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"# 10 · Economics and Econometrics\n",
"\n",
"Economists use Python to test theories against data and to forecast. **statsmodels** provides the\n",
"econometric toolkit (regression with proper standard errors, time-series models, statistical tests) on\n",
"top of pandas. This module works with fifty years of US macroeconomic data.\n",
"\n",
"**You will learn**\n",
"1. Turning levels into growth rates and handling quarterly dates\n",
"2. Testing an economic law with regression: Okun's law (output and unemployment)\n",
"3. Reading a regression honestly: coefficients, confidence intervals, robust standard errors, residual checks\n",
"4. Forecasting GDP growth with an ARIMA model, and checking it against naive forecasts with a proper backtest"
]
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"## 1. The data\n",
"`macrodata` ships with statsmodels: US quarterly series from 1959 to 2009, including real GDP, the\n",
"unemployment rate, inflation and interest rates."
]
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"::\n",
" Number of Observations - 203\n"
]
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"\n",
"\n",
"
\n",
" \n",
" \n",
" realgdp \n",
" unemp \n",
" infl \n",
" tbilrate \n",
" \n",
" \n",
" \n",
" \n",
" 2008Q3 \n",
" 13324.600 \n",
" 6.0 \n",
" -3.16 \n",
" 1.17 \n",
" \n",
" \n",
" 2008Q4 \n",
" 13141.920 \n",
" 6.9 \n",
" -8.79 \n",
" 0.12 \n",
" \n",
" \n",
" 2009Q1 \n",
" 12925.410 \n",
" 8.1 \n",
" 0.94 \n",
" 0.22 \n",
" \n",
" \n",
" 2009Q2 \n",
" 12901.504 \n",
" 9.2 \n",
" 3.37 \n",
" 0.18 \n",
" \n",
" \n",
" 2009Q3 \n",
" 12990.341 \n",
" 9.6 \n",
" 3.56 \n",
" 0.12 \n",
" \n",
" \n",
"
\n",
"
"
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"\n",
"\n",
"
\n",
" \n",
" \n",
" gdp_growth \n",
" unemp \n",
" d_unemp \n",
" infl \n",
" \n",
" \n",
" \n",
" \n",
" count \n",
" 202.00 \n",
" 202.00 \n",
" 202.00 \n",
" 202.00 \n",
" \n",
" \n",
" mean \n",
" 3.10 \n",
" 5.89 \n",
" 0.02 \n",
" 3.98 \n",
" \n",
" \n",
" std \n",
" 3.52 \n",
" 1.46 \n",
" 0.34 \n",
" 3.25 \n",
" \n",
" \n",
" min \n",
" -8.28 \n",
" 3.40 \n",
" -0.90 \n",
" -8.79 \n",
" \n",
" \n",
" 25% \n",
" 1.34 \n",
" 4.90 \n",
" -0.20 \n",
" 2.28 \n",
" \n",
" \n",
" 50% \n",
" 3.06 \n",
" 5.65 \n",
" 0.00 \n",
" 3.24 \n",
" \n",
" \n",
" 75% \n",
" 5.09 \n",
" 6.80 \n",
" 0.10 \n",
" 4.98 \n",
" \n",
" \n",
" max \n",
" 15.43 \n",
" 10.70 \n",
" 1.60 \n",
" 14.62 \n",
" \n",
" \n",
"
\n",
"
"
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"fig, ax = plt.subplots(1, 2, figsize=(11, 3.8))\n",
"ax[0].scatter(df[\"gdp_growth\"], df[\"d_unemp\"], s=10, alpha=.6)\n",
"xs = np.linspace(df[\"gdp_growth\"].min(), df[\"gdp_growth\"].max(), 50)\n",
"ax[0].plot(xs, alpha + beta * xs, color=\"#ef4444\"); ax[0].set_xlabel(\"GDP growth, % ann.\"); ax[0].set_ylabel(\"change in unemployment\")\n",
"ax[0].set_title(\"Okun's law, 1959-2009\")\n",
"resid = okun.resid\n",
"sm.graphics.tsa.plot_acf(resid, lags=12, ax=ax[1]); ax[1].set_title(\"residual autocorrelation\")\n",
"plt.tight_layout(); plt.show()"
]
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"The relationship is strong and the sign is exactly what theory predicts. The residuals are autocorrelated\n",
"(unemployment adjusts over several quarters), which is why the standard errors above are HAC\n",
"(heteroskedasticity- and autocorrelation-consistent): ordinary errors would overstate the precision.\n",
"\n",
"**Is the law stable over time?** A quick check: estimate it on each decade separately."
]
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"\n",
"\n",
"
\n",
" \n",
" \n",
" beta \n",
" ci_low \n",
" ci_high \n",
" quarters \n",
" \n",
" \n",
" decade \n",
" \n",
" \n",
" \n",
" \n",
" 1960s \n",
" -0.045 \n",
" -0.064 \n",
" -0.026 \n",
" 40 \n",
" \n",
" \n",
" 1970s \n",
" -0.060 \n",
" -0.084 \n",
" -0.035 \n",
" 40 \n",
" \n",
" \n",
" 1980s \n",
" -0.083 \n",
" -0.103 \n",
" -0.063 \n",
" 40 \n",
" \n",
" \n",
" 1990s \n",
" -0.050 \n",
" -0.076 \n",
" -0.024 \n",
" 40 \n",
" \n",
" \n",
" 2000s \n",
" -0.094 \n",
" -0.124 \n",
" -0.063 \n",
" 39 \n",
" \n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" MAE \n",
" RMSE \n",
" \n",
" \n",
" \n",
" \n",
" ARIMA(1,0,1) \n",
" 1.739 \n",
" 2.347 \n",
" \n",
" \n",
" historical mean \n",
" 1.892 \n",
" 2.691 \n",
" \n",
" \n",
" last value \n",
" 2.132 \n",
" 2.654 \n",
" \n",
" \n",
"
\n",
"
"
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"fit = ARIMA(y, order=(1, 0, 1)).fit()\n",
"fc = fit.get_forecast(8)\n",
"ci = fc.conf_int(alpha=0.2)\n",
"hist = y.iloc[-24:]\n",
"plt.figure(figsize=(10, 3.6))\n",
"plt.plot(range(len(y) - 24, len(y)), hist, label=\"GDP growth\")\n",
"fx = range(len(y), len(y) + 8)\n",
"plt.plot(fx, fc.predicted_mean, color=\"#ef4444\", label=\"ARIMA forecast\")\n",
"plt.fill_between(fx, ci.iloc[:, 0], ci.iloc[:, 1], color=\"#ef4444\", alpha=.2, label=\"80% interval\")\n",
"plt.axhline(0, color=\"grey\", lw=.6); plt.legend(); plt.title(\"Two-year forecast after the 2008-09 recession\"); plt.tight_layout(); plt.show()"
]
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"id": "42a04a08",
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"**Reading it honestly.** ARIMA beats \"repeat the last quarter\", but only modestly beats the historical\n",
"mean: quarterly GDP growth is close to unpredictable from its own past. The forecast after 2009 reverts\n",
"to the average within a few quarters and the interval is wide. Serious macro forecasting adds other\n",
"information (surveys, financial markets, leading indicators), which is exactly what multivariate models\n",
"such as VARs and dynamic factor models in statsmodels are for.\n",
"\n",
"## Libraries worth knowing\n",
"| Area | Libraries |\n",
"|---|---|\n",
"| econometrics, time series | statsmodels, linearmodels (panel data, instrumental variables), arch (volatility) |\n",
"| forecasting | statsmodels, sktime, Darts, Prophet |\n",
"| causal inference | DoWhy, EconML, DoubleML |\n",
"| economic data | pandas-datareader, fredapi (Federal Reserve data), wbgapi (World Bank), sdmx1 (statistical agencies) |\n",
"| quantitative finance | QuantLib, PyPortfolioOpt, vectorbt |\n",
"\n",
"## Exercises\n",
"1. Estimate a Phillips curve: regress the change in inflation on the unemployment rate. Is it stable across decades?\n",
"2. Add lagged GDP growth to the Okun regression (`df[\"gdp_growth\"].shift(1)`). Does R² improve?\n",
"3. Extend the backtest to forecasts four quarters ahead. Does ARIMA still beat the mean?"
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