מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 282: how investment responds to unemployment, from OECD and Israeli data
Why. After step 281 the largest open uncertainty is demand. With the same grid, preservation ranges from 35% when autonomous investment collapses as displacement rises to 88% when it holds (step 279). In the model the knob is autonomous_decay. Autonomous planned investment, ι·P·K with ι = 0.034, falls by the share decay × min(1, u/0.2). This step estimates how investment co-moves with unemployment in the data and runs the grid at the estimated value.
Estimates by scripts/investment_v282.py. The data are downloaded in GitHub Actions (.github/workflows/wdi-investment-v282.yml) and archived in data/processed/investment_panel_v282.csv, with the manifest in investment_raw_manifest_v282.json. The simulation is scripts/investment_sim_v282.py, with output in data/processed/investment_sim_v282.json. Illustrative; not a forecast.
Data and method
- Data. World Bank WDI for the 38 OECD members, 1991–2024 (1,292 country-years):
- gross fixed capital formation as a share of GDP; - private gross fixed capital formation (7 countries only, none of them Israel); - unemployment (ILO modelled); - real GDP and real investment.
- Model. Δ(I/Y) on current and lagged Δu, with country and year fixed effects. The cumulative
coefficient is the sum of the two. Standard errors are clustered by country. Israel alone uses Newey–West standard errors with 2 lags.
- Holding output growth fixed. In a recession unemployment rises because output falls. In the
automation scenario unemployment rises while output does not fall. So the relevant coefficient is the one on Δu with current and lagged real GDP growth as controls.
- Mapping to the model. In the base year P·K/Y = 2.0. Full decay therefore removes 0.034 × 2.0 = 6.8
points of GDP of planned investment at 20 points of displacement, that is 0.34 per point. The calibrated decay is −slope / 0.34, capped at 1.5.
Estimates
Change in the investment rate (points of GDP) per point of unemployment, cumulative over two years:
| Specification | Slope (95% CI) | Implied decay |
|---|---|---|
| OECD, unconditional | −0.60 (−0.72 to −0.47) | above 1.5 |
| OECD, holding output growth fixed (central) | −0.43 (−0.64 to −0.23) | 1.27 (0.66 to above 1.5) |
| — from 2000 | −0.42 (−0.66 to −0.18) | 1.23 |
| — excluding 2009 and 2020 | −0.39 (−0.60 to −0.18) | 1.15 |
| — private investment, 7 countries | −0.21 (−0.41 to 0.00) | 0.61 |
| Israel alone, holding output growth fixed, 1993–2024 | −0.67 (−1.29 to −0.05) | above 1.5 (0.15 to above 1.5) |
| Israel interaction, holding output growth fixed, from 2000 | −0.12 (−0.26 to 0.02) | 0.35 |
The accelerator also comes out in the usual range. Real investment rises 2.3% for each 1% of real GDP growth over two years (1.9–2.6), and 2.1% in Israel.
What it shows.
- Investment falls with unemployment even when output does not. In the OECD panel the slope,
holding output growth fixed, is about 0.43 points of investment per point of unemployment. That is more than the model's full slump assumes (0.34).
- Israel is not pinned down. The full Israeli sample points to a strong response. Since 2000, the
Israeli slope is small and not significant. The 1990s combine mass immigration, high unemployment and an investment boom. The Israel interaction's standard error rests on a single cluster and understates the uncertainty.
- Private investment responds less, but only 7 countries have that series.
Results: the grid at the estimated response
| Decay | Symmetric closure: preserved | Fiscal crises | Price level in year 20 | Fixed prices: preserved | Fiscal crises |
|---|---|---|---|---|---|
| 0 (no slump; step 279) | 378 (88%) | 0 | ×1.79 | 277 (64%) | 10 |
| 0.35 (Israel since 2000) | 341 (79%) | 8 | ×1.34 | 277 (64%) | 10 |
| 0.66 (lower CI bound, OECD) | 291 (67%) | 27 | ×1.03 | 277 (64%) | 10 |
| 1.00 (full slump; step 279) | 150 (35%) | 204 | ×0.66 | 250 (58%) | 23 |
| 1.27 (central OECD estimate) | 49 (11%) | 310 | ×0.50 | 213 (49%) | 72 |
| 1.50 | 19 (4%) | 355 | ×0.48 | 190 (44%) | 144 |
The table covers 432 cases. The symmetric closure is from step 279: prices respond to the demand gap, and investment responds to Tobin's q. Under fixed prices the price level does not respond (steps 273–274). All runs complete, and money is conserved in each.
What it shows.
- The estimated response lies near or beyond the model's pessimistic end. That end was an assumption
in step 279; here it is supported by data. The central OECD estimate places the result below the slump.
- The outcome then depends on what happens to prices, and the model has no central bank.
- In the symmetric closure a persistent demand gap pushes prices down by about 3.4% a year. The price level halves over 20 years, the real burden of nominal public debt rises, and most cases end in fiscal crisis. - When the price level is held (fixed prices, which stands in for monetary policy that keeps it stable), the same slump lowers preservation from 64% to 49%. - The gap between 11% and 49% is the role of monetary policy, which the model does not yet contain.
- Productivity still decides. At decay 1.27 with fixed prices, a productivity gain of 1.0 keeps 123
of 144 cases, a gain of 0.5 keeps 82, and a gain of 0.25 keeps 8.
Limits
- This is co-movement, not a causal effect. Even holding output growth fixed, unemployment in the data
rises mostly in downturns, when demand expectations fall. In automation profits rise, which may support investment (the Tobin's q channel). The calibrated decay is closer to an upper bound than to a central causal estimate.
- Gross investment against the model's planned investment. The data measure total gross investment,
including housing and public investment. The model's knob covers only the autonomous part; depreciation and capacity growth keep their own terms.
- Extrapolation. Observed unemployment changes are a few points; the scenario adds 20.
- No monetary policy. The next step is a central-bank rule for the interest rate, with an effective
lower bound, to replace the two extreme price closures.