Heterogeneity and the Macro-Economic Effects of Changes in Loan-to-Value Limits
What this paper finds — and why it matters
Layer 1 — Overview
Research Question
De Veirman and de Jong develop a new approach to estimating the macroeconomic effects of changes in regulatory loan-to-value (LTV) limits on mortgage loans. The central questions are: (1) how do changes in an LTV cap translate into changes in the average LTV and, through that channel, into house prices and real output; and (2) how do heterogeneity in the cross-sectional LTV distribution, non-linearity, and asymmetry shape those effects?
Motivation and Gap
Prior empirical literature on macroprudential LTV policy typically pools across countries using coded indicator variables, which imposes the restriction that all LTV policy actions have the same effect regardless of the size of the change or the position of the limit relative to the distribution. Standard TANK models with homogeneous borrowers imply either full symmetry or threshold asymmetry precisely at the point where the constraint ceases to bind. The authors are the first to relate borrower heterogeneity to non-linearity and asymmetry in LTV policy effects.
Data and Setting
The empirical application focuses on the Netherlands, which introduced an LTV cap of 106 percent on August 1, 2011, subsequently reduced in annual one-percentage-point steps to 100 percent by January 2018. Cross-sectional LTV distributions are constructed from the De Nederlandsche Bank Loan Level Data (LLD), covering 77-81 percent of outstanding Dutch mortgage debt in 2012Q4-2014Q4, restricted to borrowers aged 35 or younger as a proxy for first-time buyers. A survey-based average LTV series spanning 1979-2015 was fielded in January 2016 across the CentERpanel and LISS panel (7,943 respondents combined; 2,238 usable observations after cleaning), measuring LTV at the time of first home purchase. This survey-based annual LTV series, together with the log relative house price, log real GDP, and the real mortgage rate, forms a four-variable Vector Error Correction Model (VECM) estimated over 1981-2015, with a single cointegrating vector identified by Johansen maximum likelihood.
Methodology
The authors’ core innovation is to translate changes in the LTV cap into changes in the cross-sectional average LTV by applying each successive cap level to the underlying distribution: observations above the cap are moved to the cap value (with adjustments for exceptions in the ex post variant). These implied annual changes in the average LTV serve as a succession of impulses fed into the VECM. Two variants are implemented: an ex ante approach using only the pre-cap 2010M8-2011M7 distribution, and an ex post approach that uses the most recent empirical distribution prior to each cap change. The Cholesky identification ordering is [LTV, house prices, GDP, mortgage rate].
Main Findings with Quantitative Magnitudes
Non-trivial macroeconomic effects of Dutch LTV policy: Under the ex post approach (the preferred estimate), the imposition of the cap at 106 percent in 2011 and its gradual reduction to 100 percent by 2018 imply, twenty years after the first shock, that relative house prices are 4.84 percent lower and real GDP is 1.15 percent lower than they would have been in the absence of the cap sequence. The bulk of these responses materializes within ten years, at 4.18 percent and 1.05 percent respectively.
Non-linearity: For a given underlying distribution, changes in the cap have progressively larger effects as the cap tightens. In the ex ante approach, the fraction of households constrained by the cap rises from approximately 20 percent at a limit of 105 percent to approximately 40 percent at a limit of 100 percent. A 10 percentage point tightening from 110 to 100 percent implies a long-run relative house price response of 6.12 percent, while a tightening from 100 to 90 percent implies a response of 14.27 percent — a pronounced non-linearity traceable to the substantial mass of observations in the 90-110 range of the Dutch distribution.
Heterogeneity matters substantially: In mean-preserving comparisons using Pearson-family approximations to the pre-cap Dutch distribution, the macroeconomic effects of the actual Dutch LTV policy sequence are 2.58 times larger in the high standard deviation case (standard deviation 25 percent above the Dutch baseline of 17.09) than in the low standard deviation case (standard deviation 25 percent below). Specifically, twenty-year house price responses are 12.34 percent (high SD) versus 4.79 percent (low SD), and GDP responses are 2.93 percent versus 1.14 percent.
Asymmetry is conditional on the position of the cap relative to the distribution: For the Dutch distribution, symmetry is a good approximation for LTV limits at around 80 percent or lower, where the cap is binding for the bulk of households. Asymmetry is pronounced for higher levels. At an initial cap of 100 percent, the absolute effect of a ten-percentage-point tightening is 2.33 times that of a ten-percentage-point loosening. At 80 percent, the asymmetry ratio is only 1.17. Tightenings have smaller effects when they start from a point where few households are constrained; conversely, loosenings can have larger effects when starting from a point where many are constrained.
Homogeneity assumption understates effects above the mean LTV: Under the homogeneous-borrower benchmark (all borrowers at the Dutch mean of 93.72 percent), asymmetry is infinite at cap levels of 100 and 95 percent but zero at other levels — a feature that causes effects to be entirely absent for caps above the mean. In the heterogeneous Dutch setting, an increase in the LTV limit from 95 to 105 percent raises house prices by 10.72 percent in the long run; the homogeneous case implies no effect at all.
Scope Conditions and Caveats
The paper does not address welfare or financial stability effects. The VECM impulse responses do not establish economic causality. Anticipation effects — if households front-loaded high-LTV purchases before the cap — would cause the procedure to overstate the effect. The LTI robustness check (which smooths the loan-to-income ratio due to noisy survey responses) yields twenty-year responses of 3.32 percent (house prices) and 0.74 percent (GDP), somewhat lower than the baseline, indicating that not controlling for LTI tends to overstate the LTV-macroeconomy connection. The approach requires a usable pre-cap or recent-prior LTV distribution; it is not directly portable to settings where a loosening is studied and no recent pre-cap distribution is available.
Layer 2 — Q&A
Q1: What is the fundamental identification challenge this paper faces, and how does the proposed approach address it?
A: The standard challenge is that LTV caps are changed infrequently and have no long time series suitable for regression, so panel studies typically pool countries and use coded dummy variables that impose size-independence of effects. The authors bypass this by using the cross-sectional LTV distribution itself: they measure how each cap level would truncate the underlying distribution and track the implied change in the cross-sectional mean LTV, which is then fed as a shock into a time-series VECM. This approach does not require the cap to have been in place previously, imposes no cross-country coefficient restrictions, and explicitly accounts for the size of the policy change.
Q2: What are the ex ante and ex post approaches to translating cap changes into average LTV changes, and how do their cumulative estimates differ?
A: The ex ante approach applies all successive cap levels to the single pre-cap distribution of 2010M8-2011M7 (after correcting for the June 2011 sales-tax reduction from 6 to 2 percent), without allowing for exceptions. The ex post approach uses the most recent empirical distribution prior to each cap change and accounts for the observed share of borrowers above the cap as exceptions. The ex ante approach yields a cumulative decline in the average LTV of 3.08 percentage points over 2011-2018; the ex post approach yields 1.96 percentage points, roughly one percentage point less. The difference is largely concentrated in 2011-2012 and stems from the ex ante approach not accounting for exceptions to the cap.
Q3: How does the paper correct for the coincident 2011 sales-tax reduction, and why does this matter?
A: In June 2011, the Dutch sales tax on housing purchases fell from 6 to 2 percent, approximately coinciding with the August 2011 imposition of the LTV cap. Without correction, the observed drop in high LTVs in the 106-cap period would conflate the two policy changes. The authors apply a tiered correction: LTVs at or below 100 percent are left unchanged (the data show no notable change in that range); LTVs between 100 and 110 percent are reduced proportionally to the share of total closing costs attributable to the tax; LTVs at or above 110 percent are reduced by the full magnitude of the tax decline. This yields the “tax-adjusted pre-cap distribution” with a mean of 93.72 percent, down from 94.46 percent in the unadjusted data.
Q4: Why does the fraction of constrained households matter so much, and how does it drive non-linearity?
A: The key mechanism is that the average LTV changes when and only when the cap binds for a given borrower. The larger the share of borrowers whose LTV (in the counterfactual uncapped distribution) would exceed the cap, the larger the share of individual LTVs that move in lockstep with any change in the cap, and therefore the larger the aggregate average LTV response and, through the VECM, the house price and GDP response. As the Dutch cap tightened from 105 to 100 percent, the constrained fraction rose from roughly 20 percent to roughly 40 percent, and the annual implied decline in the average LTV grew from 22 basis points to 42 basis points — illustrating monotonically increasing non-linearity within the ex ante approach.
Q5: How does the survey design address the risk of selection bias relative to alternative data sources such as the American Housing Survey?
A: The survey, fielded in January 2016 across both the CentERpanel and LISS panel, asks retrospectively about respondents’ first home purchase, irrespective of whether they still reside there. This avoids the selection bias in the American Housing Survey, where the first-time-buyer flag captures only those still living in the first home — disproportionately selecting homes that are traded less frequently. A single-wave design also avoids the methodological discontinuities that arise from combining multiple survey waves. The resulting series covers 2,238 observations over 1979-2015 (average 60.49 per year).
Q6: What does the VECM cointegration evidence suggest about the long-run relationship between LTV, house prices, GDP, and the real mortgage rate?
A: Augmented Dickey-Fuller tests do not reject a unit root in any of the four series in levels, while all four are stationary in first differences (with the borderline case of log relative house price inflation when an intercept is included). Both the Johansen L-Max and Trace tests reject no cointegration at the 1 percent level, and neither test indicates more than one cointegrating vector. The authors therefore estimate a single-cointegrating-vector VECM with one lag (selected by the Schwarz Information Criterion) over 1981-2015. The long-run relation is normalized so that the coefficient on the log relative house price is one.
Q7: What do the impulse responses in the baseline VECM specification imply for the long-run macro effects of Dutch LTV policy?
A: Under the preferred ex post approach, twenty years after the first shock in 2011 the VECM implies that relative house prices are 4.84 percent lower and real GDP is 1.15 percent lower than the no-cap counterfactual. The bulk of the response materializes within ten years, with house prices 4.18 percent lower and GDP 1.05 percent lower at the ten-year horizon. The twenty-year real mortgage rate response is positive but negligibly small. When the ex ante approach is used instead, responses are larger owing to the larger cumulative LTV impulse.
Q8: How does the paper conduct the mean-preserving heterogeneity exercise, and what are the key quantitative results?
A: The authors generate Pearson-family distributions that match the first four moments of the Dutch pre-cap distribution (mean 93.72, standard deviation 17.09, skewness -1.16, kurtosis 5.97 under the convention that a normal has kurtosis 3), truncated to support (0, 200]. Two alternative distributions are constructed with standard deviations 25 percent below (12.97) and 25 percent above (21.61) the Pearson proxy, holding mean, skewness, and kurtosis constant. The same VECM and Cholesky ordering are applied. Twenty-year house price responses are 12.34 percent (high SD), 8.46 percent (Pearson proxy), and 4.79 percent (low SD). Twenty-year GDP responses are 2.93, 2.01, and 1.14 percent respectively. The ratio of high-to-low-SD responses is 2.58 for both variables.
Q9: How does asymmetry vary across different initial levels of the LTV cap for the Dutch distribution, and what is the intuition?
A: At a starting cap of 100 percent, a ten-percentage-point tightening produces a long-run house price response 2.33 times larger (in absolute value) than a ten-percentage-point easing from the same starting point. At 80 percent the asymmetry ratio falls to 1.17, meaning the effects of tightening and easing are nearly symmetric. The intuition is that at 80 percent the cap is binding for the bulk of the distribution, so both tightenings and easings move a similarly large fraction of borrowers and have large, roughly comparable effects. At 100 percent, far fewer borrowers are currently constrained, so an easing from 100 to 110 moves almost no one whereas a tightening from 100 to 90 moves substantially more.
Q10: What does the comparison of the heterogeneous-borrower and homogeneous-borrower cases reveal about the implications for TANK and HANK models?
A: Under the homogeneous benchmark — all borrowers at the mean Dutch LTV of 93.72 percent — changes in the cap produce infinite asymmetry at cap levels of 100 and 95 percent (tightening has a full effect, easing has zero effect) but zero asymmetry and zero effect for any cap level above 95 percent. For example, an increase in the cap from 95 to 105 percent has no effect in the homogeneous case but raises house prices by 10.72 percent in the heterogeneous case. In sum, homogeneous-borrower models — including TANK frameworks and linearized models with always-binding constraints such as Iacoviello (2005) — overstate asymmetry in a narrow range around the mean LTV and simultaneously understate the effects of cap changes above the mean LTV. The results are more consistent with heterogeneous-agent frameworks, though the authors note they are not aware of any existing HANK paper that investigates asymmetry and non-linearity specifically in response to changes in the borrowing limit.
Q11: What do the robustness checks show about sensitivity of results to LTV measurement choices?
A: The results are robust to all alternative Cholesky orderings, to using the real mortgage rate computed as the nominal rate minus current (rather than two-year moving average) inflation, to using the computed LTV without cross-checking, and to using the directly reported LTV after cross-checking. The most notable alternative is the directly reported LTV without cross-checking, which yields a twenty-year house price response of 3.81 percent and a GDP response of 0.72 percent (ex post approach), somewhat lower than the baseline of 4.84 and 1.15 percent but in the same direction. A further robustness check using an LTV series that extrapolates 2011-2015 values from the Loan Level Data yields larger estimates (cumulative twenty-year house price response of 6.65 percent and GDP response of 1.40 percent), reflecting the LLD series’ more moderate drop in 2014.
Q12: What is the policy implication regarding the importance of distributional information for gauging LTV policy effects?
A: The results imply that knowing the mean of the LTV distribution is not sufficient for estimating the effects of cap changes: the variance — and specifically the fraction of borrowers constrained by the cap — is critical. This is analogous in spirit to the finding of Krueger, Mitman, and Perri (2016) that matching the tails of the wealth distribution, and not just the mean, is essential for determining the aggregate consumption effects of shocks. Existing empirical literature that focuses on the first moment of the LTV distribution will therefore systematically mismeasure the macro effects of LTV limits, and the direction of the bias depends on where the cap stands relative to the distribution.
Key Concepts
Loan-to-value (LTV) cap / limit: The regulatory maximum on the ratio of total mortgage loan amount to the purchase price of the property (excluding buyer-incurred closing costs such as sales taxes and notary fees). In the Netherlands, this was set at 106 percent from August 2011 and reduced annually by one percentage point to 100 percent by January 2018. The paper explicitly distinguishes the cap (the regulatory threshold) from the average LTV (the cross-sectional mean of the distribution, which the cap may or may not bind for all borrowers).
Underlying (or pre-cap) LTV distribution: The cross-sectional distribution of LTV ratios that would prevail in the absence of any LTV cap — approximated in the paper by the empirical distribution in the twelve months before the cap was introduced (2010M8-2011M7, adjusted for the June 2011 sales-tax cut). The shape, mean, and variance of this distribution determine the fraction of borrowers who are constrained by any given cap level and therefore govern the magnitude and symmetry of policy effects.
Mean-preserving change in heterogeneity: A change in the standard deviation of the LTV distribution that holds the mean (and, in the paper’s stylized scenarios, also the skewness and kurtosis) constant. The paper uses this construct to isolate the effect of dispersion per se on the macroeconomic consequences of cap changes, showing that a 25 percent increase in the standard deviation relative to the Dutch baseline more than doubles the macro effects relative to a 25 percent decrease.
Ex ante approach: The method of translating cap changes into average LTV changes that uses only the pre-cap distribution, applying successive cap levels to that single distribution. It does not require an LTV cap to have been in place and is therefore applicable for prospective analysis. It does not account for exceptions to the cap.
Ex post approach: The method that uses the most recent empirical LTV distribution preceding each cap change as the proxy for the counterfactual uncapped distribution, and that explicitly accounts for the observed share of borrowers above the cap (treated as exceptions). Preferred by the authors when feasible because it incorporates information about how the underlying distribution has evolved for reasons unrelated to the current cap change.
Asymmetry ratio: The ratio of the absolute value of the long-run house price (or GDP) response to a ten-percentage-point tightening in the cap to the absolute value of the response to a ten-percentage-point easing from the same initial cap level. A ratio exceeding one indicates that tightenings have larger effects than easings of equal magnitude from the same starting point. In the paper, this ratio is shown to depend critically on where the initial cap sits relative to the underlying distribution.
Non-linearity in LTV effects: The property that changes in the cap from a lower starting point have larger macroeconomic effects than changes from a higher starting point, for a given underlying distribution. This arises because the fraction of constrained borrowers increases as the cap is tightened, so a further tightening moves a larger share of individual LTVs. In the paper, this is documented through the increasing year-on-year effects in Table 1 and the large difference between the house price response to a tightening from 110 to 100 percent (6.12 percent) versus from 100 to 90 percent (14.27 percent).
Pearson system (as used in this paper): A parametric family of distributions in which every combination of the first four moments (mean, variance, skewness, kurtosis) corresponds to a unique distribution. The authors use it to construct smooth approximations to the empirical Dutch distribution with the same mean, skewness, and kurtosis but varying standard deviations, enabling a controlled comparison of heterogeneity scenarios.