| \n", " | NAEXKP01USQ652S | \n", "NAEXKP04USQ652S | \n", "NAEXKP02USQ189S | \n", "TOTLQ | \n", "GS10 | \n", "CES0500000003 | \n", "CPIAUCSL | \n", "
|---|---|---|---|---|---|---|---|
| DATE | \n", "\n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " |
| 2024-05-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.48 | \n", "34.89 | \n", "313.140 | \n", "
| 2024-06-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.31 | \n", "35.00 | \n", "313.131 | \n", "
| 2024-07-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.25 | \n", "35.07 | \n", "313.566 | \n", "
| 2024-08-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "3.87 | \n", "35.23 | \n", "314.131 | \n", "
| 2024-09-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "3.72 | \n", "35.33 | \n", "314.851 | \n", "
| 2024-10-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.10 | \n", "35.48 | \n", "315.564 | \n", "
| 2024-11-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.36 | \n", "35.61 | \n", "316.449 | \n", "
| 2024-12-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.39 | \n", "35.68 | \n", "317.603 | \n", "
| 2025-01-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.63 | \n", "35.83 | \n", "319.086 | \n", "
| 2025-02-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "4.45 | \n", "35.93 | \n", "319.775 | \n", "
| \n", " | Y | \n", "I | \n", "C | \n", "L | \n", "w | \n", "r | \n", "
|---|---|---|---|---|---|---|
| Time | \n", "\n", " | \n", " | \n", " | \n", " | \n", " | \n", " |
| 2024-01-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "11.108370 | \n", "3.783503 | \n", "
| 2024-04-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "11.177431 | \n", "4.329314 | \n", "
| 2024-07-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "11.221181 | \n", "3.756799 | \n", "
| 2024-10-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "11.234151 | \n", "3.981176 | \n", "
| 2025-01-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "11.236025 | \n", "2.770449 | \n", "
\\[A_{ss} = 1\\]
\n", "\\[mc_{ss} = 1\\]
\n", "\\[r_{ss} = \\delta - 1 + \\frac{1}{\\beta}\\]
\n", "\\[w_{ss} = - \\left(\\frac{\\alpha}{r_{ss}}\\right)^{- \\frac{\\alpha}{\\alpha - 1}} \\left(\\alpha - 1\\right)\\]
\n", "\\[Y_{ss} = \\left(w_{ss} \\left(- \\frac{w_{ss}}{\\alpha - 1}\\right)^{\\sigma_{L}}\\right)^{\\frac{1}{\\sigma_{C} + \\sigma_{L}}} \\left(- \\frac{r_{ss}}{\\alpha \\delta - r_{ss}}\\right)^{\\frac{\\sigma_{C}}{\\sigma_{C} + \\sigma_{L}}}\\]
\n", "\\[I_{ss} = \\frac{\\alpha \\delta Y_{ss}}{r_{ss}}\\]
\n", "\\[C_{ss} = Y_{ss}^{\\frac{\\left(-1\\right) \\sigma_{L}}{\\sigma_{C}}} \\left(w_{ss}^{\\sigma_{L} + 1} \\left(1 - \\alpha\\right)^{- \\sigma_{L}}\\right)^{\\frac{1}{\\sigma_{C}}}\\]
\n", "\\[K_{ss} = \\frac{\\alpha Y_{ss} mc_{ss}}{r_{ss}}\\]
\n", "\\[L_{ss} = - \\frac{Y_{ss} mc_{ss} \\left(\\alpha - 1\\right)}{w_{ss}}\\]
\n", "\\[U_{ss} = \\frac{\\frac{C_{ss}^{1 - \\sigma_{C}}}{\\sigma_{C} - 1} + \\frac{L_{ss}^{\\sigma_{L} + 1}}{\\sigma_{L} + 1}}{\\beta - 1}\\]
\n", "\\[\\lambda_{ss} = C_{ss}^{- \\sigma_{C}}\\]
\n", "\\[TC_{ss} = - K_{ss} r_{ss} - L_{ss} w_{ss}\\]
\n", "\\[u_{t} = - \\frac{C_{t}^{1 - \\sigma_{C}}}{\\sigma_{C} - 1} - \\frac{L_{t}^{\\sigma_{L} + 1}}{\\sigma_{L} + 1}\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ C_{t}, \\ L_{t}, \\ I_{t}, \\ K_{t}\\right]\\right)\\]
\n", "\\[U_{t} = \\beta U_{t+1} + u_{t}\\]
\n", "\\[C_{t} + I_{t} = K_{t-1} r_{t} + L_{t} w_{t}\\]
\n", "\\[K_{t} = I_{t} - K_{t-1} \\left(\\delta - 1\\right)\\]
\n", "\\[\\beta = 0.99\\]
\n", "\\[\\delta = 0.02\\]
\n", "\\[\\sigma_{C} = 1.5\\]
\n", "\\[\\sigma_{L} = 2.0\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ K_{t-1}, \\ L_{t}\\right]\\right)\\]
\n", "\\[TC_{t} = - K_{t-1} r_{t} - L_{t} w_{t}\\]
\n", "\\[Y_{t} = A_{t} K_{t-1}^{\\alpha} L_{t}^{1 - \\alpha}\\]
\n", "\\[mc_{t} = 1\\]
\n", "\\[\\alpha = 0.35\\]
\n", "\\[\\log{\\left(A_{t} \\right)} = \\rho_{A} \\log{\\left(A_{t-1} \\right)} + \\epsilon_{A t}\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ \\epsilon_{A t}\\right]\\right)\\]
\n", "\\[\\rho_{A} = 0.95\\]
\n", "Model Requirements \n", " \n", " Variable Shape Constraints Dimensions \n", " ──────────────────────────────────────────────────── \n", " alpha () None \n", " beta () None \n", " delta () None \n", " rho_A () None \n", " sigma_C () Positive None \n", " sigma_L () Positive None \n", " sigma_epsilon_A () Positive None \n", " error_sigma_Y () None \n", " error_sigma_I () None \n", " error_sigma_C () None \n", " error_sigma_L () None \n", " error_sigma_w () None \n", " error_sigma_r () None \n", " \n", " These parameters should be assigned priors inside a \n", " PyMC model block before calling the \n", " build_statespace_graph method. \n", "\n" ], "text/plain": [ "\u001b[3m Model Requirements \u001b[0m\n", " \n", " \u001b[1m \u001b[0m\u001b[1mVariable \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mShape\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mConstraints\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDimensions\u001b[0m\u001b[1m \u001b[0m \n", " ──────────────────────────────────────────────────── \n", " alpha \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " beta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " delta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " rho_A \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " sigma_C \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_L \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_epsilon_A \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " error_sigma_Y \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_I \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_C \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_L \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_w \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_r \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " \n", "\u001b[2;3m These parameters should be assigned priors inside a \u001b[0m\n", "\u001b[2;3m PyMC model block before calling the \u001b[0m\n", "\u001b[2;3m build_statespace_graph method. \u001b[0m\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ss_mod.configure(\n", " observed_states=df.columns,\n", " measurement_error=df.columns,\n", " mode=\"JAX\",\n", " solver=\"scan_cycle_reduction\",\n", " use_adjoint_gradients=True,\n", " max_iter=20,\n", ")" ] }, { "cell_type": "code", "execution_count": 22, "id": "5dbe4889", "metadata": { "execution": { "iopub.execute_input": "2025-03-15T12:21:09.330961Z", "iopub.status.busy": "2025-03-15T12:21:09.330885Z", "iopub.status.idle": "2025-03-15T12:21:09.332577Z", "shell.execute_reply": "2025-03-15T12:21:09.332391Z" } }, "outputs": [], "source": [ "# Save some groups of variable names for later\n", "all_params = ss_mod.param_names\n", "deep_params = list(ss_mod.param_dict.keys())\n", "shock_params = [f\"sigma_{name}\" for name in ss_mod.shock_names]\n", "error_params = [f\"error_sigma_{name}\" for name in ss_mod.error_states]" ] }, { "cell_type": "markdown", "id": "dd31e109", "metadata": {}, "source": [ "## Building PyMC model\n", "\n", "The `Model Requirements` table tells us what we need to define. We already have priors for the 6 deep parameters. These can be quickly added using `ss_mod.to_pymc()`. Then we have to define the remaining standard deviations: `sigma_epsilon_A`, `error_sigma_Y`, `error_sigma_I`, `error_sigma_C`, `error_sigma_w`, and `error_sigma_r`. \n", "\n", "The model is log-linearized, so all values are in percentage deviation from steady state. This is nice, because we can think about the errors in percentage terms. We can assume a prior that data are at most 5% off, which implies a standard deviation of at most ~5 (2 * sqrt(5) = 4.47, just round back up to 5). \n", "\n", "Probably that huge, but why not. It's just a prior!" ] }, { "cell_type": "code", "execution_count": 23, "id": "32c9af2c", "metadata": { "execution": { "iopub.execute_input": "2025-03-15T12:21:09.333647Z", "iopub.status.busy": "2025-03-15T12:21:09.333589Z", "iopub.status.idle": "2025-03-15T12:21:09.641580Z", "shell.execute_reply": "2025-03-15T12:21:09.641265Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jessegrabowski/mambaforge/envs/geconpy-dev/lib/python3.12/site-packages/pymc_extras/statespace/utils/data_tools.py:159: ImputationWarning: Provided data contains missing values and will be automatically imputed as hidden states during Kalman filtering.\n", " warnings.warn(impute_message, ImputationWarning)\n" ] } ], "source": [ "with pm.Model(coords=ss_mod.coords) as usa_rbc:\n", " ss_mod.to_pymc()\n", "\n", " # Save the pre-defined priors as a variable we can use to stay organized\n", " prior_dict = ss_mod.param_priors.copy()\n", "\n", " # pz.maxent helps us by finding the distribution in a given family with some percent of total mass between\n", " # two points. Technically infinity distribtuions will satisfy that criteria, so it gives the one with\n", " # maximum entropy. It's much easier to reason about ranges of admissible values than parameters.\n", "\n", " prior_dict[\"sigma_epsilon_A\"] = pz.maxent(pz.Gamma(), lower=0.01, upper=0.1, plot=False)\n", " prior_dict[\"sigma_epsilon_A\"].to_pymc(\"sigma_epsilon_A\")\n", "\n", " # As mentioned above, we'll make the measurement errors between 0% and 5%\n", " for var in ss_mod.error_states:\n", " d = pz.maxent(pz.Gamma(), lower=0.001, upper=0.05, plot=False)\n", " prior_dict[f\"error_sigma_{var}\"] = d\n", " d.to_pymc(f\"error_sigma_{var}\")\n", "\n", " ss_mod.build_statespace_graph(\n", " data=df_detrend[ss_mod.observed_states],\n", " add_norm_check=True,\n", " add_solver_success_check=True,\n", " add_steady_state_penalty=True,\n", " )" ] }, { "cell_type": "code", "execution_count": 24, "id": "ecdd6e30", "metadata": { "execution": { "iopub.execute_input": "2025-03-15T12:21:09.642815Z", "iopub.status.busy": "2025-03-15T12:21:09.642746Z", "iopub.status.idle": "2025-03-15T12:21:10.289526Z", "shell.execute_reply": "2025-03-15T12:21:10.289239Z" } }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "
Sampler Progress
\n", "Total Chains: 6
\n", "Active Chains: 0
\n", "\n", " Finished Chains:\n", " 6\n", "
\n", "Sampling for 6 minutes
\n", "\n", " Estimated Time to Completion:\n", " now\n", "
\n", "\n", "| Progress | \n", "Draws | \n", "Divergences | \n", "Step Size | \n", "Gradients/Draw | \n", "
|---|---|---|---|---|
| \n",
" | \n",
" 1000 | \n", "1 | \n", "0.81 | \n", "3 | \n", "
| \n",
" | \n",
" 1000 | \n", "0 | \n", "0.79 | \n", "7 | \n", "
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" 1000 | \n", "0 | \n", "0.78 | \n", "7 | \n", "
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" 1000 | \n", "0 | \n", "0.76 | \n", "7 | \n", "
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" 1000 | \n", "0 | \n", "0.75 | \n", "7 | \n", "
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" | \n",
" 1000 | \n", "0 | \n", "0.78 | \n", "7 | \n", "
\\[K_{to L ss} = \\left(\\frac{\\alpha A_{ss} mc_{ss}}{r_{ss}}\\right)^{- \\frac{1}{\\alpha - 1}}\\]
\n", "\\[A_{ss} = 1\\]
\n", "\\[shock_{I ss} = 1\\]
\n", "\\[\\beta_{ss} = \\beta\\]
\n", "\\[\\Theta_{ss} = \\Theta\\]
\n", "\\[z_{ss} = 1\\]
\n", "\\[mc_{ss} = 1\\]
\n", "\\[r_{ss} = \\delta - 1 + \\frac{1}{\\beta}\\]
\n", "\\[w_{ss} = - A_{ss} K_{to L ss}^{\\alpha} mc_{ss} \\left(\\alpha - 1\\right)\\]
\n", "\\[L_{ss} = \\left(- \\frac{w_{ss} \\left(1 - \\phi_{H}\\right)^{- \\sigma_{C}} \\left(\\beta \\phi_{H} - 1\\right) \\left(- \\delta K_{to L ss} + A_{ss} K_{to L ss}^{\\alpha}\\right)^{- \\sigma_{C}}}{\\Theta}\\right)^{\\frac{1}{\\sigma_{C} + \\sigma_{L}}}\\]
\n", "\\[K_{ss} = K_{to L ss} L_{ss}\\]
\n", "\\[K_{d ss} = K_{ss} z_{ss}\\]
\n", "\\[Y_{ss} = A_{ss} K_{d ss}^{\\alpha} L_{ss}^{1 - \\alpha}\\]
\n", "\\[I_{ss} = \\delta K_{ss}\\]
\n", "\\[C_{ss} = - I_{ss} + Y_{ss}\\]
\n", "\\[U_{ss} = \\frac{\\frac{C_{ss}^{1 - \\sigma_{C}}}{\\sigma_{C} - 1} + \\frac{L_{ss}^{\\sigma_{L} + 1}}{\\sigma_{L} + 1}}{\\beta - 1}\\]
\n", "\\[\\lambda_{ss} = - \\left(- C_{ss} \\left(\\phi_{H} - 1\\right)\\right)^{- \\sigma_{C}} \\left(\\beta \\phi_{H} - 1\\right)\\]
\n", "\\[q_{ss} = \\lambda_{ss}\\]
\n", "\\[TC_{ss} = - K_{ss} r_{ss} - L_{ss} w_{ss}\\]
\n", "\\[u_{t} = - \\frac{L_{t}^{\\sigma_{L} + 1} \\Theta_{t}}{\\sigma_{L} + 1} - \\frac{\\left(- \\phi_{H} C_{t-1} + C_{t}\\right)^{1 - \\sigma_{C}}}{\\sigma_{C} - 1}\\]
\n", "\\[\\Psi_{z t} = \\frac{\\psi_{z} \\left(z_{t} - 1\\right)^{2}}{2} + \\psi_{z 1} \\left(z_{t} - 1\\right)\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ C_{t}, \\ L_{t}, \\ I_{t}, \\ K_{t}, \\ z_{t}\\right]\\right)\\]
\n", "\\[U_{t} = U_{t+1} \\beta_{t} + u_{t}\\]
\n", "\\[C_{t} + I_{t} + K_{t-1} \\Psi_{z t} = K_{t-1} r_{t} z_{t} + L_{t} w_{t}\\]
\n", "\\[K_{t} = - I_{t} \\left(\\frac{\\gamma_{I} \\left(\\frac{I_{t} shock_{I t}}{I_{t-1}} - 1\\right)^{2}}{2} - 1\\right) - K_{t-1} \\left(\\delta - 1\\right)\\]
\n", "\\[\\log{\\left(\\beta_{t} \\right)} = \\rho_{\\beta} \\log{\\left(\\beta_{t-1} \\right)} + \\epsilon_{\\beta t} - \\left(\\rho_{\\beta} - 1\\right) \\log{\\left(\\beta \\right)}\\]
\n", "\\[\\log{\\left(shock_{I t} \\right)} = \\rho_{I} \\log{\\left(shock_{I t-1} \\right)} + \\epsilon_{I t}\\]
\n", "\\[\\log{\\left(\\Theta_{t} \\right)} = \\rho_{\\Theta} \\log{\\left(\\Theta_{t-1} \\right)} + \\epsilon_{\\Theta t} - \\left(\\rho_{\\Theta} - 1\\right) \\log{\\left(\\Theta \\right)}\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ \\epsilon_{\\beta t}, \\ \\epsilon_{I t}, \\ \\epsilon_{\\Theta t}\\right]\\right)\\]
\n", "\\[\\beta = 0.99\\]
\n", "\\[\\delta = 0.035\\]
\n", "\\[\\sigma_{C} = 3\\]
\n", "\\[\\sigma_{L} = 1.5\\]
\n", "\\[\\Theta = 1.0\\]
\n", "\\[\\gamma_{I} = 6.32\\]
\n", "\\[\\phi_{H} = 0.8\\]
\n", "\\[\\rho_{\\beta} = 0.9\\]
\n", "\\[\\rho_{\\Theta} = 0.9\\]
\n", "\\[\\rho_{I} = 0.9\\]
\n", "\\[\\psi_{z} = 0.169\\]
\n", "\\[\\psi_{z 1} = \\delta - 1 + \\frac{1}{\\beta}\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ K_{d t}, \\ L_{t}\\right]\\right)\\]
\n", "\\[TC_{t} = - K_{d t} r_{t} - L_{t} w_{t}\\]
\n", "\\[Y_{t} = A_{t} K_{d t}^{\\alpha} L_{t}^{1 - \\alpha}\\]
\n", "\\[mc_{t} = 1\\]
\n", "\\[K_{d t} = K_{t-1} z_{t}\\]
\n", "\\[\\alpha = 0.35\\]
\n", "\\[\\log{\\left(A_{t} \\right)} = \\rho_{A} \\log{\\left(A_{t-1} \\right)} + \\epsilon_{A t}\\]
\n", "\\[\\operatorname{Set}\\left(\\left[ \\epsilon_{A t}\\right]\\right)\\]
\n", "\\[\\rho_{A} = 0.95\\]
\n", "Model Requirements \n", " \n", " Variable Shape Constraints Dimensions \n", " ──────────────────────────────────────────────────────── \n", " Theta () None \n", " alpha () None \n", " beta () None \n", " delta () None \n", " gamma_I () None \n", " phi_H () None \n", " psi_z () None \n", " rho_A () None \n", " rho_I () None \n", " rho_Theta () None \n", " rho_beta () None \n", " sigma_C () Positive None \n", " sigma_L () Positive None \n", " sigma_epsilon_A () Positive None \n", " sigma_epsilon_I () Positive None \n", " sigma_epsilon_Theta () Positive None \n", " sigma_epsilon_beta () Positive None \n", " error_sigma_Y () None \n", " error_sigma_I () None \n", " error_sigma_C () None \n", " error_sigma_L () None \n", " error_sigma_w () None \n", " error_sigma_r () None \n", " \n", " These parameters should be assigned priors inside a PyMC \n", " model block before calling the build_statespace_graph \n", " method. \n", "\n" ], "text/plain": [ "\u001b[3m Model Requirements \u001b[0m\n", " \n", " \u001b[1m \u001b[0m\u001b[1mVariable \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mShape\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mConstraints\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDimensions\u001b[0m\u001b[1m \u001b[0m \n", " ──────────────────────────────────────────────────────── \n", " Theta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " alpha \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " beta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " delta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " gamma_I \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " phi_H \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " psi_z \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " rho_A \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " rho_I \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " rho_Theta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " rho_beta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " sigma_C \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_L \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_epsilon_A \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_epsilon_I \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_epsilon_Theta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " sigma_epsilon_beta \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " error_sigma_Y \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_I \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_C \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_L \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_w \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " error_sigma_r \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \u001b[3;35mNone\u001b[0m \n", " \n", "\u001b[2;3m These parameters should be assigned priors inside a PyMC \u001b[0m\n", "\u001b[2;3m model block before calling the build_statespace_graph \u001b[0m\n", "\u001b[2;3m method. \u001b[0m\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ss_mod_extended.configure(\n", " observed_states=df_detrend.columns,\n", " measurement_error=df_detrend.columns,\n", " mode=\"JAX\",\n", " solver=\"scan_cycle_reduction\",\n", " use_adjoint_gradients=True,\n", " max_iter=20,\n", ")" ] }, { "cell_type": "code", "execution_count": 34, "id": "773a0d47", "metadata": { "execution": { "iopub.execute_input": "2025-03-15T12:29:33.141958Z", "iopub.status.busy": "2025-03-15T12:29:33.141889Z", "iopub.status.idle": "2025-03-15T12:29:33.367116Z", "shell.execute_reply": "2025-03-15T12:29:33.366863Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jessegrabowski/mambaforge/envs/geconpy-dev/lib/python3.12/site-packages/pymc_extras/statespace/utils/data_tools.py:159: ImputationWarning: Provided data contains missing values and will be automatically imputed as hidden states during Kalman filtering.\n", " warnings.warn(impute_message, ImputationWarning)\n" ] } ], "source": [ "with pm.Model(coords=ss_mod_extended.coords) as usa_rbc_extended:\n", " ss_mod_extended.to_pymc()\n", "\n", " # Save the pre-defined priors as a variable we can use to stay organized\n", " prior_dict = ss_mod_extended.param_priors.copy()\n", "\n", " for shock in ss_mod_extended.shock_names:\n", " prior_dict[f\"sigma_{shock}\"] = pz.maxent(pz.Gamma(), lower=0.01, upper=0.1, plot=False)\n", " prior_dict[f\"sigma_{shock}\"].to_pymc(f\"sigma_{shock}\")\n", "\n", " # As mentioned above, we'll make the measurement errors between 0% and 5%\n", " for var in ss_mod_extended.error_states:\n", " d = pz.maxent(pz.Gamma(), lower=0.01, upper=0.05, plot=False)\n", " prior_dict[f\"error_sigma_{var}\"] = d\n", " d.to_pymc(f\"error_sigma_{var}\")\n", "\n", " ss_mod_extended.build_statespace_graph(\n", " data=df_detrend[ss_mod_extended.observed_states],\n", " add_norm_check=True,\n", " add_solver_success_check=True,\n", " add_steady_state_penalty=True,\n", " )" ] }, { "cell_type": "code", "execution_count": 35, "id": "cf442d9e", "metadata": { "execution": { "iopub.execute_input": "2025-03-15T12:29:33.368378Z", "iopub.status.busy": "2025-03-15T12:29:33.368300Z", "iopub.status.idle": "2025-03-15T12:29:34.295664Z", "shell.execute_reply": "2025-03-15T12:29:34.295371Z" } }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "
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