child abuse occurs, is it fair to turn give the child back to the abuser, even if punishing the abuser will deprive the child of a place the child wishes to be.

An alternative, not allowing minors to compete at the Olympics, is unfair to those minors, those Nations, and the adults in those Nations who have not violated the rules.  It is throwing out the baby  with the bath water.  Child abuse might occur in families.  The solution should not be to remove all children from their families.  But if the adults found guilty of child abuse are to be punished, every step should be taken to make it clear that punishing the abuser is not also punishing the child.  Saying that Kamila Valieva willing took Trimetazidine is blaming the victim in a child abuse case.  Can the abuser be punished without punishing the victim?  If it means returning the victim back to the abuser and requiring non victims to be poor sports, it doesn’t seem that justice has been served. Collateral damage is still damage. Saying that collateral damage should be ignored does not make that damage go away.

 

An Iterative Process

Try Again

If at first you don't succeed (first you don't succeed),

Dust yourself off, and try again

You can dust it off and try again, try again

'Cause if at first you don't succeed (first you don't succeed),

You can dust it off, and try again

Dust yourself off and try again, try again

In mathematics, trying again is called iterating.

The User Equilibrium assignment in Travel Demand Models is an iterative process.  Those iterations  are of the Frank-Wolfe algorithm in order to compute an equilibrium volume.  Between iterations, the IMPEDANCE is updated.  NO other attributes,  especially capacity, should be changed until the equilibrium process is completed.  Changing the formula for impedance, or any link attributes, except the volume, during this process violates the assumptions of the Frank-Wolfe algorithm that is being used.

This does not mean that the initial link capacities are absolutely correct.  Capacities on links are most often based on characteristics of the design for that link, e.g. lane width.  However there are circumstances where the capacity depends  not only on the design characteristics of the link, but on the volumes on this or other links. 

·    For example, the capacity of a link approaching a signalized intersection is a function of the green to Cycle Length, g/C, of that signal.  An initial assumption has to be made for the g/C ratio before the volumes are known, but technically the g/C ratio is a function of the approach volume on that link divided by the approach volumes of all links approaching that intstection.  Those volumes are precisely what is being computed in the assignment iterations.

·   Similarly, the capacity of truck climbing lanes depends on the truck percentage on that link as well as truck percentages of adjacent links.  These percentages will not be known until after the assignment iterations are complete.

This issue is not unique to assignment. It can occur whenever an iterative process is used.  Assumptions may be made in order to solve the process, but these assumptions may be inconsistent with the solution.  In fact the Travel Demand Modeling process often already has such a feedback loop .  In order to distribute and find the mode choice in creating a trip table, it is necessary to know the impedances, e.g. skim times, between zones for each mode, which are not really known until after that trip table is assigned.  A feedback loop uses the impedances based on the initial assignment to update the inputs to trip distribution and mode choice.

A similar process is proposed for assignment.  Assumptions are made for network link capacities in order to solve for volumes on that network.  After the assignment ( NOT DURING THE ASSIGNMENT), the capacities can be recomputed based on the volumes which were assigned.  If these capacities are significantly different than the capacities that were assumed before the assignment began, then the link capacities should be updated and a new assignment should begin. This process should continue until the capacities that were assumed as the input to the assignment are sufficiently consistent with the capacities computed from the volumes that are output from the assignment.

Time AND Reliabilty

How The Grinch  Stole Christmas

It came without ribbons, it came without tags.
It came without packages, boxes or bags.
Maybe Christmas doesn't come from a store.
Maybe Christmas (he thought) means a little bit more.

What if congested time in Travel Demand Models was a little bit more

Travel Demand Models that utilize the User Equilibrium assignment method proposed by Sparrow and Dafermos, use the Frank-Wolfe, F-W, algorithm to iteratively solve for this equilibrium. This requires the use of an impedance function.  The purpose of this impedance function is to recompute the impedance of links on paths between F-W iterations.  As implemented in Travel Demand Models, this impedance function is typically called the Volume Delay Function, VDF.  This function expresses impedance in units of time, but this time is more properly a measure of impedance, not observable times. The impedance function must have the volume for which equilibrium is being solved, as one of its independent variables.  The other variables may NOT change in value during F-W iterations. 

VDFs are typically expressed as  a function of volume to capacity ratios, v/c.  The Bureau of Public Roads, BPR, proposed an empirical impedance function which is based on v/c ratios, but the empirical observations were only for v/c ratios less than 1.2 and it was NEVER proposed that this equation be used for conditions with v/c ratios greater than 1.2.  Nonetheless, the BPR equation is the basis of the VDF that is recommended by the Travel Model Improvement Program, and is used for ALL v/c ratios.

Before proposing a theoretical impedance function, it is useful to identify those variables where the impedance will increase with increasing volumes.  The impedance function used in TDMs does not have to include all impedance choice variables, only those choice variables that cause a change in impedance with a change in volume.  If the impedance does not change with a choice variable, that variable  need not be included in the “impedance” function.  More properly what is needed is NOT an impedance function, but a CHANGE in impedance function.  This function need only consider how impedance changes in response to changes in volume.  For example, if the number of traffic control devices on a route is an impedance choice variable, the impedance associated with that choice variable does not change with a change in volumes, and that need not be considered in the UE.

The impedance as a function of volume DOES change as the reliability changes and as the travel time changes.  It is suggested that the “delay” in the BPR is more properly time, and reliability expressed in units of time, compared to the time and reliability with zero volume. If reliability and travel time are functions of volume, then a proposed equation of reliability, expressed in units of time, and a proposed equation of mean travel time, that change with increasing volume, is needed.  The function of reliability is a function of the mean time, but since the mean time is a function of volume, then reliability is, de facto, a function of volume.

It is suggested that the empirical BPR  already must include both mean time, and reliability expressed in units of time. Since the mean travel time is proposed to be a discontinuous function, any impedance function derived using mean travel time thus will also be a discontinuous function.

Azizi and Beagan  showed that route choice, was better correlated with the Planning Index, PI, than with the mean Travel Time Index, TTI.  It is proposed that the impedance function should be a function of PI. It was also shown that PI resulted in fewer assignment, F-W,  iterations before reaching essentially the same equilibrium volumes  It is proposed that the VDF should be PI and that it would include both time and reliability, e.g. be a Volume Delay AND Reliability Function, a VD(R)F.  The proposed theoretical VD(R)F,  based on the equations of travel time and reliability, is proposed to be

If v/c>=1  then TTI = FFS/TS*exp((v/c-1)/γ_T)) else TTI = 1/(γ_L*ln(1-v/c)/FFS+1))

VD(R)F =PI=TTI*(1+0.645*(1-exp(-(TTI-1)/.110171)))

where FFS, TS are link attributes similar to capacity (FFS is already coded on links),  and γ_T and γ_L are functions of FFS and TS, i.e. γ_T=( FFS-TS)/5.8 and γ_L =TS/5.8. The coefficients of reliability, δ and ε,  are shown using their theoretical values which are true for every link. 

This VD(R)F is very well correlated with the existing BPR equation for v/c ratios less than 1.2.  It is proposed that the existing validation of the VDF using the BPR formatted curve be used in this domain.  Figure 1 shows the traditional BPR curve with α =0.5 and β=4, (the original formulation of the BPR has α=0.15 but it also uses the practical capacity in the ratio.  The α =0.5 is the value consistent with the current convention of coding the physical capacity on links), and PI for a Free Flow Speed of 70 MPH, a Transition Speed of 60 MPH, and capacity of 2000 veh./hr./ln . The proposed interim BPR is the validated BPR for v/c less than 1.2,  and a simple queuing equation rotated by an angle θ,,where α=sin(θ), after a transition at v/c=1.2. The queuing equation is also coordinate translated to move the origin from (0,0) to (1.2, 1+α*1.2^β). The congestion portion of the BPR equation, α *(v/c)^β,  is itself coordinate transformed from an origin of  (0,0) to an origin of  (0,1). The proposed interim BPR is

1+α *(v/c)^β                               for v/c ≤ 1.2

and

1+α*(v/c-1.2)+α*1.2^β                for v/c > 1.2

Figure 1 Various Impedance Functions

Traffic Flow

 

Row, Row, RowYour Boat

Row, row, row your boat
Gently down the stream
Merrily merrily, merrily, merrily
Life is but a dream

Do vehicles in traffic behave like water in a stream?

This topic was rejected by a national publication, in part because one of the reviewers disagreed that people in traffic behave  like drops of water in a stream with laminar and turbulent flow. Oh, yeah?

Polynomial equations of speed/time have been proposed and are widely used. These equations describe the behavior of speed/time in two domains.  They require a Free Flow Speed, FFS, the speed at zero volume; the capacity, which separates the uncongested and congested domains; and either an explicit or implicit Transition Speed, TS. The two domains are:

·       Uncongested/ laminar flow, where the volume is less than the capacity, and

·       Congested/ turbulent flow, where the volume is greater than the capacity.

The polynomial equations adequately explain the speed/time in the uncongested domain.  Their use in the congested domain is always not necessary for Traffic Simulation models, but is necessary for Travel Demand Models.  The use of these polynomial equations creates some inconsistencies when they are used in the congested domain.  Polynomial  equations are smooth, i.e. have no discontinuities.  But the use of these equations creates a discontinuity at a v/c of 2.0, and requires the allowance of negative or imaginary, not real and positive, capacities. It is proposed that exponential equations of speed/time which are different in the uncongested and congested domains may be preferable. They will have a discontinuity at the transition between the two domains, but create no additional discontinuities and require only positive capacities.  These equations are:

Uncongested domain, v/c ≤1.

Vol/Cap = 1-exp (-1/γ_L *(FFS-Speed)))

Speed = f(Vol/Cap) = FFS*(γ_L/FFS*ln(1-Vol/Cap)+1)

where γ_L is a range ( transient) coefficient of the laminar equation.  If 99.97%, 3 Sigma, of the transition occurs during the range which is the absolute value of (FFS-TS), it has the value of

γ_L = -|FFS -TS|/ln(1-0.9997) = (FFS-TS)/5.8

This is a horizontal mirroring of the traditional exponential association of speed and a translation of the origin from (0,0) to an origin of (FFS,0), restated with v/c as a function of speed.

Congested domain, v/c >1

Vol/Cap = (1-γ_T*ln(1+(Speed-TS)/TS))

Speed=f(Vol/Cap) = TS*((1-exp((-(Vol/Cap-1))/γ_T ))+1)

where γ_T is a range ( transient) coefficient of the turbulent equation.  If 99.97%, 3 Sigma, of the transition occurs during the absolute value of the range (TS-0), it has the value of

γ_T = -|TS-0|/ln(1-0.997) =  TS/5.8

This is the traditional exponential association of transition and a translation of the origin from (0,0) to an origin of (TS,1), restated with v/c as a function of speed.