Saturday, April 15, 2017

the three class game of capitalism

Lancaster has only two

Add a class of small producers

Wednesday, April 12, 2017

take note : Latin AM populism now wrecked

For the Nth time

Z
B
A

Must take commanding heights plus

Socialize key market pricing mechanisms

With mark up warrant systems

Exim first

neutral v natural

Why these pernicious labels

For various unicorns

We can imagine the state sitting on
its hands at some conjuncture

From that point on
How will
The existing
social production system develop

Is there a determinable path range

Is there a settling down
what are
the emergent features
state variables

Self disrupting systems may make
Such attempts at simple framing impossible

Even if a neutral  rate exists at each instant
One that is stable intrinsically
it may change
thru immediate following events

The system chases a moving target

With uncertain course

transaction accounting

The base in real time :

transaction space-time

This pretentious construct
is justified
and plausible now

Tuesday, April 11, 2017

civil liberties and the dictatorship of the prole class

A nasty bit of historical dialectic

when capitalism chews up its own institutional foundations.....like those predicated on certain civil liberties. libet

Like say
Free Labor unions
rendered into a national labor front

Friday, April 7, 2017

new topic : exploitation in the twenty first century...to hell with inequality in a multi class world

revisiting vintage modeling

look at any two class toon world

wage earning producers and productive faclilities owning capitalists

Saturday, February 18, 2017

Simon from inside himself "here is the rub. If we really think there is no relationship between unemployment and inflation, why on earth are we not trying to get unemployment below 4%? We know that the government could, by spending more, raise demand and reduce unemployment. And why would we ever raise interest rates above their lower bound?"

Again it's so lapidary

here is the rub.

If we really think there is no relationship between unemployment and inflation,

why on earth are we not trying to get unemployment below 4%?

We know that the government could, by spending more,
raise demand and reduce unemployment.

And why would we ever raise interest rates above their lower bound?
obvious response

to sustain robust exploitation...!!!!!!!!!!!!!!!!!

end job scarcity and precarity and watch exploitation wither to pure innovation

`
at any rate
if we want to actually study
price kinetics

FIRST LET'S REWRITE

IF THERE IS NO RELATIONSHIP BETWEEN VARIOUS PRODUCT PRICE CHANGES
AND THE CONDITIONS ON CORRESPONDING JOB MARKETS .......

NOW JOB MARKETS IS A VERY DIFFERENT BUNCH OF CRITTER FROM UNEMPLOYMENT SCALARS
OR EVEN UE VECTORS

FOCUS ON MODELING JOB MARKETS ADEQUATELY
NOT ON SHORT CUT CORRELATIONS BETWEEN UE and product price inflation !

NAIRU bashing

"The NAIRU is the level of unemployment at which inflation is stable. Ever since economists invented the concept people have poked fun at how difficult to measure and elusive the NAIRU appears to be, and these articles often end with the proclamation that it is time we ditched the concept. Even good journalists can do it. But few of these attempts to trash the NAIRU answer a very simple and obvious question - how else do we link the real economy to inflation?

One exception are those that attempt to suggest that all we need to effectively control the economy is a nominal anchor, like the money supply or the exchange rate. But to cut a long story short, attempts to put this into practice have never worked out too well. The most recent attempt has been the Euro: just adopt a common currency, and inflation in individual countries will be forced to follow the average. This didn’t prove to be true for either Germany or the periphery, with disastrous results.

The NAIRU is one of those economic concepts which is essential to understand the economy but is extremely difficult to measure. Let’s start with the reasons for difficulty. First, unemployment is not perfectly measured (with people giving up looking for work who start looking again when the economy grows strongly), and may not capture the idea it is meant to represent, which is excess supply or demand in the labour market. Second, it looks at only the labour market, whereas inflation may also have something to do with excess demand in the goods market. Third, even if neither of these problems existed, the way unemployment interacts with inflation is still not clear.

The way economists have thought about the relationship between unemployment and inflation over the last 50 years is the Phillips curve. That says that inflation depends on expected inflation and unemployment. The importance of expected inflation means that simply drawing unemployment against inflation will always produce a mess. I remember from one of the earlier editions of Mankiw’s textbook he had a lovely plot of this for the US, that contradicted what I just said: it displayed clear ‘Phillips curve loops’. But it was always messier for other countries and it got messier for the US once we had inflation targeting (as it should with rational expectations). See this post for details.

The ubiquity of the New Keynesian Phillips Curve (NKPC) in current macroeconomics should not fool anyone that we finally have the true model of inflation. Its frequency of use reflects the obsession with microfoundations methodology and the consequent downgrading of empirical analysis. We know that workers and employers don’t like nominal wage cuts, but that aversion is not in the NKPC. If monetary policy is stuck at the Zero Lower Bound the NKPC says that inflation should become rather volatile, but that did not appear to happen, a point John Cochrane has stressed.

I could go on and on, and write my own NAIRU bashing piece. But here is the rub. If we really think there is no relationship between unemployment and inflation, why on earth are we not trying to get unemployment below 4%? We know that the government could, by spending more, raise demand and reduce unemployment. And why would we ever raise interest rates above their lower bound?

I’ve been there, done that. While we should not be obsessed by the 1970s, we should not wipe it from our minds either. Then policy makers did in effect ditch the NAIRU, and we got uncomfortably high inflation. In 1980 in the US and UK policy changed and increased unemployment, and inflation fell. There is a relationship between inflation and unemployment, but it is just very difficult to pin down. For most macroeconomists, the concept of the NAIRU really just stands for that basic macroeconomic truth.

A more subtle critique of the NAIRU would be to acknowledge that truth, but say that because the relationship is difficult to measure, we should stop using unemployment as a guide to setting monetary policy. Let’s just focus on the objective, inflation, and move rates according to what actually happens to inflation. In other words forget forecasting, and let monetary policy operate like a thermostat, raising rates when inflation is above target and vice versa.

That could lead to large oscillations in inflation, but there is a more serious problem. This tends to be forgotten, but inflation is not the only goal of monetary policy. Take what is currently happening in the UK. Inflation is rising, and is expected to soon exceed its target, but the central bank has cut interest rates because it is more concerned about the impact of Brexit on the real economy. That shows quite clearly that policy makers in reality target some measure of the output gap as well as inflation. And they are quite right to, because why create a recession just to smooth inflation.

OK, so just target some weighted average of inflation and unemployment like a thermostat. But what level of unemployment? There is a danger that would always mean we would tolerate high inflation if unemployment is low. We know that is not a good idea, because inflation would just go on rising. So why not target the difference between unemployment and some level which is consistent with stable inflation. We could call that level X, but we should try to be more descriptive. Any suggestions?

Friday, February 17, 2017

"While the average income in the country remains between 3 and 4 times lower than in Europe or in North America, the richest 10% of the Chinese population – or some 130 million persons all the same – do have an average disposable income equivalent to that of the rich countries."

However
"the share of the poorest 50% in the national income in China fell from 28% to 15% between 1978 and 2015, while the income of the 10% richest rose from 26% to 41%"

And" the share of public capital constituted 70% of national capital in 1978, and has stabilised around 30% since 2006, "

Monday, February 13, 2017

Making Deaf adder music

Paine said in reply to Sanjait...
"The Great Moderation era Fed has some good aspects but has fundamentally failed to understand how its obsession with keeping inflation from ever even thinking abut going up has suppressed wages and caused labor hysteresis.
I think they assume that all those problems just equilibriate away across the cycle but the reality is not that."
Excellent
The long run wage rate path is a historical product not the consequence of sublime
Ineluctable dynamic
Indeed
The optimal path of monetary / credit policy would run hotter
That is until we find our selfs back in the roaring 70's again
Then ?
We face up to socializing the price level path
And deal with the complex consequences of that un confronted historical necessity
Paine said in reply to Paine ...
Ken Galbraith and Jim Tobin among other worthy heads
never stopped knocking on that door
Our un socialized pricing mechanism has fatal externality problems
Any and all "absolute autonomous firm level pricing power"
must be moderated
Harnessed in fact
By an encompassing social mechanism
Harnessed into a relative pricing power only

Paine said in reply to Paine ...
Yes I write too long range but
Wage price spirals are obviously
Macro Policy induced whirl pool
we must someday navigate our way thru and out of this whirl pool
Not simply slow down and let the whirl pool unwind
Or stay slow and avoid the whirl pools all together
Slow slack and wage poor

Thursday, February 9, 2017

Van rump et again" I am far more worried by Trump. His approach is supportive of business not markets—"

This distinction is rarely so well used

Trump will destroy the social dynamics markets in order to benefit a few big outfits

Wednesday, February 8, 2017

Stem cell plants

Stem cell like outfits
that can quickly scale up to full production in various product areas
Where our domestic market place
relies entirely on foreign imports

Obviously a public project
But one that should not be restricted
to strategic security related products
We can never know when the frontier may revive a sector
We consider now to be easily off shored without consequence
to our long run social production platform

WTO allowed Legacy tax schedules for each producing bordered area based on historic contribution to global pollution by bordered market area as tax on imports from that market area

The burden of pollution ought to reflect historic contributions not just present remedies

An export from the us would pay a higher entry tax then say an identical product from Zimbabwe

Of course this is a counter current to border taxes based on carbon content of actual product

Say Zimbabwe has no pigou tax on carbon emissions
Competing products from US and Zimbabwe
the two legacy payments are set against each other
By  any third bordered market area

Friday, February 3, 2017

Oh that devil dick Nixon....Fear of politics mixing with macro nautics is a libel on " our system "

My goodness a pol gooses up the economy to get re elected and that leads to run away inflation
And / or a steep contraction post election !

What kind of system can get regularly into a phase where policy could actually deliver better performance but only if  the system convulses afterwards ?

Like a  race horse fed a speed ball

Surely other institutional arrangements should be explored
If the present system needs  substantial and yes palpable obvious slack ....
Enough Idle productive capacity and idle labor to be noticeable when removed to get votes .....

Yup sub maximal social production
Just to keep from over heating itself
Not technically or humanly
But simply
Price change wise !!!

Thursday, February 2, 2017

Letting your currency crash on forex markets .....A SIN ?

No
For a start

Imagine the jubilation among dollar denominated debtors ?

What about the import price tsunami ?

Rationing !

MM "These were not policymakers trying the exploit a permanent inflation output trade-off, but policymakers trying to escape the discipline of any kind of Phillips curve. "

They can  beat the dynamic P curve
Simply by ending untrammeled decentralized autonomous corporate dictated
spontaneous wage and output price setting

The price level path must be directly regulated
Using effective demand variation to " contain inflation"
Is a corporate class solution

One look at the end product of the great moderation ought to jar the counter cyclical demand management is bad for the wage class long run
Whether it's using stop go household credit
Or counter cyclical tax algorithms

Kalecki  macro updated by Vickrey
indeed requires Lerner mark up cap and trade

More mainly mackerel

".....politicians could not be trusted with operating such a Keynesian counter cyclical policy, essentially because they imagined they could beat the Phillips curve using direct controls on prices and incomes."

Yes the social democratic agenda had long run fiscal limits but not because of some long run inter temporal balance constraint
But

Because
"  ....we failed to raise taxes and cut spending in a boom. "

Far from a denunciation of Keynesian countercyclical fiscal policy, it was an admission that politicians could not be trusted with operating such a policy, essentially because they imagined they could beat the Phillips curve using direct controls on prices and incomes. The fact that fiscal rather than (government controlled) interest rate policy was being used as the countercyclical instrument here was incidental.

The labor party abdication of social democracy circa 1976 : "We used to think that you could spend your way out of a recession and increase employment by cutting taxes and boosting government spending. I tell you with all candour that that option no longer exists, and so far as it ever did exist, it only worked on each occasion since the war by injecting a bigger dose of inflation into the economy, followed by a higher level of unemployment as the next step”

Pure poison ?

No the poison came with the corporate fashioned remedy !

Right then and there the correct strategy
" we need to socialize the price level path "

Here however is manly mackerel ' s. Take

"As a piece of text it only makes sense to modern ears if there is a missing sentence:

that we failed to raise taxes and cut spending in a boom.

Far from a denunciation of Keynesian countercyclical fiscal policy,
it was an admission that politicians could not be trusted with operating such a policy,
essentially because they imagined they could beat the Phillips curve
using direct controls on prices and incomes. "

My my the road not traveled is blocked by a meme barrier !

One wonders what he thinks of Weintraub Lerner remedies ?

Crude analogy :
No more  massive electricity generation
It requires ruinous climate changing coal !

Nicely he does add:

" The fact that fiscal rather than (government controlled) interest rate policy
was being used as the countercyclical instrument here
was incidental."

More DBCFT chatter : will deduction of ground rent boost land values ?

We're told this tax change would  " hurt " real estate  firms ?

Really ?

Hell if I'm interested in chasing these foxes to their dens

Tax warriors are chicken shit

The job bled multitude needs
A Vickrey - Lerner macro policy juggernaut
Not tax snipers

But some one must have figured the class and sectoral implications of this by now

DBCFT chatter : What if we pin the dollar forex ?

PK CW "So one way to think of a DBCFT is as a VAT combined with a subsidy for employment of domestic factors of production. The VAT part has no competitive effect, but the subsidy part would lead to expanded domestic production if wages and exchange rates didn’t change.
But of course wages and/or the exchange rate would, in fact, change. If the US went to a DBCFT, we should expect the dollar to rise by enough to wipe out any competitive advantage. After the currency adjustment, the trade effect should once again be nil. But there might be a lot of short-to-medium term financial consequences from a stronger dollar."

But why not lean against the appreciation like the PRC might ?

Would Yellen accommodate a trump  "protectionist " dollar

Wednesday, February 1, 2017

Temp price freeze as real life NK macro

Why not pull a Nixon -Connolly  ? A temporary price freeze at the time of injection ?

Ya ya the rat ex swinging Panglossians will predict enfeeblement

I'd bet on a real effect

The impoverished dynamics of mainstream macro models

I'll leave it at that except to add

Models that restore some steady path are doomed to remove the basis for real comp dynamics

Hint
Try building a model
With  internally generated convulsions
And variable sim paths with and without optionally operated multiple intensity homeostatic sub systems

Forget multiple equilibria stick to comparative dynamics

Roger farmer wants us to condemn Paul Samuelson for his belief in spontaneous ie endogenous
Recovery from contractions

Nonsense !

The problem with leaving it to the corporations and households is obvious
It's too SLOW
too long between trough and recovery yes too long
and too deep a drop from peak to trough too !

The state with correct macro nautics can do better !
In fact the state can end the output and employment cycle as we know it

And we know it and have known it ..more or less ..
since the  late 1930's and early 40's

After thirty years of reactionary NEW DEMOCRAT hegemony
The prog wing of the  Democrats ...the new majority democrats....
The new hegemonic democrats ....need to thrust
this self evident truth
on a long suffering long awaiting multitude
of job class dis illusionists

Perpetual full employment !

The horrid fiscal deficit / state debt mass phobia : If social democracy is synonymous with tax and transfer systems what's not synonymous unfortunately is a full power autostab use of this system for perpetual full mobilization of social production factors

Thesis

Social democracy stalled out because the implementation of perpetual mobilization max was never an explicit goal
And the dynamics of such a system was never fearlessly explored and advocated against its
Shrewd class enemies scare tactics dis info and reliance on received embedded superstitions
Reinvigorated with half truths and damnable out right falsehoods !

Keeping the system safe for bountiful corporate profits is NOT a reasonable job class objective

The output pricing system is best kept decentralized
But nothing suggests it can't be interconnected by a  mark up warrant exchange

Yes viable sustainable average mark ups vary from industry to industry
But at the margin they can be tagged with a tax or subsidy to reflect system wide conditions

It's really that simple

Of course we'd best start with a sector like health
Where obvious social control would have immediate and substantial benefits
Always of course
With the clear objective
of expanding the range of the exchange step by step
to commodities and industrial imports and exports and then to the rest of the economy

Typical meme toxins "Wages aren’t in that description. Wages are primarily a guide to estimating full employment (economic slack). Rising wage growth indicates the economy is approaching full employment. Wage growth in excess of the inflation target plus productivity growth raises warning signs that the economy is operating beyond full employment. Also, commodity prices are included as idiosyncratic shocks. Finally, the labor market data is very clearly not the ultimate arbiter of price stability. In the long-run, inflation expectations are the ultimate arbiter of price stability."

Some  use the term employment max v full employment

Others say sustainable employment

All mean just to the north edge of the estimated
"nominal wage acceleration zone "

Surprisingly this contrivance of 70's macro nautics
The NAIRU
Rarely gets the credit it may deserve for the relative decline
in real wage rates
secular climb thru time

This taboo zone  is sacred
willfully violated only once ( late 90's )  since the volcker Dammerung
During the dot com bubble up
and the fabulous fiscal surplus soar

Attempts to dive to the " true bottom "
Just to see what's real and what's fantasy
have never even been broached by establishment Merlins

Step one of any new macro for job class pols should be
To undertake such an expedition
A vickrey drive toward full mobilization

If we need a output price freeze pro temp
So be it

Society must from time to time
Probe  the alleged  operational boundaries of its various instituted systems

If certain institutions need to be modified as a result

Bravo !

Tuesday, January 31, 2017

Capture the DP power core but bring along some new economic thinkers

This capture of the DP commanding heights needs a new economic think tank
Drawn “broadly ” from the several currents of real progressive economists
As a macro economist I see the necessity to re found macro policy
We have fore fathers
like Kalecki Lerner and Vickrey
And a wide range of contemporaneous eclectic allies
From the likes of theorist joe Stiglitz to policy Merlins like bobby Reich and Jamie Galbraith
Obama built his policy team basically out of inherited Clinton cadre
They must be pushed out …completely
Example
Senators Warren or Brown or Sanders
Despite rooted job class orientations

Lack
a real economics brain trust
steeped in potential progressive best practices

"Low taxes merely liberated income from taxation to pay for higher levels of debt service, "

Nice little card trick of our times

"Social democracy and market liberalism offered different solutions to the same problem: how to provide for life-cycle dependency. Social democracy makes lateral transfers from producers to dependents by means of progressive taxation. Market liberalism uses financial markets to transfer financial entitlement over time. Social democracy came up against the limits of public expenditure in the 1970s. The ‘market turn’ from social democracy to market liberalism was enabled by easy credit in the 1980s. Much of this was absorbed into homeownership, which attracted majorities of households (and voters) in the developed world. Early movers did well, but easy credit eventually drove house prices beyond the reach of younger cohorts. Debt service diminished effective demand, which instigated financial instability. Both social democracy and market liberalism are in crisis."

Oxbridge take on the past 40 years

Sunday, January 29, 2017

Capitalists dictate prosperity or misery

Rog farmer uses wealth to drive spending around not income

He relies on beliefs about the future !

Beliefs in a future prosperity are self fulfilling
Similarly beliefs in future dirth are self fulfilling

He grabs the easiest existing ready to hand lever to move this system

The stock market

Essentially he surrenders the system to the capitalists
Motivating their firm level spending
thru state manipulation
of the equity value
of public corporations  !

Friday, January 27, 2017

Flash back pause : Ken's hierarchy of systems

1. Frameworks. The geography and anatomy of the universe : the patterns of electrons around a nucleus, the pattern of atoms in a molecular formula, the arrangement of atoms in a crystal, the anatomy of the gene, the mapping of the earth, etc.
2. Clockworks. The solar system or simple machines such as the lever and the pulley, even quite complicated machines like steam engines and dynamos fall mostly under this category.
3. Thermostats. Control Mechanisms or Cybernetic Systems : the system will move to the maintenance of any given equilibrium, within limits.
4. Cells. Open systems or self-maintaining structures. This is the level at which life begins to differentiate itself from not life.
5. Plants. The outstanding characteristics of these systems (studied by the botanists) are first, a division of labor with differentiated and mutually dependent parts (roots, leaves, seeds, etc.), and second, a sharp differentiation between the genotype and the phenotype, associated with the phenomenon of equifinal or "blueprinted" growth.
6. Animals. Level characterized by increased mobility, teleological behavior and self-awareness, with the development of specialized 'information receptors (eyes, ears, etc.) leading to an enormous increase in the intake of information.
7. Human Beings. In, addition to all, or nearly all, of the characteristics of animal systems man possesses self consciousness, which is something different from mere awareness.
8. Social Organizations. The unit of such systems is not perhaps the person but the "role" - that part of the person which is concerned with the organization or situation in question. Social organizations might be defined as a set of roles tied together with channels of communication.
9. Trascendental Systems. The ultimates and absolutes and the inescapable unknowables, that also exhibit systematic structure and relationship.

Beware cloud 9 !!!

Ancient Ken Boulding "Conventions of generality and mathematical elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity and literary vagueness... It may well be that the slovenly and literary borderland between economics and sociology will be the most fruitful building ground during the years to come and that mathematical economics will remain too flawless in its perfection to be very fruitful."

I doubt the development of  frigidly formal ( with or without fudge sauce )
single rep
rat ex macro models
from what ..
The mid 70's to the late or mid 80's......

....Add in of course
the concurrent and subsequent elite smothering of alternatives ......
......Until September 2008 finally popped this most cunning of brain zits....

Has many peers for clog effect

Surely this interval
Will challenge scholars to find a better fulfillment
of stammer' Ken's prophecy

Third leg ism "modernize progressive politics and government for the Information Age. Leaving behind the stale left-right debates of the industrial era,"

Third leg ideology

Black "If Wall Street remains in charge of the DNC, the democratic wing of the Democratic Party should found a new party free from Wall Street and big corporate influence."

No

Just set up a "counter national committee " of  " Real Democrats "
With a real Democrat manifesto

Declare " the bought DNC " anti Democrat anti democratic anti people power

Force  Dembots  in elective positions to choose between the two national committees

Never surrender the party to Wall Street !

Thursday, January 26, 2017

Big racket opportunity buy up existing life insurance policies and inject drugs

The gaps in the life insurance market can be exploited more efficiently
If an effort is made to shorten life expectancies by increased drug use

The Dembot party needs a brand new economic brain trust

Forever at Full blast job markets

Perpetual high utilization production

A green Industrial policy

Tied to

Based on globally equalized  PPP guided forex

Tax wealth not work
Etc

Smarket algorithms that max social welfare objectives will be child's play .....once the market system is socialized

The endless dialectic
of competition and cooperation
of autonomy and integration
Of bottom up and top down
Etc etc
Can be codified and re codified
instituted and mutated incessantly

Undervalued forex leads to import substitution obviously

As forex falls domestic production of inputs into exportable outputs should rise

Cross put : the value of cross border transactions

The sum total of all transactions back and forth
across any bordered region of the global marketplace

Cross put

The degree of open ness is not well measured by ratio to GDP
if we have lots of intermediate imports as inputs  to exported outputs and visa versa

An estimate of  total domestic product transactions makes a better denominator

Sounds like I'm still shaken here

But the present formula import vale plus export value over GDP is too sensitive to
The amount of intermediate ins and outs

Once trade was in mostly final products not products that once productively consumed
Are headed back out into inter border commerce

Wednesday, January 25, 2017

Wage rates accelerate in 2017?

"We haven't been hearing reports from firms where the typical worker's wage increase in 2017 is expected to be above 4 percent. However, we did get readings for the Wage Growth Tracker pretty close to 4 percent in October and November of last year. As the following chart shows, a sharp increase in women's median wage growth (hitting 4.3 percent in October 2016) drove the overall increase. In contrast, the median wage increase for men was 3.5 percent."

Higher innovation rates among New research teams at new firms

Assume the productivity of a  research outfit
falls as the size of the outfit gets larger and the duration of the outfit gets longer

Producing new memes decreasing returns ? Why ?

Very unlikely

"In green is the relative number of researchers compared to the number in 1930. This isn’t the number of researchers, its a measure of effective researchers, found by dividing total R and D spending by the nominal wage of high-skilled workers. Relative to 1930, we have almost 25 times as many (effective) researchers at work today. This leads to the author’s title question - “Are ideas getting harder to find?”. And the author’s answer is “Yes”."

Thus looking at individual industries/lines will help us sort out what is happening. The first example is transistors, and the count of transistors per square inch on a chip. Famously, this appears to obey Moore’s Law, which is that the number of transistors per square inch doubles every 18 months. If we count the number of transistors per square inch as “ideas”, then this translates to a growth rate of 35% per year. At the same time, the effective number of researchers working at chip companies (Intel, AMD, etc..) has grown by a factor of about 80 since 1970. Plotting this together yields their next figure.
Maybe discovery is only partly connected to total effort All you get with more research mind hours Is redundancy and tight interval  between rival teams  in the same races
Maybe large teams slow the rate of discovery
Much to ponder

Even if global pop growthslows to zero Of course as available free labor ratios rise Thru increased productivity for necessary labor The research effort can increase $\frac{{\stackrel{}{I}}_{t}}{{I}_{t}}\frac{\alpha }{{I}_{t}^{\beta }}{S}_{t}$