Solving a question with more unknowns than equations
$begingroup$
I am not sure if I am thick in the head or not, but I am trying to replicate this paper: https://www.nber.org/papers/w19086.pdf. The equations characterising the equilibrium are given on Page $22$.
Unfortunately it seems as though there are 7 unknowns but only 6 equations (well I am trying to calculate the steady state, so for any time varying variable $X$ which is time varying $X_{t+1} = X_t = X$ and thats how it becomes only 7 unknowns.)
The unknowns are:
$widetilde{K}, widetilde{Q}, widetilde{C}, widetilde{Y},tau_k,tau_l and L$
I am omitting the time subscripts because I am trying to solve for the steady state, so again, variables are constant through time.
I tried going through the paper again and how we got to the equations but to no avail. I may be missing something super basic here but any help would be great!
ordinary-differential-equations economics steady-state
edited Jan 8 at 9:20
Sauhard Sharma
953318
asked Jan 8 at 7:47
HariharanHariharan
312
$endgroup$
|
show 3 more comments
$begingroup$
I am not sure if I am thick in the head or not, but I am trying to replicate this paper: https://www.nber.org/papers/w19086.pdf. The equations characterising the equilibrium are given on Page $22$.
Unfortunately it seems as though there are 7 unknowns but only 6 equations (well I am trying to calculate the steady state, so for any time varying variable $X$ which is time varying $X_{t+1} = X_t = X$ and thats how it becomes only 7 unknowns.)
The unknowns are:
$widetilde{K}, widetilde{Q}, widetilde{C}, widetilde{Y},tau_k,tau_l and L$
I am omitting the time subscripts because I am trying to solve for the steady state, so again, variables are constant through time.
I tried going through the paper again and how we got to the equations but to no avail. I may be missing something super basic here but any help would be great!
ordinary-differential-equations economics steady-state
edited Jan 8 at 9:20
Sauhard Sharma
953318
asked Jan 8 at 7:47
HariharanHariharan
312
$endgroup$
$begingroup$
What are the unknowns? $K,Q,C,Y$ with subscripts $t$ and $t+1$? which variable are you referring to as $X$?
$endgroup$
– Dylan
Jan 8 at 8:14
$begingroup$
@Dylan Hi, I have edited in some more information into the answers. X is just an example variable, but but it applies to all the variables with the subscript t in the system of equations. I've listed the unknowns above.
$endgroup$
– Hariharan
Jan 8 at 9:05
1
$begingroup$
The variables are normalized, so if you want $Q_{t+1}=Q_t$, wouldn't $widetilde{Q}_{t+1} = frac{Q_{t+1}}{Q_t} = 1$?
$endgroup$
– Dylan
Jan 8 at 9:35
$begingroup$
@Dylan You're a genius. That was quite silly of me! Thanks!
$endgroup$
– Hariharan
Jan 8 at 9:58
1
$begingroup$
Seems to me that $tau_l$ and $tau_k$ are policy instruments. The definition of equilibrium takes them as given. You then look for $tau_l$ and $tau_k$ that solve some objective of the planner/government.
$endgroup$
– Mdoc
Jan 10 at 6:39
|
show 3 more comments
$begingroup$
I am not sure if I am thick in the head or not, but I am trying to replicate this paper: https://www.nber.org/papers/w19086.pdf. The equations characterising the equilibrium are given on Page $22$.
Unfortunately it seems as though there are 7 unknowns but only 6 equations (well I am trying to calculate the steady state, so for any time varying variable $X$ which is time varying $X_{t+1} = X_t = X$ and thats how it becomes only 7 unknowns.)
The unknowns are:
$widetilde{K}, widetilde{Q}, widetilde{C}, widetilde{Y},tau_k,tau_l and L$
I am omitting the time subscripts because I am trying to solve for the steady state, so again, variables are constant through time.
I tried going through the paper again and how we got to the equations but to no avail. I may be missing something super basic here but any help would be great!
ordinary-differential-equations economics steady-state
edited Jan 8 at 9:20
Sauhard Sharma
953318
asked Jan 8 at 7:47
HariharanHariharan
312
$endgroup$
I am not sure if I am thick in the head or not, but I am trying to replicate this paper: https://www.nber.org/papers/w19086.pdf. The equations characterising the equilibrium are given on Page $22$.
Unfortunately it seems as though there are 7 unknowns but only 6 equations (well I am trying to calculate the steady state, so for any time varying variable $X$ which is time varying $X_{t+1} = X_t = X$ and thats how it becomes only 7 unknowns.)
The unknowns are:
$widetilde{K}, widetilde{Q}, widetilde{C}, widetilde{Y},tau_k,tau_l and L$
I am omitting the time subscripts because I am trying to solve for the steady state, so again, variables are constant through time.
I tried going through the paper again and how we got to the equations but to no avail. I may be missing something super basic here but any help would be great!
ordinary-differential-equations economics steady-state
ordinary-differential-equations economics steady-state
edited Jan 8 at 9:20
Sauhard Sharma
953318
asked Jan 8 at 7:47
HariharanHariharan
312
edited Jan 8 at 9:20
Sauhard Sharma
953318
asked Jan 8 at 7:47
HariharanHariharan
312
edited Jan 8 at 9:20
Sauhard Sharma
953318
edited Jan 8 at 9:20
Sauhard Sharma
953318
edited Jan 8 at 9:20
Sauhard Sharma
953318
953318
asked Jan 8 at 7:47
HariharanHariharan
312
asked Jan 8 at 7:47
HariharanHariharan
312
asked Jan 8 at 7:47
HariharanHariharan
312
312
$begingroup$
What are the unknowns? $K,Q,C,Y$ with subscripts $t$ and $t+1$? which variable are you referring to as $X$?
$endgroup$
– Dylan
Jan 8 at 8:14
$begingroup$
@Dylan Hi, I have edited in some more information into the answers. X is just an example variable, but but it applies to all the variables with the subscript t in the system of equations. I've listed the unknowns above.
$endgroup$
– Hariharan
Jan 8 at 9:05
1
$begingroup$
The variables are normalized, so if you want $Q_{t+1}=Q_t$, wouldn't $widetilde{Q}_{t+1} = frac{Q_{t+1}}{Q_t} = 1$?
$endgroup$
– Dylan
Jan 8 at 9:35
$begingroup$
@Dylan You're a genius. That was quite silly of me! Thanks!
$endgroup$
– Hariharan
Jan 8 at 9:58
1
$begingroup$
Seems to me that $tau_l$ and $tau_k$ are policy instruments. The definition of equilibrium takes them as given. You then look for $tau_l$ and $tau_k$ that solve some objective of the planner/government.
$endgroup$
– Mdoc
Jan 10 at 6:39
|
show 3 more comments
$begingroup$
What are the unknowns? $K,Q,C,Y$ with subscripts $t$ and $t+1$? which variable are you referring to as $X$?
$endgroup$
– Dylan
Jan 8 at 8:14
$begingroup$
@Dylan Hi, I have edited in some more information into the answers. X is just an example variable, but but it applies to all the variables with the subscript t in the system of equations. I've listed the unknowns above.
$endgroup$
– Hariharan
Jan 8 at 9:05
1
$begingroup$
The variables are normalized, so if you want $Q_{t+1}=Q_t$, wouldn't $widetilde{Q}_{t+1} = frac{Q_{t+1}}{Q_t} = 1$?
$endgroup$
– Dylan
Jan 8 at 9:35
$begingroup$
@Dylan You're a genius. That was quite silly of me! Thanks!
$endgroup$
– Hariharan
Jan 8 at 9:58
1
$begingroup$
Seems to me that $tau_l$ and $tau_k$ are policy instruments. The definition of equilibrium takes them as given. You then look for $tau_l$ and $tau_k$ that solve some objective of the planner/government.
$endgroup$
– Mdoc
Jan 10 at 6:39
$begingroup$
What are the unknowns? $K,Q,C,Y$ with subscripts $t$ and $t+1$? which variable are you referring to as $X$?
$endgroup$
– Dylan
Jan 8 at 8:14
$begingroup$
What are the unknowns? $K,Q,C,Y$ with subscripts $t$ and $t+1$? which variable are you referring to as $X$?
$endgroup$
– Dylan
Jan 8 at 8:14
$begingroup$
@Dylan Hi, I have edited in some more information into the answers. X is just an example variable, but but it applies to all the variables with the subscript t in the system of equations. I've listed the unknowns above.
$endgroup$
– Hariharan
Jan 8 at 9:05
$begingroup$
@Dylan Hi, I have edited in some more information into the answers. X is just an example variable, but but it applies to all the variables with the subscript t in the system of equations. I've listed the unknowns above.
$endgroup$
– Hariharan
Jan 8 at 9:05
1
1
$begingroup$
The variables are normalized, so if you want $Q_{t+1}=Q_t$, wouldn't $widetilde{Q}_{t+1} = frac{Q_{t+1}}{Q_t} = 1$?
$endgroup$
– Dylan
Jan 8 at 9:35
$begingroup$
The variables are normalized, so if you want $Q_{t+1}=Q_t$, wouldn't $widetilde{Q}_{t+1} = frac{Q_{t+1}}{Q_t} = 1$?
$endgroup$
– Dylan
Jan 8 at 9:35
$begingroup$
@Dylan You're a genius. That was quite silly of me! Thanks!
$endgroup$
– Hariharan
Jan 8 at 9:58
$begingroup$
@Dylan You're a genius. That was quite silly of me! Thanks!
$endgroup$
– Hariharan
Jan 8 at 9:58
1
1
$begingroup$
Seems to me that $tau_l$ and $tau_k$ are policy instruments. The definition of equilibrium takes them as given. You then look for $tau_l$ and $tau_k$ that solve some objective of the planner/government.
$endgroup$
– Mdoc
Jan 10 at 6:39
$begingroup$
Seems to me that $tau_l$ and $tau_k$ are policy instruments. The definition of equilibrium takes them as given. You then look for $tau_l$ and $tau_k$ that solve some objective of the planner/government.
$endgroup$
– Mdoc
Jan 10 at 6:39
|
show 3 more comments
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3065901%2fsolving-a-question-with-more-unknowns-than-equations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3065901%2fsolving-a-question-with-more-unknowns-than-equations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
What are the unknowns? $K,Q,C,Y$ with subscripts $t$ and $t+1$? which variable are you referring to as $X$?
$endgroup$
– Dylan
Jan 8 at 8:14
$begingroup$
@Dylan Hi, I have edited in some more information into the answers. X is just an example variable, but but it applies to all the variables with the subscript t in the system of equations. I've listed the unknowns above.
$endgroup$
– Hariharan
Jan 8 at 9:05
1
$begingroup$
The variables are normalized, so if you want $Q_{t+1}=Q_t$, wouldn't $widetilde{Q}_{t+1} = frac{Q_{t+1}}{Q_t} = 1$?
$endgroup$
– Dylan
Jan 8 at 9:35
$begingroup$
@Dylan You're a genius. That was quite silly of me! Thanks!
$endgroup$
– Hariharan
Jan 8 at 9:58
1
$begingroup$
Seems to me that $tau_l$ and $tau_k$ are policy instruments. The definition of equilibrium takes them as given. You then look for $tau_l$ and $tau_k$ that solve some objective of the planner/government.
$endgroup$
– Mdoc
Jan 10 at 6:39