# COVID-19 Shocks, Monetary Policy, and Real Estate Price Volatility: Analysis Based on a Dynamic Stochastic General Equilibrium Perspective

Authors: Zhe Hou; Yu Song; Wen Xin
Journal: Scientific Programming
 (2022)

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## Abstract

The COVID-19 pneumonia epidemic in early 2020 severely affected all sectors of the Chinese economy, with economic growth plummeting but the property market continuing to heat up after a brief contraction. How to formulate an effective monetary policy in the face of the COVID-19 shock to achieve stable economic growth while curbing excessive real estate price inflation has become a pressing issue for Chinese policymakers today. To this end, this paper focuses on the impact of two types of monetary policy, price-based and quantity-based, on macro-economic variables such as real estate prices and aggregate output by developing a multi-sectoral DSGE model incorporating the COVID-19 shock and comparing them. The analysis finds that both monetary policy rules can achieve the objective of dampening real estate prices. Nevertheless, while causing the same magnitude of real estate price contraction, quantity-based monetary policy leads to greater volatility in variables such as aggregate output, while other economic variables are less volatile under the price-based monetary policy.


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## Body

## 1. Introduction

In the first quarter of 2020, the COVID-19 outbreak resulted in a nationwide shutdown to combat the epidemic and negative GDP growth for the first time in over 40 years. The government introduced a series of macro-economic policies, including active fiscal policy and flexible monetary policy, to counter the impact of the epidemic. Proactive fiscal policy promoted production recovery in tax and fee cuts and increased market capitalization to help enterprises ease their difficulties and resume production. Promoting demand recovery through flexible monetary policy, the People’s Bank of China implemented a series of accommodative monetary policies, such as lowering refinancing rates and lowering the reserve requirement ratio to drive the economy back to life. Under this policy, the Chinese economy as a whole showed a steady recovery, but structurally, there was a clear divergence between different economic sectors. In 2020, China’s disposable income, consumption, and manufacturing investment as a whole showed negative growth, while real estate investment bucks the trend. In 2021, as China's economy as a whole continues to pick up, real estate investment gets a further boost in the first half of this year, with commercial property sales growing at a much faster rate than before the outbreak, while real estate prices also show an upward trend. However, concerns about the impact of the epidemic are likely to continue, and pressure for continued slow growth in China’s economy remains in the future.Affected by the epidemic, the deep adjustment of the world economic and political landscape, and the deep overlap of domestic conflicts, the uncertainty of China’s economy has increased. The Fifth Plenary Session of the 19th CPC Central Committee clearly proposed to “maintain financial security and guard the bottom line of no systemic risk.” Furthermore, real estate is an important source of financial risk in China. Since the housing reform in 1998, the real estate market has experienced more than 20 years of booming development, and real estate prices have continued to rise, which has seriously affected residents’ spending power. High prices characterize the real estate industry, high leverage, and high financialization, which has exacerbated distortions in the real estate market, spawned price bubbles, and generated a great shock to economic and financial stability. Against this realistic background, effectively curbing real estate prices, defusing real estate risks, and maintaining macro-economic stability through policy implementation have become a common concern for future policy researchers and policymakers.Since 2012, China has repeatedly regulated the real estate market through macro-control measures, but the changes in real estate prices have not been satisfactory. From 2012 to 2013, the growth rate of real estate prices was basically stable; from 2014 to 2016, the growth rate of real estate prices rose to 10.1%. In the second half of 2016, the government’s regulation and control efforts escalated again. Restrictions on purchasing and lending policies were introduced, raising policy interest rates in all provinces and cities. In 2017, General Secretary Xi Jinping proposed the policy of “housing is for living in, not speculation” in the report of the 19th National Congress, which brought the momentum of the rapid rise in real estate prices under control to some extent. However, since the outbreak of COVID-19, the real estate market has again seen the momentum of price increases. Although each regulation has played a role in stabilizing housing prices in the short term, housing prices have fallen into the strange circle of more and more adjustments in the medium and long term. It is not difficult to find that the real estate development investment accounted for the proportion of the total social fixed asset investment from 12.5% in 1998 to 27.26% the real estate industry after 20 years of rapid development in 2020 with depth analysis. The real estate industry has penetrated all fields of the national economy and become an important part of driving economic growth, promoting employment, and government revenue. China’s economic development has entered a new normal with significant downward pressure on the economy in recent years. Loose macro-policies have effectively eased some of the pressure while tightening policies will inevitably add to the downward pressure on the economy. Therefore, the market generally expects that the tightening policy will not last, so there is a tendency for real estate prices to continue to rise in the medium to long term. Therefore, under the current complex and changing the background of domestic economic development, establishing a balance between the real estate market and economic development, i.e., regulating the real estate market and ensuring the smooth operation of China’s economy, has become a major problem for policymakers and academics.Because of this, this paper attempts to construct a DSGE model incorporating COVID-19 shocks, real estate market, and financial frictions based on the latest monetary policy theory research in the context of the current reality of global epidemic shocks and the new normal of China’s economy. By studying the monetary policy transmission mechanism and its effectiveness, this paper examines the impact of different monetary policies on the real estate market and the macro-economy. Based on the analysis results, it selects the optimal policy conducive to calming housing prices and stabilizing economic development.


## 2. Related Literature

### 2.1. COVID-19 Shock and Monetary Policy

Since 2020, the catastrophic impact of COVID-19 on the global economy has become the focus of attention of macro-economic scholars at home and abroad. Studies on the impact of COVID-19 on the economy can be broadly divided into two categories [1]; one is from a micro-perspective, examining the impact of the epidemic shock on the behavior of micro-subjects and industrial structure through survey data information and other methods [2–4]. Another part of scholars establishing DSGE models from a macroperspective for the characteristics of the epidemic examine the impact of the epidemic shock on the macroeconomy and try to propose relevant policies to mitigate the negative impact of the epidemic.While earlier literature on catastrophe shocks mainly deals with natural disasters such as earthquakes and floods, COVID-19 is significantly different from other catastrophic events in terms of the scope, magnitude, and duration of impact [5]. At present, it seems that the impact of COVID-19 on the global economy is comprehensive, from the internal circulation of economies to external exchange and from the demand side of the macro-economy (residential consumption, etc.) to the supply side (enterprise production, etc.) being seriously affected. On the demand side, from the perspective of household production, the COVID-19 shock brings more uncertainty by affecting the decision-making behavior of residents, such as consumption, leading to a decline in consumption [6, 7]. It forces households to restructure their assets and increase their holdings of lower-risk assets, resulting in the supply side of the economy also being affected, with investment and output trending downwards [8]. Zhu et al. proposed a characteristic of COVID-19 that distinguishes it from other disasters, namely, the sudden quiescence of the labor force, and introduced the labor force trilogy into the DSGE model [5]. However, as far as the current economic data are concerned, the impact of sudden labor force quiescence on the overall economy is not significant (with the rise of online offices, the Internet economy has defused this impact to some extent). Chen and Zhong combined the contagion (SIR) model with the DSGE model to depict the changes in aggregate supply and aggregate demand in the Chinese economy under the influence of COVID-19 and analyzed the impact of monetary policy under the interest rate rule [9]. However, the impact of quantitative monetary policy and mixed monetary policy is not discussed in depth.In summary, although some of the literature analyzes the COVID-19 shock economy and the corresponding policy choices for domestic and international studies on the epidemic, there is no specific discussion on the optimal choice of multiple monetary policies under COVID-19 shocks. Examining optimal monetary policies based on the COVID-19 context to mitigate macro-economic volatility and quantitatively analyzing the impact of COVID-19 on the effectiveness of traditional monetary policies are still topics less covered in current studies. In addition, the possible real estate price volatility triggered by COVID-19 has been even less explored.


### 2.2. Real Estate Price Volatility and Monetary Policy

In recent years, many scholars at home and abroad have studied the relationship between real estate prices, monetary policy, and economic fluctuations, mainly using DSGE model analysis. However, different scholars have different views on the impact of monetary policy on the real estate market. Most of the early literature concluded that monetary policy need not respond to real estate price volatility and that monetary policy regulations that dampened asset price volatility reduced output volatility, albeit marginally. However, this led to more dramatic inflationary fluctuations and did not stabilize the economy [10, 11]. After an in-depth analysis of the above literature, it is not difficult to find that their models have the following two common features. First, incremental changes in assets such as real estate are not considered separately, which is clearly not in line with the current economic reality, where the real estate firms have become an important pillar of the national economy in many important economies. Second, many important financial market frictions were not attended to, which may lead to biased policy transmission paths and ultimately yield expected results inconsistent with reality. Therefore, later scholars continued their research to address the above issues by adding the real estate market as an important productive sector to the model for analysis. As the uncertainty of the economy increased after the subprime mortgage crisis, more scholars introduced financial frictions such as credit constraints and monetary policy shocks into the DSGE model. They began to focus on the financial stirrup effect and various types of shocks on the macro-economic regulation effect. It has been found that the inclusion of heterogeneous production sectors can better model the transmission path of monetary policy and multiple shocks to the real economy, and real estate prices have become an important transmission medium for monetary policy shocks [12–14]. This view gradually gained influence after 2008, with a growing literature affirming the role of monetary policy on asset prices and its macro-economic implications.They analyzed the U.S. real estate market by building a DSGE model that includes credit constraints and found that real estate price volatility has a significant impact on the cyclical fluctuations of the economy [15]. Others focused on two frictions, asset collateral and external financing premium, and argued that negative fluctuations in asset prices lead to homogeneous fluctuations in investment and output, exacerbating negative fluctuations in the economy [16]. Real estate mortgages have a significant financial stirrup effect in economies where the macro-economic impact of real estate price volatility is more dramatic and that this spillover effect is more pronounced in countries with more developed real estate financial markets [17]. Some scholars obtained similar conclusions from their analysis in the context of the Chinese economy: price-based monetary policy shocks are a key determinant of real estate price volatility, and excessive real estate price increases can be curbed through the formulation of appropriate monetary policies [18]. The shocks such as mortgage rate shocks and preference shocks to real estate have a significant impact on macro-economic fluctuations in China [19]. Monetary policy shocks affect consumption and real estate demand through the medium of nominal interest rates, ultimately leading to fluctuations in real estate prices and aggregate demand [20, 21]. The government can use monetary policy and financial shock effects to achieve stability in the real estate market. Therefore, some scholars argue that expectations affect cyclical fluctuations in the real estate market and even the macro-economy [22]. Active use of monetary policy tools such as lending rates can effectively reduce the volatility of household debt and aggregate consumption and GDP. There are significant effects in dampening expectation-driven cyclical fluctuations in the real estate market and the macro-economy [23]. Starting from the correlation between real estate prices and variables such as interest rates, exchange rates, and financing size, scholars have also argued that monetary policy is significantly effective in smoothing real estate prices as well as stabilizing the macro-economy and have discussed the linkage mechanism between these three [24].It is clear from the review of the above literature that while most early scholars and policymakers did not advocate intervention in asset price volatility with the help of monetary policy, the mainstream view changed significantly after the 2008 crisis. Using DSGE models that incorporate financial frictions, many scholars have affirmed the moderating role of monetary policy on real estate prices as well as macro-economic stability. Since most of the studies mentioned above discuss the impact of a single type of monetary policy on real estate prices, few articles compare and analyze the impact of different monetary policies. Therefore, there is no uniform analysis on the choice of the optimal monetary policy.


## 2.1. COVID-19 Shock and Monetary Policy

Since 2020, the catastrophic impact of COVID-19 on the global economy has become the focus of attention of macro-economic scholars at home and abroad. Studies on the impact of COVID-19 on the economy can be broadly divided into two categories [1]; one is from a micro-perspective, examining the impact of the epidemic shock on the behavior of micro-subjects and industrial structure through survey data information and other methods [2–4]. Another part of scholars establishing DSGE models from a macroperspective for the characteristics of the epidemic examine the impact of the epidemic shock on the macroeconomy and try to propose relevant policies to mitigate the negative impact of the epidemic.While earlier literature on catastrophe shocks mainly deals with natural disasters such as earthquakes and floods, COVID-19 is significantly different from other catastrophic events in terms of the scope, magnitude, and duration of impact [5]. At present, it seems that the impact of COVID-19 on the global economy is comprehensive, from the internal circulation of economies to external exchange and from the demand side of the macro-economy (residential consumption, etc.) to the supply side (enterprise production, etc.) being seriously affected. On the demand side, from the perspective of household production, the COVID-19 shock brings more uncertainty by affecting the decision-making behavior of residents, such as consumption, leading to a decline in consumption [6, 7]. It forces households to restructure their assets and increase their holdings of lower-risk assets, resulting in the supply side of the economy also being affected, with investment and output trending downwards [8]. Zhu et al. proposed a characteristic of COVID-19 that distinguishes it from other disasters, namely, the sudden quiescence of the labor force, and introduced the labor force trilogy into the DSGE model [5]. However, as far as the current economic data are concerned, the impact of sudden labor force quiescence on the overall economy is not significant (with the rise of online offices, the Internet economy has defused this impact to some extent). Chen and Zhong combined the contagion (SIR) model with the DSGE model to depict the changes in aggregate supply and aggregate demand in the Chinese economy under the influence of COVID-19 and analyzed the impact of monetary policy under the interest rate rule [9]. However, the impact of quantitative monetary policy and mixed monetary policy is not discussed in depth.In summary, although some of the literature analyzes the COVID-19 shock economy and the corresponding policy choices for domestic and international studies on the epidemic, there is no specific discussion on the optimal choice of multiple monetary policies under COVID-19 shocks. Examining optimal monetary policies based on the COVID-19 context to mitigate macro-economic volatility and quantitatively analyzing the impact of COVID-19 on the effectiveness of traditional monetary policies are still topics less covered in current studies. In addition, the possible real estate price volatility triggered by COVID-19 has been even less explored.


## 2.2. Real Estate Price Volatility and Monetary Policy

In recent years, many scholars at home and abroad have studied the relationship between real estate prices, monetary policy, and economic fluctuations, mainly using DSGE model analysis. However, different scholars have different views on the impact of monetary policy on the real estate market. Most of the early literature concluded that monetary policy need not respond to real estate price volatility and that monetary policy regulations that dampened asset price volatility reduced output volatility, albeit marginally. However, this led to more dramatic inflationary fluctuations and did not stabilize the economy [10, 11]. After an in-depth analysis of the above literature, it is not difficult to find that their models have the following two common features. First, incremental changes in assets such as real estate are not considered separately, which is clearly not in line with the current economic reality, where the real estate firms have become an important pillar of the national economy in many important economies. Second, many important financial market frictions were not attended to, which may lead to biased policy transmission paths and ultimately yield expected results inconsistent with reality. Therefore, later scholars continued their research to address the above issues by adding the real estate market as an important productive sector to the model for analysis. As the uncertainty of the economy increased after the subprime mortgage crisis, more scholars introduced financial frictions such as credit constraints and monetary policy shocks into the DSGE model. They began to focus on the financial stirrup effect and various types of shocks on the macro-economic regulation effect. It has been found that the inclusion of heterogeneous production sectors can better model the transmission path of monetary policy and multiple shocks to the real economy, and real estate prices have become an important transmission medium for monetary policy shocks [12–14]. This view gradually gained influence after 2008, with a growing literature affirming the role of monetary policy on asset prices and its macro-economic implications.They analyzed the U.S. real estate market by building a DSGE model that includes credit constraints and found that real estate price volatility has a significant impact on the cyclical fluctuations of the economy [15]. Others focused on two frictions, asset collateral and external financing premium, and argued that negative fluctuations in asset prices lead to homogeneous fluctuations in investment and output, exacerbating negative fluctuations in the economy [16]. Real estate mortgages have a significant financial stirrup effect in economies where the macro-economic impact of real estate price volatility is more dramatic and that this spillover effect is more pronounced in countries with more developed real estate financial markets [17]. Some scholars obtained similar conclusions from their analysis in the context of the Chinese economy: price-based monetary policy shocks are a key determinant of real estate price volatility, and excessive real estate price increases can be curbed through the formulation of appropriate monetary policies [18]. The shocks such as mortgage rate shocks and preference shocks to real estate have a significant impact on macro-economic fluctuations in China [19]. Monetary policy shocks affect consumption and real estate demand through the medium of nominal interest rates, ultimately leading to fluctuations in real estate prices and aggregate demand [20, 21]. The government can use monetary policy and financial shock effects to achieve stability in the real estate market. Therefore, some scholars argue that expectations affect cyclical fluctuations in the real estate market and even the macro-economy [22]. Active use of monetary policy tools such as lending rates can effectively reduce the volatility of household debt and aggregate consumption and GDP. There are significant effects in dampening expectation-driven cyclical fluctuations in the real estate market and the macro-economy [23]. Starting from the correlation between real estate prices and variables such as interest rates, exchange rates, and financing size, scholars have also argued that monetary policy is significantly effective in smoothing real estate prices as well as stabilizing the macro-economy and have discussed the linkage mechanism between these three [24].It is clear from the review of the above literature that while most early scholars and policymakers did not advocate intervention in asset price volatility with the help of monetary policy, the mainstream view changed significantly after the 2008 crisis. Using DSGE models that incorporate financial frictions, many scholars have affirmed the moderating role of monetary policy on real estate prices as well as macro-economic stability. Since most of the studies mentioned above discuss the impact of a single type of monetary policy on real estate prices, few articles compare and analyze the impact of different monetary policies. Therefore, there is no uniform analysis on the choice of the optimal monetary policy.


## 3. The DSGE Model

### 3.1. Model Frame

Compared with previous models, this paper constructed a DSGE model including COVID-19 shocks, the real estate market, and financial frictions. The model includes multiple macro-economic sectors, such as households, firms, commercial banks, and central banks. We try to compare and analyze the impact of different monetary policies. As seen in the 2020 Chinese and global economic data and related reports, the COVID-19 shock triggers a reduction in the rate of technological upgrading, human resource mismatch, and different proportions of original stock capital accumulation in each sector of production firms, and the overall performance of the economy is severely affected by the level of output. The impact of COVID-19 on the economy is similar to previous disasters in that it causes a reduction in the level of output in the economy and a decline in capital accumulation. However, the impact of this epidemic is much broader, and its negative impact is no less than that of any previous disaster. Consequently, the model in this paper will introduce variablesust for COVID-19 shocks in the real estate firms, the consumer goods sector, and household capital accumulation, which result in sectoral total factor productivity and capital stock being affected, as shown in Figure 1.Figure 1
Model structure diagram.


### 3.2. Households

Drawing on Iacoviello’s model setup, heterogeneous household characteristics are introduced in the household sector, considering the differences between Chinese and U.S. households: savings-type households and loan-type households [11]. The discount factor β′ is larger for savings-type households than for loan-type households β″. When making utility maximization choices, loan-type households are more inclined to consume than savings-type households, while savings-type households are more inclined to save for investment. Thus, saving households accumulate physical capital through investment and save in commercial banks. In contrast, loan-based households do not accumulate physical capital and borrow from commercial banks as collateral for their only real estate asset that has a collateral function. Therefore, a financial stirrup mechanism is introduced in the model. The proportion of saving households is denoted as α and the proportion of loan households is 1−α.


#### 3.2.1. Savings-Type Households

Saving-type households’ discount factorsβ′ is saving-type households' discount factor. Subjecting to the budget constraints, saving-type households rationally choose consumption Ct′, housing Ht′, labor Nt′, assets: physical assets, and financial assets (including monetary Mt′, deposits bt′, etc.) subject to budget constraints. Maximizing household lifetime utility:(1)maxEt∑t=0∞β′tlnCt′+JtlnHt′+lnMt′−Nt′1+ϕ1+ϕ,where ϕ is the inverse of the real wage elasticity and Jt is a housing preference shock that obeys the AR(1) process lnJt=ρtlnJt−1+υj,t (υj,t ∼ N0,σj2)(Exogenous shocks in the text take the same setting, i.e., they obey the first-order autoregressive process.). The labor supply of a saving household is the sum of its labor supply in the real estate and consumer goods sectors, assuming that labor supply is invested according to this equation:(2)Nt′=Nct′1+τ+Nht′1+τ1/1+τ,where τ is the elasticity of substitution of labor inputs between sectors and Nct′ and Nht′ represent the household’s labor supply in the consumer goods and real estate firms. The saving household faces the following budget constraint:(3)Ct′+bt′+Mt′+QtHt′=Nct′Wct′+Nht′Wht′+Mt−1′Πt+rt−1b′bt−1′Πt+Qt1−δhHt−1′,where δh is the depreciation rate of real estate, Wct′ and Wht′ represent the level of real wages in the consumer goods sector and the real estate firms, Πt is the inflation rate, rtb′ is the interest rate on bank deposits, and Qt is the level of real estate prices.


#### 3.2.2. Loan-Type Households

Loan-type households have a discount factor ofβ″. Loan-type households have no capital holdings and mortgage their homes bt″ (to commercial banks). Maximizing process lifetime utility:(4)maxEt∑t=0∞β″tlnCt″+JtlnHt″+lnMt″−Nt″1+ϕ1+ϕ.Similar to the saving-type household, the labor supply of the loan-type household is invested according to this equation:(5)Nt″=Nct″1+τ+Nht″1+τ1/1+τ.The budget constraints faced by loan-based households are as follows:(6)Ct″+rt−1b″bt−1″Πt+Mt″+QtHt″=Nct″Wct″+Nht″Wht″+Mt−1″Πt+bt″+Qt1−δhHt−1″,where rtb″ is the bank’s lending rate. Loan-type households prefer to consume and use home mortgages, so they face the following credit constraints (m″ is the mortgage rate):(7)bt″=m″EtQt+11−δhHt″Πt+1rtb″.


### 3.3. Labor Supply and Wage Setting

These two household sectors are the only labor supply sectors in the economy, providing labor for the real estate and consumer goods sectors. Assume a Calvo-type stickiness setup for households: assume that the proportion of households with adjustable wages in each period is1−θw. θw is the wage stickiness index, i.e., the larger θw is, the stickier the wage is. In period t, households that can adjust their wages choose the actual optimal wage Wt∗. For households that cannot adjust their wages, wages are indexed to the inflation rate of the previous period (inflation inertia) and set to Wt−1Πt−1 (the fully indexed setting) [25].A large and competing class of labor integration agents in the economy adds up the heterogeneous labor supplied by each householdi into homogeneous labor and supplies it to other sectors. εw can be understood as the wage elasticity of labor demand.(8)Wc,h,t=∫01Wc,h,ti1−εwdi1/1−εw,where Wc,h,t denotes the real wage index for both sectors, assuming that the labor demand function faced by the first representative household is defined as(9)Nc,h,ti=Wc,h,tiWc,h,t−εwNc,h,t,where Nc,h,t is the aggregate demand in the labor market for both sectors. Solving the problem of setting the household optimal wage yields the real wage inflation equation for the household sector:(10)W^c,h,t=β′1+β′EtW^c,h,t+1+Π^t−1−Π^t+11+β′EtW^c,h,t+1+Π^t−1−1−β′θw1−θwθw1+β′1+εwϕW^c,h,t−ϕN^c,h,t−C^t.


### 3.4. Representative Enterprises

#### 3.4.1. Real Estate Firms

The real estate firm produces housing, referring to the setting in the article by Wang and Hou [26]. The real estate firm is assumed to consist of monopolistically competitive manufacturers continuously distributed on the interval [0,1], with homogeneous and divisible products and non-sticky housing prices. Real estate manufacturers produce by hiring labor, renting capital from savers, and providing land. The manufacturer’s production function can be expressed in the following form:(11)Yht=LtKh,t−1αhNht′αNht″1−α1−αh.The COVID-19 shock has hit the global economy since the beginning of 2020. As shown in the Chinese and global economic data for 2020 and related reports, the COVID-19 shock triggered a reduction in the rate of technological upgrading, human resource mismatch, and a different proportion of the original stock of capital accumulation in production enterprises in various sectors, resulting in an overall severe shock to the output level of the economy. The shock of COVID-19 on the economy is similar to that of previous catastrophes in that both have caused a decline in output levels and capital accumulation in the economy. However, the shock of the COVID-19 was more widespread and caused as much negative shock as any of the previous catastrophes. Therefore, in two production sectors, namely, the real estate sector and the consumer goods sector, a variableuts representing a COVID-19 shock is introduced to denote the probability of a COVID-19 shock occurring in period t [27]. This shock leads to a decrease in total factor productivity by a proportion syh. Since this COVID-19 shock has a greater impact than other previous catastrophic shocks, it can be distinguished by adjusting the size of the impairment proportion syh. Then, the above equation can be rewritten as follows:(12)Yht=1−utssyhLtKh,t−1αhNht′αNht″1−α1−αh.Assume that wages are non-differentiable within the same sector, i.e.,Nht′αNht″1−α. Here the land supply directly affects the output of the vendor, assuming that the vendor faces a representative land supply shock Lt. Since the wages of labor in the real estate firms are non-differentiable, Wht′=Wht″=Wht. From the vendor cost minimization problem, the real marginal cost function of the vendor is obtained.(13)MCht=1Lt11−utssyh1αα1−αh1αhαh11−αh1−αh11−α1−α1−αhRhtαhWht1−αh.It is assumed above that prices in the real estate firms are not sticky, i.e., all real estate vendors can re-price each period. Therefore, it is assumed that vendors use the marginal cost-plus method for pricing and thus(14)Qt=εhεh−1MCht,where εh/εh−1 is the price plus ratio and εh is the price elasticity coefficient of housing demand.


#### 3.4.2. Consumer Goods Sector

Referring to some of the assumptions of the real estate firms, the production of goods in the consumer goods sector requires the input of capital and labor to produce and supply its products to other economic agents. Like the real estate firms, considering that the epidemic shock also impacts TFP (total factor productivity), the production function is defined in the following form:(15)Yct=1−utssycAtKc,t−1αcNct′αNct″1−α1−αc.Here the technology shockAt directly affects the level of output of the vendor. Solving the vendor cost minimization problem yields the real marginal cost function of the vendor.(16)MCct=1At11−utssyc1αα1−αc1αcαc11−αc1−αc11−α1−α1−αcRctαcWct1−αc.Since this paper sets the existence of price stickiness in the consumer goods sector, the current price stickiness characteristics refer to the Calvo stochastic price adjustment model [28]. Assume that the proportion of manufacturers who can adjust prices in each period is 1−θc, and θc is the price stickiness index. The NK Phillips curve for the consumer goods sector can be obtained as follows.(17)Π^t=β′1+β′EtΠ^t+1+11+β′Π^t+1+1−β′θc1−θcθc1+β′M^Cct.


### 3.5. Capital Accumulation and Investment Decisions

It is assumed that saving households, as owners of capital goods, invest their holdings in various production sectors and achieve capital accumulation through investment decisions in each period [29]. The COVID-19 shock introduced in the model can lead to an impairment of the capital stock by a percentage. The capital accumulation of saving households in each sector satisfies the following equation.(18)Kct=1−utsskc1−δkKc,t−1+Ict1−ψc2IctIct−1−12utI,Kht=1−utsskh1−δkKh,t−1+Iht1−ψh2IhtIht−1−12utI.δk is the capital depreciation rate. Assuming that the saving household does not separate ownership and operation of the firm, the household makes its choice of capital along with its choice of investment, ψc and ψh are the sensitivity coefficients of the capital adjustment costs of the two sectors, respectively, and utI is the investment shock. Then, the saving household makes its investment decision through the following optimization problem.(19)maxEt∑t=0∞β′tλt′Kc,t−1Rct+Kh,t−1Rht−Ict−Iht.


### 3.6. Commercial Bank

Considering the model consistency and solution problems, the commercial bank sector in the model is set to be highly simplified compared to the behavioral characteristics of commercial banks in practice. The profit sources of commercial banks are deposit and loan spreads, which are obtained by taking deposits from saving households and then extending loans to the real estate firms and lending households to maximize profits. In the course of their operations, commercial banks are subject to the required legal deposit reserveRRt=bt′ftRR, of which ftRR is the legal deposit reserve ratio. Thus, the asset-liability structure of commercial banks can be expressed as follows:(20)RRt+bt″=bt′.Commercial banks need to consider liquidity issues while generating profits. Referring to the loan stock adjustment problem proposed by Atta and Dib, banks adjust the number of deposits and loans according to various requirements such as capital adequacy ratio in their operations [30]. This adjustment cost is assumed to be ψb/2bt″/bt−1″−12bt−1″, where bt″ denotes the total amount of loans and ψb is the loan stickiness parameter. Solving the bank’s profit maximization problem yields the first-order condition as(21)rtb″−rtb′1−ftRR−ψbbt″bt−1″−1=β′ψb2bt+1″bt″−12−ψbbt+1″bt″−1bt+1″bt″.


### 3.7. Central Bank

There is no uniform conclusion on the applicability of monetary rules in China, and Huang and Xu conducted a policy analysis using a Taylor rule with additional interest rate stickiness and obtained good fitting results [31]. In contrast, others argued that a quantity rule based on monetary supply regulation is more representative of China’s macro-policy practice [32, 33]. Given the above literature, in the following analysis, the model settings are considered separately for both interest rate and quantity rules, which are commonly used in the literature.


#### 3.7.1. Interest Rule

Assuming that the lending rate is the main operating instrument of the central bank [26], the monetary policy rule takes the form of the promoted Taylor rule:(22)rtb″rssb″=rt−1b″rssb″ρbΠtΠssφΠYtYssφYQtQssφQ1−ρbutr,where rtb″ denotes the lending rate, ρb is the interest rate smoothing coefficient, which is set to avoid the impact of large fluctuations in interest rates on the economy and allows for some inertia in the adjustment of interest rates, φΠ, φY, φQ denote the response coefficients of output gap, inflation, and real estate prices, and utr is the monetary policy shock.


#### 3.7.2. Quantity Rule

Under the quantity rule, the monetary supply becomes the main operating tool of the central bank. According to the model setting of this paper, the monetary aggregate isMt=Mt′+Mt″+bt′ [33], the monetary growth rate can be expressed as gmt=Mt/Mt−1, and the monetary policy rule is as follows:(23)gmtgmss=gmt−1gmssρmΠtΠss−φπYtYss−φyQtQss−φq1−ρmutg,where ρm is the smoothing factor that regulates the monetary supply, allowing for some inertia in the adjustment of the monetary supply, and utg is the monetary policy shock at this point.


### 3.8. Equilibrium

The clearing conditions of the whole system, including the commodity market, are(24)Yt=Yct+QtYht,Yct=Ct′+Ct″+Ict+Iht,Yht=Ht′−1−δhHt−1′+Ht″−1−δhHt−1″,bt′=bt″1−ftRR,where Yt denotes real GDP. The equilibrium conditions of the above-mentioned economic agents and production sectors and the exogenous shock processes together construct an economic dynamical system.


## 3.1. Model Frame

Compared with previous models, this paper constructed a DSGE model including COVID-19 shocks, the real estate market, and financial frictions. The model includes multiple macro-economic sectors, such as households, firms, commercial banks, and central banks. We try to compare and analyze the impact of different monetary policies. As seen in the 2020 Chinese and global economic data and related reports, the COVID-19 shock triggers a reduction in the rate of technological upgrading, human resource mismatch, and different proportions of original stock capital accumulation in each sector of production firms, and the overall performance of the economy is severely affected by the level of output. The impact of COVID-19 on the economy is similar to previous disasters in that it causes a reduction in the level of output in the economy and a decline in capital accumulation. However, the impact of this epidemic is much broader, and its negative impact is no less than that of any previous disaster. Consequently, the model in this paper will introduce variablesust for COVID-19 shocks in the real estate firms, the consumer goods sector, and household capital accumulation, which result in sectoral total factor productivity and capital stock being affected, as shown in Figure 1.Figure 1
Model structure diagram.


## 3.2. Households

Drawing on Iacoviello’s model setup, heterogeneous household characteristics are introduced in the household sector, considering the differences between Chinese and U.S. households: savings-type households and loan-type households [11]. The discount factor β′ is larger for savings-type households than for loan-type households β″. When making utility maximization choices, loan-type households are more inclined to consume than savings-type households, while savings-type households are more inclined to save for investment. Thus, saving households accumulate physical capital through investment and save in commercial banks. In contrast, loan-based households do not accumulate physical capital and borrow from commercial banks as collateral for their only real estate asset that has a collateral function. Therefore, a financial stirrup mechanism is introduced in the model. The proportion of saving households is denoted as α and the proportion of loan households is 1−α.


### 3.2.1. Savings-Type Households

Saving-type households’ discount factorsβ′ is saving-type households' discount factor. Subjecting to the budget constraints, saving-type households rationally choose consumption Ct′, housing Ht′, labor Nt′, assets: physical assets, and financial assets (including monetary Mt′, deposits bt′, etc.) subject to budget constraints. Maximizing household lifetime utility:(1)maxEt∑t=0∞β′tlnCt′+JtlnHt′+lnMt′−Nt′1+ϕ1+ϕ,where ϕ is the inverse of the real wage elasticity and Jt is a housing preference shock that obeys the AR(1) process lnJt=ρtlnJt−1+υj,t (υj,t ∼ N0,σj2)(Exogenous shocks in the text take the same setting, i.e., they obey the first-order autoregressive process.). The labor supply of a saving household is the sum of its labor supply in the real estate and consumer goods sectors, assuming that labor supply is invested according to this equation:(2)Nt′=Nct′1+τ+Nht′1+τ1/1+τ,where τ is the elasticity of substitution of labor inputs between sectors and Nct′ and Nht′ represent the household’s labor supply in the consumer goods and real estate firms. The saving household faces the following budget constraint:(3)Ct′+bt′+Mt′+QtHt′=Nct′Wct′+Nht′Wht′+Mt−1′Πt+rt−1b′bt−1′Πt+Qt1−δhHt−1′,where δh is the depreciation rate of real estate, Wct′ and Wht′ represent the level of real wages in the consumer goods sector and the real estate firms, Πt is the inflation rate, rtb′ is the interest rate on bank deposits, and Qt is the level of real estate prices.


### 3.2.2. Loan-Type Households

Loan-type households have a discount factor ofβ″. Loan-type households have no capital holdings and mortgage their homes bt″ (to commercial banks). Maximizing process lifetime utility:(4)maxEt∑t=0∞β″tlnCt″+JtlnHt″+lnMt″−Nt″1+ϕ1+ϕ.Similar to the saving-type household, the labor supply of the loan-type household is invested according to this equation:(5)Nt″=Nct″1+τ+Nht″1+τ1/1+τ.The budget constraints faced by loan-based households are as follows:(6)Ct″+rt−1b″bt−1″Πt+Mt″+QtHt″=Nct″Wct″+Nht″Wht″+Mt−1″Πt+bt″+Qt1−δhHt−1″,where rtb″ is the bank’s lending rate. Loan-type households prefer to consume and use home mortgages, so they face the following credit constraints (m″ is the mortgage rate):(7)bt″=m″EtQt+11−δhHt″Πt+1rtb″.


## 3.2.1. Savings-Type Households

Saving-type households’ discount factorsβ′ is saving-type households' discount factor. Subjecting to the budget constraints, saving-type households rationally choose consumption Ct′, housing Ht′, labor Nt′, assets: physical assets, and financial assets (including monetary Mt′, deposits bt′, etc.) subject to budget constraints. Maximizing household lifetime utility:(1)maxEt∑t=0∞β′tlnCt′+JtlnHt′+lnMt′−Nt′1+ϕ1+ϕ,where ϕ is the inverse of the real wage elasticity and Jt is a housing preference shock that obeys the AR(1) process lnJt=ρtlnJt−1+υj,t (υj,t ∼ N0,σj2)(Exogenous shocks in the text take the same setting, i.e., they obey the first-order autoregressive process.). The labor supply of a saving household is the sum of its labor supply in the real estate and consumer goods sectors, assuming that labor supply is invested according to this equation:(2)Nt′=Nct′1+τ+Nht′1+τ1/1+τ,where τ is the elasticity of substitution of labor inputs between sectors and Nct′ and Nht′ represent the household’s labor supply in the consumer goods and real estate firms. The saving household faces the following budget constraint:(3)Ct′+bt′+Mt′+QtHt′=Nct′Wct′+Nht′Wht′+Mt−1′Πt+rt−1b′bt−1′Πt+Qt1−δhHt−1′,where δh is the depreciation rate of real estate, Wct′ and Wht′ represent the level of real wages in the consumer goods sector and the real estate firms, Πt is the inflation rate, rtb′ is the interest rate on bank deposits, and Qt is the level of real estate prices.


## 3.2.2. Loan-Type Households

Loan-type households have a discount factor ofβ″. Loan-type households have no capital holdings and mortgage their homes bt″ (to commercial banks). Maximizing process lifetime utility:(4)maxEt∑t=0∞β″tlnCt″+JtlnHt″+lnMt″−Nt″1+ϕ1+ϕ.Similar to the saving-type household, the labor supply of the loan-type household is invested according to this equation:(5)Nt″=Nct″1+τ+Nht″1+τ1/1+τ.The budget constraints faced by loan-based households are as follows:(6)Ct″+rt−1b″bt−1″Πt+Mt″+QtHt″=Nct″Wct″+Nht″Wht″+Mt−1″Πt+bt″+Qt1−δhHt−1″,where rtb″ is the bank’s lending rate. Loan-type households prefer to consume and use home mortgages, so they face the following credit constraints (m″ is the mortgage rate):(7)bt″=m″EtQt+11−δhHt″Πt+1rtb″.


## 3.3. Labor Supply and Wage Setting

These two household sectors are the only labor supply sectors in the economy, providing labor for the real estate and consumer goods sectors. Assume a Calvo-type stickiness setup for households: assume that the proportion of households with adjustable wages in each period is1−θw. θw is the wage stickiness index, i.e., the larger θw is, the stickier the wage is. In period t, households that can adjust their wages choose the actual optimal wage Wt∗. For households that cannot adjust their wages, wages are indexed to the inflation rate of the previous period (inflation inertia) and set to Wt−1Πt−1 (the fully indexed setting) [25].A large and competing class of labor integration agents in the economy adds up the heterogeneous labor supplied by each householdi into homogeneous labor and supplies it to other sectors. εw can be understood as the wage elasticity of labor demand.(8)Wc,h,t=∫01Wc,h,ti1−εwdi1/1−εw,where Wc,h,t denotes the real wage index for both sectors, assuming that the labor demand function faced by the first representative household is defined as(9)Nc,h,ti=Wc,h,tiWc,h,t−εwNc,h,t,where Nc,h,t is the aggregate demand in the labor market for both sectors. Solving the problem of setting the household optimal wage yields the real wage inflation equation for the household sector:(10)W^c,h,t=β′1+β′EtW^c,h,t+1+Π^t−1−Π^t+11+β′EtW^c,h,t+1+Π^t−1−1−β′θw1−θwθw1+β′1+εwϕW^c,h,t−ϕN^c,h,t−C^t.


## 3.4. Representative Enterprises

### 3.4.1. Real Estate Firms

The real estate firm produces housing, referring to the setting in the article by Wang and Hou [26]. The real estate firm is assumed to consist of monopolistically competitive manufacturers continuously distributed on the interval [0,1], with homogeneous and divisible products and non-sticky housing prices. Real estate manufacturers produce by hiring labor, renting capital from savers, and providing land. The manufacturer’s production function can be expressed in the following form:(11)Yht=LtKh,t−1αhNht′αNht″1−α1−αh.The COVID-19 shock has hit the global economy since the beginning of 2020. As shown in the Chinese and global economic data for 2020 and related reports, the COVID-19 shock triggered a reduction in the rate of technological upgrading, human resource mismatch, and a different proportion of the original stock of capital accumulation in production enterprises in various sectors, resulting in an overall severe shock to the output level of the economy. The shock of COVID-19 on the economy is similar to that of previous catastrophes in that both have caused a decline in output levels and capital accumulation in the economy. However, the shock of the COVID-19 was more widespread and caused as much negative shock as any of the previous catastrophes. Therefore, in two production sectors, namely, the real estate sector and the consumer goods sector, a variableuts representing a COVID-19 shock is introduced to denote the probability of a COVID-19 shock occurring in period t [27]. This shock leads to a decrease in total factor productivity by a proportion syh. Since this COVID-19 shock has a greater impact than other previous catastrophic shocks, it can be distinguished by adjusting the size of the impairment proportion syh. Then, the above equation can be rewritten as follows:(12)Yht=1−utssyhLtKh,t−1αhNht′αNht″1−α1−αh.Assume that wages are non-differentiable within the same sector, i.e.,Nht′αNht″1−α. Here the land supply directly affects the output of the vendor, assuming that the vendor faces a representative land supply shock Lt. Since the wages of labor in the real estate firms are non-differentiable, Wht′=Wht″=Wht. From the vendor cost minimization problem, the real marginal cost function of the vendor is obtained.(13)MCht=1Lt11−utssyh1αα1−αh1αhαh11−αh1−αh11−α1−α1−αhRhtαhWht1−αh.It is assumed above that prices in the real estate firms are not sticky, i.e., all real estate vendors can re-price each period. Therefore, it is assumed that vendors use the marginal cost-plus method for pricing and thus(14)Qt=εhεh−1MCht,where εh/εh−1 is the price plus ratio and εh is the price elasticity coefficient of housing demand.


### 3.4.2. Consumer Goods Sector

Referring to some of the assumptions of the real estate firms, the production of goods in the consumer goods sector requires the input of capital and labor to produce and supply its products to other economic agents. Like the real estate firms, considering that the epidemic shock also impacts TFP (total factor productivity), the production function is defined in the following form:(15)Yct=1−utssycAtKc,t−1αcNct′αNct″1−α1−αc.Here the technology shockAt directly affects the level of output of the vendor. Solving the vendor cost minimization problem yields the real marginal cost function of the vendor.(16)MCct=1At11−utssyc1αα1−αc1αcαc11−αc1−αc11−α1−α1−αcRctαcWct1−αc.Since this paper sets the existence of price stickiness in the consumer goods sector, the current price stickiness characteristics refer to the Calvo stochastic price adjustment model [28]. Assume that the proportion of manufacturers who can adjust prices in each period is 1−θc, and θc is the price stickiness index. The NK Phillips curve for the consumer goods sector can be obtained as follows.(17)Π^t=β′1+β′EtΠ^t+1+11+β′Π^t+1+1−β′θc1−θcθc1+β′M^Cct.


## 3.4.1. Real Estate Firms

The real estate firm produces housing, referring to the setting in the article by Wang and Hou [26]. The real estate firm is assumed to consist of monopolistically competitive manufacturers continuously distributed on the interval [0,1], with homogeneous and divisible products and non-sticky housing prices. Real estate manufacturers produce by hiring labor, renting capital from savers, and providing land. The manufacturer’s production function can be expressed in the following form:(11)Yht=LtKh,t−1αhNht′αNht″1−α1−αh.The COVID-19 shock has hit the global economy since the beginning of 2020. As shown in the Chinese and global economic data for 2020 and related reports, the COVID-19 shock triggered a reduction in the rate of technological upgrading, human resource mismatch, and a different proportion of the original stock of capital accumulation in production enterprises in various sectors, resulting in an overall severe shock to the output level of the economy. The shock of COVID-19 on the economy is similar to that of previous catastrophes in that both have caused a decline in output levels and capital accumulation in the economy. However, the shock of the COVID-19 was more widespread and caused as much negative shock as any of the previous catastrophes. Therefore, in two production sectors, namely, the real estate sector and the consumer goods sector, a variableuts representing a COVID-19 shock is introduced to denote the probability of a COVID-19 shock occurring in period t [27]. This shock leads to a decrease in total factor productivity by a proportion syh. Since this COVID-19 shock has a greater impact than other previous catastrophic shocks, it can be distinguished by adjusting the size of the impairment proportion syh. Then, the above equation can be rewritten as follows:(12)Yht=1−utssyhLtKh,t−1αhNht′αNht″1−α1−αh.Assume that wages are non-differentiable within the same sector, i.e.,Nht′αNht″1−α. Here the land supply directly affects the output of the vendor, assuming that the vendor faces a representative land supply shock Lt. Since the wages of labor in the real estate firms are non-differentiable, Wht′=Wht″=Wht. From the vendor cost minimization problem, the real marginal cost function of the vendor is obtained.(13)MCht=1Lt11−utssyh1αα1−αh1αhαh11−αh1−αh11−α1−α1−αhRhtαhWht1−αh.It is assumed above that prices in the real estate firms are not sticky, i.e., all real estate vendors can re-price each period. Therefore, it is assumed that vendors use the marginal cost-plus method for pricing and thus(14)Qt=εhεh−1MCht,where εh/εh−1 is the price plus ratio and εh is the price elasticity coefficient of housing demand.


## 3.4.2. Consumer Goods Sector

Referring to some of the assumptions of the real estate firms, the production of goods in the consumer goods sector requires the input of capital and labor to produce and supply its products to other economic agents. Like the real estate firms, considering that the epidemic shock also impacts TFP (total factor productivity), the production function is defined in the following form:(15)Yct=1−utssycAtKc,t−1αcNct′αNct″1−α1−αc.Here the technology shockAt directly affects the level of output of the vendor. Solving the vendor cost minimization problem yields the real marginal cost function of the vendor.(16)MCct=1At11−utssyc1αα1−αc1αcαc11−αc1−αc11−α1−α1−αcRctαcWct1−αc.Since this paper sets the existence of price stickiness in the consumer goods sector, the current price stickiness characteristics refer to the Calvo stochastic price adjustment model [28]. Assume that the proportion of manufacturers who can adjust prices in each period is 1−θc, and θc is the price stickiness index. The NK Phillips curve for the consumer goods sector can be obtained as follows.(17)Π^t=β′1+β′EtΠ^t+1+11+β′Π^t+1+1−β′θc1−θcθc1+β′M^Cct.


## 3.5. Capital Accumulation and Investment Decisions

It is assumed that saving households, as owners of capital goods, invest their holdings in various production sectors and achieve capital accumulation through investment decisions in each period [29]. The COVID-19 shock introduced in the model can lead to an impairment of the capital stock by a percentage. The capital accumulation of saving households in each sector satisfies the following equation.(18)Kct=1−utsskc1−δkKc,t−1+Ict1−ψc2IctIct−1−12utI,Kht=1−utsskh1−δkKh,t−1+Iht1−ψh2IhtIht−1−12utI.δk is the capital depreciation rate. Assuming that the saving household does not separate ownership and operation of the firm, the household makes its choice of capital along with its choice of investment, ψc and ψh are the sensitivity coefficients of the capital adjustment costs of the two sectors, respectively, and utI is the investment shock. Then, the saving household makes its investment decision through the following optimization problem.(19)maxEt∑t=0∞β′tλt′Kc,t−1Rct+Kh,t−1Rht−Ict−Iht.


## 3.6. Commercial Bank

Considering the model consistency and solution problems, the commercial bank sector in the model is set to be highly simplified compared to the behavioral characteristics of commercial banks in practice. The profit sources of commercial banks are deposit and loan spreads, which are obtained by taking deposits from saving households and then extending loans to the real estate firms and lending households to maximize profits. In the course of their operations, commercial banks are subject to the required legal deposit reserveRRt=bt′ftRR, of which ftRR is the legal deposit reserve ratio. Thus, the asset-liability structure of commercial banks can be expressed as follows:(20)RRt+bt″=bt′.Commercial banks need to consider liquidity issues while generating profits. Referring to the loan stock adjustment problem proposed by Atta and Dib, banks adjust the number of deposits and loans according to various requirements such as capital adequacy ratio in their operations [30]. This adjustment cost is assumed to be ψb/2bt″/bt−1″−12bt−1″, where bt″ denotes the total amount of loans and ψb is the loan stickiness parameter. Solving the bank’s profit maximization problem yields the first-order condition as(21)rtb″−rtb′1−ftRR−ψbbt″bt−1″−1=β′ψb2bt+1″bt″−12−ψbbt+1″bt″−1bt+1″bt″.


## 3.7. Central Bank

There is no uniform conclusion on the applicability of monetary rules in China, and Huang and Xu conducted a policy analysis using a Taylor rule with additional interest rate stickiness and obtained good fitting results [31]. In contrast, others argued that a quantity rule based on monetary supply regulation is more representative of China’s macro-policy practice [32, 33]. Given the above literature, in the following analysis, the model settings are considered separately for both interest rate and quantity rules, which are commonly used in the literature.


### 3.7.1. Interest Rule

Assuming that the lending rate is the main operating instrument of the central bank [26], the monetary policy rule takes the form of the promoted Taylor rule:(22)rtb″rssb″=rt−1b″rssb″ρbΠtΠssφΠYtYssφYQtQssφQ1−ρbutr,where rtb″ denotes the lending rate, ρb is the interest rate smoothing coefficient, which is set to avoid the impact of large fluctuations in interest rates on the economy and allows for some inertia in the adjustment of interest rates, φΠ, φY, φQ denote the response coefficients of output gap, inflation, and real estate prices, and utr is the monetary policy shock.


### 3.7.2. Quantity Rule

Under the quantity rule, the monetary supply becomes the main operating tool of the central bank. According to the model setting of this paper, the monetary aggregate isMt=Mt′+Mt″+bt′ [33], the monetary growth rate can be expressed as gmt=Mt/Mt−1, and the monetary policy rule is as follows:(23)gmtgmss=gmt−1gmssρmΠtΠss−φπYtYss−φyQtQss−φq1−ρmutg,where ρm is the smoothing factor that regulates the monetary supply, allowing for some inertia in the adjustment of the monetary supply, and utg is the monetary policy shock at this point.


## 3.7.1. Interest Rule

Assuming that the lending rate is the main operating instrument of the central bank [26], the monetary policy rule takes the form of the promoted Taylor rule:(22)rtb″rssb″=rt−1b″rssb″ρbΠtΠssφΠYtYssφYQtQssφQ1−ρbutr,where rtb″ denotes the lending rate, ρb is the interest rate smoothing coefficient, which is set to avoid the impact of large fluctuations in interest rates on the economy and allows for some inertia in the adjustment of interest rates, φΠ, φY, φQ denote the response coefficients of output gap, inflation, and real estate prices, and utr is the monetary policy shock.


## 3.7.2. Quantity Rule

Under the quantity rule, the monetary supply becomes the main operating tool of the central bank. According to the model setting of this paper, the monetary aggregate isMt=Mt′+Mt″+bt′ [33], the monetary growth rate can be expressed as gmt=Mt/Mt−1, and the monetary policy rule is as follows:(23)gmtgmss=gmt−1gmssρmΠtΠss−φπYtYss−φyQtQss−φq1−ρmutg,where ρm is the smoothing factor that regulates the monetary supply, allowing for some inertia in the adjustment of the monetary supply, and utg is the monetary policy shock at this point.


## 3.8. Equilibrium

The clearing conditions of the whole system, including the commodity market, are(24)Yt=Yct+QtYht,Yct=Ct′+Ct″+Ict+Iht,Yht=Ht′−1−δhHt−1′+Ht″−1−δhHt−1″,bt′=bt″1−ftRR,where Yt denotes real GDP. The equilibrium conditions of the above-mentioned economic agents and production sectors and the exogenous shock processes together construct an economic dynamical system.


## 4. Parameter Calibration and Estimation

### 4.1. Parameter Calibration

When calculating the steady state, it is necessary to calibrate the relevant parameters to determine the steady state. In this paper, the data related to the Chinese economic variables are matched to the relevant parameters in the steady-state model and are summarized in Table1.Table 1
Parameter calibration.
CalibrationMeaningCalibration valueBasis for taking valuesβ′Savings-based household discount factor0.988Iacoviello and Neri [15]β″Loan-based household discount factor0.95Wang and Hou [26]δkElasticity of substitution between labor inputs in each sector1ϕQuarterly depreciation rate of real estate0.8%τCapital depreciation rate (quarterly)2.5%Xu and Liu [33]δhThe inverse of the real wage elasticity of labor1Bernanke et al. [10], Peng and Fang [39]m″Mortgage ratio0.7According to the current lending policy in China, the downpayment ratio for the first suite is usually 30%εhElasticity of output with respect to capital for the real estate firms0.5Iacoviello and Neri [15]αhElasticity of output of the consumer goods sector with respect to capital0.5αcPrice elasticity of demand for housing6Iacoviello [11]φΠInflation under the interest rate rule0.15Hou and Gong [18]φYOutput gap under the interest rate rule1.5φQReal estate price response coefficient under the interest rate rule1.5φπInterest rate smoothing coefficient0.8φyInflation under the quantity rule0.5Xu and Liu [33]φqOutput gap under the quantity rule1.5ρbReal estate price response coefficient under the quantity rule1.5ρmMonetary supply smoothing coefficient0.8syProportion of TFP declines in both sectors due to epidemic shocks0.0678Estimation based on Barro [35] estimation method with actual data from China.skProportion of capital stock impaired due to epidemic shocks0.0678Chen et al. [34]Among them,sy, sk are estimated based on the estimation method of Barro using Chinese real GDP per capita growth rate data [35]. Figure 2 shows China’s real GDP per capita growth rate indicators during 1953–2020. The average value of the nine negative values is taken as the percentage of total factor productivity loss due to disaster shocks in China, and the estimated percentage of total factor productivity loss is 0.0678. Therefore, the above percentage of loss is set to 0.0678.Figure 2
Trends in real GDP per capita growth rates(Data source: Calculated based on data from the official website of the National Bureau of Statistics.).


### 4.2. Parameter Simulation

There are seven external shocks included in the model. This paper selects relevant data from seven primary data such as consumer price index, total retail sales of consumer goods, fixed asset investment, gross domestic product, average price of commercial housing (calculated from sales of commercial housing/area of commercial housing sales), and monetary and quasi-monetary (M2) supply to estimate the model. The data sample period is from the first quarter of 2000 to the fourth quarter of 2020. Since the model variables are all real values, the above nominal data are processed and converted to real values. Quarterly data are used for all data characterized by seasonal fluctuations, except for the monetary supply and interest rates, which do not have significant seasonal characteristics. Therefore, X12 is used to adjust these data seasonally. Next, the natural logarithm of the above-adjusted data was taken, and finally, HP filtering was applied to remove long-term trends from the data and convert them into observable variable information.The parameters to be estimated by the model were estimated using Bayes methods to compare the posterior estimates under the price-based rule and the quantity-based rule, as shown in Table2.Table 2
Bayes estimation results of the model.
ParameterPrior distributionInterest ruleQuantity ruleDistr.MeanPosterior meanConfidence intervalPosterior meanConfidence intervalρjBeta0.80.7662(0.7633, 0.7686)0.8386(0.7320, 0.9502)ρuIBeta0.70.9193(0.9158, 0.9226)0.8313(0.8151, 0.8439)ρusBeta0.80.7455(0.7445, 0.7465)0.8447(0.8319, 0.8563)ρlBeta0.80.9973(0.9951, 0.9993)0.8972(0.8809, 0.9180)ρaBeta0.80.8218(0.8197, 0.8238)0.4369(0.4063, 0.4737)ρfRRBeta0.80.9152(0.9117, 0.9181)0.8700(0.8295, 0.9208)ρur/ρugBeta0.80.9991(0.9986, 0.9998)0.8471(0.8145, 0.8770)σjInv.Gamma0.10.0059(0.0026, 0.0092)0.0078(0.0024, 0.0139)σuIInv.Gamma0.10.0070(0.0060, 0.0079)0.2996(0.2453, 0.3526)σusInv.Gamma0.10.0017(0.0015, 0.0020)0.2346(0.1774, 0.3195)σlInv.Gamma0.10.0019(0.0018, 0.0020)0.0929(0.0778, 0.1081)σaInv.Gamma0.10.2271(0.2142, 0.2409)0.1476(0.0832, 0.1789)σfRRInv.Gamma0.10.1827(0.1715, 0.1911)0.0079(0.0022, 0.0135)σur/σugInv.Gamma0.10.0057(0.0050, 0.0065)0.0355(0.0290, 0.0418)


## 4.1. Parameter Calibration

When calculating the steady state, it is necessary to calibrate the relevant parameters to determine the steady state. In this paper, the data related to the Chinese economic variables are matched to the relevant parameters in the steady-state model and are summarized in Table1.Table 1
Parameter calibration.
CalibrationMeaningCalibration valueBasis for taking valuesβ′Savings-based household discount factor0.988Iacoviello and Neri [15]β″Loan-based household discount factor0.95Wang and Hou [26]δkElasticity of substitution between labor inputs in each sector1ϕQuarterly depreciation rate of real estate0.8%τCapital depreciation rate (quarterly)2.5%Xu and Liu [33]δhThe inverse of the real wage elasticity of labor1Bernanke et al. [10], Peng and Fang [39]m″Mortgage ratio0.7According to the current lending policy in China, the downpayment ratio for the first suite is usually 30%εhElasticity of output with respect to capital for the real estate firms0.5Iacoviello and Neri [15]αhElasticity of output of the consumer goods sector with respect to capital0.5αcPrice elasticity of demand for housing6Iacoviello [11]φΠInflation under the interest rate rule0.15Hou and Gong [18]φYOutput gap under the interest rate rule1.5φQReal estate price response coefficient under the interest rate rule1.5φπInterest rate smoothing coefficient0.8φyInflation under the quantity rule0.5Xu and Liu [33]φqOutput gap under the quantity rule1.5ρbReal estate price response coefficient under the quantity rule1.5ρmMonetary supply smoothing coefficient0.8syProportion of TFP declines in both sectors due to epidemic shocks0.0678Estimation based on Barro [35] estimation method with actual data from China.skProportion of capital stock impaired due to epidemic shocks0.0678Chen et al. [34]Among them,sy, sk are estimated based on the estimation method of Barro using Chinese real GDP per capita growth rate data [35]. Figure 2 shows China’s real GDP per capita growth rate indicators during 1953–2020. The average value of the nine negative values is taken as the percentage of total factor productivity loss due to disaster shocks in China, and the estimated percentage of total factor productivity loss is 0.0678. Therefore, the above percentage of loss is set to 0.0678.Figure 2
Trends in real GDP per capita growth rates(Data source: Calculated based on data from the official website of the National Bureau of Statistics.).


## 4.2. Parameter Simulation

There are seven external shocks included in the model. This paper selects relevant data from seven primary data such as consumer price index, total retail sales of consumer goods, fixed asset investment, gross domestic product, average price of commercial housing (calculated from sales of commercial housing/area of commercial housing sales), and monetary and quasi-monetary (M2) supply to estimate the model. The data sample period is from the first quarter of 2000 to the fourth quarter of 2020. Since the model variables are all real values, the above nominal data are processed and converted to real values. Quarterly data are used for all data characterized by seasonal fluctuations, except for the monetary supply and interest rates, which do not have significant seasonal characteristics. Therefore, X12 is used to adjust these data seasonally. Next, the natural logarithm of the above-adjusted data was taken, and finally, HP filtering was applied to remove long-term trends from the data and convert them into observable variable information.The parameters to be estimated by the model were estimated using Bayes methods to compare the posterior estimates under the price-based rule and the quantity-based rule, as shown in Table2.Table 2
Bayes estimation results of the model.
ParameterPrior distributionInterest ruleQuantity ruleDistr.MeanPosterior meanConfidence intervalPosterior meanConfidence intervalρjBeta0.80.7662(0.7633, 0.7686)0.8386(0.7320, 0.9502)ρuIBeta0.70.9193(0.9158, 0.9226)0.8313(0.8151, 0.8439)ρusBeta0.80.7455(0.7445, 0.7465)0.8447(0.8319, 0.8563)ρlBeta0.80.9973(0.9951, 0.9993)0.8972(0.8809, 0.9180)ρaBeta0.80.8218(0.8197, 0.8238)0.4369(0.4063, 0.4737)ρfRRBeta0.80.9152(0.9117, 0.9181)0.8700(0.8295, 0.9208)ρur/ρugBeta0.80.9991(0.9986, 0.9998)0.8471(0.8145, 0.8770)σjInv.Gamma0.10.0059(0.0026, 0.0092)0.0078(0.0024, 0.0139)σuIInv.Gamma0.10.0070(0.0060, 0.0079)0.2996(0.2453, 0.3526)σusInv.Gamma0.10.0017(0.0015, 0.0020)0.2346(0.1774, 0.3195)σlInv.Gamma0.10.0019(0.0018, 0.0020)0.0929(0.0778, 0.1081)σaInv.Gamma0.10.2271(0.2142, 0.2409)0.1476(0.0832, 0.1789)σfRRInv.Gamma0.10.1827(0.1715, 0.1911)0.0079(0.0022, 0.0135)σur/σugInv.Gamma0.10.0057(0.0050, 0.0065)0.0355(0.0290, 0.0418)


## 5. Impulse Response Analysis

This paper compares the impulse response results of monetary policy shocks of two rules, price-based and quantity-based (the dynamic responses of each variable in the figure are shown as percentage deviations from the steady state), to analyze the different impacts of the two monetary policy shocks on China’s macro-economic fluctuations in terms of both the magnitude of fluctuations and the duration period and further analyzes the applicability of the two monetary policy rules in China.


### 5.1. COVID-19 Shock

Figure3 shows in comparison the dynamic impact of COVID-19 shock on macro-economic variables under both models. The simulation results above show that the onset of the epidemic has a significant short-term impact on the real estate market and the economy as a whole. Real estate prices contract more significantly under the epidemic shock but for a shorter duration. Aggregate output and consumption also fall sharply in a short period, which confirms the market performance since 2020, and the household sector does not experience post-disaster panic consumption. As can be seen, the impact of the epidemic shock on real estate prices and aggregate consumption and investment is similar in magnitude in both models, but the volatility of output is more pronounced in the quantity-based model. Hence, the price-based model effectively regulates real estate prices and stabilizes the economy under an epidemic shock. In contrast, the quantity-based model can achieve the objective of regulating real estate prices but may cause drastic fluctuations in the total economy in the short run, which is not conducive to stabilizing economic development.Figure 3
Impulse responses to COVID-19 shock. The figure on the left shows the interest rate rule model and that on the right is the quantity rule model.


### 5.2. Monetary Shock

Figure4 shows the dynamic effects of different monetary policy shocks on macro-economic variables. In the model, including the impact of the epidemic, real estate prices show a significant increase and a long duration when a positive interest rate shock occurs. Aggregate output and aggregate investment show varying degrees of decline, and aggregate consumption shows a rise followed by a decline. When a positive monetary growth rate shock hits the economy, real estate prices show a more pronounced rise and last longer. Aggregate output, aggregate investment, etc. show varying degrees of increase, and aggregate consumption shows a tendency to fall and then rise.Figure 4
Impulse responses to monetary shock.From the above simulation results, it can be seen that a tight monetary policy can be more effective in curbing the overheated development of real estate prices, but it also has a dampening effect on the total output of the economy, and the impact is relatively long-lasting. Thus, in the face of a pandemic shock, raising interest rates will dampen real estate prices in the short run, but it will also cause a certain degree of economic contraction. When using this type of monetary policy, attention needs to be paid to the negative effects on the economy. An accommodative quantitative monetary policy shock can positively impact investment and output, with real estate prices tending to rise and the impact having a high degree of permanence. However, the side effects of the policy are also evident, leading to persistent and significant inflation.


### 5.3. Investment Shock

Figure5 compares the macro-economic dynamics of investment shocks in the two models. As can be seen, both models exhibit similar results when subjected to investment shocks, both affecting aggregate consumption in the short run and having some dampening effect on real estate prices. However, as higher interest rates reverse the dampening effect on investment, a slight rebound in housing prices ensues. The volatility of aggregate investment suggests that the long-run impact of the current positive investment shock is poor and may be dragged down by the subsequent decline in aggregate social investment, which creates an awkward situation of early use, leading to a subsequent slippage in aggregate output as well.Figure 5
Impulse responses to investment shock.


### 5.4. Land Supply Shock

As can be seen from the simulation results below, a positive land supply shock effectively suppressed real estate prices over a longer period in both models. It also has a strong, persistent effect on all variables, which positively affects the overall adjustment of the economy. However, the drawback is also evident in that it causes inflation to remain at a high level for a longer period, which in the long run must prevent the economy from overheating, as shown in Figure6.Figure 6
Impulse responses to land supply shock.In summary, in terms of stabilizing the real estate market as well as macro-economic fluctuations, the above shocks of both price-based and quantity-based rule models have produced certain effects on achieving real estate price regulation and stabilizing the economy, but the effects of each shock on aggregate output are more drastic under the quantity-based rule. Therefore, in practice, it is necessary to choose the optimal regulation instruments according to the current economic development and macro-economic regulation objectives in different periods while paying attention to the abnormal fluctuations of other variables.


## 5.1. COVID-19 Shock

Figure3 shows in comparison the dynamic impact of COVID-19 shock on macro-economic variables under both models. The simulation results above show that the onset of the epidemic has a significant short-term impact on the real estate market and the economy as a whole. Real estate prices contract more significantly under the epidemic shock but for a shorter duration. Aggregate output and consumption also fall sharply in a short period, which confirms the market performance since 2020, and the household sector does not experience post-disaster panic consumption. As can be seen, the impact of the epidemic shock on real estate prices and aggregate consumption and investment is similar in magnitude in both models, but the volatility of output is more pronounced in the quantity-based model. Hence, the price-based model effectively regulates real estate prices and stabilizes the economy under an epidemic shock. In contrast, the quantity-based model can achieve the objective of regulating real estate prices but may cause drastic fluctuations in the total economy in the short run, which is not conducive to stabilizing economic development.Figure 3
Impulse responses to COVID-19 shock. The figure on the left shows the interest rate rule model and that on the right is the quantity rule model.


## 5.2. Monetary Shock

Figure4 shows the dynamic effects of different monetary policy shocks on macro-economic variables. In the model, including the impact of the epidemic, real estate prices show a significant increase and a long duration when a positive interest rate shock occurs. Aggregate output and aggregate investment show varying degrees of decline, and aggregate consumption shows a rise followed by a decline. When a positive monetary growth rate shock hits the economy, real estate prices show a more pronounced rise and last longer. Aggregate output, aggregate investment, etc. show varying degrees of increase, and aggregate consumption shows a tendency to fall and then rise.Figure 4
Impulse responses to monetary shock.From the above simulation results, it can be seen that a tight monetary policy can be more effective in curbing the overheated development of real estate prices, but it also has a dampening effect on the total output of the economy, and the impact is relatively long-lasting. Thus, in the face of a pandemic shock, raising interest rates will dampen real estate prices in the short run, but it will also cause a certain degree of economic contraction. When using this type of monetary policy, attention needs to be paid to the negative effects on the economy. An accommodative quantitative monetary policy shock can positively impact investment and output, with real estate prices tending to rise and the impact having a high degree of permanence. However, the side effects of the policy are also evident, leading to persistent and significant inflation.


## 5.3. Investment Shock

Figure5 compares the macro-economic dynamics of investment shocks in the two models. As can be seen, both models exhibit similar results when subjected to investment shocks, both affecting aggregate consumption in the short run and having some dampening effect on real estate prices. However, as higher interest rates reverse the dampening effect on investment, a slight rebound in housing prices ensues. The volatility of aggregate investment suggests that the long-run impact of the current positive investment shock is poor and may be dragged down by the subsequent decline in aggregate social investment, which creates an awkward situation of early use, leading to a subsequent slippage in aggregate output as well.Figure 5
Impulse responses to investment shock.


## 5.4. Land Supply Shock

As can be seen from the simulation results below, a positive land supply shock effectively suppressed real estate prices over a longer period in both models. It also has a strong, persistent effect on all variables, which positively affects the overall adjustment of the economy. However, the drawback is also evident in that it causes inflation to remain at a high level for a longer period, which in the long run must prevent the economy from overheating, as shown in Figure6.Figure 6
Impulse responses to land supply shock.In summary, in terms of stabilizing the real estate market as well as macro-economic fluctuations, the above shocks of both price-based and quantity-based rule models have produced certain effects on achieving real estate price regulation and stabilizing the economy, but the effects of each shock on aggregate output are more drastic under the quantity-based rule. Therefore, in practice, it is necessary to choose the optimal regulation instruments according to the current economic development and macro-economic regulation objectives in different periods while paying attention to the abnormal fluctuations of other variables.


## 6. Conclusions

Since the outbreak of COVID-19, the economies of various countries have been hit to varying degrees, and the recent rapid heating of the real estate market has drawn the attention of scholars. In this context, regulating the real estate market while stabilizing the economy has become a key problem faced by China's policy makers. This paper focuses on the effects of two types of monetary policies, price-based and quantity-based, on variables such as real estate prices and aggregate output by building a multi-sectoral DSGE model that includes COVID-19 shocks. The following conclusions are drawn.First, price-based monetary policy is more effective in regulating real estate prices and stabilizing the economy. The analysis finds that both monetary policy rules achieve the goal of curbing real estate prices to some extent, but variables such as aggregate output are more volatile under the quantity-based rule, which is detrimental to economic stability. In contrast, in the model with the price-based rule, other variables such as aggregate output are less volatile under the same degree of real estate price volatility. Price-based monetary policy can curb real estate prices while having a milder impact on the overall economy.Second, the COVID-19 shock dampened real estate prices in the short run but simultaneously had serious effects on other parts of the Chinese economy, and the effects lasted longer. Impulse response analysis finds that the impact of the epidemic shock on real estate prices lasts only about 4 periods, while the impact on aggregate consumption, aggregate investment, and aggregate output lasts more than 10. This finding is supported by economic reality, as China’s real estate market heated up rapidly in the first quarter of the year, with real estate prices and volumes rising in many places, while the rest of the economy recovered more slowly.Third, investment and land supply shocks can effectively curb real estate prices while not having much negative impact on other economic variables and can better cope with the current situation. While aggressive monetary policy can effectively stimulate the economy in the short run, it may lead to further increases in real estate prices. In contrast, investment and land supply shocks can stabilize the economy while dampening real estate prices in response to the epidemic.This paper puts forward the following policy recommendations based on the above findings. First, given that the effects of COVID-19 are still ongoing, it is more appropriate to choose price-based monetary policies for macro-economic control at this time. Both types of monetary policies can effectively curb the rise of real estate prices under normal circumstances. However, in the face of a special period like COVID-19, the monetary authorities should minimize the impact on economic fluctuations in their policy operations to curb real estate prices. Obviously, at this time, price-based monetary policy is more effective and can achieve real estate price regulation while having a more moderate impact on the economy. Second, regulating real estate prices in the context of COVID-19 requires appropriate monetary policy and the coordination and cooperation of various other sectors better stabilize real estate prices in the long run, for example, stimulating investment through relevant policies and targeted increases in land supply by local governments at all levels.



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*Source: 7625465-2022-03-11.xml*