2.1 Households

The households maximize the expected present value of lifetime utility, which is given by:

(1)

where C_t denotes households’ consumption other than housing, H_t represents the housing stock purchased by households, and L_t indicates the labor supply. measures the housing preference of households. is the discount factor, while represents the Frisch elasticity of labor supply.

In the process of household investment, the adjustment cost of investment in the form of CEE (Christiano et al., 2005 [18]) is generated, which satisfies the following constraints in decision-making:

(2)

(3)

where P_t is the non-housing goods price so that the inflation rate is defined by . P_h,t denotes the housing price. I_t is the investment amount, while W_t is the labor wage. K_t is the household capital holdings, which yield a capital return rate of R_k,t. The households still hold bonds B_p,t domestically and B_f,t internationally, corresponding to the interest rates R_t and R_f,t, separately. is the stamp duty rate based on the housing transaction amount for households. For households, stamp duty is payable only upon purchasing or transferring a residential property. This tax is levied concurrently with the transaction, with both parties bearing the tax liability. The tax base is determined by the transaction value of the property. and are the depreciation rates of houses and capital, and measures the size of the adjustment cost of the investment.

Referring to Grohé and Uribe (2003) [19], we introduce the concept of debt elastic interest rate, where the domestic interest rate is defined as the sum of the foreign interest rate R_f,t and an increasing function . Consequently, the interest rate differential between domestic and foreign markets depends on the magnitude of foreign bond holdings B_f,t relative to the steady-state value , that is:

(4)

Households choose the contingent sequence to maximize Eq. (1) subject to Eq. (2) and Eq. (3). The first order conditions for households are:

(5)

(6)

(7)

(8)

(9)

(10)

(11)

where and are Lagrange multipliers associated with two budget constraints Eq. (1) and Eq. (2). U_c,t represents the marginal utility of a unit of non-housing consumption, and U_h,t represents the marginal utility of holding an additional unit of housing. Eq. (5) and Eq. (6) are first order conditions for non-housing consumption and housing dynamics. Eq. (7) relates to household labor choice, while Eq. (8) and Eq. (9) pertain to investment and domestic bonds. Eq. (10) and Eq. (11) respectively reflect the optimal choices for capital and foreign bonds.

2.2 Firms

2.2.1 Non-housing sector.

Suppose that the non-housing sector invests capital and employs labor to produce goods, which consists of monopolistically competitive intermediate goods producers indexed by a continuum of . The government promotes non-housing production by enhancing investment efficiency; the size of its direct or indirect effects is uniformly measured by . It is an important manifestation of the government expenditure multiplier effects (Wang and Wen, 2013 [20]; Guo et al., 2015 [2]). The production function is set in the form of Cobb-Douglas:

(12)

where Y_t(j) denotes the non-housing output from intermediate goods producers. Non-housing factor productivity A_t follows the AR(1) process . is the logarithmic deviation from the steady state, . L_n,t and K_t are the labor and capital inputs of non-housing firms, and G_t represents the public expenditure of the government. We suppose that the agents of non-housing firms know the magnitude of government expenditure before each period of production decision-making. The parameter represents the output elasticity of capital, and represents the degree to which government expenditure increases output.

The first-order conditions for maximizing profits are given by:

(13)(14)

2.2.2 Housing sector.

We assume that the government imposes the stamp duty on housing transaction amounts between housing firms and households at a tax rate of . Referring to Guo et al.(2015) [2], it is assumed that the housing firms also follow the production function in the form of Cobb-Douglas, and employ labor and land to produce housing for households. Thus, the dynamic process of housing stock is:

(15)

where L_h,t and Z_t represent the labor and land input, respectively. The parameter is the output elasticity of land in the housing sector.

Similarly, as the land prices P_z,t are given, the first order conditions for housing firms to maximize profits are:

(16)(17)

2.3 Government

Assuming the government implements a balanced budget, its revenue derives from stamp duties from households, land sale income, and borrowed debt D_t, while expenditures stem from government spending and the repayment of prior-period debt with accrued interest. The balanced budget is given by:

(18)

In the study by Iacoviello and Neri (2010) [14], collateral constraints primarily focused on the household level and the housing market, while Liu et al. (2013) [21] incorporated land into the collateral constraints of firm debt. Drawing on the characteristics of land-based fiscal systems, we integrate land into the collateral constraints of government debt. The government’s debt ceiling is determined by the expected value of the remaining land as collateral and the LTV ratio:

(19)

where the supply quota S_t is decided by the government in each period.

The fiscal policies primarily considered in this paper focus on three aspects: government expenditures, stamp duty rates, and land supply constraints. We denote the logarithms of these policies as , where are the corresponding steady-state values. For fiscal policy formulation, we consider three distinct approaches. The first is the most common specification in DSGE literature, where fiscal policy is viewed as a random exogenous shock independent of endogenous economic indicators. It is denoted as Rule 1 as follows:

(20)

Here, represents the first-order autoregressive coefficient of the AR(1) process, indicating the response of the current fiscal policy to the previous period. Furthermore, according to Han (2021) [22], fiscal policymaking is more purposeful than a simple AR(1) process. In the second case, for the sake of elaboration, we adopt the most common standard fiscal rule that responds to output (Guerguil et al., 2017 [23]; Combes et al., 2017 [24]), which is denoted as Rule 2 and takes the form of:

(21)

The parameter represents the degree to which the policy responds to output. Beyond this, policy interventions may target not only output but also debt (Kliem and Kriwoluzky, 2014 [25]). In the third case, fiscal policies designed based on existing debt levels reflect the government’s concern for fiscal sustainability, which is given by:

(22)

The parameter represents the degree to which the policy responds to existing government debt.

2.4 International sector

In the international sector, following Gali and Monacelli (2005) [13] and Obstfeld et al.(2010) [26], consumption consists of domestic goods C_d,t and imports IM_t. We assume its aggregation follows a CES form:

(23)

where indicates the allocation parameter for domestic and foreign goods, while stands for the elasticity of substitution. Let P_d,t and P_f,t denote the prices of domestic goods and foreign goods. The budget constraint is given by:

(24)

Then, the optimal quantities of C_d,t and IM_t are obtained as follows:

(25)

(26)

According to the symmetry, export EX_t equals foreign import. Similarly, the export can be derived from Eq. (23) and Eq. (24) as:

(27)

where C_f,t represents the foreign consumption. indicates the allocation parameter for goods in foreign countries, while stands for the foreign elasticity of substitution.

Exogenous shocks originating abroad are transmitted through price and consumption channels. Assuming P_f,t, C_f,t and R_f,t follow AR(1) processes:

(28)

(29)

(30)

where , , and are the autoregressive coefficients of foreign prices, consumption, and interest rate, , , .

Moreover, under the balance of payments, the dynamic process of foreign bonds satisfies the following condition:

(31)

2.5 Equilibrium

The competitive equilibrium consists of the price sequence , the allocation sequence and the fiscal policy sequence such that (i) taking all prices and fiscal policies as given, households’ allocations maximize their utility, (ii) taking all prices and fiscal policies as given, firms’ allocations maximize their profits, and (iii) all markets clear. In addition to the first-order conditions listed above in this article, the market clearing conditions need to be satisfied in equilibrium.

The labor force provided by households is the sum of employed labor in the non-housing sector and the housing sector. The labor market clearing condition is:

(32)

The clearing condition for the goods market is:

(33)

4.1 Impulse responses

This section builds upon the four-sector model constructed earlier to conduct impulse response analysis under three fiscal rules (Rule 1: fully exogenous rule; Rule 2: output-responsive rule; Rule 3: debt-responsive rule). It examines the dynamic effects of the government expenditure shock, stamp duty shock, and land supply shock on key variables of the Hong Kong economy. All impulse responses are simulated based on the posterior parameter means obtained through Bayesian estimation.

We find that under each rule, government expenditure exhibits the crowding-out effect to some extent, as shown in Fig 2. Under balanced budget rules, the government incurs debt to cover deficits, which primarily drives up market interest rates. Consequently, household investment declines due to high interest rates, and consumption shrinks as investment income decreases. The crowding-out effect is most pronounced under Rule 1; conversely, under Rule 3, the government will tighten spending more rapidly after shocks to maintain debt sustainability, interest rate fluctuations are relatively stable, and government expenditures exert less crowding-out pressure on consumption and investment. Meanwhile, due to the temporary rise in domestic inflation, imports increased while exports decreased in the international sector, causing net exports to follow a downward trend in the short term. In addition, government expenditures spur short-term growth in employment. This is attributable both to the stimulus of government expenditures on production and to households undertaking additional work to compensate for losses in investment income. We also note that the impact of government expenditures on housing price fluctuations varies distinctly under different policy rules. Under Rule 1 and Rule 2, fiscal rules do not prioritize fiscal sustainability. Consequently, increased government expenditures lead to heightened debt repayment pressures and potential deficit risks. Since debt levels are tied to the value of mortgaged land, expectations for the land and housing markets decline. Under Rule 3, however, government expenditures are adjusted in a timely manner based on current debt levels, thereby playing a greater role in stimulating the housing market.

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Fig 2. Impulse responses of government expenditure shock under different fiscal rules (The horizontal axis in the figure represents the number of periods following the shock, while the vertical axis indicates the deviation of the variable relative to the steady state. The solid line is the case of Rule 1, the dashed line is the case of Rule 2, and the dash-dot line is the case of Rule 3).

https://doi.org/10.1371/journal.pone.0346966.g002

Stamp duty is another crucial component of the fiscal system. In Fig 3, a positive stamp duty shock demonstrates a dampening effect on consumption and a stimulating effect on investment. The underlying logic is straightforward: higher stamp duty directly increases the cost of home purchases for households, thereby reducing the disposable income available for consumption. Simultaneously, a less heated housing market encourages investors to channel more capital into the real economy, ultimately elevating overall investment levels in the macroeconomy. Rules 2 and 3 enable stamp duty policy to respond to macroeconomic conditions and debt levels, thereby smoothing fluctuations and stabilizing consumption and investment dynamics. We further observe that regardless of the rule applied, the impact of stamp duty, a tax associated with housing transactions, suppresses housing prices, which aligns with existing empirical findings (Besley et al., 2014 [30]; Kopczuk and Munroe, 2015 [31]; Best and Kleven, 2018 [32]). Under Rule 3, the government determines stamp duty rates based on debt levels relative to housing and land prices, thereby minimizing the decline in housing prices. For the land market, the increase in stamp duty reduces housing demand. This shrinking demand further translates into a decrease in land requirements for housing construction firms, leading to a corresponding decline in land prices. Subsequently, the contraction of the land market also triggers a downsizing of government debt, thereby reducing the debt-to-revenue ratio.

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Fig 3. Impulse responses of stamp duty shock under different fiscal rules (The horizontal axis in the figure represents the number of periods following the shock, while the vertical axis indicates the deviation of the variable relative to the steady state. The solid line is the case of Rule 1, the dashed line is the case of Rule 2, and the dash-dot line is the case of Rule 3).

https://doi.org/10.1371/journal.pone.0346966.g003

We now turn to the implications of government land supply policies. In fact, positive land supply shocks primarily manifest as a demand-pulling effect. This manifests as increased household consumption and a temporary rise in investment levels driven by falling interest rates. Compared to Rule 1 and Rule 2, implementing land supply policies under Rule 3 exerts a gentler impact on economic fundamentals. As shown in Fig 4, the IRFs for consumption, investment, and interest rates under Rule 3 exhibit relatively flatter trajectories, further underscoring Rule 3’s policy orientation toward stabilizing fluctuations. Furthermore, the loosened land supply eases constraints on land use for construction by housing enterprises, enabling firms to expand their capacity and thereby employ more labor. Under Rule 1 and Rule 2, the land supply shock conveys the signal of economic expansion, fostering positive future expectations in the market and consequently driving up housing prices and land prices. Under Rule 3, however, the land supply shock is translated into a signal of fiscal deficit pressure. Since land transactions are directly linked to fiscal debt under the established rules, this instead fosters negative expectations in the housing market, thus depressing prices. This counterintuitive outcome precisely highlights the peculiarity of the “land finance” development pattern. Moreover, raising the land supply cap also implies an increase in the debt ceiling determined by the collateral value of surplus land. As the government further expands its debt, the debt-to-revenue ratio rises, and fiscal sustainability weakens.

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Fig 4. Impulse responses of land supply shock under different fiscal rules (The horizontal axis in the figure represents the number of periods following the shock, while the vertical axis indicates the deviation of the variable relative to the steady state. The solid line is the case of Rule 1, the dashed line is the case of Rule 2, and the dash-dot line is the case of Rule 3).

https://doi.org/10.1371/journal.pone.0346966.g004

4.2 Variance decomposition

We adopt variance decomposition to analyze the contribution of different fiscal shocks to the volatility of essential economic components, thereby identifying the sources of shocks affecting Hong Kong’s economic fluctuations. Table 3 presents the percentage of theoretical variance contributed by the government expenditure shock (), stamp duty shock (), and land supply shock () to the movements of key macroeconomic variables under three fiscal rule scenarios.

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Table 3. Variance decomposition of fiscal shocks in percent.

https://doi.org/10.1371/journal.pone.0346966.t003

Overall, stamp duty shocks appear to be the primary fiscal contributor to macroeconomic volatility in Hong Kong. Under all three rules, their contribution to fluctuations in variables such as the net export, labor, land price, and debt-to-revenue ratio remains significant and consistently high. For instance, under Rule 1, the stamp duty shock accounted for 45.70% fluctuations of net export, 46.15% of the labor, and 47.70% of the debt-to-revenue ratio. This finding underscores that tax policies closely tied to housing transactions possess powerful spillover effects – not only directly impacting the housing market but also broadly affecting the balance of payments, the labor market, and the sustainability of the government finance.

The contribution of land supply shocks exhibits pronounced rule dependency. Under Rules 1 and 2, their impact on fundamentals such as consumption, investment, and interest rates remains relatively moderate. Under Rule 3, the contribution of land supply shocks to land price and debt-to-revenue ratio fluctuations rises to 1.85% and 3.39%. This indicates that when fiscal rules prioritize debt sustainability, the link between land supply policies and government indebtedness is significantly strengthened. Changes in land supply directly impact government borrowing capacity and debt burdens through the collateral value channel, therefore becoming a significant source of fiscal volatility.

In contrast, the contribution of the government expenditure shock is relatively mild under all three rules, particularly under Rule 3. Its explanatory power for fluctuations in core macroeconomic variables such as consumption and investment generally falls below 0.1%. This reflects that, within Hong Kong’s land finance framework, fiscal expenditures are not the primary drivers of economic fluctuations. When fiscal rules incorporate feedback mechanisms for debt (Rules 3), government expenditures tend to function more as “automatic stabilizers” or “debt smoothers,” and their own characteristics as independent shock sources are weakened.

The variance decomposition results above indicate that Hong Kong’s macroeconomic fluctuations are closely linked to land-related fiscal instruments, particularly stamp duty. While a simple output-responsive fiscal rule (Rule 2) can moderate some fluctuations, only by explicitly anchoring the fiscal rule to debt levels (Rule 3) can the transmission of various fiscal shocks be systematically reduced. This provides a more binding policy framework to mitigate reliance on the “land finance” pattern which depends on stamp duty and land sale revenues, thereby enhancing fiscal sustainability.

4.3 Forecasts

This section uses the posterior parameter means obtained from Bayesian estimation (see Table 3) to forecast the equilibrium paths of the model under three different fiscal rules. The projections simulate the percentage deviation paths of key macroeconomic variables relative to their steady-state values over the next 40 quarters, with results presented in Fig 5. The forecast path begins with the final observed value of the sample, namely Q4 2023. We employ a mean forecast, accounting solely for parameter uncertainty rather than uncertainty surrounding future shocks. The impact of shocks is neutralized by setting them to zero.

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Fig 5. Forecasts from the posterior mean under different fiscal rules (The horizontal axis in the figure represents the number of periods following the shock, while the vertical axis indicates the deviation of the variable relative to the steady state. The solid line is the case of Rule 1, the dashed line is the case of Rule 2, and the dash-dot line is the case of Rule 3).

https://doi.org/10.1371/journal.pone.0346966.g005

By and large, Rule 3 exhibits the most pronounced stabilizing effect. Under this rule, the forecast paths of actual variables such as consumption and investment show the smallest fluctuations and converge more rapidly toward steady states. This indicates that fiscal rules targeting government debt levels directly can effectively reduce policy-induced uncertainty by constraining government expenditures and land finance practices. By providing the private sector with more stable long-term expectations, such rules help curb excessive volatility in the economy.

Specifically, we have three key findings:

First, under Rule 1, the projected paths of output and consumption exhibit persistent cyclical fluctuations. Rule 2 partially smooths these fluctuations by linking fiscal policy to the output gap, though its effect diminishes after the medium term. In contrast, Rule 3 manages to suppress fluctuations in consumption, interest rates, and inflation within an extremely narrow range, resulting in nearly smooth paths. The underlying mechanism is that under Rule 3, the government’s adjustments to stabilize debt automatically offset other shocks in the economy, thereby maintaining intrinsic stability.

Second, regarding housing and land prices, the forecast results further highlight the divergence in policy outcomes under the land finance pattern. Under Rules 1 and 2, the forecast paths for housing and land prices exhibit sustained moderate upward pressure, paralleling the rise in government debt levels. Under Rule 3, however, as policies respond to debt accumulation, fiscal policy becomes more effective in monitoring debt dynamics, while the forecast paths for housing and land prices stabilize.

Third, the forecast paths for the government debt-to-revenue ratio show stark differences. Under Rules 1 and 2, this ratio exhibits a long-term upward trend, which portends persistent pressure on fiscal sustainability. Meanwhile, under Rule 3, the debt-to-revenue ratio is strictly anchored and stabilized near a steady-state level. This contrast strongly indicates that without explicitly linking fiscal rules to debt measures, Hong Kong’s current land finance pattern will drive continuous increases in government leverage, accumulating long-term risks. Conversely, debt-responsive rules can effectively curb this trend and provide safeguards for fiscal sustainability.

4.4 Welfare comparison

In the preceding discussion, we conducted only a formal qualitative analysis of the ranking of the three rules from different perspectives. To enable the rules to more intuitively reflect their overall effects quantitatively, we further calculate welfare losses using the methods of Woodford (2003) [33], Gali and Monacelli (2005) [13], and Gali and Monacelli (2008) [34], thereby illustrating the economy’s deviation from an efficient equilibrium. Specifically, we define the logarithmic deviation of variables relative to steady state as and . We can rewrite the single-period utility corresponding to Eq. (1) as:

(35)

Perform a second-order Taylor expansion of L_t at to obtain:

(36)

Since all variables return to their long-term steady state, . Therefore, the welfare loss function is ultimately expressed as:

(37)

The calculation results show significant differences in welfare losses under the three rules: Rule 1 incurs the highest welfare loss, reaching 3.36%. This indicates that when fiscal policy operates entirely independently of endogenous economic indicators, the inherent uncertainty of the policy amplifies economic fluctuations,especially in the labor market, which leads to substantial welfare losses. Under Rule 2, the welfare loss decreased significantly to 1.75%. This demonstrates that linking fiscal policy to the output gap can function as an automatic stabilizer, which smooths economic cycles, mitigates excessive fluctuations in the labor market, and thereby enhances welfare. Rule 3 yields the lowest welfare loss at only 1.02%. This demonstrates that fiscal rules responsive to government debt are most effective in stabilizing the economy and reducing volatility. By monitoring government spending and land-based fiscal practices, Rule 3 provides the private sector with more stable long-term expectations, thereby significantly reducing fluctuations in the labor market and the aggregate economy.

5.1 Identification tests

To determine whether all parameters to be estimated are effectively identified, we first conducted identification tests on all parameters, following the methods of Iskrev (2010) [35], Komunjer and Ng (2011) [36], and Qu and Tkachenko (2012) [37]. The results show that under three distinct levels of testing, all parameters are identified in the Jacobian of the first two moments, the steady-state and minimal system, and the Jacobian of mean and spectrum. Then, by examining the overlap plots of prior-posterior distributions for each parameter under three different rules, we observe that the posterior distribution of each parameter shares overlapping regions with its prior distribution but does not fully coincide with it. This indicates that the posterior distribution can adjust within a given interval during the estimation process, which validates the reasonableness of prior distribution selection and the identifiability of parameters to some extent. S2 Fig details the results of the identification tests.

5.2 Robustness tests

To verify the consistency of the preceding results, we conducted robustness tests in two aspects, following the approach of Smets and Wouters (2007) [38]. Initially, we examined the sensitivity of the prior distribution. Specifically, we tested the sensitivity of the estimation results to prior assumptions by relaxing the standard deviation of the prior distribution to 1.1 times its original value. Re-estimation revealed that even with a more lenient standard deviation, the parameter estimates remained highly similar to the original results. This indicates that our parameter estimates exhibit no significant sensitivity to the chosen prior distribution range. Subsequently, we also take note of the critique by Ramey and Zubairy (2018) [39], carefully considering the possibility of divergent outcomes under different initial economic conditions when analyzing the economic impacts of fiscal policies. Thus, we further examined the stability of the estimates across different sample sizes. Considering the substantial impact of the SARS pandemic on the Hong Kong economy, we re-estimated the model using a subsample from 2004 onward. We find that after reducing the sample size by one seventh, the estimation results remain similar to the original estimates, indicating robustness across sample lengths. Detailed estimated results from robustness tests are presented in S3 Table.