Fix continuous DiD tutorial formatting

docs/tutorials/14_continuous_did.ipynb

@@ -301,8 +301,8 @@
    "source": [
     "### Interpreting the dose-response curves\n",
     "\n",
-    "- **Left panel (ATT):** The total effect of training rises roughly linearly with dose, closely tracking the true curve (dashed). A worker with 3 hours of training gains about $7 in earnings; a worker with 5 hours gains about $11.\n",
-    "- **Right panel (ACRT):** The marginal return to one additional hour is approximately constant at $2, matching the true DGP. The confidence band is wider at extreme doses where fewer workers are observed.\n",
+    "- **Left panel (ATT):** The total effect of training rises roughly linearly with dose, closely tracking the true curve (dashed). A worker with 3 hours of training gains about \\$7 in earnings; a worker with 5 hours gains about \\$11.\n",
+    "- **Right panel (ACRT):** The marginal return to one additional hour is approximately constant at \\$2, matching the true DGP. The confidence band is wider at extreme doses where fewer workers are observed.\n",
     "\n",
     "These curves require the **strong parallel trends** assumption. Under standard PT only, the overall binarized effect is identified — this is ATT_loc (the local average across dose groups). The dose-response curve and ACRT_glob are not identified under standard PT because they involve cross-dose comparisons and counterfactual dose-response derivatives. The ATT_glob reported by the estimator is mechanically the binarized DiD: under standard PT it equals ATT_loc, while under strong PT it additionally equals the global average ATT_glob."
    ]
@@ -563,7 +563,13 @@
    "cell_type": "markdown",
    "id": "a5230e69",
    "metadata": {},
-   "source": "## 7. Comparison to Binary DiD\n\nWhat if we ignore dose entirely and just run a standard binary Callaway-Sant'Anna estimator? Both approaches should give a similar **binarized ATT** (treated vs. untreated), but the binary approach discards all dose information — no dose-response curve, no marginal effects.\n\nNote: both estimators compute the binarized ATT by aggregating group-time effects, so the values should be very close. Under standard PT this identifies ATT_loc (the local average); under strong PT it additionally equals ATT_glob. Any small differences arise from weighting or aggregation choices, control group or base period settings, or finite-sample variation — not from spline smoothing. The continuous approach provides the full dose-response curve on top of the binarized effect."
+   "source": [
+    "## 7. Comparison to Binary DiD\n",
+    "\n",
+    "What if we ignore dose entirely and just run a standard binary Callaway-Sant'Anna estimator? Both approaches should give a similar **binarized ATT** (treated vs. untreated), but the binary approach discards all dose information — no dose-response curve, no marginal effects.\n",
+    "\n",
+    "Note: both estimators compute the binarized ATT by aggregating group-time effects, so the values should be very close. Under standard PT this identifies ATT_loc (the local average); under strong PT it additionally equals ATT_glob. Any small differences arise from weighting or aggregation choices, control group or base period settings, or finite-sample variation — not from spline smoothing. The continuous approach provides the full dose-response curve on top of the binarized effect."
+   ]
   },
   {
    "cell_type": "code",
@@ -621,10 +627,15 @@
     "    ax.legend()\n",
     "\n",
     "    plt.tight_layout()\n",
-    "    plt.show()\n",
-    "\n",
-    "    print(\"The red dashed line (binary DiD) collapses the entire dose-response curve\")\n",
-    "    print(\"into a single number, losing the relationship between dose and effect.\")"
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "s8qmrof6v0f",
+   "metadata": {},
+   "source": [
+    "The red dashed line (binary DiD) collapses the entire dose-response curve into a single number, losing the relationship between dose and effect."
    ]
   },
   {
@@ -704,4 +715,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}