gEconpy. Install them into the same environment before running the cells below:\n",
"\n",
"pip install time_series_transformers\n",
"pip install git+https://github.com/jessegrabowski/pandas-datareader.git@main\n",
"\n",
"time_series_transformers provides the sklearn-style, invertible log and detrend transformers we use to preprocess the data. pandas-datareader pulls the Senegalese national-accounts series straight from the World Bank’s World Development Indicators API (we install from a fork because the upstream package does not yet run under pandas 3).\n",
"| \n", " | Y | \n", "C | \n", "I | \n", "
|---|---|---|---|
| Time | \n", "\n", " | \n", " | \n", " |
| 2020-01-01 | \n", "13374044739200 | \n", "9317054028600 | \n", "5.373646e+12 | \n", "
| 2021-01-01 | \n", "14249242374000 | \n", "9630093933000 | \n", "5.991010e+12 | \n", "
| 2022-01-01 | \n", "14797899753200 | \n", "10000187002300 | \n", "7.010006e+12 | \n", "
| 2023-01-01 | \n", "15427910099900 | \n", "10500062199900 | \n", "7.215624e+12 | \n", "
| 2024-01-01 | \n", "16362926523300 | \n", "10811669266800 | \n", "7.590262e+12 | \n", "
| \n", " | Y | \n", "C | \n", "I | \n", "
|---|---|---|---|
| Time | \n", "\n", " | \n", " | \n", " |
| 2020-01-01 | \n", "-0.033306 | \n", "-0.019595 | \n", "0.014944 | \n", "
| 2021-01-01 | \n", "-0.016471 | \n", "-0.024871 | \n", "0.110304 | \n", "
| 2022-01-01 | \n", "0.007551 | \n", "-0.010507 | \n", "0.107608 | \n", "
| 2023-01-01 | \n", "-0.016181 | \n", "0.004544 | \n", "0.024588 | \n", "
| 2024-01-01 | \n", "0.003663 | \n", "-0.004697 | \n", "-0.086461 | \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 () None \n", " sigma_L () None \n", " sigma_epsilon_A () Positive None \n", " error_sigma_Y () Positive None \n", " error_sigma_C () Positive None \n", " error_sigma_I () Positive 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 \u001b[3;35mNone\u001b[0m \n", " sigma_L \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m \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 Positive \u001b[3;35mNone\u001b[0m \n", " error_sigma_C \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \u001b[3;35mNone\u001b[0m \n", " error_sigma_I \u001b[1m(\u001b[0m\u001b[1m)\u001b[0m Positive \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=[\"Y\", \"C\", \"I\"],\n", " measurement_error=[\"Y\", \"C\", \"I\"],\n", " temporal_aggregation={\"Y\": \"mean\", \"C\": \"mean\", \"I\": \"mean\"},\n", " aggregation_period=4,\n", " mode=\"NUMBA\",\n", " solver=\"gensys\",\n", " use_adjoint_gradients=True,\n", " max_iter=20,\n", ")" ] }, { "cell_type": "code", "execution_count": 11, "id": "ff095f77", "metadata": {}, "outputs": [], "source": [ "# Variable groups for plotting\n", "deep_parameters = list(ss_mod.param_dict.keys())\n", "shock_sigmas = [f\"sigma_{name}\" for name in ss_mod.shock_names]\n", "noise_sigmas = [f\"error_sigma_{name}\" for name in ss_mod.error_states]" ] }, { "cell_type": "markdown", "id": "b308b369", "metadata": {}, "source": [ "## Shaping the data\n", "\n", "The Kalman filter runs on the quarterly grid, so we expand the annual series onto a quarterly index, leaving the three unobserved quarters of each year as `NaN`. `ge.prepare_mixed_frequency_data` does this; `observation_position=\"last\"` places each annual value in the fourth quarter, where the four-quarter cumulator window completes. The filter treats every `NaN`, including the empty quarters, the Hamilton-filter warmup, and the missing early investment figures, as a missing observation and skips the update step." ] }, { "cell_type": "code", "execution_count": 12, "id": "03f62a19", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
| \n", " | Y | \n", "C | \n", "I | \n", "
|---|---|---|---|
| 2023-01-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
| 2023-04-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
| 2023-07-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
| 2023-10-01 | \n", "-0.016181 | \n", "0.004544 | \n", "0.024588 | \n", "
| 2024-01-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
| 2024-04-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
| 2024-07-01 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
| 2024-10-01 | \n", "0.003663 | \n", "-0.004697 | \n", "-0.086461 | \n", "