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Remove Sphinx cross-references from notebook and docs
Replaced Sphinx-style {ref} cross-references with plain text in code/notebook.ipynb and code/notebook.md for improved compatibility outside Sphinx. Added missing section anchors in content/paper/moderation.md to preserve reference targets. Updated PDF files with corresponding changes.
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code/notebook.ipynb

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"\n",
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"### Figure 1: The EGM Extrapolation Problem\n",
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"\n",
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"The **precautionary saving gap** (optimist minus realist consumption) must be positive: income risk induces additional saving. As {ref}`demonstrated in the paper <benchmark-the-method-of-endogenous-gridpoints>` and shown in [](#fig:egm-extrapolation-problem) ({ref}`Figure 1 <fig:ExtrapProblem>` in the paper), standard EGM violates this constraint when extrapolating {cite:p}`carrollEGM`."
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"The **precautionary saving gap** (optimist minus realist consumption) must be positive: income risk induces additional saving. As demonstrated in the paper and shown in [](#fig:egm-extrapolation-problem), standard EGM violates this constraint when extrapolating {cite:p}`carrollEGM`."
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]
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},
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{
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"5. Interpolate $\\logitModRte(\\logmNrmEx)$ with derivatives\n",
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"6. Reconstruct: $\\cFuncReal = \\cFuncPes + \\modRte \\cdot (\\cFuncOpt - \\cFuncPes)$\n",
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"\n",
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"This ensures bound compliance via asymptotically linear extrapolation, as {ref}`derived in the paper <the-consumption-function>`. HARK uses **cubic Hermite interpolation** {cite:p}`Fritsch1980,FritschButland1984` for accuracy; see {cite:p}`Santos2000,JuddMaliarMaliar2017` on function approximation and error bounding.\n",
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"This ensures bound compliance via asymptotically linear extrapolation, as derived in the paper. HARK uses **cubic Hermite interpolation** {cite:p}`Fritsch1980,FritschButland1984` for accuracy; see {cite:p}`Santos2000,JuddMaliarMaliar2017` on function approximation and error bounding.\n",
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"```\n",
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"\n",
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"```{note} The Transformation\n",

code/notebook.md

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### Figure 1: The EGM Extrapolation Problem
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The **precautionary saving gap** (optimist minus realist consumption) must be positive: income risk induces additional saving. As {ref}`demonstrated in the paper <benchmark-the-method-of-endogenous-gridpoints>` and shown in [](#fig:egm-extrapolation-problem) ({ref}`Figure 1 <fig:ExtrapProblem>` in the paper), standard EGM violates this constraint when extrapolating {cite:p}`carrollEGM`.
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The **precautionary saving gap** (optimist minus realist consumption) must be positive: income risk induces additional saving. As demonstrated in the paper and shown in [](#fig:egm-extrapolation-problem), standard EGM violates this constraint when extrapolating {cite:p}`carrollEGM`.
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```python
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# | label: fig:egm-extrapolation-problem
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5. Interpolate $\logitModRte(\logmNrmEx)$ with derivatives
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6. Reconstruct: $\cFuncReal = \cFuncPes + \modRte \cdot (\cFuncOpt - \cFuncPes)$
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This ensures bound compliance via asymptotically linear extrapolation, as {ref}`derived in the paper <the-consumption-function>`. HARK uses **cubic Hermite interpolation** {cite:p}`Fritsch1980,FritschButland1984` for accuracy; see {cite:p}`Santos2000,JuddMaliarMaliar2017` on function approximation and error bounding.
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This ensures bound compliance via asymptotically linear extrapolation, as derived in the paper. HARK uses **cubic Hermite interpolation** {cite:p}`Fritsch1980,FritschButland1984` for accuracy; see {cite:p}`Santos2000,JuddMaliarMaliar2017` on function approximation and error bounding.
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```
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```{note} The Transformation

content/paper/appendix_letters.pdf

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content/paper/moderation.md

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[^crra-not-one]:
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For notational simplicity, we henceforth assume $\CRRA \neq 1$. Most subsequent derivations involving transformations of the value function (such as $\vInvOpt$ and $\vInvReal$) contain expressions with denominators $(1-\CRRA)$ that are undefined when $\CRRA=1$. The case $\CRRA=1$ (logarithmic utility) requires parallel derivations that exploit the simplifications arising from $\log$ utility; the economic insights remain analogous.
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(benchmark-the-method-of-endogenous-gridpoints)=
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# Benchmark: The Method of Endogenous Gridpoints
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For comparison to our new solution method, we use the endogenous gridpoints
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\end{aligned}
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```
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(the-consumption-function)=
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## The Consumption Function
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It seems obvious that the spending of the realist will be strictly greater than
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