6 Empirical strategy
The descriptive chapter establishes that there is a rural leverage gap, that it is not composition, and that there is enormous variation in CDE-level rural orientation. The natural research question is whether the gap is a market-structure phenomenon (rural markets are structurally less leverageable) or an intermediary-selection phenomenon (the CDEs that go rural are systematically different from the ones that stay urban).
Both stories are consistent with the descriptive evidence. They have very different policy implications — and a fixed-effects decomposition can distinguish them.
6.1 The measurement framework
Project-level leverage and the implied mobilization ratio are directly observable from the CDFI Fund release:
\Leverage_i \;=\; \frac{\ProjectCost_i}{\QLICI_i} \qquad \Mobilization_i \;=\; \Leverage_i - 1
Note that \Leverage_i \geq 1 by construction — the QLICI is part of the project cost by definition. A leverage of 1 means the project was 100% NMTC-financed (zero private mobilization). A leverage of 3 means each federal dollar pulled in $2 of non-federal capital. The mobilization ratio is the central blended-finance quantity that the OECD, World Bank, Convergence Finance, and ODI report annually but that is rarely directly observed at the project level.
6.2 The layered fixed-effects regressions
We estimate a sequence of OLS specifications, each adding a layer of fixed effects. The unit of observation is the project. The outcome is project-level leverage, winsorized at [1, 20]. The treatment indicator R_i equals 1 if project i is in a non-metropolitan census tract.
| Spec | Equation | Adds |
|---|---|---|
| M0 | L_i = \alpha + \beta R_i + \varepsilon_i | nothing |
| M1 | L_i = \alpha + \beta R_i + \delta_{t(i)} + \varepsilon_i | year FE |
| M2 | L_i = \alpha + \beta R_i + \delta_{t(i)} + \eta_{q(i)} + \varepsilon_i | + QALICB type |
| M3 | L_i = \alpha + \beta R_i + \delta_{t(i)} + \eta_{q(i)} + \mu_{s(i)} + \varepsilon_i | + state |
| M4 | L_i = \alpha + \beta R_i + \delta_{t(i)} + \eta_{q(i)} + \gamma_{c(i)} + \varepsilon_i | + CDE (workhorse) |
where:
- L_i: leverage of project i (winsorized [1, 20])
- R_i \in \{0, 1\}: 1 if non-metro
- \delta_{t(i)}: year fixed effect (a separate intercept for each origination year)
- \eta_{q(i)}: QALICB-type fixed effect (RE / NRE / SPE / CDE)
- \mu_{s(i)}: state fixed effect
- \gamma_{c(i)}: CDE fixed effect (a separate intercept for each of ~600 CDEs)
Standard errors are HC1 for M0–M3 and clustered at the CDE level for M4 — the conservative choice given that \gamma_c absorbs persistent within-CDE error correlation.
6.3 What each fixed effect absorbs
- Year FE (\delta_t): macro credit cycle. The 2008 financial crisis depressed leverage everywhere. Without year FE, if rural deals are over-represented in low-leverage years, the rural coefficient picks that up.
- QALICB-type FE (\eta_q): project type. RE projects stack more leverage than NRE; rural is more NRE-heavy. Without project-type FE, the rural coefficient picks up the composition difference.
- State FE (\mu_s): state-level capital-market depth. New York has deeper capital markets than Mississippi regardless of metro/non- metro.
- CDE FE (\gamma_c): which intermediary deploys the credit. This is the load-bearing fixed effect. If rural-specialist CDEs are systematically less effective at private-capital mobilization than the urban-specialist CDEs, the rural coefficient before CDE FE picks up that organization-level skill difference. CDE FE absorbs it.
The economic content of going M3 → M4 is the decomposition. The shrinkage in \hat\beta from M3 to M4 is the between-CDE selection component. The remaining \hat\beta in M4 is the within-CDE rural penalty — the gap that persists for the same CDE deploying both rural and urban.
6.4 Quantile regression at the median
The OLS specifications target the conditional mean of leverage. Because the leverage distribution has a long right tail (winsorized at 20×, but still heavily right-skewed), the mean is influenced by outlier-ish high-leverage deals. The median is less sensitive. We re-estimate M4 at the conditional median:
Q_{0.5}(L_i \mid X_i) = \alpha + \beta R_i + \delta_{t(i)} + \eta_{q(i)} + \gamma_{c(i)}
6.5 Rural × QALICB-type interaction
To check whether the within-CDE rural penalty differs across project types:
L_i = \alpha + \beta R_i + \sum_{q \in \{NRE, RE, SPE\}} \theta_q (R_i \times \mathbf{1}\{\text{Type}_i = q\}) + \delta_{t(i)} + \gamma_{c(i)} + \varepsilon_i
The \theta_q coefficients tell us how much larger or smaller the rural penalty is for each project type relative to the baseline. From the Chapter 3 figures we expect the largest within-type gap in real estate and the smallest in CDE-to-CDE deals.
6.6 The 20% mandate as a Kleven–Waseem notch
The 20% non-metropolitan deployment statute is, in form, a notch in the Kleven–Waseem (Kleven and Waseem 2013) sense: it imposes a cliff in required behavior. We test whether it binds at the cumulative-deployment level by computing, for each CDE j with at least five QLICI transactions:
s_j = \frac{n_{j,\text{non-metro}}}{n_{j,\text{total}}}
If the mandate is just a paper rule, the cross-CDE distribution of s_j is smooth through 0.20. If it binds, there should be excess mass piling up at exactly s_j = 0.20. The Chetty–Kleven excess-mass estimator (Chetty et al. 2011; Kleven 2016):
B = \int_{0.20-h}^{0.20+h} \left[\hat f(s) - \tilde f(s)\right] ds
where \hat f is the empirical density of s_j and \tilde f is a polynomial fit excluding the \pm h window around 0.20. B > 0 is the excess mass — the share of CDEs bunched at the mandate floor.
6.7 Identification assumptions and limitations
- The fixed-effects strategy is selection on observables within CDE × year × type cells. Within-CDE deal allocation (rural vs. urban) is not random; we are not claiming a causal interpretation of \hat\beta_{M4} in the LATE sense. The decomposition is descriptive but framed economically.
- The fully causal piece — a regression-discontinuity design at the LIC-eligibility cutoff — requires merging in tract-level demographics from the American Community Survey (Imbens and Lemieux 2008). This is a planned extension; a forthcoming version of the paper will add Chapter 6.5 with the metro-vs-non-metro RDD interaction estimate.
- The bunching test addresses one form of the 20% mandate; the realized-deployment-share test we run does not capture binding behavior at the allocation-award stage (which CDFI does not disclose in the public release).