A small open-economy DSGE model with a mortgage market for Mongolia

Mongolia’s housing and credit markets feature (1) high borrower payment burdens (debt service-to-income [DSTI] near 0.7), (2) substantial government support for mortgage rates and (3) inflation that tends to run above advanced-economy targets. In this environment, the interaction between mortgage design, borrower constraints and open-economy shocks is central for both monetary and macroprudential policies.

We develop a small open-economy (SOE) New Keynesian dynamic stochastic general equilibrium (DSGE) model with a housing sector. Borrowers face both loan-to-value (LTV) and DSTI limits at origination and receive an interest-payment subsidy. Following Greenwald (2018) and Greenwald and Guren (2021), the mortgage block captures prepayment and spread movements that shape monetary-policy transmission through the mortgage credit channel. We augment this with open-economy features (imports/exports, terms of trade, foreign interest rate) and standard nominal rigidities.

The paper makes three contributions. First, we embed a mortgage market structure into a small open-economy model with explicit LTV/DSTI constraints and a calibrated subsidy wedge for Mongolia. Second, we quantify policy trade-offs between cutting subsidies and tightening borrower-based tools, alongside standard monetary and external shocks. Third, we propose policy sequencing – scale down subsidies before lowering DSTI limits – to reduce volatility while curbing leverage. The framework is calibrated to Mongolian moments and can be used by the central bank as an ex ante policy laboratory.

A large literature studies how housing collateral and borrower heterogeneity amplify business cycles. Iacoviello (2005) introduces a New Keynesian model with a collateral constraint linking house prices to borrowing. Iacoviello and Neri (2010) estimate a richer version with a separate housing sector, showing that collateral effects propagate to consumption and output. Ingholt (2022) estimates a DSGE with both LTV and DTI/DSTI limits and shows that the binding constraint switches over time with the state of the economy. Greenwald (2018) and Greenwald and Guren (2021) show that mortgage design – fixed rates with prepayment/refinancing and time-varying spreads – critically shapes the monetary transmission mechanism. They also demonstrate that models with only a collateral constraint struggle to match certain housing dynamics, and they introduce a tractable setup with both LTV and DSTI constraints suitable for policy experiments.

This paper is also related to a literature study on SOE models. A classic contribution is Adolfson et al. (2007), which estimates an open-economy DSGE for Sweden. Bahadir and Gumus (2022) use emerging-market data and a two-sector SOE model to show that house-price increases disproportionately lift non-tradable output via collateral-driven demand, with muted effects on tradables.

A substantial body of work finds that borrower-based tools curb leverage and house-price growth with relatively modest output costs. In small or open economies, Alpanda et al. (2018) show that tighter LTV caps are particularly effective at containing household debt. In an estimated model for Hong Kong, Rabanal (2018) attributes sizable reductions in house-price and credit pressures to implemented LTV/DSR rules and housing transaction taxes.

In sum, this paper builds on Greenwald (2018) and Greenwald and Guren (2021), embeds it in a small open economy and introduces mortgage subsidies calibrated to Mongolia. This yields a policy laboratory to study the joint design of monetary, macroprudential and subsidy policies under country-specific constraints.

This model extends the work of Greenwald (2018) to develop an SOE New Keynesian DSGE model.

The economy consists of two types: (representative) borrowers and savers. Borrowers are relatively impatient and denoted with subscript b and savers are relatively patient and denoted with subscript s so that the preference parameters satisfy β_b < β_s. The measure of each type is given by χ_b and χ_s = 1 − χ_b, respectively. The household of type $j∈b,s$ seeks to maximize

where

n_t denotes employment. Z is an exogenous preference shifter.

Under the fixed-rate mortgage contract, the saver gives the borrower $1 at origination. In exchange, the saver receives $$1−vk1−△q,trt+vqt*$ at time t + k, for all k > 0 until prepayment, where r_t is a mortgage interest rate at origination and v is the fraction of principal paid each period. Mortgage loans are prepayable, and a random fraction ρ of households prepay their mortgages.

A new loan for borrower i must satisfy both an LTV and a DSTI constraint:

where $mi,t*$ is the balance on the new loan and θ^LTV and θ^DSTI are the maximum LTV and DSTI ratios, respectively. This constraint is applied at origination of the loan only so that borrowers are not forced to deliver if they violate these constraints later on.

The LTV ratio divides the loan balance by the borrower’s house value, given by the product of house price $pth$ and the quantity of housing purchased $hi,t*$⁠. The key property of the LTV limit is that it moves proportionally with $pth$ so that a rise in house prices loosens this constraint.

For the DSTI ratio, the numerator is the borrower’s initial payment, while the denominator is the borrower’s labor income, equal to the product of the wage w_t, labor supply n_i,t and an idiosyncratic labor efficiency shock e_i,t, drawn i.i.d. across borrowers and time with mean equal to unity and distribution Γ_e. The term α is used to account for taxes and insurance included in DSTI calculations. The offsetting term κ adjusts for the underwriting convention that the numerator of DSTI typically includes payments on all recurring debt (e.g. auto loans, student loans, etc.) by assuming that these payments require a fixed fraction of borrwer income.

Note that $m¯i,tLTV$ and $m¯i,tDSTI$ are the maximum debt balances, for which the inequalities (1) and (2) are satisfied with equality, respectively.

In addition to mortgages, households can trade a one-period nominal bond, whose balances are denoted as b_t. One unit of this bond costs $1 at time t and pays $R_t with certainty at time t+1. This bond is in zero net supply and is used by the monetary authority as a policy instrument. Since the focus of the paper is on mortgage debt, I assume that positions in the one-period bond must be non-negative so that it is traded by savers only at equilibrium.

The final asset in the economy is housing, which produces a service flow each period equal to its stock, and can be owned by both types. A constant fraction δ of house value must be paid as a maintenance cost at the start of each period. Borrower and saver holdings of housing are denoted as h_b,t and h_s,t, respectively. To simplify the analysis, I fix the total housing stock to be $H¯$⁠, which implies that the price of housing fully characterizes the state of the housing market. Additionally, to focus on the use of housing as a collateral asset, I assume that saver demand is fixed at $hs,t,=H¯s$ so that a borrower is always the marginal buyer of housing. Saver demand is fixed for both owned housing and housing services so that borrowers do not rent from savers at equilibrium. Finally, each loan is linked to a specific house so that only prepaying households can adjust their housing holdings.

Taxation. Both types are subject to proportional taxation of labor income at rate τ_y. All taxes are returned in lump sum transfers equal to the amount paid by that type. Borrower interest payments, defined as $r¯B,t−1mi,t−1$⁠, are tax deductible.

Representative borrower’s problem. The borrower’s problem conveniently aggregates to that of a single representative borrower.

subject to

Debt constraint:

where

Additionally, borrowers receive the government subsidy $△tS$ on their mortgage interest payments. The laws of motion for the state variables m_t, x_b,t,, h_b,t are as follows:

Representative saver’s problem. The saver’s problem also aggregates to the problem of a representative saver.

subject to

where the wedge ∆_t is a time-varying tax, rebated to the saver lump sum at equilibrium, that allows for time variation in mortgage spreads. A value of ∆_t > 0 implies that the mortgage rate exceeds the rate on risk-free bonds with the payment structure, allowing for exogenous variation in mortgage spreads. In addition to the budget constraint, the saver must also satisfy the fixed housing demand constraint $hs,t=h¯s$ at all times.

Note that $xs,t−1=r¯b,t−1mt−1$⁠, where

We use the following definitions to denote variables: $wt≡WtPtc,mt≡MtPtc,mt*≡Mt*Ptc,πtc≡PtcPt−1c,pth≡PthPtc,bt−1≡Bt−1Ptc,at−1f≡At−1fPtc$⁠.

Final good firms: (Y_t = C_t) (competitive)

where C_t is a composite consumption aggregator defined by

and $Ctd$ is an index of consumption of domestic goods. $Ctm$ denotes the quantity of imported goods consumed. $ωc∈0,1$ may be interpreted as a measure of openness. η_c > 0 measures the substitutability between domestic and foreign goods.

FOCs:

Domestic final good firms: (competitive)

where $Ctd$ is given by the constant elasticity of consumption function

where $i∈0,1$ denotes the good variety. Parameter ɛ > 1 denotes the elasticity of substitution between varieties produced domestically.

Intermediate good firms: monopolistically competitive

Imports and exports: Competitive firms produce imported good $Ctm$ with price $Ptm,c$⁠, and their profit functions are given by

where S_t is the nominal exchange rate, $Ptf$ is the price of foreign good and ψ^f is a foreign adjustment cost parameter.

Competitive firms produce exported good X_t, and their profits are given by

where $Ptx$ is the price of export and ψ^x is an export adjustment cost parameter.

We also define the real exchange rate $qt≡StPtfPtc$⁠, terms of trade $ptx≡PtxPtf$ and $st=StSt−1$⁠.

Monetary authority. The monetary authority follows a Taylor rule, similar to that of Smets and Wouters (2007), of the form

where the subscript “ss” refers to steady state values and $π¯c,t$ is a time-varying inflation target defined by

where $επ¯,t$ is an inflation target shock.

Equilibrium. A competitive equilibrium economy consists of endogenous states $mt−1,xt−1,hb,t−1$⁠, borrower controls $cB,t,nB,t,ht,hb,t*,mt*$⁠, saver controls $cS,t,nS,t,mt*$ and prices $πt,wt,pth,Rt,rt*$ that jointly solve the borrower, saver and firm problems, as well as the market clearing conditions:

I have set the parameter values of the model as shown in Tables 1–4. Some internal parameters were calibrated to match their respective targets.

In the context of Mongolia’s economic framework, the nation currently accommodates a notably high payment-to-income (DSTI) ratio of approximately 0.7, contrasting sharply with the more conservative thresholds near 0.4 observed in advanced economies. Coupled with this, Mongolia contends with inflation rates oscillating between 6 and 7%, significantly above the more stable target range of 3–4% seen as optimal by many economic standards. The government’s extensive mortgage subsidies, where rates are set at nearly half of policy rates, also highlight potential vulnerabilities in fiscal sustainability. Addressing these challenges necessitates a comprehensive evaluation of policy responses using advanced economic models. This paper aims to simulate potential impacts on the housing market and the broader economy through a variety of economic shocks, including adjustments to inflation targets, country spread, DSTI ratios, terms of trade, domestic demand, productivity and reductions in subsidy levels. By exploring these dimensions, the analysis will provide a robust framework for strategic economic decision-making in Mongolia.

I first generate the impulse responses of key economic variables to a 1% (annualized) inflation target shock, comparing two hypothetical scenarios – one characterized by high government subsidies on mortgage interest payments (50%) and another with low subsidies (20%). By assessing various economic indicators over a series of quarters, we uncover the interplay between government intervention in the housing market and broader economic dynamics.

Figure 1 shows that in the high subsidy environment, the impulse response exhibits a pronounced and volatile reaction in house prices and the price-to-rent ratio following the inflation target shock. The heightened amplitude of fluctuations suggests a greater sensitivity of the housing market to changes in inflation expectations. Conversely, in the low subsidy setting, the response in house prices and the price-to-rent ratio is significantly more subdued, indicating a more stable housing market less influenced by shifts in monetary policy due to reduced fiscal distortion.

In environments with high subsidies, output and consumption exhibit higher peaks and deeper troughs, underscoring the economy’s increased exposure to cyclical fluctuations. The trade balance deteriorates more sharply. On the other hand, in low subsidy settings, both output and consumption increase more gradually, suggesting that economic activity is better insulated from the inflation shock. The trade balance shows a less pronounced decline, pointing to a relatively stable external sector.

The findings suggest that high subsidy levels amplify economic volatility in response to inflation target shocks (see Figure 2).

A decrease the DSTI ratio may be needed to prevent financial distress among consumers. A high DSTI ratio often leads to increased financial burden on households, making them more susceptible to defaults, especially in times of economic downturn or rising interest rates.

Here, I analyze the impact of a 10% reduction in the payment-to-income (DSTI) ratio on the economy. The comparative analysis underscores the heightened sensitivity of high subsidy economies to changes in the DSTI regulation, which raises crucial arguments for the sequencing of policy adjustments – specifically, the reduction of housing subsidies prior to changes in the DSTI ratio.

This policy measure directly impacts households’ borrowing capabilities in the model. The model’s impulse responses highlight a notable decline in new mortgages, which drops sharply immediately following the DSTI ratio cut. This reduction is a direct consequence of tightened borrowing conditions, which restrict households’ ability to finance new home purchases. Concurrently, overall household debt shows a decrease, reflecting a reduction in new borrowing. The price-to-rent ratio and house prices also exhibit a significant downward adjustment, signaling a cooling off in the housing market driven by decreased demand.

Interest rates in the model show a downward trajectory, which may indicate a responsive easing by the central bank to counterbalance the contractionary effects of the DSTI cut on the economy. Despite this, the outputs in terms of inflation, overall economic output and consumption reveal a downturn. This suggests that the reduced leverage in household finances leads to lower spending power, subsequently damping economic activity and reducing consumer demand. The trade balance shows a positive shift. This is due to decreased domestic demand leading to lower import consumption.

A reduction in the LTV ratio yields qualitatively similar results, as illustrated in Figure 3.

Here, I analyze the impact of a 10% reduction in the government subsidies.

The immediate response in the housing market to a subsidy cut is evident from the reduction in new mortgages and a decline in house prices. This is accompanied by a downward adjustment in the price-to-rent ratio, illustrating a direct contraction in housing demand.

Comparing Figures 2 with 4, we find the differential impacts of the two policy adjustments. The comparison reveals that while both policies impact the housing market and consumer debt, a subsidy cut appears to be less detrimental to overall economic activity compared to a DSTI ratio reduction in the high subsidy economy. This may be due to their targeted impact on specific segments of the housing market.

In contrast, changes to the DSTI ratio, which directly affect the borrowing limits of a broader swath of consumers, seem to have deeper and more widespread economic ramifications. This underscores the need for careful calibration of such policies to avoid significant disruptions in economic activity.

In Figures 5–8, I also analyze the impact of various kinds of demand shock, such as shocks on a domestic interest rate shock (negative), country spread (negative), terms of trade (positive) and productivity (positive). The model responses provide nuanced insights into how these shocks affect high and low subsidy economies. The broader economic impacts across different subsidy levels are similar. But we still find that distinct differences are evident in housing market responses.

This section delves into the sensitivity analysis conducted using our DSGE model, focusing on the impulse responses to an inflation target shock under various financial conditions. We explore how economies with differing DSTI ratios, saver’s housing price-to-income ratios and borrower discount factors respond to changes in the inflation target.

In response to a decrease in the inflation target, the impulse response plots reveal notable differences between economies with low and high DSTI ratios. Over a period of 20 quarters, the inflation rate decreases more sharply in high DSTI economies, illustrating a pronounced disinflationary effect due to the target reduction.

The economic impact extends to output and consumption, both of which decrease following the shock, with high DSTI economies facing a deeper and more prolonged contraction. This outcome highlights the heavier burden of debt service in these economies, potentially restricting consumer spending and investment more severely than low DSTI economies. Additionally, house prices and the price-to-rent ratio experience significant reductions, particularly in high DSTI areas, indicating a heightened sensitivity of real estate markets to interest rate changes and economic slowdowns.

This analysis underscores the role of higher indebtedness in amplifying the impacts of monetary policy changes in high DSTI economies. The results indicate more acute economic fluctuations across various sectors, including real estate and consumer behavior, than their low DSTI counterparts, highlighting the differential effects of monetary policy based on economic indebtedness.

This sensitivity analysis explores the impulse responses to a decrease in the inflation target under different saver’s housing price-to-income ratios – specifically comparing a benchmark ratio of 7 to an alternative ratio of 5.5. Although the data for setting these ratios are somewhat arbitrarily determined due to lack of available data, the analysis still offers insights into how monetary policy impacts different economic environments.

The impulse responses show that declines in house prices, the price-rent ratio and inflation are evident in both scenarios, but their magnitudes and durations are quite similar across the two scenarios. This suggests that the housing price-to-income ratio, within the range examined, does not significantly alter the sensitivity of the housing market to shifts in inflation targets.

The sensitivity analysis examines the impulse responses to a decrease in the inflation target under different borrower discount factors, comparing a baseline value of 0.95 to a scenario with a smaller beta of 0.935, with these values set based on existing literature due to the unavailability of specific data for Mongolia.

While reductions in the inflation target lead to decreases across economic indicators such as house prices, the price-to-rent ratio and new mortgages, these impacts are less pronounced in the scenario with the smaller beta. This suggests that a lower discount factor somewhat cushions the economic response to changes in monetary policy. The declines in house prices and the price-to-rent ratio are notably less steep under the smaller beta, indicating a dampened sensitivity to monetary shifts.

Output and consumption responses exhibit relative stability, suggesting overall economic activity is resilient to variations in the discount factor. Similarly, the trade balance remains largely unaffected, indicating that these internal financial adjustments do not significantly impact external economic transactions.

This analysis underscores that a smaller discount factor can moderate the sensitivity of economic outcomes to monetary policy changes, particularly in financial metrics closely tied to housing and borrowing.

SOE DSGE with a housing sector shows that high mortgage subsidies amplify housing and aggregate volatility. When subsidies are large, inflation-target or rate shocks generate bigger swings in house prices, consumption and external balances.

Comparing subsidy cuts to DSTI/LTV tightening, we find that reducing subsidies lowers leverage and cools house prices at lower output and consumption costs than a DSTI tightening in a high-subsidy environment. This supports policy sequencing: scale down subsidies first, then consider tighter DSTI (or LTV) caps if further cooling is needed. The same ranking persists under open-economy shocks (terms of trade, country spread).

For policy, the model recommends (1) gradually reducing mortgage subsidies to temper cyclical amplification, (2) using borrower-based tools as targeted complements rather than first-best substitutes for subsidy reform and (3) coordinating monetary, macroprudential and fiscal housing policies to manage volatility while preserving access to credit.

I thank colleagues at the Bank of Korea and the Bank of Mongolia for helpful comments and discussions. The views expressed are those of the author and do not necessarily represent those of the BOK or the Bank of Mongolia. Any remaining errors are my own.