Replies: 52 comments
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Yes. Attributes named in poststate_vars are the ones that are initialized
at birth, and thus also when initializeSim() is called. They are the
variables that describe the agents' state at the moment that time t becomes
time t+1: they're the end of time t and the beginning of time t+1, and thus
the variables that are mandated to exist for a new agent who comes into
existence at some time.
The permanent income level `pLvlNow` is a state variable in the sense that
its value in time t is a function of the post-state variable from t-1 and
the shock variables from time t. For an IndShockConsumerType, `pLvlNow` is
only trivially used to make a consumption decision, as the problem is
normalized by permanent income. For a GenIncProcessConsumerType, `pLvlNow`
is a direct argument into the consumption function in a non-trivial way.
But it's *also* a post-state variable in the sense that it exists at the
moment of intertemporal transition. Non-trivial post-state variables are
determined as a function of period t state variables and period t control
variables, e.g. end-of-period assets are market resources less
consumption. But permanent income as a post-state variable is a trivial
(identity) function of its value as a state variable: permanent income at t
equals permanent income at t.
…On Thu, Aug 13, 2020 at 5:36 PM Sebastian Benthall ***@***.***> wrote:
The PerfForesightConsumerType has two poststate_vars: aNrmNow and pLvlNow
https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py#L1450
However pLvlNow is set in getStates():
https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py#L1665
...and not in getPostStates(). Rather, aLvlNow is updated as a poststate
in the code:
https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py#L1706
Correcting the poststate_var field to list aLvlNow instead of pLvlNow
raises an AttributeError.
I guess this is because the class is depending on the automatic
initialization of the poststates, to create the attribute.
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Hmmm. For context, I bumped into this while working on #761. If I understand correctly, you are saying:
I find this confusing. If the variable is being used intertemporally, wouldn't its value in the previous period be I.e., why not:
(I expect that once the state variables are all properly listed out, it should be possible to automatically store the previous value for all of them. But that would be a separate issue.) Also, what about |
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I think I do that exact thing in some of the models, where there's a line
of code in getStates:
`pLvlPrev = self.pLvlNow`
`pLvlNow = pLvlPrev*self.PermShkNow`
The span of time in the code where what *was* pLvlNow is now pLvlPrev
is extremely short. That can be moved to `getPostStates` if you want. In
some sense it would make things more explicit, *but* it would introduce the
bad feature that if you added `pLvlPrev` to track_vars, hoping it would
track p_{t-1}, it would instead track p_t.
`aLvlNow` isn't in poststate_vars for an IndShockConsumerType because it
isn't needed at simulation initialization; note that it *is* in
poststate_vars for GenIncProcessConsumerType. It's calculated here merely
for user convenience. I guess it's also a slight code speedup for when the
simulation is being run for a AggShockConsumerType as part of a Market
being solved, and thus might be computed in parallel (to other instances of
AggShockConsumerType).
…On Fri, Aug 14, 2020 at 11:56 AM Sebastian Benthall < ***@***.***> wrote:
Hmmm.
For context, I bumped into this while working on #761
<#761>.
I'm trying to functionalize out some of the behavior and that requires
consistency as to how the functions used in simulations and variable
designations are used.
If I understand correctly, you are saying:
- pLvlNow is a state variable because it is a function of past state
and stochastic shocks and is an input to the determination of a period's
control values.
- It is also an intertemporal transition, so is in that respect a
'poststate'
I find this confusing. If the variable is being used intertemporally,
wouldn't its value in the previous period be pLvlPrev, or $p_{t-1}$, and
the new value be pLvlNow, or p? It seems like some notational slippage
was introduced into the code here.
I.e., why not:
- in getStates, assign a value to state variable pLvlNow based on
pLvlPrev and the stochastic shocks
- in getPostStates, assign to poststate variable pLvlPrev that value
of pLvlNow.
(I expect that once the state variables are all properly listed out, it
should be possible to automatically store the previous value for all of
them. But that would be a separate issue.)
Also, what about aLvlNow? Can you explain why that is being set in
getPostStates(), but not listed as a poststate_var?
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Ok. As I said, the main thing that's needed for refactoring is consistency. That's interesting about the tracking issue.
In the short term, I'd like to go ahead with having the previous state stored in |
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This is related to the discussion Seb and I had with @albop last week. I believe we agreed to move to a system in which there was a clearly defined point at which each exogenous shock was realized and at which each endogenous decision was made. The transition equations would define the state variables. But we would need to have a name for every state variable that exists at any point -- including some that might not have names in the mathematical formulation of the problem. For example, in the portfolio problem:
There are several virtues of disarticulating things in this way:
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I support what Chris just wrote, with the extension that I'd like to make
*every single thing* its own subperiod or step or whatever we call it.
Then there are only three basic kinds of operations:
1) Assign: Determining a variable as a *function* of other variables.
2) Draw: Determining variable(s) by drawing from a distribution.
3) Choose: Determine a variable by selecting among alternatives.
In some sense, Choose is a subset of Assign: `cNrm = cFunc(mNrm)`. When
"acted out", assigning consumption based on the consumption function
evaluated at market resources is just another kind of assignment. However,
`cFunc` is not part of the agent's problem, but is instead determined as
part of its solution. All Assign and Draw steps could be executed once the
*problem* has been specified, but any Choose step only has a value when the
model has been "solved" in some sense.
This is also the way to indicate to the future "magic solver" that *this
thing* is to be optimized, and *these* are the variables in the information
set at the time the choice is made.
Note that I specifically wrote Draw as potentially multivariate, whereas
the other ones have one variable on the LHS. Any multivariable
distribution can be written as a sequence of conditional multivariate
distributions, but that can add work for the user if we mandate that.
Somewhat related, a Choose step might have a multivariate LHS purely for
computational speed reasons.
…On Mon, Aug 17, 2020 at 1:40 PM Christopher Llorracc Carroll < ***@***.***> wrote:
This is related to the discussion Seb and I had with @albop
<https://github.com/albop> last week.
I believe we agreed to move to a system in which there was a clearly
defined point at which each exogenous shock was realized and at which each
endogenous decision was made.
The transition equations would define the state variables. But we would
need to have a name for every state variable that exists at any point --
including some that might not have names in the mathematical formulation of
the problem.
For example, in the portfolio problem:
Subperiod State Shock Operation
0 b_{t} = a_{t-1} \RPort \Risky Transition
1 p_{t}=p_{t-1}\PermShk_{t} \PermShk_{t} Transition
2 y_{t} = p_{t}\TranShk_{t} TranShk Transition
3 m_{t} = b_{t} + y_{t} Transition
4 a_{t} = m_{t} - c_{t} c_{t} is chosen
5 \PortShare \PortShare chosen optimally
There are several virtues of disarticulating things in this way:
1. There are no more "post-state" and "pre-state" variables. There are
just the states at each subperiod.
2. The state variables are all defined by the transition equations --
there's no need to have any separate articulation of what is a state and
what is a control
3. All the variables have a unique value within the period. So we
don't need to have extra notation to decide whether the value in question
is a "pre" or a "post" value
4. In the case of models where we are really thinking of shocks as
being realized simultaneously (like the risky return, the transitory shock,
and the permanent shock, the order in which we lay out the draws of those
shocks in sequence does not matter for the mathematical solution, but might
matter sometimes for computational purposes.
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Ok cool. I think this is something we are getting consensus around then. I'm working towards making this happen. I'm trying to start with some more basic refactoring: #760 #761 #660 When everything has been standardized around that, it should be possible to write a "magic simulator" that uses them, along with a decision rule for the control variables. Then "magic solvers" can be written that algorithmically find good decision rules. |
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@mnwhite makes a good point about multivariate statistical draws, and that for computational efficiency we might want to have several LHS variables rather than one. Let me expound a point that I forgot to make earlier, then elaborate on it in light of Matt's response. The point was that we should refer to subperiods by the name of the product(s) returned therein, rather than by a numerical order (0, 1, etc). So the earlier figure should have been
If (counterfactually) the most efficient way to solve this problem were a simultaneous method that produced both c and portshare, the last line could be modified as below. And if it were necessary to draw the transitory and permanent shocks jointly (because they are mutually correlated, we could modify the representation as below
Then we would be able to write sentences like "In the period labeled c_portshare, both the level of consumption and the share of the portfolio invested in risky assets are jointly determined." |
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I'd prefer more descriptive indexing/naming, but I agree they shouldn't be
absolutely numbered (at least by us; the code will look at their order and
number them).
…On Mon, Aug 17, 2020 at 5:11 PM Christopher Llorracc Carroll < ***@***.***> wrote:
@mnwhite <https://github.com/mnwhite> makes a good point about
multivariate statistical draws, and that for computational efficiency we
might want to have several LHS variables rather than one.
Let me expound a point that I forgot to make earlier, then elaborate on it
in light of Matt's response.
The point was that we should refer to subperiods by the name of the
product(s) returned therein, rather than by a numerical order (0, 1, etc).
So the earlier figure should have been
Subperiod State Shock Operation
b b_{t} = a_{t-1} \RPort \Risky Transition
p p_{t}=p_{t-1}\PermShk_{t} \PermShk_{t} Transition
y y_{t} = p_{t}\TranShk_{t} TranShk Transition
m m_{t} = b_{t} + y_{t} Transition
a a_{t} = m_{t} - c_{t} c_{t} is chosen
portshare \PortShare \PortShare chosen optimally
If (counterfactually) the most efficient way to solve this problem were a
simultaneous method that produced both c and portshare, the last line could
be modified as below. And if it were necessary to draw the transitory and
permanent shocks jointly (because they are mutually correlated, we could
modify the representation as below
Subperiod State Shock Operation
b b_{t} = a_{t-1} \RPort \Risky Transition
PermShk_TranShk $\psi,\theta$ \PermShkTranShkMatrix Draw
p p_{t}=p_{t-1}\PermShk_{t} \PermShk_{t} Transition
y y_{t} = p_{t}\TranShk_{t} TranShk Transition
m m_{t} = b_{t} + y_{t} Transition
c_portshare \PortShare c and \PortShare chosen optimally
a a_{t} = m_{t} - c_{t} Transition
Then we would be able to write sentences like "In the period labeled
c_portshare, both the level of consumption and the share of the portfolio
invested in risky assets are jointly determined."
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The equations/rules for assignments will specify a partial order, but not necessarily a total order, on the variables. In my view, this means we should not consider them to be numbered. It also means that the exogenous shocks can be both "simultaneous" and at differentiated. What's important is that they can be evaluated prior to state or control variables. |
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I might not get to the full refactor of post-post-state glory in the next PR. For the transitional work, @mnwhite could you tell me if |
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I'm getting back to this discussion by pure chance. There is one argument I
didn't convey properly.
In my view, the definition of a subperiod does not result from a
succession of operations, but rather by a change n the state-space that
does not correspond to a change in the information set (information set
being indexed by t). It defines the succession of functional spaces that
you are going to go through when doing your time-iteration.
When you do $m_{t} = b_{t} + y_{t}$ you move to a new subperiod, not
because there is a new subperiod (there isn't) but because the state-space
has changed from $b_t$ to $m_t$. It defines how you iterate "backward":
i..e you start by functions of m_t (`c(m_t)`, then functions of `b_t`
(psi(b_t), p(b_t), ...). Conceptually, all these function could be
computed as a function of m_t or b_t, but we would loose useful information.
So this is not the same as defining an order in which you compute the
transitions (b then p then y then m). It is possible to keep this order to
compute transitions from one subperiod to the next. When doing
time-iteration, if there is a system of several functions to solve for,
which have the same state-space, one can also look for the right succession
of operation (either provide it or autodetect it).
Now, the idea of labeling implicitly subperiod (in the sense I introduced),
with the name of the last computed variable does make some sense: after you
have computed `m` then `m` is the new state-space where functions are
defined. But what if you have more than one state ? Which variables do you
keep to define the state-space in a given subperiod ? I suppose when could
name subperiod, $(m,p)$ the period obtained just after m and p have both
been computed. I'm not saying it doesn't work but it requires a bit
more some thought compared to the 0,1,2,3... version which certainly does.
…On Mon, Sep 14, 2020 at 10:20 PM Sebastian Benthall < ***@***.***> wrote:
I might not get to the full refactor of post-post-state glory in the next
PR.
For the transitional work, @mnwhite <https://github.com/mnwhite> could
you tell me if aLvlNow is a state or a post-state in AggShockConsumerType
?
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In my view, there is not a linear series of subperiods. Rather, over a period at time t, there is a directed acyclic graph of variables. In simulation, a decision rule induces the choice variables into a normal random variable with conditional dependencies on its inputs. State variables are like this as well. Exogenous shocks are the roots (no parents) of the DAG structure. Simulation proceeds down the DAG. In principle, the evaluation of two nodes at the same "depth" can be parallelized at the computational level. Nothing makes it sequential, necessarily. When doing the solution, I expect you can work in reverse in a similar way. Start with the "deepest" nodes in the DAG, solve them, then go by backwards induction to "back" of the graph. So I think I agree with what @albop is saying, in that what matters about a "period" is which variable's states are being sampled/solved. But calling them "subperiods" imposes a linearity on this process needlessly. |
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I've renamed this issue to make it clear that it is now about the new proposed architecture. |
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Actually I find the term subperiod confusing. I prefer post-state which is less ambiguous. How to generalize it ? Post-post-state or post-k-state or just k-state ? |
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On Fri, Sep 18, 2020 at 4:00 PM Sebastian Benthall ***@***.***> wrote:
The definitions still work for natural numbers. You could define 1,2,3,4
to be a period then 1,2 and 3,4 would be subperiods. And, anyway, it would
be nice if naming conventions for a subcategory of problems (discrete time)
matched ones for the broader class (continuous time), especially when the
latter matches physical experience.
I would certainly not deny that intervals are well defined on the natural
numbers.
There is, in the natural numbers, a minimum non-degenerate interval size,
1, which cannot be subdivided. Maybe this is what you meant by an "atomic
period".
Speaking strictly from the point of convention:
- The MDP formalism defines the relationship between States and
Actions ordered by their atomic periods. Because of how this formalism is
defined, the problem at t is isomorphic to the problem at t+1, and there is
not much redundant information. It's a natural way to break the problem
down.
- It may be possible to transform an MDP into a different "time-scale"
by aggregating N atomic periods into larger intervals. It's not clear why
anybody would do this.
- Time at the sub-atomic level simply does not work in the same way
that it works at the atomic level. It is different because: (a) it is not
totally ordered, and (b) it has no periodic structure--i.e., it is not
repeating itself frame by frame.
I hesitate to assert the following, as it may muddy the waters, but:
"Physical experience" is a bit of an oxymoron. The phenomenology of time is
quite different from the social consensus around it, and indeed if we were
*truly* physicists we concede time to be much more complex than the real
number system (i.e., "space-time"). So I don't think "physical experience"
is solid ground for choice of mathematical formalism in this case.
I just suspected that if we look at "frames" coming from the splitting of
one max operation over several argument into several max operators we are
naturally getting ordered frames.
Considering a DAG of variables, as determined by the transition function,
the following will be true:
- There exists at least one valid linear ordering of the variables
based on topological sorting
<https://en.wikipedia.org/wiki/Topological_sorting>.
- If we consider "framings" to be a partitioning of the variables and
each subset in the partition a "frame", there will exist a framing such
- that the frames will have a unique topological order.
Problem is not whether frames are clearly and uniquely defined by
transitions but which set of frames are useful.
…
Do you have one easy characterization of one if the models you are working
on ?
Not yet. Thank you for the prompt to derive one.
The difficulty I have had is that I have not been able to find the
mathematical definition of the classes of models that "Economists find
interesting", in this context. I am now digging for a formal description of
the scope of heterogeneous agent models (HAM), as opposed to ABMs, and
MDPs, but have not found one yet.
My hope is that as the formal constraints crystalize in the software, it
will be expressive enough for me construct such a model.
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On Fri, Sep 18, 2020 at 4:00 PM Sebastian Benthall ***@***.***> wrote:
The definitions still work for natural numbers. You could define 1,2,3,4
to be a period then 1,2 and 3,4 would be subperiods. And, anyway, it would
be nice if naming conventions for a subcategory of problems (discrete time)
matched ones for the broader class (continuous time), especially when the
latter matches physical experience.
I would certainly not deny that intervals are well defined on the natural
numbers.
There is, in the natural numbers, a minimum non-degenerate interval size,
1, which cannot be subdivided. Maybe this is what you meant by an "atomic
period".
I defined "atomic period" earlier in this discussion as a
continuous interval that doesn't contain any new information. I'm not
pushing for this vocable by the way, just clarifying what I meant. With
this definitions, frames can live within one atomic period.
Speaking strictly from the point of convention:
- The MDP formalism defines the relationship between States and
Actions ordered by their atomic periods. Because of how this formalism is
defined, the problem at t is isomorphic to the problem at t+1, and there is
not much redundant information. It's a natural way to break the problem
down.
There is an alternative formulation of the Markov property where the
future distribution of of a process can be forecast using (X_t, X_{t-1},
... X_{t-k}) with some finite k. By redefining the states, it can be recast
as a one-period memory process but when formulating a model it is sometimes
easier to refer to states that are not in the immediate past.
- It may be possible to transform an MDP into a different "time-scale"
by aggregating N atomic periods into larger intervals. It's not clear why
anybody would do this.
seasonality for instance. As a modeller you might want to refer to t+1 as
the next quarter, while t+4 would be the next year.
- Time at the sub-atomic level simply does not work in the same way
that it works at the atomic level. It is different because: (a) it is not
totally ordered, and (b) it has no periodic structure--i.e., it is not
repeating itself frame by frame.
I hesitate to assert the following, as it may muddy the waters, but:
"Physical experience" is a bit of an oxymoron. The phenomenology of time is
quite different from the social consensus around it, and indeed if we were
*truly* physicists we concede time to be much more complex than the real
number system (i.e., "space-time"). So I don't think "physical experience"
is solid ground for choice of mathematical formalism in this case.
This is a quite useless comment. By physical experience, I mean day to day
life, not general relativity or Planck units.
I just suspected that if we look at "frames" coming from the splitting of
… one max operation over several argument into several max operators we are
naturally getting ordered frames.
Considering a DAG of variables, as determined by the transition function,
the following will be true:
- There exists at least one valid linear ordering of the variables
based on topological sorting
<https://en.wikipedia.org/wiki/Topological_sorting>.
- If we consider "framings" to be a partitioning of the variables and
each subset in the partition a "frame", there will exist a framing such
that the frames will have a unique topological order.
Do you have one easy characterization of one if the models you are working
on ?
Not yet. Thank you for the prompt to derive one.
The difficulty I have had is that I have not been able to find the
mathematical definition of the classes of models that "Economists find
interesting", in this context. I am now digging for a formal description of
the scope of heterogeneous agent models (HAM), as opposed to ABMs, and
MDPs, but have not found one yet.
My hope is that as the formal constraints crystalize in the software, it
will be expressive enough for me construct such a model.
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What is "F" in this notation?
True.
I see. Yes, seasonality. This case has been quite tricky. My impression of this discussion so far is that there are many equivalent ways to model the seasonality problem, and that the sticking point is computational tractability. My own preference would be, in terms of setting up the model:
But then have the solver and simulator know how to handle these cases intelligently and not waste time on, say, computing what happens if s_(t+1) = s_(t) + 2 because that never happens. I.e., separate the model definition and computational levels of abstraction cleverly.
I will wait at least a decade before trying to debate this point with you further.
Ah. This gets to the heart of the matter. Is there a way to formulate what "usefulness" is? If so, maybe there's a way to programmatically discover the best framings of a particular model. |
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Trying to get at this more directly... suppose you have a problem with several control variables:
I wonder if it matters whether:
Maybe the consumer can only investigate their asset allocations on days that they don't labor. |
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On Fri, Sep 18, 2020, 4:47 PM Sebastian Benthall ***@***.***> wrote:
1. d. in discrete time, one can define natural ("atomic") periods as
intervals [t1, t2[ such that F_t = F_t1 for any t in [t1,t2[ and F_t1 ⊄F_t2
. With these notations, t+1 is "one unit of time later", but does not
necessarily denote the "next" period, as in "the next time information will
be released.
What is "F" in this notation?
The infamous filtration ;-) in other words a sigma-algebra used to measure
information up to date t. In France we usually call it a "tribe" and there
is a recurring joke that most annoying questions in a math seminar can be
answered by "it is a custom of my tribe".
It is the standard mathematical apparatus to define random processes both
in discrete and continuous time.
There is an alternative formulation of the Markov property where the
future distribution of of a process can be forecast using (X_t, X_{t-1},
... X_{t-k}) with some finite k.
True.
seasonality for instance. As a modeller you might want to refer to t+1 as
the next quarter, while t+4 would be the next year.
I see. Yes, seasonality. This case has been quite tricky.
My impression of this discussion so far is that there are many equivalent
ways to model the seasonality problem, and that the sticking point is
computational tractability.
Not necessarily. There is a difference between the modeling language, and
the convention we take and the internal representation. The internal
representation can be a markov chain while the user-facing formalism could
be expressed differently.
My own preference would be, in terms of setting up the model:
- reserve *t* (time, time step) as the natural numbers, scoped such
that the k=1 Markov property holds
- a different variable, such as *c*, be used to represent the number
of time steps within a cyclical superperiod (i.e, c = 4 for four seasons,
where one time step (t) is a season.
- a different variable, such as *s*, advances deterministically as *t*
mod *c*.
But then have the solver and simulator know how to handle these cases
intelligently and not waste time on, say, computing what happens if s_(t+1)
= s_(t) + 2 because that never happens.
I.e., separate the model definition and computational levels of
abstraction cleverly.
Yes it is the kind of of things we need to differentiate physical time and
computational ticks.
This is a quite useless comment.
I will wait at least a decade before trying to debate this point with you
further.
But at that point, interplanetary macroeconomics may be viable and I would
like to revisit the topic.
By then quantum computing might be a thing which will probably allow for
conflicting opinions to be simultaneously true.
Problem is not whether frames are clearly and uniquely defined by
transitions but which set of frames are useful.
Ah. This gets to the heart of the matter.
Is there a way to formulate what "usefulness" is?
No that is to be defined.
It is probably not about simulating a model though but rather about
specifying additional informations to solve it.
… If so, maybe there's a way to programmatically discover the best framings
of a particular model.
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Yes it is this kind of example which could make a difference. Some quick
comments :
- if it's about changing the order of arrival of new information or about
taking all decisions at date t, to me it is a problem of type 1, i.e. about
cycles and about language shortcuts to define and redefine them
- if it's about ignoring selectively some shocks when taking some decisions
it becomes about "decision frames" (I actually like the addition of
"decision" there)
…On Fri, Sep 18, 2020, 5:22 PM Sebastian Benthall ***@***.***> wrote:
And I wanted to have an example in mind where this is not the case. I can
see why it would be the case for some limited information problem though.
In the basic consumption-savings model it is not the case. In fact there
another condition is met that a frame does not loose information w.r.t. its
parent frame. Do you have one easy characterization of one if the models
you are working on ?
Trying to get at this more directly... suppose you have a problem with
several control variables:
- consumption, informed by current market assets
- endogenous labor quantity, informed by an exogenous physical energy
level
- risky asset allocation share, informed by an exogenous and
intermittent selective attention to stock prices.
I wonder if it matters whether:
- (a) these variables are determined in sequential order, each made
with knowledge of the preceding choices, or
- (b) if the variables are determined only in light of the state at
t-1.
Maybe the consumer can only investigate their asset allocations on days
that they don't labor.
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It is getting to the point where it will be possible to implement a general framework for this. I expect it will be viable to work on it soon after #836 is pulled. I'm wondering, from a software design standpoint, how we would like to support this in HARK. My preference would be for this architecture to ultimately be in My understanding is that the status quo is to support the overwriting of the core functionality for custom models in cases like this. See the work of @Mv77 on the new multi-stage portfolio model, this comment from @mnwhite, and the work in PR #832 Recall that the goal for this work is twofold:
I'm somewhat ambivalent between trying to modify the Speaking of #696, I wonder how its experimental approach to dictionary-based model configuration looks in light of the more recent discussions in this thread. While in that experimental PR each state has its own individual transition function--because the dictionary of transition functions uses single variable names as keys--it would also be possible for it to use tuples of variables names as keys, allowing for transition functions that determine multiple variables 'at once'. |
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I'm now trying to figure out a generic data structure for the frame architecture (this is informed by work on #862). @Mv77 wondering if you could weigh in on this especially. I think we have consensus about what a frame is. The question is how to design the implementation so that it elegantly does all the things we want it to do. This is a list of desiderata for what a Frame implementation might have: I have been playing with implementations in terms of the basic data structures that come with Python. But now I'm wondering if we should have a dedicated Frame class that can capture all this information. The other question that's coming up for me is that when listing the variables that a transition function depends on, it needs to distinguish between current time values and previous time values for any referenced model variables. This can be done structurally (i.e., separate lists of variable names for 'now' and previous values) or notationally (i.e., adding 'prev' to indicate a previous value). I can see pros or cons to either approach. I have a prototype implementation ready for your review at PR #865 but it sidesteps these issues, which I do think will matter moving forward. |
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On the data-structure question, my own uninformed prior is that the most future-proof way to do things would be for frames to have their own class. They seem like a complex enough object that at some point in the future you might want to add properties or attributes to it that might not be accommodated by primitive structures without substantial changes. It might also make it more user friendly in the sense of, e.g., knowing that the 'target' is at |
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Thanks @Mv77 that does sound right. The implementations in #865 and #866 don't yet use a dedicated class, but I will move them in that direction. I think we can get the best of both worlds with a sensible constructor. I.e. initialize the Frame with something like
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Just a broader example of what the Frame initialization fragment may look like |
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One point to make here is that "arbitrage equation" is a legacy from the Representative Agent world in which one of the chief cheats is that all optimization solutions are interior solutions for which a first order condition holds. That often will not be true. (Like, in our dcegm tool). So I think I'd advocate replacing "arbitrage" with "optimality" in the above, which allows for the possibility of dcegm-like tools. |
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Roger that. |
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Definition of an objective function that should be maximized by the agent.
Maybe the category should be "objective" or something like that rather than
"optimality". We should consult Pablo on this.
…On Tue, Nov 17, 2020 at 6:50 PM Sebastian Benthall ***@***.***> wrote:
Roger that.
What does 'optimality' refer to in general? A function to be optimized?
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I have another question about the design of frames. Control variables may be subject to bounds that functions of other state variables. https://dolo.readthedocs.io/en/latest/model_specification.html#boundaries In @llorracc 's examples in this thread, which I'm working from, it's not clear where the bounds are specified. My intuition is:
What I'm unclear about is how a frame-specific constraint would impact the complexity of a frame's solution problem, and whether these constraints are any impediment to the composability of frame solutions in backwards induction. |
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The
PerfForesightConsumerTypehas twopoststate_vars:aNrmNowandpLvlNowhttps://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py#L1450
However
pLvlNowis set in getStates():https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py#L1665
...and not in getPostStates(). Rather,
aLvlNowis updated as a poststate in the code:https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py#L1706
Correcting the
poststate_varfield to listaLvlNowinstead ofpLvlNowraises anAttributeError.I guess this is because the class is depending on the automatic initialization of the poststates, to create the attribute.
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